TSTP Solution File: ITP246^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP246^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 03:25:13 EDT 2023
% Result : Theorem 171.19s 171.54s
% Output : Proof 171.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.53/2.57 % Problem : ITP246^1 : TPTP v8.1.2. Released v8.1.0.
% 2.53/2.58 % Command : do_cvc5 %s %d
% 2.57/2.79 % Computer : n008.cluster.edu
% 2.57/2.79 % Model : x86_64 x86_64
% 2.57/2.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.57/2.79 % Memory : 8042.1875MB
% 2.57/2.79 % OS : Linux 3.10.0-693.el7.x86_64
% 2.57/2.79 % CPULimit : 300
% 2.57/2.79 % WCLimit : 300
% 2.57/2.79 % DateTime : Sun Aug 27 12:51:34 EDT 2023
% 2.57/2.79 % CPUTime :
% 5.41/5.61 %----Proving TH0
% 5.41/5.62 %------------------------------------------------------------------------------
% 5.41/5.62 % File : ITP246^1 : TPTP v8.1.2. Released v8.1.0.
% 5.41/5.62 % Domain : Interactive Theorem Proving
% 5.41/5.62 % Problem : Sledgehammer problem VEBT_Succ 00795_053196
% 5.41/5.62 % Version : [Des22] axioms.
% 5.41/5.62 % English :
% 5.41/5.62
% 5.41/5.62 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.41/5.62 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.41/5.62 % Source : [Des22]
% 5.41/5.62 % Names : 0070_VEBT_Succ_00795_053196 [Des22]
% 5.41/5.62
% 5.41/5.62 % Status : Theorem
% 5.41/5.62 % Rating : 0.69 v8.1.0
% 5.41/5.62 % Syntax : Number of formulae : 11234 (6275 unt; 977 typ; 0 def)
% 5.41/5.62 % Number of atoms : 26809 (11987 equ; 0 cnn)
% 5.41/5.62 % Maximal formula atoms : 71 ( 2 avg)
% 5.41/5.62 % Number of connectives : 104965 (2569 ~; 512 |;1523 &;91781 @)
% 5.41/5.62 % ( 0 <=>;8580 =>; 0 <=; 0 <~>)
% 5.41/5.62 % Maximal formula depth : 39 ( 5 avg)
% 5.41/5.62 % Number of types : 85 ( 84 usr)
% 5.41/5.62 % Number of type conns : 3106 (3106 >; 0 *; 0 +; 0 <<)
% 5.41/5.62 % Number of symbols : 896 ( 893 usr; 69 con; 0-8 aty)
% 5.41/5.62 % Number of variables : 23057 (1889 ^;20505 !; 663 ?;23057 :)
% 5.41/5.62 % SPC : TH0_THM_EQU_NAR
% 5.41/5.62
% 5.41/5.62 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.41/5.62 % from the van Emde Boas Trees session in the Archive of Formal
% 5.41/5.62 % proofs -
% 5.41/5.62 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.41/5.62 % 2022-02-18 01:26:33.043
% 5.41/5.62 %------------------------------------------------------------------------------
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 5.41/5.62 archim3151403230148437115or_rat: rat > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
% 5.41/5.62 archim6058952711729229775r_real: real > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
% 5.41/5.62 archimedean_frac_rat: rat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Archimedean__Field_Ofrac_001t__Real__Oreal,type,
% 5.41/5.62 archim2898591450579166408c_real: real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 5.41/5.62 archim7778729529865785530nd_rat: rat > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
% 5.41/5.62 archim8280529875227126926d_real: real > int ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 bNF_re895249473297799549at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 bNF_re4695409256820837752l_real: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( real > real > real ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_Eo_J_001_062_It__Real__Oreal_M_Eo_J,type,
% 5.41/5.62 bNF_re4521903465945308077real_o: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > $o ) > ( real > $o ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( real > real > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 bNF_re3023117138289059399t_real: ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_Eo_001_Eo,type,
% 5.41/5.62 bNF_re4297313714947099218al_o_o: ( ( nat > rat ) > real > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( real > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.41/5.62 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.41/5.62 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.41/5.62 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 5.41/5.62 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 5.41/5.62 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 5.41/5.62 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 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 ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Binomial_Obinomial,type,
% 5.41/5.62 binomial: nat > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Binomial_Ogbinomial_001t__Complex__Ocomplex,type,
% 5.41/5.62 gbinomial_complex: complex > nat > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 5.41/5.62 gbinomial_int: int > nat > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 5.41/5.62 gbinomial_nat: nat > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
% 5.41/5.62 gbinomial_rat: rat > nat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Binomial_Ogbinomial_001t__Real__Oreal,type,
% 5.41/5.62 gbinomial_real: real > nat > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 5.41/5.62 bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Bit__Operations_Oand__not__num,type,
% 5.41/5.62 bit_and_not_num: num > num > option_num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Bit__Operations_Oand__not__num__rel,type,
% 5.41/5.62 bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 5.41/5.62 bit_concat_bit: nat > int > int > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
% 5.41/5.62 bit_or_not_num_neg: num > num > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Bit__Operations_Oor__not__num__neg__rel,type,
% 5.41/5.62 bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 bit_ri7632146776885996613nteger: code_integer > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 5.41/5.62 bit_ri7919022796975470100ot_int: int > int ).
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% 5.41/5.62 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Nat__Onat,type,
% 5.41/5.62 comm_s4663373288045622133er_nat: nat > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Rat__Orat,type,
% 5.41/5.62 comm_s4028243227959126397er_rat: rat > nat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Real__Oreal,type,
% 5.41/5.62 comm_s7457072308508201937r_real: real > nat > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 semiri3624122377584611663nteger: nat > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex,type,
% 5.41/5.62 semiri5044797733671781792omplex: nat > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Int__Oint,type,
% 5.41/5.62 semiri1406184849735516958ct_int: nat > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 5.41/5.62 semiri1408675320244567234ct_nat: nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Rat__Orat,type,
% 5.41/5.62 semiri773545260158071498ct_rat: nat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 5.41/5.62 semiri2265585572941072030t_real: nat > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 5.41/5.62 invers8013647133539491842omplex: complex > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 5.41/5.62 inverse_inverse_rat: rat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 5.41/5.62 inverse_inverse_real: real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 5.41/5.62 at_bot_real: filter_real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 5.41/5.62 at_top_nat: filter_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 5.41/5.62 at_top_real: filter_real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 5.41/5.62 eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.62 eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 5.41/5.62 eventually_real: ( real > $o ) > filter_real > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.41/5.62 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.62 filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.62 filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.41/5.62 princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.41/5.62 princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Filter_Oprod__filter_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 5.41/5.62 finite_card_o: set_o > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 5.41/5.62 finite_card_complex: set_complex > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 5.41/5.62 finite_card_int: set_int > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.62 finite_card_list_nat: set_list_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 5.41/5.62 finite_card_nat: set_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 5.41/5.62 finite410649719033368117t_unit: set_Product_unit > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 5.41/5.62 finite_card_char: set_char > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 5.41/5.62 finite3207457112153483333omplex: set_complex > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Extended____Nat__Oenat,type,
% 5.41/5.62 finite4001608067531595151d_enat: set_Extended_enat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 5.41/5.62 finite_finite_int: set_int > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 5.41/5.62 finite_finite_nat: set_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.41/5.62 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.41/5.62 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 5.41/5.62 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.62 comp_int_real_real: ( int > real ) > ( real > int ) > real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.41/5.62 comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Oid_001_Eo,type,
% 5.41/5.62 id_o: $o > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 5.41/5.62 id_nat: nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
% 5.41/5.62 inj_on_nat_char: ( nat > char ) > set_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.62 inj_on_real_real: ( real > real ) > set_real > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.41/5.62 map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.41/5.62 map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 5.41/5.62 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.41/5.62 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 5.41/5.62 map_fu4333342158222067775at_rat: ( rat > product_prod_int_int ) > ( ( product_prod_int_int > product_prod_int_int ) > rat > rat ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > rat > rat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 5.41/5.62 map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 5.41/5.62 map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J_001_062_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.41/5.62 map_fu1532550112467129777l_real: ( real > nat > rat ) > ( ( ( nat > rat ) > nat > rat ) > real > real ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > real > real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.41/5.62 map_fu7146612038024189824t_real: ( real > nat > rat ) > ( ( nat > rat ) > real ) > ( ( nat > rat ) > nat > rat ) > real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_Eo_001_Eo,type,
% 5.41/5.62 map_fu1856342031159181835at_o_o: ( real > nat > rat ) > ( $o > $o ) > ( ( nat > rat ) > $o ) > real > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.62 the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun__Def_Opair__leq,type,
% 5.41/5.62 fun_pair_leq: set_Pr8693737435421807431at_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Fun__Def_Opair__less,type,
% 5.41/5.62 fun_pair_less: set_Pr8693737435421807431at_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 5.41/5.62 gcd_Gcd_nat: set_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_GCD_Obezw,type,
% 5.41/5.62 bezw: nat > nat > product_prod_int_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_GCD_Obezw__rel,type,
% 5.41/5.62 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 5.41/5.62 gcd_gcd_int: int > int > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 5.41/5.62 gcd_gcd_nat: nat > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 gcd_lcm_Code_integer: code_integer > code_integer > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Int__Oint,type,
% 5.41/5.62 gcd_lcm_int: int > int > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Nat__Onat,type,
% 5.41/5.62 gcd_lcm_nat: nat > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_GCD_Ogcd__nat__rel,type,
% 5.41/5.62 gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 abs_abs_Code_integer: code_integer > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex,type,
% 5.41/5.62 abs_abs_complex: complex > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 5.41/5.62 abs_abs_int: int > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 5.41/5.62 abs_abs_rat: rat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 5.41/5.62 abs_abs_real: real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 5.41/5.62 minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Extended____Nat__Oenat_M_Eo_J,type,
% 5.41/5.62 minus_2020553357622893040enat_o: ( extended_enat > $o ) > ( extended_enat > $o ) > extended_enat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Int__Oint_M_Eo_J,type,
% 5.41/5.62 minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
% 5.41/5.62 minus_1139252259498527702_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).
% 5.41/5.62
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% 5.41/5.62 if_list_nat: $o > list_nat > list_nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Nat__Onat,type,
% 5.41/5.62 if_nat: $o > nat > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Num__Onum,type,
% 5.41/5.62 if_num: $o > num > num > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.41/5.62 if_option_nat: $o > option_nat > option_nat > option_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.41/5.62 if_option_num: $o > option_num > option_num > option_num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.41/5.62 if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.41/5.62 if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.41/5.62 if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.62 if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Rat__Orat,type,
% 5.41/5.62 if_rat: $o > rat > rat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Real__Oreal,type,
% 5.41/5.62 if_real: $o > real > real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 5.41/5.62 if_set_int: $o > set_int > set_int > set_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.62 if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Infinite__Set_Owellorder__class_Oenumerate_001t__Nat__Onat,type,
% 5.41/5.62 infini8530281810654367211te_nat: set_nat > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_OAbs__Integ,type,
% 5.41/5.62 abs_Integ: product_prod_nat_nat > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_ORep__Integ,type,
% 5.41/5.62 rep_Integ: int > product_prod_nat_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oint__ge__less__than,type,
% 5.41/5.62 int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oint__ge__less__than2,type,
% 5.41/5.62 int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Ointrel,type,
% 5.41/5.62 intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Onat,type,
% 5.41/5.62 nat2: int > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Opcr__int,type,
% 5.41/5.62 pcr_int: product_prod_nat_nat > int > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Opower__int_001t__Real__Oreal,type,
% 5.41/5.62 power_int_real: real > int > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oring__1__class_OInts_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 ring_11222124179247155820nteger: set_Code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oring__1__class_OInts_001t__Complex__Ocomplex,type,
% 5.41/5.62 ring_1_Ints_complex: set_complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oring__1__class_OInts_001t__Int__Oint,type,
% 5.41/5.62 ring_1_Ints_int: set_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oring__1__class_OInts_001t__Rat__Orat,type,
% 5.41/5.62 ring_1_Ints_rat: set_rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 5.41/5.62 ring_1_Ints_real: set_real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 ring_18347121197199848620nteger: int > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 5.41/5.62 ring_17405671764205052669omplex: int > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 5.41/5.62 ring_1_of_int_int: int > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 5.41/5.62 ring_1_of_int_rat: int > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 5.41/5.62 ring_1_of_int_real: int > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Extended____Nat__Oenat,type,
% 5.41/5.62 inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 5.41/5.62 inf_inf_nat: nat > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 5.41/5.62 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 5.41/5.62 sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 5.41/5.62 sup_sup_nat: nat > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.62 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.41/5.62 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Extended____Nat__Oenat,type,
% 5.41/5.62 lattic921264341876707157d_enat: set_Extended_enat > extended_enat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.41/5.62 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Lifting_OQuotient_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.41/5.62 quotie3684837364556693515t_real: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > real ) > ( real > nat > rat ) > ( ( nat > rat ) > real > $o ) > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.41/5.62 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 5.41/5.62 append_int: list_int > list_int > list_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 5.41/5.62 append_nat: list_nat > list_nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 5.41/5.62 drop_nat: nat > list_nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 5.41/5.62 last_nat: list_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.41/5.62 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.41/5.62 cons_int: int > list_int > list_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.41/5.62 cons_nat: nat > list_nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 5.41/5.62 nil_int: list_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.41/5.62 nil_nat: list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 5.41/5.62 hd_nat: list_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.62 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.62 map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.41/5.62 set_o2: list_o > set_o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.41/5.62 set_complex2: list_complex > set_complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Oset_001t__Extended____Nat__Oenat,type,
% 5.41/5.62 set_Extended_enat2: list_Extended_enat > set_Extended_enat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.41/5.62 set_int2: list_int > set_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.62 set_list_nat2: list_list_nat > set_list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.41/5.62 set_nat2: list_nat > set_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.41/5.62 set_real2: list_real > set_real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.62 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.62 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 5.41/5.62 tl_nat: list_nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.62 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001_Eo,type,
% 5.41/5.62 nth_o: list_o > nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.41/5.62 nth_complex: list_complex > nat > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Extended____Nat__Oenat,type,
% 5.41/5.62 nth_Extended_enat: list_Extended_enat > nat > extended_enat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.41/5.62 nth_int: list_int > nat > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.62 nth_list_nat: list_list_nat > nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.41/5.62 nth_nat: list_nat > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.41/5.62 nth_num: list_num > nat > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 5.41/5.62 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 5.41/5.62 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.41/5.62 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.41/5.62 nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num ).
% 5.41/5.62
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
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% 5.41/5.62
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.41/5.62 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__Real__Oreal,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.41/5.62 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
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% 5.41/5.62 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Num__Onum,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
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% 5.41/5.62
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.62 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.62 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.41/5.62 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.41/5.62 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.41/5.62 take_nat: nat > list_nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.62 take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oupt,type,
% 5.41/5.62 upt: nat > nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oupto,type,
% 5.41/5.62 upto: int > int > list_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oupto__aux,type,
% 5.41/5.62 upto_aux: int > int > list_int > list_int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_List_Oupto__rel,type,
% 5.41/5.62 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_OSuc,type,
% 5.41/5.62 suc: nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.62 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.41/5.62 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.41/5.62 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.41/5.62 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Onat_Opred,type,
% 5.41/5.62 pred: nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 semiri4939895301339042750nteger: nat > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.41/5.62 semiri8010041392384452111omplex: nat > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.41/5.62 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.41/5.62 semiri1314217659103216013at_int: nat > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.41/5.62 semiri1316708129612266289at_nat: nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.41/5.62 semiri681578069525770553at_rat: nat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.41/5.62 semiri5074537144036343181t_real: nat > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.41/5.62 size_size_list_o: list_o > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.41/5.62 size_s3451745648224563538omplex: list_complex > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Extended____Nat__Oenat_J,type,
% 5.41/5.62 size_s3941691890525107288d_enat: list_Extended_enat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.41/5.62 size_size_list_int: list_int > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 5.41/5.62 size_s3023201423986296836st_nat: list_list_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.62 size_size_list_nat: list_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 5.41/5.62 size_size_list_num: list_num > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.41/5.62 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.41/5.62 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 5.41/5.62 size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.41/5.62 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 5.41/5.62 size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.41/5.62 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.41/5.62 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 5.41/5.62 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 5.41/5.62 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 5.41/5.62
% 5.41/5.62 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,
% 5.41/5.62 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.41/5.62 size_size_list_real: list_real > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.41/5.62 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.41/5.62 size_size_num: num > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.62 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Olist__decode,type,
% 5.41/5.62 nat_list_decode: nat > list_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 5.41/5.62 nat_list_decode_rel: nat > nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.41/5.62 nat_list_encode: list_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.41/5.62 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 5.41/5.62 nat_prod_decode: nat > product_prod_nat_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.41/5.62 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.41/5.62 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.41/5.62 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.41/5.62 nat_set_decode: nat > set_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.41/5.62 nat_set_encode: set_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.41/5.62 nat_triangle: nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_NthRoot_Oroot,type,
% 5.41/5.62 root: nat > real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_NthRoot_Osqrt,type,
% 5.41/5.62 sqrt: real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_OBitM,type,
% 5.41/5.62 bitM: num > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oinc,type,
% 5.41/5.62 inc: num > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.41/5.62 neg_nu7009210354673126013omplex: complex > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.41/5.62 neg_numeral_dbl_int: int > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.41/5.62 neg_numeral_dbl_rat: rat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.41/5.62 neg_numeral_dbl_real: real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.41/5.62 neg_nu6511756317524482435omplex: complex > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 5.41/5.62 neg_nu3811975205180677377ec_int: int > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.41/5.62 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.41/5.62 neg_nu6075765906172075777c_real: real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.41/5.62 neg_nu8557863876264182079omplex: complex > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 5.41/5.62 neg_nu5851722552734809277nc_int: int > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.41/5.62 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 5.41/5.62 neg_nu8295874005876285629c_real: real > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.41/5.62 neg_numeral_sub_int: num > num > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onum_OBit0,type,
% 5.41/5.62 bit0: num > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onum_OBit1,type,
% 5.41/5.62 bit1: num > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onum_OOne,type,
% 5.41/5.62 one: num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.41/5.62 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onum_Osize__num,type,
% 5.41/5.62 size_num: num > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onum__of__nat,type,
% 5.41/5.62 num_of_nat: nat > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 5.41/5.62 numera6620942414471956472nteger: num > code_integer ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 5.41/5.62 numera6690914467698888265omplex: num > complex ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 5.41/5.62 numera1916890842035813515d_enat: num > extended_enat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 5.41/5.62 numeral_numeral_int: num > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 5.41/5.62 numeral_numeral_nat: num > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 5.41/5.62 numeral_numeral_rat: num > rat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 5.41/5.62 numeral_numeral_real: num > real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Opow,type,
% 5.41/5.62 pow: num > num > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Opred__numeral,type,
% 5.41/5.62 pred_numeral: num > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Num_Osqr,type,
% 5.41/5.62 sqr: num > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 5.41/5.62 none_nat: option_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 5.41/5.62 none_num: option_num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.62 none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 5.41/5.62 some_nat: nat > option_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 5.41/5.62 some_num: num > option_num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.62 some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.62 case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 5.41/5.62 case_option_int_num: int > ( num > int ) > option_num > int ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 5.41/5.62 case_option_num_num: num > ( num > num ) > option_num > num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 5.41/5.62 case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
% 5.41/5.62 map_option_num_num: ( num > num ) > option_num > option_num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
% 5.41/5.62 the_nat: option_nat > nat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Extended____Nat__Oenat,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Extended____Nat__Oenat_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Num__Onum_J,type,
% 5.41/5.62 bot_bot_set_num: set_num ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Rat__Orat_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.41/5.62 bot_bot_set_real: set_real ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_OLeast_001t__Extended____Nat__Oenat,type,
% 5.41/5.62 ord_Le1955565732374568822d_enat: ( extended_enat > $o ) > extended_enat ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_OLeast_001t__Nat__Onat,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_OLeast_001t__Real__Oreal,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Complex__Ocomplex_M_Eo_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Extended____Nat__Oenat_M_Eo_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Int__Oint_M_Eo_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Nat__Onat_M_Eo_J,type,
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% 5.41/5.62
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% 5.41/5.62
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
% 5.41/5.62 ord_less_num: num > num > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Extended____Nat__Oenat_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Num__Onum_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Rat__Orat_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Real__Oreal_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Ointeger,type,
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% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 5.41/5.62 ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 5.41/5.62 ord_less_eq_int: int > int > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 5.41/5.62 ord_less_eq_nat: nat > nat > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 5.41/5.62 ord_less_eq_num: num > num > $o ).
% 5.41/5.62
% 5.41/5.62 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
% 5.41/5.62 ord_less_eq_rat: rat > rat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 5.41/5.63 ord_less_eq_real: real > real > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.41/5.63 ord_le211207098394363844omplex: set_complex > set_complex > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Extended____Nat__Oenat_J,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Num__Onum_J,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Rat__Orat_J,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.41/5.63 ord_less_eq_set_real: set_real > set_real > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Omax_001t__Extended____Nat__Oenat,type,
% 5.41/5.63 ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
% 5.41/5.63 ord_max_int: int > int > int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Omin_001t__Extended____Nat__Oenat,type,
% 5.41/5.63 ord_mi8085742599997312461d_enat: extended_enat > extended_enat > extended_enat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
% 5.41/5.63 ord_min_nat: nat > nat > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 5.41/5.63 order_Greatest_nat: ( nat > $o ) > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.41/5.63 order_9091379641038594480t_real: ( nat > real ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oorder__class_Omono_001t__Extended____Nat__Oenat_001t__Extended____Nat__Oenat,type,
% 5.41/5.63 order_4130057895858720880d_enat: ( extended_enat > extended_enat ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.63 order_mono_nat_nat: ( nat > nat ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.41/5.63 order_mono_nat_real: ( nat > real ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.63 order_5726023648592871131at_nat: ( nat > nat ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.63 order_7092887310737990675l_real: ( real > real ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Oordering__top_001t__Nat__Onat,type,
% 5.41/5.63 ordering_top_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Otop__class_Otop_001t__Extended____Nat__Oenat,type,
% 5.41/5.63 top_to3028658606643905974d_enat: extended_enat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 5.41/5.63 top_top_set_o: set_o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.63 top_top_set_nat: set_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 5.41/5.63 top_to1996260823553986621t_unit: set_Product_unit ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.41/5.63 top_top_set_real: set_real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__String__Ochar_J,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
% 5.41/5.63 power_8256067586552552935nteger: code_integer > nat > code_integer ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
% 5.41/5.63 power_power_complex: complex > nat > complex ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 5.41/5.63 power_power_int: int > nat > int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 5.41/5.63 power_power_rat: rat > nat > rat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 5.41/5.63 power_power_real: real > nat > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.41/5.63 produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Num__Onum_Mt__Num__Onum_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
% 5.41/5.63 product_Pair_o_o: $o > $o > product_prod_o_o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
% 5.41/5.63 product_Pair_o_int: $o > int > product_prod_o_int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
% 5.41/5.63 product_Pair_o_nat: $o > nat > product_prod_o_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.63 produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
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% 5.41/5.63 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
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% 5.41/5.63
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
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% 5.41/5.63
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Extended____Nat__Oenat,type,
% 5.41/5.63 produc581526299967858633d_enat: vEBT_VEBT > extended_enat > produc7272778201969148633d_enat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.41/5.63 produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.41/5.63 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.63 produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.63 produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.41/5.63 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.41/5.63 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.41/5.63 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.41/5.63 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 5.41/5.63
% 5.41/5.63 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,
% 5.41/5.63 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.41/5.63
% 5.41/5.63 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,
% 5.41/5.63 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 5.41/5.63 produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.41/5.63 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.41/5.63 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.41/5.63
% 5.41/5.63 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,
% 5.41/5.63 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.41/5.63
% 5.41/5.63 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,
% 5.41/5.63 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.41/5.63
% 5.41/5.63 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,
% 5.41/5.63 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.41/5.63 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.63 produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.63 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.41/5.63
% 5.41/5.63 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,
% 5.41/5.63 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.41/5.63 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 5.41/5.63 produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ofst_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.41/5.63 produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.41/5.63 product_fst_int_int: product_prod_int_int > int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.63 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.41/5.63 produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.41/5.63 product_snd_int_int: product_prod_int_int > int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.63 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_OAbs__Rat,type,
% 5.41/5.63 abs_Rat: product_prod_int_int > rat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_OFract,type,
% 5.41/5.63 fract: int > int > rat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_OFrct,type,
% 5.41/5.63 frct: product_prod_int_int > rat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_ORep__Rat,type,
% 5.41/5.63 rep_Rat: rat > product_prod_int_int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 5.41/5.63 field_5140801741446780682s_real: set_real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 5.41/5.63 field_7254667332652039916t_real: rat > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_Onormalize,type,
% 5.41/5.63 normalize: product_prod_int_int > product_prod_int_int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_Opcr__rat,type,
% 5.41/5.63 pcr_rat: product_prod_int_int > rat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_Opositive,type,
% 5.41/5.63 positive: rat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_Oquotient__of,type,
% 5.41/5.63 quotient_of: rat > product_prod_int_int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rat_Oratrel,type,
% 5.41/5.63 ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real_OReal,type,
% 5.41/5.63 real2: ( nat > rat ) > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real_Ocauchy,type,
% 5.41/5.63 cauchy: ( nat > rat ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real_Ocr__real,type,
% 5.41/5.63 cr_real: ( nat > rat ) > real > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real_Opcr__real,type,
% 5.41/5.63 pcr_real: ( nat > rat ) > real > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real_Opositive,type,
% 5.41/5.63 positive2: real > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real_Orealrel,type,
% 5.41/5.63 realrel: ( nat > rat ) > ( nat > rat ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real_Orep__real,type,
% 5.41/5.63 rep_real: real > nat > rat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real_Ovanishes,type,
% 5.41/5.63 vanishes: ( nat > rat ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.41/5.63 real_V2521375963428798218omplex: set_complex ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.63 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 5.41/5.63 real_V3694042436643373181omplex: complex > complex > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 5.41/5.63 real_V975177566351809787t_real: real > real > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.41/5.63 real_V1022390504157884413omplex: complex > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.41/5.63 real_V7735802525324610683m_real: real > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.41/5.63 real_V4546457046886955230omplex: real > complex ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 5.41/5.63 real_V1803761363581548252l_real: real > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 5.41/5.63 real_V2046097035970521341omplex: real > complex > complex ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 5.41/5.63 real_V1485227260804924795R_real: real > real > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Relation_Otransp_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.41/5.63 transp_nat_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
% 5.41/5.63 algebr932160517623751201me_int: int > int > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
% 5.41/5.63 algebr934650988132801477me_nat: nat > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.41/5.63 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.41/5.63 divide1717551699836669952omplex: complex > complex > complex ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 5.41/5.63 divide_divide_int: int > int > int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.41/5.63 divide_divide_nat: nat > nat > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.41/5.63 divide_divide_rat: rat > rat > rat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.41/5.63 divide_divide_real: real > real > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.41/5.63 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.41/5.63 dvd_dvd_complex: complex > complex > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.41/5.63 dvd_dvd_int: int > int > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.41/5.63 dvd_dvd_nat: nat > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.41/5.63 dvd_dvd_rat: rat > rat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.41/5.63 dvd_dvd_real: real > real > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.41/5.63 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.41/5.63 modulo_modulo_int: int > int > int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.41/5.63 modulo_modulo_nat: nat > nat > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 5.41/5.63 zero_n356916108424825756nteger: $o > code_integer ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 5.41/5.63 zero_n1201886186963655149omplex: $o > complex ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.41/5.63 zero_n2684676970156552555ol_int: $o > int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.41/5.63 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.41/5.63 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.41/5.63 zero_n3304061248610475627l_real: $o > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 5.41/5.63 suminf_complex: ( nat > complex ) > complex ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.41/5.63 suminf_real: ( nat > real ) > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 5.41/5.63 summable_complex: ( nat > complex ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.41/5.63 summable_real: ( nat > real ) > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.41/5.63 sums_real: ( nat > real ) > real > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set_OCollect_001_Eo,type,
% 5.41/5.63 collect_o: ( $o > $o ) > set_o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 5.41/5.63 collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.41/5.63 collect_complex: ( complex > $o ) > set_complex ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set_OCollect_001t__Extended____Nat__Oenat,type,
% 5.41/5.63 collec4429806609662206161d_enat: ( extended_enat > $o ) > set_Extended_enat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 5.41/5.63 collect_int: ( int > $o ) > set_int ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.63 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
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% 5.41/5.63
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% 5.41/5.63
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% 5.41/5.63
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
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% 5.41/5.63
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% 5.41/5.63 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
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% 5.41/5.63 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Complex__Ocomplex,type,
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% 5.41/5.63 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
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% 5.41/5.63 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Oarccos,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Oarcsin,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Oarctan,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Ocos__coeff,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Ocosh_001t__Complex__Ocomplex,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Ocot_001t__Complex__Ocomplex,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Olog,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Opi,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Opowr__real,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Osin__coeff,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Osinh_001t__Complex__Ocomplex,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.41/5.63 tanh_complex: complex > complex ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.41/5.63 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
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% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead,type,
% 5.41/5.63 vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oelim__dead__rel,type,
% 5.41/5.63 vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.41/5.63 vEBT_VEBT_high: nat > nat > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.41/5.63 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.41/5.63 vEBT_VEBT_low: nat > nat > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.41/5.63 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.41/5.63 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.41/5.63 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.41/5.63 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.41/5.63 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.41/5.63 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.41/5.63 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.41/5.63 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.41/5.63 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.41/5.63 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.41/5.63 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.41/5.63 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.41/5.63 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.41/5.63 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.41/5.63 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.41/5.63 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.41/5.63 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.41/5.63 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.41/5.63 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.41/5.63 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.41/5.63 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.41/5.63 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.41/5.63 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.41/5.63 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.41/5.63 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 5.41/5.63 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 5.41/5.63 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.41/5.63 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.41/5.63 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.41/5.63 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 5.41/5.63 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 5.41/5.63 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 5.41/5.63 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.63 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.41/5.63 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.41/5.63 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.63 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.41/5.63 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Extended____Nat__Oenat_J,type,
% 5.41/5.63 accp_P6183159247885693666d_enat: ( produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ) > produc7272778201969148633d_enat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.41/5.63 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.63 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Wellfounded_Oless__than,type,
% 5.41/5.63 less_than: set_Pr1261947904930325089at_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.41/5.63 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.41/5.63 fChoice_real: ( real > $o ) > real ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001_Eo,type,
% 5.41/5.63 member_o: $o > set_o > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 5.41/5.63 member_Code_integer: code_integer > set_Code_integer > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.41/5.63 member_complex: complex > set_complex > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Extended____Nat__Oenat,type,
% 5.41/5.63 member_Extended_enat: extended_enat > set_Extended_enat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Int__Oint,type,
% 5.41/5.63 member_int: int > set_int > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.63 member_list_nat: list_nat > set_list_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Nat__Onat,type,
% 5.41/5.63 member_nat: nat > set_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Num__Onum,type,
% 5.41/5.63 member_num: num > set_num > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.63 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.41/5.63 member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Rat__Orat,type,
% 5.41/5.63 member_rat: rat > set_rat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Real__Oreal,type,
% 5.41/5.63 member_real: real > set_real > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.63 member_set_nat: set_nat > set_set_nat > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.63 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_deg____,type,
% 5.41/5.63 deg: nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_m____,type,
% 5.41/5.63 m: nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_ma____,type,
% 5.41/5.63 ma: nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_mi____,type,
% 5.41/5.63 mi: nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_miny____,type,
% 5.41/5.63 miny: nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_na____,type,
% 5.41/5.63 na: nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_res____,type,
% 5.41/5.63 res: nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_sc____,type,
% 5.41/5.63 sc: nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_summary____,type,
% 5.41/5.63 summary: vEBT_VEBT ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_treeList____,type,
% 5.41/5.63 treeList: list_VEBT_VEBT ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_xa____,type,
% 5.41/5.63 xa: nat ).
% 5.41/5.63
% 5.41/5.63 thf(sy_v_za____,type,
% 5.41/5.63 za: nat ).
% 5.41/5.63
% 5.41/5.63 % Relevant facts (10210)
% 5.41/5.63 thf(fact_0_bbbb,axiom,
% 5.41/5.63 ord_less_eq_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % bbbb
% 5.41/5.63 thf(fact_1__092_060open_0622_A_092_060le_062_Adeg_092_060close_062,axiom,
% 5.41/5.63 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.41/5.63
% 5.41/5.63 % \<open>2 \<le> deg\<close>
% 5.41/5.63 thf(fact_2_aaaa,axiom,
% 5.41/5.63 ord_less_eq_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % aaaa
% 5.41/5.63 thf(fact_3_max__in__set__def,axiom,
% 5.41/5.63 ( vEBT_VEBT_max_in_set
% 5.41/5.63 = ( ^ [Xs: set_nat,X: nat] :
% 5.41/5.63 ( ( member_nat @ X @ Xs )
% 5.41/5.63 & ! [Y: nat] :
% 5.41/5.63 ( ( member_nat @ Y @ Xs )
% 5.41/5.63 => ( ord_less_eq_nat @ Y @ X ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % max_in_set_def
% 5.41/5.63 thf(fact_4_min__in__set__def,axiom,
% 5.41/5.63 ( vEBT_VEBT_min_in_set
% 5.41/5.63 = ( ^ [Xs: set_nat,X: nat] :
% 5.41/5.63 ( ( member_nat @ X @ Xs )
% 5.41/5.63 & ! [Y: nat] :
% 5.41/5.63 ( ( member_nat @ Y @ Xs )
% 5.41/5.63 => ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % min_in_set_def
% 5.41/5.63 thf(fact_5__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062,axiom,
% 5.41/5.63 ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = na ) ).
% 5.41/5.63
% 5.41/5.63 % \<open>deg div 2 = n\<close>
% 5.41/5.63 thf(fact_6_semiring__norm_I85_J,axiom,
% 5.41/5.63 ! [M: num] :
% 5.41/5.63 ( ( bit0 @ M )
% 5.41/5.63 != one ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(85)
% 5.41/5.63 thf(fact_7_semiring__norm_I83_J,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( one
% 5.41/5.63 != ( bit0 @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(83)
% 5.41/5.63 thf(fact_8_numeral__Bit0__div__2,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( numeral_numeral_nat @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_Bit0_div_2
% 5.41/5.63 thf(fact_9_numeral__Bit0__div__2,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( numeral_numeral_int @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_Bit0_div_2
% 5.41/5.63 thf(fact_10_high__def,axiom,
% 5.41/5.63 ( vEBT_VEBT_high
% 5.41/5.63 = ( ^ [X: nat,N2: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % high_def
% 5.41/5.63 thf(fact_11__092_060open_062high_Az_A_Ideg_Adiv_A2_J_A_060_Asc_092_060close_062,axiom,
% 5.41/5.63 ord_less_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc ).
% 5.41/5.63
% 5.41/5.63 % \<open>high z (deg div 2) < sc\<close>
% 5.41/5.63 thf(fact_12_divide__numeral__1,axiom,
% 5.41/5.63 ! [A: complex] :
% 5.41/5.63 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % divide_numeral_1
% 5.41/5.63 thf(fact_13_divide__numeral__1,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % divide_numeral_1
% 5.41/5.63 thf(fact_14_divide__numeral__1,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % divide_numeral_1
% 5.41/5.63 thf(fact_15_verit__eq__simplify_I8_J,axiom,
% 5.41/5.63 ! [X2: num,Y2: num] :
% 5.41/5.63 ( ( ( bit0 @ X2 )
% 5.41/5.63 = ( bit0 @ Y2 ) )
% 5.41/5.63 = ( X2 = Y2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_eq_simplify(8)
% 5.41/5.63 thf(fact_16_semiring__norm_I87_J,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ( bit0 @ M )
% 5.41/5.63 = ( bit0 @ N ) )
% 5.41/5.63 = ( M = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(87)
% 5.41/5.63 thf(fact_17_numeral__eq__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ( numera6690914467698888265omplex @ M )
% 5.41/5.63 = ( numera6690914467698888265omplex @ N ) )
% 5.41/5.63 = ( M = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_eq_iff
% 5.41/5.63 thf(fact_18_numeral__eq__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ( numeral_numeral_real @ M )
% 5.41/5.63 = ( numeral_numeral_real @ N ) )
% 5.41/5.63 = ( M = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_eq_iff
% 5.41/5.63 thf(fact_19_numeral__eq__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ( numeral_numeral_rat @ M )
% 5.41/5.63 = ( numeral_numeral_rat @ N ) )
% 5.41/5.63 = ( M = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_eq_iff
% 5.41/5.63 thf(fact_20_numeral__eq__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ( numeral_numeral_nat @ M )
% 5.41/5.63 = ( numeral_numeral_nat @ N ) )
% 5.41/5.63 = ( M = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_eq_iff
% 5.41/5.63 thf(fact_21_numeral__eq__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ( numeral_numeral_int @ M )
% 5.41/5.63 = ( numeral_numeral_int @ N ) )
% 5.41/5.63 = ( M = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_eq_iff
% 5.41/5.63 thf(fact_22_numeral__le__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.63 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_le_iff
% 5.41/5.63 thf(fact_23_numeral__le__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.63 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_le_iff
% 5.41/5.63 thf(fact_24_numeral__le__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.63 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_le_iff
% 5.41/5.63 thf(fact_25_numeral__le__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.63 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_le_iff
% 5.41/5.63 thf(fact_26_numeral__less__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.63 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_less_iff
% 5.41/5.63 thf(fact_27_numeral__less__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.63 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_less_iff
% 5.41/5.63 thf(fact_28_numeral__less__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.63 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_less_iff
% 5.41/5.63 thf(fact_29_numeral__less__iff,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.63 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_less_iff
% 5.41/5.63 thf(fact_30__092_060open_062z_A_060_A2_A_094_Adeg_092_060close_062,axiom,
% 5.41/5.63 ord_less_nat @ za @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.41/5.63
% 5.41/5.63 % \<open>z < 2 ^ deg\<close>
% 5.41/5.63 thf(fact_31__C5_Ohyps_C_I10_J,axiom,
% 5.41/5.63 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.41/5.63
% 5.41/5.63 % "5.hyps"(10)
% 5.41/5.63 thf(fact_32_verit__comp__simplify1_I3_J,axiom,
% 5.41/5.63 ! [B: real,A2: real] :
% 5.41/5.63 ( ( ~ ( ord_less_eq_real @ B @ A2 ) )
% 5.41/5.63 = ( ord_less_real @ A2 @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(3)
% 5.41/5.63 thf(fact_33_verit__comp__simplify1_I3_J,axiom,
% 5.41/5.63 ! [B: rat,A2: rat] :
% 5.41/5.63 ( ( ~ ( ord_less_eq_rat @ B @ A2 ) )
% 5.41/5.63 = ( ord_less_rat @ A2 @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(3)
% 5.41/5.63 thf(fact_34_verit__comp__simplify1_I3_J,axiom,
% 5.41/5.63 ! [B: num,A2: num] :
% 5.41/5.63 ( ( ~ ( ord_less_eq_num @ B @ A2 ) )
% 5.41/5.63 = ( ord_less_num @ A2 @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(3)
% 5.41/5.63 thf(fact_35_verit__comp__simplify1_I3_J,axiom,
% 5.41/5.63 ! [B: nat,A2: nat] :
% 5.41/5.63 ( ( ~ ( ord_less_eq_nat @ B @ A2 ) )
% 5.41/5.63 = ( ord_less_nat @ A2 @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(3)
% 5.41/5.63 thf(fact_36_verit__comp__simplify1_I3_J,axiom,
% 5.41/5.63 ! [B: int,A2: int] :
% 5.41/5.63 ( ( ~ ( ord_less_eq_int @ B @ A2 ) )
% 5.41/5.63 = ( ord_less_int @ A2 @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(3)
% 5.41/5.63 thf(fact_37_verit__comp__simplify1_I2_J,axiom,
% 5.41/5.63 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(2)
% 5.41/5.63 thf(fact_38_verit__comp__simplify1_I2_J,axiom,
% 5.41/5.63 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(2)
% 5.41/5.63 thf(fact_39_verit__comp__simplify1_I2_J,axiom,
% 5.41/5.63 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(2)
% 5.41/5.63 thf(fact_40_verit__comp__simplify1_I2_J,axiom,
% 5.41/5.63 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(2)
% 5.41/5.63 thf(fact_41_verit__comp__simplify1_I2_J,axiom,
% 5.41/5.63 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(2)
% 5.41/5.63 thf(fact_42_verit__comp__simplify1_I1_J,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ~ ( ord_less_real @ A @ A ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(1)
% 5.41/5.63 thf(fact_43_verit__comp__simplify1_I1_J,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ~ ( ord_less_rat @ A @ A ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(1)
% 5.41/5.63 thf(fact_44_verit__comp__simplify1_I1_J,axiom,
% 5.41/5.63 ! [A: num] :
% 5.41/5.63 ~ ( ord_less_num @ A @ A ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(1)
% 5.41/5.63 thf(fact_45_verit__comp__simplify1_I1_J,axiom,
% 5.41/5.63 ! [A: nat] :
% 5.41/5.63 ~ ( ord_less_nat @ A @ A ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(1)
% 5.41/5.63 thf(fact_46_verit__comp__simplify1_I1_J,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ~ ( ord_less_int @ A @ A ) ).
% 5.41/5.63
% 5.41/5.63 % verit_comp_simplify1(1)
% 5.41/5.63 thf(fact_47_verit__la__disequality,axiom,
% 5.41/5.63 ! [A: rat,B2: rat] :
% 5.41/5.63 ( ( A = B2 )
% 5.41/5.63 | ~ ( ord_less_eq_rat @ A @ B2 )
% 5.41/5.63 | ~ ( ord_less_eq_rat @ B2 @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_la_disequality
% 5.41/5.63 thf(fact_48_verit__la__disequality,axiom,
% 5.41/5.63 ! [A: num,B2: num] :
% 5.41/5.63 ( ( A = B2 )
% 5.41/5.63 | ~ ( ord_less_eq_num @ A @ B2 )
% 5.41/5.63 | ~ ( ord_less_eq_num @ B2 @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_la_disequality
% 5.41/5.63 thf(fact_49_verit__la__disequality,axiom,
% 5.41/5.63 ! [A: nat,B2: nat] :
% 5.41/5.63 ( ( A = B2 )
% 5.41/5.63 | ~ ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.63 | ~ ( ord_less_eq_nat @ B2 @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_la_disequality
% 5.41/5.63 thf(fact_50_verit__la__disequality,axiom,
% 5.41/5.63 ! [A: int,B2: int] :
% 5.41/5.63 ( ( A = B2 )
% 5.41/5.63 | ~ ( ord_less_eq_int @ A @ B2 )
% 5.41/5.63 | ~ ( ord_less_eq_int @ B2 @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_la_disequality
% 5.41/5.63 thf(fact_51_div__le__dividend,axiom,
% 5.41/5.63 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.41/5.63
% 5.41/5.63 % div_le_dividend
% 5.41/5.63 thf(fact_52_div__le__mono,axiom,
% 5.41/5.63 ! [M: nat,N: nat,K: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.63 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_le_mono
% 5.41/5.63 thf(fact_53_verit__eq__simplify_I10_J,axiom,
% 5.41/5.63 ! [X2: num] :
% 5.41/5.63 ( one
% 5.41/5.63 != ( bit0 @ X2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % verit_eq_simplify(10)
% 5.41/5.63 thf(fact_54__092_060open_062high_Ares_A_Ideg_Adiv_A2_J_A_061_Asc_092_060close_062,axiom,
% 5.41/5.63 ( ( vEBT_VEBT_high @ res @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = sc ) ).
% 5.41/5.63
% 5.41/5.63 % \<open>high res (deg div 2) = sc\<close>
% 5.41/5.63 thf(fact_55__092_060open_062x_A_060_Ares_092_060close_062,axiom,
% 5.41/5.63 ord_less_nat @ xa @ res ).
% 5.41/5.63
% 5.41/5.63 % \<open>x < res\<close>
% 5.41/5.63 thf(fact_56__092_060open_062sc_A_060_A2_A_094_Am_092_060close_062,axiom,
% 5.41/5.63 ord_less_nat @ sc @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 5.41/5.63
% 5.41/5.63 % \<open>sc < 2 ^ m\<close>
% 5.41/5.63 thf(fact_57_power2__nat__le__imp__le,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.41/5.63 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_nat_le_imp_le
% 5.41/5.63 thf(fact_58_power2__nat__le__eq__le,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_nat_le_eq_le
% 5.41/5.63 thf(fact_59_self__le__ge2__pow,axiom,
% 5.41/5.63 ! [K: nat,M: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.41/5.63 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % self_le_ge2_pow
% 5.41/5.63 thf(fact_60_less__exp,axiom,
% 5.41/5.63 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_exp
% 5.41/5.63 thf(fact_61_high__bound__aux,axiom,
% 5.41/5.63 ! [Ma: nat,N: nat,M: nat] :
% 5.41/5.63 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.41/5.63 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % high_bound_aux
% 5.41/5.63 thf(fact_62_power__minus__is__div,axiom,
% 5.41/5.63 ! [B2: nat,A: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ B2 @ A )
% 5.41/5.63 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B2 ) )
% 5.41/5.63 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_minus_is_div
% 5.41/5.63 thf(fact_63_pow__sum,axiom,
% 5.41/5.63 ! [A: nat,B2: nat] :
% 5.41/5.63 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % pow_sum
% 5.41/5.63 thf(fact_64__092_060open_0621_A_092_060le_062_An_092_060close_062,axiom,
% 5.41/5.63 ord_less_eq_nat @ one_one_nat @ na ).
% 5.41/5.63
% 5.41/5.63 % \<open>1 \<le> n\<close>
% 5.41/5.63 thf(fact_65__092_060open_062mi_A_092_060le_062_Ax_092_060close_062,axiom,
% 5.41/5.63 ord_less_eq_nat @ mi @ xa ).
% 5.41/5.63
% 5.41/5.63 % \<open>mi \<le> x\<close>
% 5.41/5.63 thf(fact_66__C5_Ohyps_C_I9_J,axiom,
% 5.41/5.63 ord_less_eq_nat @ mi @ ma ).
% 5.41/5.63
% 5.41/5.63 % "5.hyps"(9)
% 5.41/5.63 thf(fact_67__C5_Ohyps_C_I6_J,axiom,
% 5.41/5.63 ( deg
% 5.41/5.63 = ( plus_plus_nat @ na @ m ) ) ).
% 5.41/5.63
% 5.41/5.63 % "5.hyps"(6)
% 5.41/5.63 thf(fact_68__092_060open_062z_A_092_060noteq_062_Ami_092_060close_062,axiom,
% 5.41/5.63 za != mi ).
% 5.41/5.63
% 5.41/5.63 % \<open>z \<noteq> mi\<close>
% 5.41/5.63 thf(fact_69__092_060open_062mi_A_092_060noteq_062_Ama_092_060close_062,axiom,
% 5.41/5.63 mi != ma ).
% 5.41/5.63
% 5.41/5.63 % \<open>mi \<noteq> ma\<close>
% 5.41/5.63 thf(fact_70__092_060open_062res_A_092_060le_062_Ama_092_060close_062,axiom,
% 5.41/5.63 ord_less_eq_nat @ res @ ma ).
% 5.41/5.63
% 5.41/5.63 % \<open>res \<le> ma\<close>
% 5.41/5.63 thf(fact_71_mem__Collect__eq,axiom,
% 5.41/5.63 ! [A: extended_enat,P: extended_enat > $o] :
% 5.41/5.63 ( ( member_Extended_enat @ A @ ( collec4429806609662206161d_enat @ P ) )
% 5.41/5.63 = ( P @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % mem_Collect_eq
% 5.41/5.63 thf(fact_72_mem__Collect__eq,axiom,
% 5.41/5.63 ! [A: complex,P: complex > $o] :
% 5.41/5.63 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.41/5.63 = ( P @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % mem_Collect_eq
% 5.41/5.63 thf(fact_73_mem__Collect__eq,axiom,
% 5.41/5.63 ! [A: real,P: real > $o] :
% 5.41/5.63 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.41/5.63 = ( P @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % mem_Collect_eq
% 5.41/5.63 thf(fact_74_mem__Collect__eq,axiom,
% 5.41/5.63 ! [A: list_nat,P: list_nat > $o] :
% 5.41/5.63 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.41/5.63 = ( P @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % mem_Collect_eq
% 5.41/5.63 thf(fact_75_mem__Collect__eq,axiom,
% 5.41/5.63 ! [A: nat,P: nat > $o] :
% 5.41/5.63 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.41/5.63 = ( P @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % mem_Collect_eq
% 5.41/5.63 thf(fact_76_mem__Collect__eq,axiom,
% 5.41/5.63 ! [A: int,P: int > $o] :
% 5.41/5.63 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.41/5.63 = ( P @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % mem_Collect_eq
% 5.41/5.63 thf(fact_77_Collect__mem__eq,axiom,
% 5.41/5.63 ! [A3: set_Extended_enat] :
% 5.41/5.63 ( ( collec4429806609662206161d_enat
% 5.41/5.63 @ ^ [X: extended_enat] : ( member_Extended_enat @ X @ A3 ) )
% 5.41/5.63 = A3 ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_mem_eq
% 5.41/5.63 thf(fact_78_Collect__mem__eq,axiom,
% 5.41/5.63 ! [A3: set_complex] :
% 5.41/5.63 ( ( collect_complex
% 5.41/5.63 @ ^ [X: complex] : ( member_complex @ X @ A3 ) )
% 5.41/5.63 = A3 ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_mem_eq
% 5.41/5.63 thf(fact_79_Collect__mem__eq,axiom,
% 5.41/5.63 ! [A3: set_real] :
% 5.41/5.63 ( ( collect_real
% 5.41/5.63 @ ^ [X: real] : ( member_real @ X @ A3 ) )
% 5.41/5.63 = A3 ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_mem_eq
% 5.41/5.63 thf(fact_80_Collect__mem__eq,axiom,
% 5.41/5.63 ! [A3: set_list_nat] :
% 5.41/5.63 ( ( collect_list_nat
% 5.41/5.63 @ ^ [X: list_nat] : ( member_list_nat @ X @ A3 ) )
% 5.41/5.63 = A3 ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_mem_eq
% 5.41/5.63 thf(fact_81_Collect__mem__eq,axiom,
% 5.41/5.63 ! [A3: set_nat] :
% 5.41/5.63 ( ( collect_nat
% 5.41/5.63 @ ^ [X: nat] : ( member_nat @ X @ A3 ) )
% 5.41/5.63 = A3 ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_mem_eq
% 5.41/5.63 thf(fact_82_Collect__mem__eq,axiom,
% 5.41/5.63 ! [A3: set_int] :
% 5.41/5.63 ( ( collect_int
% 5.41/5.63 @ ^ [X: int] : ( member_int @ X @ A3 ) )
% 5.41/5.63 = A3 ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_mem_eq
% 5.41/5.63 thf(fact_83_Collect__cong,axiom,
% 5.41/5.63 ! [P: complex > $o,Q: complex > $o] :
% 5.41/5.63 ( ! [X3: complex] :
% 5.41/5.63 ( ( P @ X3 )
% 5.41/5.63 = ( Q @ X3 ) )
% 5.41/5.63 => ( ( collect_complex @ P )
% 5.41/5.63 = ( collect_complex @ Q ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_cong
% 5.41/5.63 thf(fact_84_Collect__cong,axiom,
% 5.41/5.63 ! [P: real > $o,Q: real > $o] :
% 5.41/5.63 ( ! [X3: real] :
% 5.41/5.63 ( ( P @ X3 )
% 5.41/5.63 = ( Q @ X3 ) )
% 5.41/5.63 => ( ( collect_real @ P )
% 5.41/5.63 = ( collect_real @ Q ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_cong
% 5.41/5.63 thf(fact_85_Collect__cong,axiom,
% 5.41/5.63 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.41/5.63 ( ! [X3: list_nat] :
% 5.41/5.63 ( ( P @ X3 )
% 5.41/5.63 = ( Q @ X3 ) )
% 5.41/5.63 => ( ( collect_list_nat @ P )
% 5.41/5.63 = ( collect_list_nat @ Q ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_cong
% 5.41/5.63 thf(fact_86_Collect__cong,axiom,
% 5.41/5.63 ! [P: nat > $o,Q: nat > $o] :
% 5.41/5.63 ( ! [X3: nat] :
% 5.41/5.63 ( ( P @ X3 )
% 5.41/5.63 = ( Q @ X3 ) )
% 5.41/5.63 => ( ( collect_nat @ P )
% 5.41/5.63 = ( collect_nat @ Q ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_cong
% 5.41/5.63 thf(fact_87_Collect__cong,axiom,
% 5.41/5.63 ! [P: int > $o,Q: int > $o] :
% 5.41/5.63 ( ! [X3: int] :
% 5.41/5.63 ( ( P @ X3 )
% 5.41/5.63 = ( Q @ X3 ) )
% 5.41/5.63 => ( ( collect_int @ P )
% 5.41/5.63 = ( collect_int @ Q ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Collect_cong
% 5.41/5.63 thf(fact_88__092_060open_062mi_A_060_Ares_092_060close_062,axiom,
% 5.41/5.63 ord_less_nat @ mi @ res ).
% 5.41/5.63
% 5.41/5.63 % \<open>mi < res\<close>
% 5.41/5.63 thf(fact_89_add__numeral__left,axiom,
% 5.41/5.63 ! [V: num,W: num,Z: complex] :
% 5.41/5.63 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.41/5.63 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_numeral_left
% 5.41/5.63 thf(fact_90_add__numeral__left,axiom,
% 5.41/5.63 ! [V: num,W: num,Z: real] :
% 5.41/5.63 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.41/5.63 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_numeral_left
% 5.41/5.63 thf(fact_91_add__numeral__left,axiom,
% 5.41/5.63 ! [V: num,W: num,Z: rat] :
% 5.41/5.63 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.41/5.63 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_numeral_left
% 5.41/5.63 thf(fact_92_add__numeral__left,axiom,
% 5.41/5.63 ! [V: num,W: num,Z: nat] :
% 5.41/5.63 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.41/5.63 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_numeral_left
% 5.41/5.63 thf(fact_93_add__numeral__left,axiom,
% 5.41/5.63 ! [V: num,W: num,Z: int] :
% 5.41/5.63 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.41/5.63 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_numeral_left
% 5.41/5.63 thf(fact_94_numeral__plus__numeral,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.41/5.63 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_plus_numeral
% 5.41/5.63 thf(fact_95_numeral__plus__numeral,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.63 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_plus_numeral
% 5.41/5.63 thf(fact_96_numeral__plus__numeral,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.63 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_plus_numeral
% 5.41/5.63 thf(fact_97_numeral__plus__numeral,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.63 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_plus_numeral
% 5.41/5.63 thf(fact_98_numeral__plus__numeral,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.63 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_plus_numeral
% 5.41/5.63 thf(fact_99_power__one,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( power_power_rat @ one_one_rat @ N )
% 5.41/5.63 = one_one_rat ) ).
% 5.41/5.63
% 5.41/5.63 % power_one
% 5.41/5.63 thf(fact_100_power__one,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( power_power_nat @ one_one_nat @ N )
% 5.41/5.63 = one_one_nat ) ).
% 5.41/5.63
% 5.41/5.63 % power_one
% 5.41/5.63 thf(fact_101_power__one,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( power_power_real @ one_one_real @ N )
% 5.41/5.63 = one_one_real ) ).
% 5.41/5.63
% 5.41/5.63 % power_one
% 5.41/5.63 thf(fact_102_power__one,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( power_power_int @ one_one_int @ N )
% 5.41/5.63 = one_one_int ) ).
% 5.41/5.63
% 5.41/5.63 % power_one
% 5.41/5.63 thf(fact_103_power__one,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( power_power_complex @ one_one_complex @ N )
% 5.41/5.63 = one_one_complex ) ).
% 5.41/5.63
% 5.41/5.63 % power_one
% 5.41/5.63 thf(fact_104_power__one__right,axiom,
% 5.41/5.63 ! [A: nat] :
% 5.41/5.63 ( ( power_power_nat @ A @ one_one_nat )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % power_one_right
% 5.41/5.63 thf(fact_105_power__one__right,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( power_power_real @ A @ one_one_nat )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % power_one_right
% 5.41/5.63 thf(fact_106_power__one__right,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( power_power_int @ A @ one_one_nat )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % power_one_right
% 5.41/5.63 thf(fact_107_power__one__right,axiom,
% 5.41/5.63 ! [A: complex] :
% 5.41/5.63 ( ( power_power_complex @ A @ one_one_nat )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % power_one_right
% 5.41/5.63 thf(fact_108_semiring__norm_I78_J,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.63 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(78)
% 5.41/5.63 thf(fact_109_semiring__norm_I71_J,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.63 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(71)
% 5.41/5.63 thf(fact_110_semiring__norm_I75_J,axiom,
% 5.41/5.63 ! [M: num] :
% 5.41/5.63 ~ ( ord_less_num @ M @ one ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(75)
% 5.41/5.63 thf(fact_111_semiring__norm_I68_J,axiom,
% 5.41/5.63 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(68)
% 5.41/5.63 thf(fact_112_numeral__eq__one__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ( numera6690914467698888265omplex @ N )
% 5.41/5.63 = one_one_complex )
% 5.41/5.63 = ( N = one ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_eq_one_iff
% 5.41/5.63 thf(fact_113_numeral__eq__one__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ( numeral_numeral_real @ N )
% 5.41/5.63 = one_one_real )
% 5.41/5.63 = ( N = one ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_eq_one_iff
% 5.41/5.63 thf(fact_114_numeral__eq__one__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ( numeral_numeral_rat @ N )
% 5.41/5.63 = one_one_rat )
% 5.41/5.63 = ( N = one ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_eq_one_iff
% 5.41/5.63 thf(fact_115_numeral__eq__one__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ( numeral_numeral_nat @ N )
% 5.41/5.63 = one_one_nat )
% 5.41/5.63 = ( N = one ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_eq_one_iff
% 5.41/5.63 thf(fact_116_numeral__eq__one__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ( numeral_numeral_int @ N )
% 5.41/5.63 = one_one_int )
% 5.41/5.63 = ( N = one ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_eq_one_iff
% 5.41/5.63 thf(fact_117_one__eq__numeral__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( one_one_complex
% 5.41/5.63 = ( numera6690914467698888265omplex @ N ) )
% 5.41/5.63 = ( one = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_eq_numeral_iff
% 5.41/5.63 thf(fact_118_one__eq__numeral__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( one_one_real
% 5.41/5.63 = ( numeral_numeral_real @ N ) )
% 5.41/5.63 = ( one = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_eq_numeral_iff
% 5.41/5.63 thf(fact_119_one__eq__numeral__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( one_one_rat
% 5.41/5.63 = ( numeral_numeral_rat @ N ) )
% 5.41/5.63 = ( one = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_eq_numeral_iff
% 5.41/5.63 thf(fact_120_one__eq__numeral__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( one_one_nat
% 5.41/5.63 = ( numeral_numeral_nat @ N ) )
% 5.41/5.63 = ( one = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_eq_numeral_iff
% 5.41/5.63 thf(fact_121_one__eq__numeral__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( one_one_int
% 5.41/5.63 = ( numeral_numeral_int @ N ) )
% 5.41/5.63 = ( one = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_eq_numeral_iff
% 5.41/5.63 thf(fact_122_power__inject__exp,axiom,
% 5.41/5.63 ! [A: real,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.63 => ( ( ( power_power_real @ A @ M )
% 5.41/5.63 = ( power_power_real @ A @ N ) )
% 5.41/5.63 = ( M = N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_inject_exp
% 5.41/5.63 thf(fact_123_power__inject__exp,axiom,
% 5.41/5.63 ! [A: rat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.63 => ( ( ( power_power_rat @ A @ M )
% 5.41/5.63 = ( power_power_rat @ A @ N ) )
% 5.41/5.63 = ( M = N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_inject_exp
% 5.41/5.63 thf(fact_124_power__inject__exp,axiom,
% 5.41/5.63 ! [A: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.63 => ( ( ( power_power_nat @ A @ M )
% 5.41/5.63 = ( power_power_nat @ A @ N ) )
% 5.41/5.63 = ( M = N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_inject_exp
% 5.41/5.63 thf(fact_125_power__inject__exp,axiom,
% 5.41/5.63 ! [A: int,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.63 => ( ( ( power_power_int @ A @ M )
% 5.41/5.63 = ( power_power_int @ A @ N ) )
% 5.41/5.63 = ( M = N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_inject_exp
% 5.41/5.63 thf(fact_126_semiring__norm_I76_J,axiom,
% 5.41/5.63 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(76)
% 5.41/5.63 thf(fact_127_semiring__norm_I69_J,axiom,
% 5.41/5.63 ! [M: num] :
% 5.41/5.63 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(69)
% 5.41/5.63 thf(fact_128__C5_Ohyps_C_I5_J,axiom,
% 5.41/5.63 ( m
% 5.41/5.63 = ( suc @ na ) ) ).
% 5.41/5.63
% 5.41/5.63 % "5.hyps"(5)
% 5.41/5.63 thf(fact_129_numeral__plus__one,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.41/5.63 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_plus_one
% 5.41/5.63 thf(fact_130_numeral__plus__one,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.41/5.63 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_plus_one
% 5.41/5.63 thf(fact_131_numeral__plus__one,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.41/5.63 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_plus_one
% 5.41/5.63 thf(fact_132_numeral__plus__one,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.41/5.63 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_plus_one
% 5.41/5.63 thf(fact_133_numeral__plus__one,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.41/5.63 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_plus_one
% 5.41/5.63 thf(fact_134_one__plus__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.41/5.63 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_plus_numeral
% 5.41/5.63 thf(fact_135_one__plus__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.41/5.63 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_plus_numeral
% 5.41/5.63 thf(fact_136_one__plus__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.41/5.63 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_plus_numeral
% 5.41/5.63 thf(fact_137_one__plus__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.41/5.63 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_plus_numeral
% 5.41/5.63 thf(fact_138_one__plus__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.41/5.63 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_plus_numeral
% 5.41/5.63 thf(fact_139_power__strict__increasing__iff,axiom,
% 5.41/5.63 ! [B2: real,X4: nat,Y3: nat] :
% 5.41/5.63 ( ( ord_less_real @ one_one_real @ B2 )
% 5.41/5.63 => ( ( ord_less_real @ ( power_power_real @ B2 @ X4 ) @ ( power_power_real @ B2 @ Y3 ) )
% 5.41/5.63 = ( ord_less_nat @ X4 @ Y3 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_increasing_iff
% 5.41/5.63 thf(fact_140_power__strict__increasing__iff,axiom,
% 5.41/5.63 ! [B2: rat,X4: nat,Y3: nat] :
% 5.41/5.63 ( ( ord_less_rat @ one_one_rat @ B2 )
% 5.41/5.63 => ( ( ord_less_rat @ ( power_power_rat @ B2 @ X4 ) @ ( power_power_rat @ B2 @ Y3 ) )
% 5.41/5.63 = ( ord_less_nat @ X4 @ Y3 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_increasing_iff
% 5.41/5.63 thf(fact_141_power__strict__increasing__iff,axiom,
% 5.41/5.63 ! [B2: nat,X4: nat,Y3: nat] :
% 5.41/5.63 ( ( ord_less_nat @ one_one_nat @ B2 )
% 5.41/5.63 => ( ( ord_less_nat @ ( power_power_nat @ B2 @ X4 ) @ ( power_power_nat @ B2 @ Y3 ) )
% 5.41/5.63 = ( ord_less_nat @ X4 @ Y3 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_increasing_iff
% 5.41/5.63 thf(fact_142_power__strict__increasing__iff,axiom,
% 5.41/5.63 ! [B2: int,X4: nat,Y3: nat] :
% 5.41/5.63 ( ( ord_less_int @ one_one_int @ B2 )
% 5.41/5.63 => ( ( ord_less_int @ ( power_power_int @ B2 @ X4 ) @ ( power_power_int @ B2 @ Y3 ) )
% 5.41/5.63 = ( ord_less_nat @ X4 @ Y3 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_increasing_iff
% 5.41/5.63 thf(fact_143_one__add__one,axiom,
% 5.41/5.63 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.41/5.63 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_add_one
% 5.41/5.63 thf(fact_144_one__add__one,axiom,
% 5.41/5.63 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.41/5.63 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_add_one
% 5.41/5.63 thf(fact_145_one__add__one,axiom,
% 5.41/5.63 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.41/5.63 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_add_one
% 5.41/5.63 thf(fact_146_one__add__one,axiom,
% 5.41/5.63 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.41/5.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_add_one
% 5.41/5.63 thf(fact_147_one__add__one,axiom,
% 5.41/5.63 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.41/5.63 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_add_one
% 5.41/5.63 thf(fact_148_power__increasing__iff,axiom,
% 5.41/5.63 ! [B2: real,X4: nat,Y3: nat] :
% 5.41/5.63 ( ( ord_less_real @ one_one_real @ B2 )
% 5.41/5.63 => ( ( ord_less_eq_real @ ( power_power_real @ B2 @ X4 ) @ ( power_power_real @ B2 @ Y3 ) )
% 5.41/5.63 = ( ord_less_eq_nat @ X4 @ Y3 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_increasing_iff
% 5.41/5.63 thf(fact_149_power__increasing__iff,axiom,
% 5.41/5.63 ! [B2: rat,X4: nat,Y3: nat] :
% 5.41/5.63 ( ( ord_less_rat @ one_one_rat @ B2 )
% 5.41/5.63 => ( ( ord_less_eq_rat @ ( power_power_rat @ B2 @ X4 ) @ ( power_power_rat @ B2 @ Y3 ) )
% 5.41/5.63 = ( ord_less_eq_nat @ X4 @ Y3 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_increasing_iff
% 5.41/5.63 thf(fact_150_power__increasing__iff,axiom,
% 5.41/5.63 ! [B2: nat,X4: nat,Y3: nat] :
% 5.41/5.63 ( ( ord_less_nat @ one_one_nat @ B2 )
% 5.41/5.63 => ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ X4 ) @ ( power_power_nat @ B2 @ Y3 ) )
% 5.41/5.63 = ( ord_less_eq_nat @ X4 @ Y3 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_increasing_iff
% 5.41/5.63 thf(fact_151_power__increasing__iff,axiom,
% 5.41/5.63 ! [B2: int,X4: nat,Y3: nat] :
% 5.41/5.63 ( ( ord_less_int @ one_one_int @ B2 )
% 5.41/5.63 => ( ( ord_less_eq_int @ ( power_power_int @ B2 @ X4 ) @ ( power_power_int @ B2 @ Y3 ) )
% 5.41/5.63 = ( ord_less_eq_nat @ X4 @ Y3 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_increasing_iff
% 5.41/5.63 thf(fact_152_add__self__div__2,axiom,
% 5.41/5.63 ! [M: nat] :
% 5.41/5.63 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = M ) ).
% 5.41/5.63
% 5.41/5.63 % add_self_div_2
% 5.41/5.63 thf(fact_153_numeral__le__one__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.41/5.63 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_le_one_iff
% 5.41/5.63 thf(fact_154_numeral__le__one__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.41/5.63 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_le_one_iff
% 5.41/5.63 thf(fact_155_numeral__le__one__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.41/5.63 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_le_one_iff
% 5.41/5.63 thf(fact_156_numeral__le__one__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.41/5.63 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_le_one_iff
% 5.41/5.63 thf(fact_157_one__less__numeral__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.41/5.63 = ( ord_less_num @ one @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_less_numeral_iff
% 5.41/5.63 thf(fact_158_one__less__numeral__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.41/5.63 = ( ord_less_num @ one @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_less_numeral_iff
% 5.41/5.63 thf(fact_159_one__less__numeral__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.41/5.63 = ( ord_less_num @ one @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_less_numeral_iff
% 5.41/5.63 thf(fact_160_one__less__numeral__iff,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.41/5.63 = ( ord_less_num @ one @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_less_numeral_iff
% 5.41/5.63 thf(fact_161_is__num__normalize_I1_J,axiom,
% 5.41/5.63 ! [A: real,B2: real,C: real] :
% 5.41/5.63 ( ( plus_plus_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 5.41/5.63 = ( plus_plus_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % is_num_normalize(1)
% 5.41/5.63 thf(fact_162_is__num__normalize_I1_J,axiom,
% 5.41/5.63 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.63 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B2 ) @ C )
% 5.41/5.63 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % is_num_normalize(1)
% 5.41/5.63 thf(fact_163_is__num__normalize_I1_J,axiom,
% 5.41/5.63 ! [A: int,B2: int,C: int] :
% 5.41/5.63 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.41/5.63 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % is_num_normalize(1)
% 5.41/5.63 thf(fact_164_one__plus__numeral__commute,axiom,
% 5.41/5.63 ! [X4: num] :
% 5.41/5.63 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X4 ) )
% 5.41/5.63 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X4 ) @ one_one_complex ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_plus_numeral_commute
% 5.41/5.63 thf(fact_165_one__plus__numeral__commute,axiom,
% 5.41/5.63 ! [X4: num] :
% 5.41/5.63 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X4 ) )
% 5.41/5.63 = ( plus_plus_real @ ( numeral_numeral_real @ X4 ) @ one_one_real ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_plus_numeral_commute
% 5.41/5.63 thf(fact_166_one__plus__numeral__commute,axiom,
% 5.41/5.63 ! [X4: num] :
% 5.41/5.63 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X4 ) )
% 5.41/5.63 = ( plus_plus_rat @ ( numeral_numeral_rat @ X4 ) @ one_one_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_plus_numeral_commute
% 5.41/5.63 thf(fact_167_one__plus__numeral__commute,axiom,
% 5.41/5.63 ! [X4: num] :
% 5.41/5.63 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X4 ) )
% 5.41/5.63 = ( plus_plus_nat @ ( numeral_numeral_nat @ X4 ) @ one_one_nat ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_plus_numeral_commute
% 5.41/5.63 thf(fact_168_one__plus__numeral__commute,axiom,
% 5.41/5.63 ! [X4: num] :
% 5.41/5.63 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X4 ) )
% 5.41/5.63 = ( plus_plus_int @ ( numeral_numeral_int @ X4 ) @ one_one_int ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_plus_numeral_commute
% 5.41/5.63 thf(fact_169_le__num__One__iff,axiom,
% 5.41/5.63 ! [X4: num] :
% 5.41/5.63 ( ( ord_less_eq_num @ X4 @ one )
% 5.41/5.63 = ( X4 = one ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_num_One_iff
% 5.41/5.63 thf(fact_170_le__numeral__extra_I4_J,axiom,
% 5.41/5.63 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.41/5.63
% 5.41/5.63 % le_numeral_extra(4)
% 5.41/5.63 thf(fact_171_le__numeral__extra_I4_J,axiom,
% 5.41/5.63 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.41/5.63
% 5.41/5.63 % le_numeral_extra(4)
% 5.41/5.63 thf(fact_172_le__numeral__extra_I4_J,axiom,
% 5.41/5.63 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.41/5.63
% 5.41/5.63 % le_numeral_extra(4)
% 5.41/5.63 thf(fact_173_le__numeral__extra_I4_J,axiom,
% 5.41/5.63 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.41/5.63
% 5.41/5.63 % le_numeral_extra(4)
% 5.41/5.63 thf(fact_174_less__numeral__extra_I4_J,axiom,
% 5.41/5.63 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.41/5.63
% 5.41/5.63 % less_numeral_extra(4)
% 5.41/5.63 thf(fact_175_less__numeral__extra_I4_J,axiom,
% 5.41/5.63 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.41/5.63
% 5.41/5.63 % less_numeral_extra(4)
% 5.41/5.63 thf(fact_176_less__numeral__extra_I4_J,axiom,
% 5.41/5.63 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.41/5.63
% 5.41/5.63 % less_numeral_extra(4)
% 5.41/5.63 thf(fact_177_less__numeral__extra_I4_J,axiom,
% 5.41/5.63 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.41/5.63
% 5.41/5.63 % less_numeral_extra(4)
% 5.41/5.63 thf(fact_178_one__le__power,axiom,
% 5.41/5.63 ! [A: real,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.41/5.63 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_le_power
% 5.41/5.63 thf(fact_179_one__le__power,axiom,
% 5.41/5.63 ! [A: rat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.41/5.63 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_le_power
% 5.41/5.63 thf(fact_180_one__le__power,axiom,
% 5.41/5.63 ! [A: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.41/5.63 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_le_power
% 5.41/5.63 thf(fact_181_one__le__power,axiom,
% 5.41/5.63 ! [A: int,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.41/5.63 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_le_power
% 5.41/5.63 thf(fact_182_power__one__over,axiom,
% 5.41/5.63 ! [A: complex,N: nat] :
% 5.41/5.63 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 5.41/5.63 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_one_over
% 5.41/5.63 thf(fact_183_power__one__over,axiom,
% 5.41/5.63 ! [A: real,N: nat] :
% 5.41/5.63 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 5.41/5.63 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_one_over
% 5.41/5.63 thf(fact_184_power__one__over,axiom,
% 5.41/5.63 ! [A: rat,N: nat] :
% 5.41/5.63 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 5.41/5.63 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_one_over
% 5.41/5.63 thf(fact_185_nat__1__add__1,axiom,
% 5.41/5.63 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.41/5.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nat_1_add_1
% 5.41/5.63 thf(fact_186_numeral__Bit0,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.41/5.63 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_Bit0
% 5.41/5.63 thf(fact_187_numeral__Bit0,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.41/5.63 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_Bit0
% 5.41/5.63 thf(fact_188_numeral__Bit0,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.41/5.63 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_Bit0
% 5.41/5.63 thf(fact_189_numeral__Bit0,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.41/5.63 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_Bit0
% 5.41/5.63 thf(fact_190_numeral__Bit0,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.41/5.63 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_Bit0
% 5.41/5.63 thf(fact_191_power__strict__increasing,axiom,
% 5.41/5.63 ! [N: nat,N3: nat,A: real] :
% 5.41/5.63 ( ( ord_less_nat @ N @ N3 )
% 5.41/5.63 => ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.63 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N3 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_increasing
% 5.41/5.63 thf(fact_192_power__strict__increasing,axiom,
% 5.41/5.63 ! [N: nat,N3: nat,A: rat] :
% 5.41/5.63 ( ( ord_less_nat @ N @ N3 )
% 5.41/5.63 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.63 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N3 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_increasing
% 5.41/5.63 thf(fact_193_power__strict__increasing,axiom,
% 5.41/5.63 ! [N: nat,N3: nat,A: nat] :
% 5.41/5.63 ( ( ord_less_nat @ N @ N3 )
% 5.41/5.63 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.63 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N3 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_increasing
% 5.41/5.63 thf(fact_194_power__strict__increasing,axiom,
% 5.41/5.63 ! [N: nat,N3: nat,A: int] :
% 5.41/5.63 ( ( ord_less_nat @ N @ N3 )
% 5.41/5.63 => ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.63 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N3 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_increasing
% 5.41/5.63 thf(fact_195_power__less__imp__less__exp,axiom,
% 5.41/5.63 ! [A: real,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.63 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.41/5.63 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_less_imp_less_exp
% 5.41/5.63 thf(fact_196_power__less__imp__less__exp,axiom,
% 5.41/5.63 ! [A: rat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.63 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.41/5.63 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_less_imp_less_exp
% 5.41/5.63 thf(fact_197_power__less__imp__less__exp,axiom,
% 5.41/5.63 ! [A: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.63 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.41/5.63 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_less_imp_less_exp
% 5.41/5.63 thf(fact_198_power__less__imp__less__exp,axiom,
% 5.41/5.63 ! [A: int,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.63 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.41/5.63 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_less_imp_less_exp
% 5.41/5.63 thf(fact_199_power__increasing,axiom,
% 5.41/5.63 ! [N: nat,N3: nat,A: real] :
% 5.41/5.63 ( ( ord_less_eq_nat @ N @ N3 )
% 5.41/5.63 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.41/5.63 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N3 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_increasing
% 5.41/5.63 thf(fact_200_power__increasing,axiom,
% 5.41/5.63 ! [N: nat,N3: nat,A: rat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ N @ N3 )
% 5.41/5.63 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.41/5.63 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N3 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_increasing
% 5.41/5.63 thf(fact_201_power__increasing,axiom,
% 5.41/5.63 ! [N: nat,N3: nat,A: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ N @ N3 )
% 5.41/5.63 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.41/5.63 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N3 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_increasing
% 5.41/5.63 thf(fact_202_power__increasing,axiom,
% 5.41/5.63 ! [N: nat,N3: nat,A: int] :
% 5.41/5.63 ( ( ord_less_eq_nat @ N @ N3 )
% 5.41/5.63 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.41/5.63 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N3 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_increasing
% 5.41/5.63 thf(fact_203_one__le__numeral,axiom,
% 5.41/5.63 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_le_numeral
% 5.41/5.63 thf(fact_204_one__le__numeral,axiom,
% 5.41/5.63 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_le_numeral
% 5.41/5.63 thf(fact_205_one__le__numeral,axiom,
% 5.41/5.63 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_le_numeral
% 5.41/5.63 thf(fact_206_one__le__numeral,axiom,
% 5.41/5.63 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_le_numeral
% 5.41/5.63 thf(fact_207_not__numeral__less__one,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.41/5.63
% 5.41/5.63 % not_numeral_less_one
% 5.41/5.63 thf(fact_208_not__numeral__less__one,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.41/5.63
% 5.41/5.63 % not_numeral_less_one
% 5.41/5.63 thf(fact_209_not__numeral__less__one,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.41/5.63
% 5.41/5.63 % not_numeral_less_one
% 5.41/5.63 thf(fact_210_not__numeral__less__one,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.41/5.63
% 5.41/5.63 % not_numeral_less_one
% 5.41/5.63 thf(fact_211_numeral__One,axiom,
% 5.41/5.63 ( ( numera6690914467698888265omplex @ one )
% 5.41/5.63 = one_one_complex ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_One
% 5.41/5.63 thf(fact_212_numeral__One,axiom,
% 5.41/5.63 ( ( numeral_numeral_real @ one )
% 5.41/5.63 = one_one_real ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_One
% 5.41/5.63 thf(fact_213_numeral__One,axiom,
% 5.41/5.63 ( ( numeral_numeral_rat @ one )
% 5.41/5.63 = one_one_rat ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_One
% 5.41/5.63 thf(fact_214_numeral__One,axiom,
% 5.41/5.63 ( ( numeral_numeral_nat @ one )
% 5.41/5.63 = one_one_nat ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_One
% 5.41/5.63 thf(fact_215_numeral__One,axiom,
% 5.41/5.63 ( ( numeral_numeral_int @ one )
% 5.41/5.63 = one_one_int ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_One
% 5.41/5.63 thf(fact_216_numerals_I1_J,axiom,
% 5.41/5.63 ( ( numeral_numeral_nat @ one )
% 5.41/5.63 = one_one_nat ) ).
% 5.41/5.63
% 5.41/5.63 % numerals(1)
% 5.41/5.63 thf(fact_217_ex__power__ivl1,axiom,
% 5.41/5.63 ! [B2: nat,K: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.41/5.63 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.41/5.63 => ? [N4: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ N4 ) @ K )
% 5.41/5.63 & ( ord_less_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % ex_power_ivl1
% 5.41/5.63 thf(fact_218_ex__power__ivl2,axiom,
% 5.41/5.63 ! [B2: nat,K: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.41/5.63 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.41/5.63 => ? [N4: nat] :
% 5.41/5.63 ( ( ord_less_nat @ ( power_power_nat @ B2 @ N4 ) @ K )
% 5.41/5.63 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % ex_power_ivl2
% 5.41/5.63 thf(fact_219_power2__commute,axiom,
% 5.41/5.63 ! [X4: complex,Y3: complex] :
% 5.41/5.63 ( ( power_power_complex @ ( minus_minus_complex @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( power_power_complex @ ( minus_minus_complex @ Y3 @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_commute
% 5.41/5.63 thf(fact_220_power2__commute,axiom,
% 5.41/5.63 ! [X4: real,Y3: real] :
% 5.41/5.63 ( ( power_power_real @ ( minus_minus_real @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( power_power_real @ ( minus_minus_real @ Y3 @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_commute
% 5.41/5.63 thf(fact_221_power2__commute,axiom,
% 5.41/5.63 ! [X4: rat,Y3: rat] :
% 5.41/5.63 ( ( power_power_rat @ ( minus_minus_rat @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( power_power_rat @ ( minus_minus_rat @ Y3 @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_commute
% 5.41/5.63 thf(fact_222_power2__commute,axiom,
% 5.41/5.63 ! [X4: int,Y3: int] :
% 5.41/5.63 ( ( power_power_int @ ( minus_minus_int @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( power_power_int @ ( minus_minus_int @ Y3 @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_commute
% 5.41/5.63 thf(fact_223_power__le__imp__le__exp,axiom,
% 5.41/5.63 ! [A: real,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.63 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.41/5.63 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_le_imp_le_exp
% 5.41/5.63 thf(fact_224_power__le__imp__le__exp,axiom,
% 5.41/5.63 ! [A: rat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.63 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.41/5.63 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_le_imp_le_exp
% 5.41/5.63 thf(fact_225_power__le__imp__le__exp,axiom,
% 5.41/5.63 ! [A: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.63 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.41/5.63 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_le_imp_le_exp
% 5.41/5.63 thf(fact_226_power__le__imp__le__exp,axiom,
% 5.41/5.63 ! [A: int,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.63 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.41/5.63 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_le_imp_le_exp
% 5.41/5.63 thf(fact_227_one__power2,axiom,
% 5.41/5.63 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_rat ) ).
% 5.41/5.63
% 5.41/5.63 % one_power2
% 5.41/5.63 thf(fact_228_one__power2,axiom,
% 5.41/5.63 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_nat ) ).
% 5.41/5.63
% 5.41/5.63 % one_power2
% 5.41/5.63 thf(fact_229_one__power2,axiom,
% 5.41/5.63 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_real ) ).
% 5.41/5.63
% 5.41/5.63 % one_power2
% 5.41/5.63 thf(fact_230_one__power2,axiom,
% 5.41/5.63 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_int ) ).
% 5.41/5.63
% 5.41/5.63 % one_power2
% 5.41/5.63 thf(fact_231_one__power2,axiom,
% 5.41/5.63 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_complex ) ).
% 5.41/5.63
% 5.41/5.63 % one_power2
% 5.41/5.63 thf(fact_232_diff__le__diff__pow,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.41/5.63 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_le_diff_pow
% 5.41/5.63 thf(fact_233_power__divide,axiom,
% 5.41/5.63 ! [A: complex,B2: complex,N: nat] :
% 5.41/5.63 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B2 ) @ N )
% 5.41/5.63 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B2 @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_divide
% 5.41/5.63 thf(fact_234_power__divide,axiom,
% 5.41/5.63 ! [A: real,B2: real,N: nat] :
% 5.41/5.63 ( ( power_power_real @ ( divide_divide_real @ A @ B2 ) @ N )
% 5.41/5.63 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B2 @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_divide
% 5.41/5.63 thf(fact_235_power__divide,axiom,
% 5.41/5.63 ! [A: rat,B2: rat,N: nat] :
% 5.41/5.63 ( ( power_power_rat @ ( divide_divide_rat @ A @ B2 ) @ N )
% 5.41/5.63 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_divide
% 5.41/5.63 thf(fact_236_Nat_Oadd__diff__assoc,axiom,
% 5.41/5.63 ! [K: nat,J: nat,I: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.63 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.41/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Nat.add_diff_assoc
% 5.41/5.63 thf(fact_237_Nat_Oadd__diff__assoc2,axiom,
% 5.41/5.63 ! [K: nat,J: nat,I: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.63 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.41/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Nat.add_diff_assoc2
% 5.41/5.63 thf(fact_238_Nat_Odiff__diff__right,axiom,
% 5.41/5.63 ! [K: nat,J: nat,I: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.63 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.41/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Nat.diff_diff_right
% 5.41/5.63 thf(fact_239__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,
% 5.41/5.63 ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.41/5.63 & ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % \<open>high x n < 2 ^ m \<and> low x n < 2 ^ n\<close>
% 5.41/5.63 thf(fact_240_le__add__diff__inverse,axiom,
% 5.41/5.63 ! [B2: real,A: real] :
% 5.41/5.63 ( ( ord_less_eq_real @ B2 @ A )
% 5.41/5.63 => ( ( plus_plus_real @ B2 @ ( minus_minus_real @ A @ B2 ) )
% 5.41/5.63 = A ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_add_diff_inverse
% 5.41/5.63 thf(fact_241_le__add__diff__inverse,axiom,
% 5.41/5.63 ! [B2: rat,A: rat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ B2 @ A )
% 5.41/5.63 => ( ( plus_plus_rat @ B2 @ ( minus_minus_rat @ A @ B2 ) )
% 5.41/5.63 = A ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_add_diff_inverse
% 5.41/5.63 thf(fact_242_le__add__diff__inverse,axiom,
% 5.41/5.63 ! [B2: nat,A: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ B2 @ A )
% 5.41/5.63 => ( ( plus_plus_nat @ B2 @ ( minus_minus_nat @ A @ B2 ) )
% 5.41/5.63 = A ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_add_diff_inverse
% 5.41/5.63 thf(fact_243_le__add__diff__inverse,axiom,
% 5.41/5.63 ! [B2: int,A: int] :
% 5.41/5.63 ( ( ord_less_eq_int @ B2 @ A )
% 5.41/5.63 => ( ( plus_plus_int @ B2 @ ( minus_minus_int @ A @ B2 ) )
% 5.41/5.63 = A ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_add_diff_inverse
% 5.41/5.63 thf(fact_244_le__add__diff__inverse2,axiom,
% 5.41/5.63 ! [B2: real,A: real] :
% 5.41/5.63 ( ( ord_less_eq_real @ B2 @ A )
% 5.41/5.63 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B2 ) @ B2 )
% 5.41/5.63 = A ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_add_diff_inverse2
% 5.41/5.63 thf(fact_245_le__add__diff__inverse2,axiom,
% 5.41/5.63 ! [B2: rat,A: rat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ B2 @ A )
% 5.41/5.63 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B2 ) @ B2 )
% 5.41/5.63 = A ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_add_diff_inverse2
% 5.41/5.63 thf(fact_246_le__add__diff__inverse2,axiom,
% 5.41/5.63 ! [B2: nat,A: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ B2 @ A )
% 5.41/5.63 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B2 ) @ B2 )
% 5.41/5.63 = A ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_add_diff_inverse2
% 5.41/5.63 thf(fact_247_le__add__diff__inverse2,axiom,
% 5.41/5.63 ! [B2: int,A: int] :
% 5.41/5.63 ( ( ord_less_eq_int @ B2 @ A )
% 5.41/5.63 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B2 ) @ B2 )
% 5.41/5.63 = A ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_add_diff_inverse2
% 5.41/5.63 thf(fact_248_div__exp__eq,axiom,
% 5.41/5.63 ! [A: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( 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 ) )
% 5.41/5.63 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_exp_eq
% 5.41/5.63 thf(fact_249_div__exp__eq,axiom,
% 5.41/5.63 ! [A: int,M: nat,N: nat] :
% 5.41/5.63 ( ( 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 ) )
% 5.41/5.63 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_exp_eq
% 5.41/5.63 thf(fact_250_field__less__half__sum,axiom,
% 5.41/5.63 ! [X4: real,Y3: real] :
% 5.41/5.63 ( ( ord_less_real @ X4 @ Y3 )
% 5.41/5.63 => ( ord_less_real @ X4 @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % field_less_half_sum
% 5.41/5.63 thf(fact_251_field__less__half__sum,axiom,
% 5.41/5.63 ! [X4: rat,Y3: rat] :
% 5.41/5.63 ( ( ord_less_rat @ X4 @ Y3 )
% 5.41/5.63 => ( ord_less_rat @ X4 @ ( divide_divide_rat @ ( plus_plus_rat @ X4 @ Y3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % field_less_half_sum
% 5.41/5.63 thf(fact_252_high__inv,axiom,
% 5.41/5.63 ! [X4: nat,N: nat,Y3: nat] :
% 5.41/5.63 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.63 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X4 ) @ N )
% 5.41/5.63 = Y3 ) ) ).
% 5.41/5.63
% 5.41/5.63 % high_inv
% 5.41/5.63 thf(fact_253_diff__diff__left,axiom,
% 5.41/5.63 ! [I: nat,J: nat,K: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.41/5.63 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_diff_left
% 5.41/5.63 thf(fact_254_diff__diff__cancel,axiom,
% 5.41/5.63 ! [I: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ I @ N )
% 5.41/5.63 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 5.41/5.63 = I ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_diff_cancel
% 5.41/5.63 thf(fact_255_nat__add__left__cancel__le,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.41/5.63 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % nat_add_left_cancel_le
% 5.41/5.63 thf(fact_256_even__odd__cases,axiom,
% 5.41/5.63 ! [X4: nat] :
% 5.41/5.63 ( ! [N4: nat] :
% 5.41/5.63 ( X4
% 5.41/5.63 != ( plus_plus_nat @ N4 @ N4 ) )
% 5.41/5.63 => ~ ! [N4: nat] :
% 5.41/5.63 ( X4
% 5.41/5.63 != ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % even_odd_cases
% 5.41/5.63 thf(fact_257_bit__split__inv,axiom,
% 5.41/5.63 ! [X4: nat,D: nat] :
% 5.41/5.63 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X4 @ D ) @ ( vEBT_VEBT_low @ X4 @ D ) @ D )
% 5.41/5.63 = X4 ) ).
% 5.41/5.63
% 5.41/5.63 % bit_split_inv
% 5.41/5.63 thf(fact_258_nat_Oinject,axiom,
% 5.41/5.63 ! [X2: nat,Y2: nat] :
% 5.41/5.63 ( ( ( suc @ X2 )
% 5.41/5.63 = ( suc @ Y2 ) )
% 5.41/5.63 = ( X2 = Y2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % nat.inject
% 5.41/5.63 thf(fact_259_old_Onat_Oinject,axiom,
% 5.41/5.63 ! [Nat: nat,Nat2: nat] :
% 5.41/5.63 ( ( ( suc @ Nat )
% 5.41/5.63 = ( suc @ Nat2 ) )
% 5.41/5.63 = ( Nat = Nat2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % old.nat.inject
% 5.41/5.63 thf(fact_260_numeral__times__numeral,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.41/5.63 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_times_numeral
% 5.41/5.63 thf(fact_261_numeral__times__numeral,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.63 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_times_numeral
% 5.41/5.63 thf(fact_262_numeral__times__numeral,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.63 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_times_numeral
% 5.41/5.63 thf(fact_263_numeral__times__numeral,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.63 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_times_numeral
% 5.41/5.63 thf(fact_264_numeral__times__numeral,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.63 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % numeral_times_numeral
% 5.41/5.63 thf(fact_265_mult__numeral__left__semiring__numeral,axiom,
% 5.41/5.63 ! [V: num,W: num,Z: complex] :
% 5.41/5.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.41/5.63 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_numeral_left_semiring_numeral
% 5.41/5.63 thf(fact_266_mult__numeral__left__semiring__numeral,axiom,
% 5.41/5.63 ! [V: num,W: num,Z: real] :
% 5.41/5.63 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.41/5.63 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_numeral_left_semiring_numeral
% 5.41/5.63 thf(fact_267_mult__numeral__left__semiring__numeral,axiom,
% 5.41/5.63 ! [V: num,W: num,Z: rat] :
% 5.41/5.63 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.41/5.63 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_numeral_left_semiring_numeral
% 5.41/5.63 thf(fact_268_mult__numeral__left__semiring__numeral,axiom,
% 5.41/5.63 ! [V: num,W: num,Z: nat] :
% 5.41/5.63 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.41/5.63 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_numeral_left_semiring_numeral
% 5.41/5.63 thf(fact_269_mult__numeral__left__semiring__numeral,axiom,
% 5.41/5.63 ! [V: num,W: num,Z: int] :
% 5.41/5.63 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.41/5.63 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_numeral_left_semiring_numeral
% 5.41/5.63 thf(fact_270_low__inv,axiom,
% 5.41/5.63 ! [X4: nat,N: nat,Y3: nat] :
% 5.41/5.63 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.63 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X4 ) @ N )
% 5.41/5.63 = X4 ) ) ).
% 5.41/5.63
% 5.41/5.63 % low_inv
% 5.41/5.63 thf(fact_271_bits__div__by__1,axiom,
% 5.41/5.63 ! [A: nat] :
% 5.41/5.63 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % bits_div_by_1
% 5.41/5.63 thf(fact_272_bits__div__by__1,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( divide_divide_int @ A @ one_one_int )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % bits_div_by_1
% 5.41/5.63 thf(fact_273_div__by__1,axiom,
% 5.41/5.63 ! [A: complex] :
% 5.41/5.63 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % div_by_1
% 5.41/5.63 thf(fact_274_div__by__1,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( divide_divide_real @ A @ one_one_real )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % div_by_1
% 5.41/5.63 thf(fact_275_div__by__1,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % div_by_1
% 5.41/5.63 thf(fact_276_div__by__1,axiom,
% 5.41/5.63 ! [A: nat] :
% 5.41/5.63 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % div_by_1
% 5.41/5.63 thf(fact_277_div__by__1,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( divide_divide_int @ A @ one_one_int )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % div_by_1
% 5.41/5.63 thf(fact_278_lessI,axiom,
% 5.41/5.63 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % lessI
% 5.41/5.63 thf(fact_279_Suc__mono,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ M @ N )
% 5.41/5.63 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Suc_mono
% 5.41/5.63 thf(fact_280_Suc__less__eq,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.41/5.63 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % Suc_less_eq
% 5.41/5.63 thf(fact_281_Suc__le__mono,axiom,
% 5.41/5.63 ! [N: nat,M: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.41/5.63 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.41/5.63
% 5.41/5.63 % Suc_le_mono
% 5.41/5.63 thf(fact_282_add__Suc__right,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.41/5.63 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_Suc_right
% 5.41/5.63 thf(fact_283_nat__add__left__cancel__less,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.41/5.63 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % nat_add_left_cancel_less
% 5.41/5.63 thf(fact_284_diff__Suc__Suc,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.41/5.63 = ( minus_minus_nat @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_Suc_Suc
% 5.41/5.63 thf(fact_285_Suc__diff__diff,axiom,
% 5.41/5.63 ! [M: nat,N: nat,K: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.41/5.63 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.41/5.63
% 5.41/5.63 % Suc_diff_diff
% 5.41/5.63 thf(fact_286_nat__1__eq__mult__iff,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( one_one_nat
% 5.41/5.63 = ( times_times_nat @ M @ N ) )
% 5.41/5.63 = ( ( M = one_one_nat )
% 5.41/5.63 & ( N = one_one_nat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nat_1_eq_mult_iff
% 5.41/5.63 thf(fact_287_nat__mult__eq__1__iff,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( ( times_times_nat @ M @ N )
% 5.41/5.63 = one_one_nat )
% 5.41/5.63 = ( ( M = one_one_nat )
% 5.41/5.63 & ( N = one_one_nat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nat_mult_eq_1_iff
% 5.41/5.63 thf(fact_288_semiring__norm_I6_J,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.63 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(6)
% 5.41/5.63 thf(fact_289_bit__concat__def,axiom,
% 5.41/5.63 ( vEBT_VEBT_bit_concat
% 5.41/5.63 = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % bit_concat_def
% 5.41/5.63 thf(fact_290_distrib__left__numeral,axiom,
% 5.41/5.63 ! [V: num,B2: complex,C: complex] :
% 5.41/5.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B2 @ C ) )
% 5.41/5.63 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B2 ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % distrib_left_numeral
% 5.41/5.63 thf(fact_291_distrib__left__numeral,axiom,
% 5.41/5.63 ! [V: num,B2: real,C: real] :
% 5.41/5.63 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B2 @ C ) )
% 5.41/5.63 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B2 ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % distrib_left_numeral
% 5.41/5.63 thf(fact_292_distrib__left__numeral,axiom,
% 5.41/5.63 ! [V: num,B2: rat,C: rat] :
% 5.41/5.63 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B2 @ C ) )
% 5.41/5.63 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B2 ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % distrib_left_numeral
% 5.41/5.63 thf(fact_293_distrib__left__numeral,axiom,
% 5.41/5.63 ! [V: num,B2: nat,C: nat] :
% 5.41/5.63 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B2 @ C ) )
% 5.41/5.63 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % distrib_left_numeral
% 5.41/5.63 thf(fact_294_distrib__left__numeral,axiom,
% 5.41/5.63 ! [V: num,B2: int,C: int] :
% 5.41/5.63 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B2 @ C ) )
% 5.41/5.63 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % distrib_left_numeral
% 5.41/5.63 thf(fact_295_distrib__right__numeral,axiom,
% 5.41/5.63 ! [A: complex,B2: complex,V: num] :
% 5.41/5.63 ( ( times_times_complex @ ( plus_plus_complex @ A @ B2 ) @ ( numera6690914467698888265omplex @ V ) )
% 5.41/5.63 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B2 @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % distrib_right_numeral
% 5.41/5.63 thf(fact_296_distrib__right__numeral,axiom,
% 5.41/5.63 ! [A: real,B2: real,V: num] :
% 5.41/5.63 ( ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.63 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B2 @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % distrib_right_numeral
% 5.41/5.63 thf(fact_297_distrib__right__numeral,axiom,
% 5.41/5.63 ! [A: rat,B2: rat,V: num] :
% 5.41/5.63 ( ( times_times_rat @ ( plus_plus_rat @ A @ B2 ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.63 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B2 @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % distrib_right_numeral
% 5.41/5.63 thf(fact_298_distrib__right__numeral,axiom,
% 5.41/5.63 ! [A: nat,B2: nat,V: num] :
% 5.41/5.63 ( ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ ( numeral_numeral_nat @ V ) )
% 5.41/5.63 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B2 @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % distrib_right_numeral
% 5.41/5.63 thf(fact_299_distrib__right__numeral,axiom,
% 5.41/5.63 ! [A: int,B2: int,V: num] :
% 5.41/5.63 ( ( times_times_int @ ( plus_plus_int @ A @ B2 ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.63 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B2 @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % distrib_right_numeral
% 5.41/5.63 thf(fact_300_left__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [A: complex,B2: complex,V: num] :
% 5.41/5.63 ( ( times_times_complex @ ( minus_minus_complex @ A @ B2 ) @ ( numera6690914467698888265omplex @ V ) )
% 5.41/5.63 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B2 @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib_numeral
% 5.41/5.63 thf(fact_301_left__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [A: real,B2: real,V: num] :
% 5.41/5.63 ( ( times_times_real @ ( minus_minus_real @ A @ B2 ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.63 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B2 @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib_numeral
% 5.41/5.63 thf(fact_302_left__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [A: rat,B2: rat,V: num] :
% 5.41/5.63 ( ( times_times_rat @ ( minus_minus_rat @ A @ B2 ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.63 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B2 @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib_numeral
% 5.41/5.63 thf(fact_303_left__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [A: int,B2: int,V: num] :
% 5.41/5.63 ( ( times_times_int @ ( minus_minus_int @ A @ B2 ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.63 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B2 @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib_numeral
% 5.41/5.63 thf(fact_304_right__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [V: num,B2: complex,C: complex] :
% 5.41/5.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B2 @ C ) )
% 5.41/5.63 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B2 ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib_numeral
% 5.41/5.63 thf(fact_305_right__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [V: num,B2: real,C: real] :
% 5.41/5.63 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B2 @ C ) )
% 5.41/5.63 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B2 ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib_numeral
% 5.41/5.63 thf(fact_306_right__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [V: num,B2: rat,C: rat] :
% 5.41/5.63 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B2 @ C ) )
% 5.41/5.63 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B2 ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib_numeral
% 5.41/5.63 thf(fact_307_right__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [V: num,B2: int,C: int] :
% 5.41/5.63 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B2 @ C ) )
% 5.41/5.63 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib_numeral
% 5.41/5.63 thf(fact_308_mult__Suc__right,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.41/5.63 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_Suc_right
% 5.41/5.63 thf(fact_309_diff__Suc__1,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.41/5.63 = N ) ).
% 5.41/5.63
% 5.41/5.63 % diff_Suc_1
% 5.41/5.63 thf(fact_310_semiring__norm_I2_J,axiom,
% 5.41/5.63 ( ( plus_plus_num @ one @ one )
% 5.41/5.63 = ( bit0 @ one ) ) ).
% 5.41/5.63
% 5.41/5.63 % semiring_norm(2)
% 5.41/5.63 thf(fact_311_le__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [A: real,B2: real,W: num] :
% 5.41/5.63 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.63 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_divide_eq_numeral1(1)
% 5.41/5.63 thf(fact_312_le__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [A: rat,B2: rat,W: num] :
% 5.41/5.63 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.63 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_divide_eq_numeral1(1)
% 5.41/5.63 thf(fact_313_divide__le__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [B2: real,W: num,A: real] :
% 5.41/5.63 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) ) @ A )
% 5.41/5.63 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_le_eq_numeral1(1)
% 5.41/5.63 thf(fact_314_divide__le__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [B2: rat,W: num,A: rat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.41/5.63 = ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_le_eq_numeral1(1)
% 5.41/5.63 thf(fact_315_less__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [A: real,B2: real,W: num] :
% 5.41/5.63 ( ( ord_less_real @ A @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.63 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_divide_eq_numeral1(1)
% 5.41/5.63 thf(fact_316_less__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [A: rat,B2: rat,W: num] :
% 5.41/5.63 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.63 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_divide_eq_numeral1(1)
% 5.41/5.63 thf(fact_317_divide__less__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [B2: real,W: num,A: real] :
% 5.41/5.63 ( ( ord_less_real @ ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) ) @ A )
% 5.41/5.63 = ( ord_less_real @ B2 @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_less_eq_numeral1(1)
% 5.41/5.63 thf(fact_318_divide__less__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [B2: rat,W: num,A: rat] :
% 5.41/5.63 ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.41/5.63 = ( ord_less_rat @ B2 @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_less_eq_numeral1(1)
% 5.41/5.63 thf(fact_319_diff__Suc__diff__eq2,axiom,
% 5.41/5.63 ! [K: nat,J: nat,I: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.63 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 5.41/5.63 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_Suc_diff_eq2
% 5.41/5.63 thf(fact_320_diff__Suc__diff__eq1,axiom,
% 5.41/5.63 ! [K: nat,J: nat,I: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.63 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.41/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_Suc_diff_eq1
% 5.41/5.63 thf(fact_321_power__add__numeral,axiom,
% 5.41/5.63 ! [A: complex,M: num,N: num] :
% 5.41/5.63 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.41/5.63 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_add_numeral
% 5.41/5.63 thf(fact_322_power__add__numeral,axiom,
% 5.41/5.63 ! [A: real,M: num,N: num] :
% 5.41/5.63 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.41/5.63 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_add_numeral
% 5.41/5.63 thf(fact_323_power__add__numeral,axiom,
% 5.41/5.63 ! [A: rat,M: num,N: num] :
% 5.41/5.63 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.41/5.63 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_add_numeral
% 5.41/5.63 thf(fact_324_power__add__numeral,axiom,
% 5.41/5.63 ! [A: nat,M: num,N: num] :
% 5.41/5.63 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.41/5.63 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_add_numeral
% 5.41/5.63 thf(fact_325_power__add__numeral,axiom,
% 5.41/5.63 ! [A: int,M: num,N: num] :
% 5.41/5.63 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.41/5.63 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_add_numeral
% 5.41/5.63 thf(fact_326_power__add__numeral2,axiom,
% 5.41/5.63 ! [A: complex,M: num,N: num,B2: complex] :
% 5.41/5.63 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.41/5.63 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_add_numeral2
% 5.41/5.63 thf(fact_327_power__add__numeral2,axiom,
% 5.41/5.63 ! [A: real,M: num,N: num,B2: real] :
% 5.41/5.63 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.41/5.63 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_add_numeral2
% 5.41/5.63 thf(fact_328_power__add__numeral2,axiom,
% 5.41/5.63 ! [A: rat,M: num,N: num,B2: rat] :
% 5.41/5.63 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.41/5.63 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_add_numeral2
% 5.41/5.63 thf(fact_329_power__add__numeral2,axiom,
% 5.41/5.63 ! [A: nat,M: num,N: num,B2: nat] :
% 5.41/5.63 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.41/5.63 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_add_numeral2
% 5.41/5.63 thf(fact_330_power__add__numeral2,axiom,
% 5.41/5.63 ! [A: int,M: num,N: num,B2: int] :
% 5.41/5.63 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B2 ) )
% 5.41/5.63 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B2 ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_add_numeral2
% 5.41/5.63 thf(fact_331_Suc__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.41/5.63 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Suc_numeral
% 5.41/5.63 thf(fact_332_add__2__eq__Suc_H,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( suc @ ( suc @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_2_eq_Suc'
% 5.41/5.63 thf(fact_333_add__2__eq__Suc,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.63 = ( suc @ ( suc @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_2_eq_Suc
% 5.41/5.63 thf(fact_334_div2__Suc__Suc,axiom,
% 5.41/5.63 ! [M: nat] :
% 5.41/5.63 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div2_Suc_Suc
% 5.41/5.63 thf(fact_335_Suc__1,axiom,
% 5.41/5.63 ( ( suc @ one_one_nat )
% 5.41/5.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Suc_1
% 5.41/5.63 thf(fact_336_Suc__mult__le__cancel1,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.41/5.63 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % Suc_mult_le_cancel1
% 5.41/5.63 thf(fact_337_Suc__mult__less__cancel1,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.41/5.63 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % Suc_mult_less_cancel1
% 5.41/5.63 thf(fact_338_mult__Suc,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.41/5.63 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_Suc
% 5.41/5.63 thf(fact_339_Suc__inject,axiom,
% 5.41/5.63 ! [X4: nat,Y3: nat] :
% 5.41/5.63 ( ( ( suc @ X4 )
% 5.41/5.63 = ( suc @ Y3 ) )
% 5.41/5.63 => ( X4 = Y3 ) ) ).
% 5.41/5.63
% 5.41/5.63 % Suc_inject
% 5.41/5.63 thf(fact_340_n__not__Suc__n,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( N
% 5.41/5.63 != ( suc @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % n_not_Suc_n
% 5.41/5.63 thf(fact_341_Suc__mult__cancel1,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.41/5.63 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.41/5.63 = ( M = N ) ) ).
% 5.41/5.63
% 5.41/5.63 % Suc_mult_cancel1
% 5.41/5.63 thf(fact_342_power__Suc2,axiom,
% 5.41/5.63 ! [A: complex,N: nat] :
% 5.41/5.63 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.41/5.63 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_Suc2
% 5.41/5.63 thf(fact_343_power__Suc2,axiom,
% 5.41/5.63 ! [A: real,N: nat] :
% 5.41/5.63 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.41/5.63 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_Suc2
% 5.41/5.63 thf(fact_344_power__Suc2,axiom,
% 5.41/5.63 ! [A: rat,N: nat] :
% 5.41/5.63 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.41/5.63 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_Suc2
% 5.41/5.63 thf(fact_345_power__Suc2,axiom,
% 5.41/5.63 ! [A: nat,N: nat] :
% 5.41/5.63 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.41/5.63 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_Suc2
% 5.41/5.63 thf(fact_346_power__Suc2,axiom,
% 5.41/5.63 ! [A: int,N: nat] :
% 5.41/5.63 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.41/5.63 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_Suc2
% 5.41/5.63 thf(fact_347_power__Suc,axiom,
% 5.41/5.63 ! [A: complex,N: nat] :
% 5.41/5.63 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.41/5.63 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_Suc
% 5.41/5.63 thf(fact_348_power__Suc,axiom,
% 5.41/5.63 ! [A: real,N: nat] :
% 5.41/5.63 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.41/5.63 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_Suc
% 5.41/5.63 thf(fact_349_power__Suc,axiom,
% 5.41/5.63 ! [A: rat,N: nat] :
% 5.41/5.63 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.41/5.63 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_Suc
% 5.41/5.63 thf(fact_350_power__Suc,axiom,
% 5.41/5.63 ! [A: nat,N: nat] :
% 5.41/5.63 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.41/5.63 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_Suc
% 5.41/5.63 thf(fact_351_power__Suc,axiom,
% 5.41/5.63 ! [A: int,N: nat] :
% 5.41/5.63 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.41/5.63 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_Suc
% 5.41/5.63 thf(fact_352_ring__class_Oring__distribs_I2_J,axiom,
% 5.41/5.63 ! [A: real,B2: real,C: real] :
% 5.41/5.63 ( ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 5.41/5.63 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % ring_class.ring_distribs(2)
% 5.41/5.63 thf(fact_353_ring__class_Oring__distribs_I2_J,axiom,
% 5.41/5.63 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.63 ( ( times_times_rat @ ( plus_plus_rat @ A @ B2 ) @ C )
% 5.41/5.63 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % ring_class.ring_distribs(2)
% 5.41/5.63 thf(fact_354_ring__class_Oring__distribs_I2_J,axiom,
% 5.41/5.63 ! [A: int,B2: int,C: int] :
% 5.41/5.63 ( ( times_times_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ring_class.ring_distribs(2)
% 5.41/5.64 thf(fact_355_ring__class_Oring__distribs_I1_J,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( times_times_real @ A @ ( plus_plus_real @ B2 @ C ) )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ A @ B2 ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ring_class.ring_distribs(1)
% 5.41/5.64 thf(fact_356_ring__class_Oring__distribs_I1_J,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( times_times_rat @ A @ ( plus_plus_rat @ B2 @ C ) )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ A @ B2 ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ring_class.ring_distribs(1)
% 5.41/5.64 thf(fact_357_ring__class_Oring__distribs_I1_J,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( times_times_int @ A @ ( plus_plus_int @ B2 @ C ) )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ A @ B2 ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ring_class.ring_distribs(1)
% 5.41/5.64 thf(fact_358_comm__semiring__class_Odistrib,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % comm_semiring_class.distrib
% 5.41/5.64 thf(fact_359_comm__semiring__class_Odistrib,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( times_times_rat @ ( plus_plus_rat @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % comm_semiring_class.distrib
% 5.41/5.64 thf(fact_360_comm__semiring__class_Odistrib,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % comm_semiring_class.distrib
% 5.41/5.64 thf(fact_361_comm__semiring__class_Odistrib,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( times_times_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % comm_semiring_class.distrib
% 5.41/5.64 thf(fact_362_distrib__left,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( times_times_real @ A @ ( plus_plus_real @ B2 @ C ) )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ A @ B2 ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % distrib_left
% 5.41/5.64 thf(fact_363_distrib__left,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( times_times_rat @ A @ ( plus_plus_rat @ B2 @ C ) )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ A @ B2 ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % distrib_left
% 5.41/5.64 thf(fact_364_distrib__left,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( times_times_nat @ A @ ( plus_plus_nat @ B2 @ C ) )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ A @ B2 ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % distrib_left
% 5.41/5.64 thf(fact_365_distrib__left,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( times_times_int @ A @ ( plus_plus_int @ B2 @ C ) )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ A @ B2 ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % distrib_left
% 5.41/5.64 thf(fact_366_distrib__right,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % distrib_right
% 5.41/5.64 thf(fact_367_distrib__right,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( times_times_rat @ ( plus_plus_rat @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % distrib_right
% 5.41/5.64 thf(fact_368_distrib__right,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % distrib_right
% 5.41/5.64 thf(fact_369_distrib__right,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( times_times_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % distrib_right
% 5.41/5.64 thf(fact_370_combine__common__factor,axiom,
% 5.41/5.64 ! [A: real,E: real,B2: real,C: real] :
% 5.41/5.64 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ C ) )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ E ) @ C ) ) ).
% 5.41/5.64
% 5.41/5.64 % combine_common_factor
% 5.41/5.64 thf(fact_371_combine__common__factor,axiom,
% 5.41/5.64 ! [A: rat,E: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ C ) )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B2 ) @ E ) @ C ) ) ).
% 5.41/5.64
% 5.41/5.64 % combine_common_factor
% 5.41/5.64 thf(fact_372_combine__common__factor,axiom,
% 5.41/5.64 ! [A: nat,E: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B2 @ E ) @ C ) )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ E ) @ C ) ) ).
% 5.41/5.64
% 5.41/5.64 % combine_common_factor
% 5.41/5.64 thf(fact_373_combine__common__factor,axiom,
% 5.41/5.64 ! [A: int,E: int,B2: int,C: int] :
% 5.41/5.64 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ C ) )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B2 ) @ E ) @ C ) ) ).
% 5.41/5.64
% 5.41/5.64 % combine_common_factor
% 5.41/5.64 thf(fact_374_left__diff__distrib,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( times_times_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 5.41/5.64 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_diff_distrib
% 5.41/5.64 thf(fact_375_left__diff__distrib,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( times_times_rat @ ( minus_minus_rat @ A @ B2 ) @ C )
% 5.41/5.64 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_diff_distrib
% 5.41/5.64 thf(fact_376_left__diff__distrib,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( times_times_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 5.41/5.64 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_diff_distrib
% 5.41/5.64 thf(fact_377_right__diff__distrib,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( times_times_real @ A @ ( minus_minus_real @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_real @ ( times_times_real @ A @ B2 ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % right_diff_distrib
% 5.41/5.64 thf(fact_378_right__diff__distrib,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( times_times_rat @ A @ ( minus_minus_rat @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_rat @ ( times_times_rat @ A @ B2 ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % right_diff_distrib
% 5.41/5.64 thf(fact_379_right__diff__distrib,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( times_times_int @ A @ ( minus_minus_int @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_int @ ( times_times_int @ A @ B2 ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % right_diff_distrib
% 5.41/5.64 thf(fact_380_left__diff__distrib_H,axiom,
% 5.41/5.64 ! [B2: real,C: real,A: real] :
% 5.41/5.64 ( ( times_times_real @ ( minus_minus_real @ B2 @ C ) @ A )
% 5.41/5.64 = ( minus_minus_real @ ( times_times_real @ B2 @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_diff_distrib'
% 5.41/5.64 thf(fact_381_left__diff__distrib_H,axiom,
% 5.41/5.64 ! [B2: rat,C: rat,A: rat] :
% 5.41/5.64 ( ( times_times_rat @ ( minus_minus_rat @ B2 @ C ) @ A )
% 5.41/5.64 = ( minus_minus_rat @ ( times_times_rat @ B2 @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_diff_distrib'
% 5.41/5.64 thf(fact_382_left__diff__distrib_H,axiom,
% 5.41/5.64 ! [B2: nat,C: nat,A: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( minus_minus_nat @ B2 @ C ) @ A )
% 5.41/5.64 = ( minus_minus_nat @ ( times_times_nat @ B2 @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_diff_distrib'
% 5.41/5.64 thf(fact_383_left__diff__distrib_H,axiom,
% 5.41/5.64 ! [B2: int,C: int,A: int] :
% 5.41/5.64 ( ( times_times_int @ ( minus_minus_int @ B2 @ C ) @ A )
% 5.41/5.64 = ( minus_minus_int @ ( times_times_int @ B2 @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_diff_distrib'
% 5.41/5.64 thf(fact_384_right__diff__distrib_H,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( times_times_real @ A @ ( minus_minus_real @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_real @ ( times_times_real @ A @ B2 ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % right_diff_distrib'
% 5.41/5.64 thf(fact_385_right__diff__distrib_H,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( times_times_rat @ A @ ( minus_minus_rat @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_rat @ ( times_times_rat @ A @ B2 ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % right_diff_distrib'
% 5.41/5.64 thf(fact_386_right__diff__distrib_H,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( times_times_nat @ A @ ( minus_minus_nat @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_nat @ ( times_times_nat @ A @ B2 ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % right_diff_distrib'
% 5.41/5.64 thf(fact_387_right__diff__distrib_H,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( times_times_int @ A @ ( minus_minus_int @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_int @ ( times_times_int @ A @ B2 ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % right_diff_distrib'
% 5.41/5.64 thf(fact_388_Nat_OlessE,axiom,
% 5.41/5.64 ! [I: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I @ K )
% 5.41/5.64 => ( ( K
% 5.41/5.64 != ( suc @ I ) )
% 5.41/5.64 => ~ ! [J2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I @ J2 )
% 5.41/5.64 => ( K
% 5.41/5.64 != ( suc @ J2 ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.lessE
% 5.41/5.64 thf(fact_389_Suc__lessD,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.41/5.64 => ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_lessD
% 5.41/5.64 thf(fact_390_Suc__lessE,axiom,
% 5.41/5.64 ! [I: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 5.41/5.64 => ~ ! [J2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I @ J2 )
% 5.41/5.64 => ( K
% 5.41/5.64 != ( suc @ J2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_lessE
% 5.41/5.64 thf(fact_391_Suc__lessI,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ N )
% 5.41/5.64 => ( ( ( suc @ M )
% 5.41/5.64 != N )
% 5.41/5.64 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_lessI
% 5.41/5.64 thf(fact_392_less__SucE,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.41/5.64 => ( ~ ( ord_less_nat @ M @ N )
% 5.41/5.64 => ( M = N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_SucE
% 5.41/5.64 thf(fact_393_less__SucI,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ N )
% 5.41/5.64 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_SucI
% 5.41/5.64 thf(fact_394_Ex__less__Suc,axiom,
% 5.41/5.64 ! [N: nat,P: nat > $o] :
% 5.41/5.64 ( ( ? [I2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.41/5.64 & ( P @ I2 ) ) )
% 5.41/5.64 = ( ( P @ N )
% 5.41/5.64 | ? [I2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I2 @ N )
% 5.41/5.64 & ( P @ I2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Ex_less_Suc
% 5.41/5.64 thf(fact_395_less__Suc__eq,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.41/5.64 = ( ( ord_less_nat @ M @ N )
% 5.41/5.64 | ( M = N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_Suc_eq
% 5.41/5.64 thf(fact_396_not__less__eq,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.41/5.64 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % not_less_eq
% 5.41/5.64 thf(fact_397_All__less__Suc,axiom,
% 5.41/5.64 ! [N: nat,P: nat > $o] :
% 5.41/5.64 ( ( ! [I2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.41/5.64 => ( P @ I2 ) ) )
% 5.41/5.64 = ( ( P @ N )
% 5.41/5.64 & ! [I2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I2 @ N )
% 5.41/5.64 => ( P @ I2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % All_less_Suc
% 5.41/5.64 thf(fact_398_Suc__less__eq2,axiom,
% 5.41/5.64 ! [N: nat,M: nat] :
% 5.41/5.64 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.64 = ( ? [M2: nat] :
% 5.41/5.64 ( ( M
% 5.41/5.64 = ( suc @ M2 ) )
% 5.41/5.64 & ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_less_eq2
% 5.41/5.64 thf(fact_399_less__antisym,axiom,
% 5.41/5.64 ! [N: nat,M: nat] :
% 5.41/5.64 ( ~ ( ord_less_nat @ N @ M )
% 5.41/5.64 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.41/5.64 => ( M = N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_antisym
% 5.41/5.64 thf(fact_400_Suc__less__SucD,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.41/5.64 => ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_less_SucD
% 5.41/5.64 thf(fact_401_less__trans__Suc,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I @ J )
% 5.41/5.64 => ( ( ord_less_nat @ J @ K )
% 5.41/5.64 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_trans_Suc
% 5.41/5.64 thf(fact_402_less__Suc__induct,axiom,
% 5.41/5.64 ! [I: nat,J: nat,P: nat > nat > $o] :
% 5.41/5.64 ( ( ord_less_nat @ I @ J )
% 5.41/5.64 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 5.41/5.64 => ( ! [I3: nat,J2: nat,K2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I3 @ J2 )
% 5.41/5.64 => ( ( ord_less_nat @ J2 @ K2 )
% 5.41/5.64 => ( ( P @ I3 @ J2 )
% 5.41/5.64 => ( ( P @ J2 @ K2 )
% 5.41/5.64 => ( P @ I3 @ K2 ) ) ) ) )
% 5.41/5.64 => ( P @ I @ J ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_Suc_induct
% 5.41/5.64 thf(fact_403_strict__inc__induct,axiom,
% 5.41/5.64 ! [I: nat,J: nat,P: nat > $o] :
% 5.41/5.64 ( ( ord_less_nat @ I @ J )
% 5.41/5.64 => ( ! [I3: nat] :
% 5.41/5.64 ( ( J
% 5.41/5.64 = ( suc @ I3 ) )
% 5.41/5.64 => ( P @ I3 ) )
% 5.41/5.64 => ( ! [I3: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I3 @ J )
% 5.41/5.64 => ( ( P @ ( suc @ I3 ) )
% 5.41/5.64 => ( P @ I3 ) ) )
% 5.41/5.64 => ( P @ I ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % strict_inc_induct
% 5.41/5.64 thf(fact_404_not__less__less__Suc__eq,axiom,
% 5.41/5.64 ! [N: nat,M: nat] :
% 5.41/5.64 ( ~ ( ord_less_nat @ N @ M )
% 5.41/5.64 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.41/5.64 = ( N = M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % not_less_less_Suc_eq
% 5.41/5.64 thf(fact_405_Suc__leD,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.41/5.64 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_leD
% 5.41/5.64 thf(fact_406_le__SucE,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.64 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ( M
% 5.41/5.64 = ( suc @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_SucE
% 5.41/5.64 thf(fact_407_le__SucI,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_SucI
% 5.41/5.64 thf(fact_408_Suc__le__D,axiom,
% 5.41/5.64 ! [N: nat,M3: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( suc @ N ) @ M3 )
% 5.41/5.64 => ? [M4: nat] :
% 5.41/5.64 ( M3
% 5.41/5.64 = ( suc @ M4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_le_D
% 5.41/5.64 thf(fact_409_le__Suc__eq,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.64 = ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 | ( M
% 5.41/5.64 = ( suc @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_Suc_eq
% 5.41/5.64 thf(fact_410_Suc__n__not__le__n,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_n_not_le_n
% 5.41/5.64 thf(fact_411_not__less__eq__eq,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.41/5.64 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.41/5.64
% 5.41/5.64 % not_less_eq_eq
% 5.41/5.64 thf(fact_412_full__nat__induct,axiom,
% 5.41/5.64 ! [P: nat > $o,N: nat] :
% 5.41/5.64 ( ! [N4: nat] :
% 5.41/5.64 ( ! [M5: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( suc @ M5 ) @ N4 )
% 5.41/5.64 => ( P @ M5 ) )
% 5.41/5.64 => ( P @ N4 ) )
% 5.41/5.64 => ( P @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % full_nat_induct
% 5.41/5.64 thf(fact_413_nat__induct__at__least,axiom,
% 5.41/5.64 ! [M: nat,N: nat,P: nat > $o] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ( ( P @ M )
% 5.41/5.64 => ( ! [N4: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N4 )
% 5.41/5.64 => ( ( P @ N4 )
% 5.41/5.64 => ( P @ ( suc @ N4 ) ) ) )
% 5.41/5.64 => ( P @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_induct_at_least
% 5.41/5.64 thf(fact_414_transitive__stepwise__le,axiom,
% 5.41/5.64 ! [M: nat,N: nat,R: nat > nat > $o] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 5.41/5.64 => ( ! [X3: nat,Y4: nat,Z2: nat] :
% 5.41/5.64 ( ( R @ X3 @ Y4 )
% 5.41/5.64 => ( ( R @ Y4 @ Z2 )
% 5.41/5.64 => ( R @ X3 @ Z2 ) ) )
% 5.41/5.64 => ( ! [N4: nat] : ( R @ N4 @ ( suc @ N4 ) )
% 5.41/5.64 => ( R @ M @ N ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % transitive_stepwise_le
% 5.41/5.64 thf(fact_415_le__cube,axiom,
% 5.41/5.64 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_cube
% 5.41/5.64 thf(fact_416_le__square,axiom,
% 5.41/5.64 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_square
% 5.41/5.64 thf(fact_417_mult__le__mono,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_le_mono
% 5.41/5.64 thf(fact_418_mult__le__mono1,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_le_mono1
% 5.41/5.64 thf(fact_419_mult__le__mono2,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_le_mono2
% 5.41/5.64 thf(fact_420_nat__arith_Osuc1,axiom,
% 5.41/5.64 ! [A3: nat,K: nat,A: nat] :
% 5.41/5.64 ( ( A3
% 5.41/5.64 = ( plus_plus_nat @ K @ A ) )
% 5.41/5.64 => ( ( suc @ A3 )
% 5.41/5.64 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_arith.suc1
% 5.41/5.64 thf(fact_421_add__Suc,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.41/5.64 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_Suc
% 5.41/5.64 thf(fact_422_add__Suc__shift,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.41/5.64 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_Suc_shift
% 5.41/5.64 thf(fact_423_add__mult__distrib,axiom,
% 5.41/5.64 ! [M: nat,N: nat,K: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_mult_distrib
% 5.41/5.64 thf(fact_424_add__mult__distrib2,axiom,
% 5.41/5.64 ! [K: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_mult_distrib2
% 5.41/5.64 thf(fact_425_zero__induct__lemma,axiom,
% 5.41/5.64 ! [P: nat > $o,K: nat,I: nat] :
% 5.41/5.64 ( ( P @ K )
% 5.41/5.64 => ( ! [N4: nat] :
% 5.41/5.64 ( ( P @ ( suc @ N4 ) )
% 5.41/5.64 => ( P @ N4 ) )
% 5.41/5.64 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_induct_lemma
% 5.41/5.64 thf(fact_426_diff__mult__distrib,axiom,
% 5.41/5.64 ! [M: nat,N: nat,K: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.41/5.64 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_mult_distrib
% 5.41/5.64 thf(fact_427_diff__mult__distrib2,axiom,
% 5.41/5.64 ! [K: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.64 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_mult_distrib2
% 5.41/5.64 thf(fact_428_nat__mult__1,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ( ( times_times_nat @ one_one_nat @ N )
% 5.41/5.64 = N ) ).
% 5.41/5.64
% 5.41/5.64 % nat_mult_1
% 5.41/5.64 thf(fact_429_nat__mult__1__right,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ( ( times_times_nat @ N @ one_one_nat )
% 5.41/5.64 = N ) ).
% 5.41/5.64
% 5.41/5.64 % nat_mult_1_right
% 5.41/5.64 thf(fact_430_two__realpow__ge__one,axiom,
% 5.41/5.64 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % two_realpow_ge_one
% 5.41/5.64 thf(fact_431_add__One__commute,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ( ( plus_plus_num @ one @ N )
% 5.41/5.64 = ( plus_plus_num @ N @ one ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_One_commute
% 5.41/5.64 thf(fact_432_power__commutes,axiom,
% 5.41/5.64 ! [A: complex,N: nat] :
% 5.41/5.64 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 5.41/5.64 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_commutes
% 5.41/5.64 thf(fact_433_power__commutes,axiom,
% 5.41/5.64 ! [A: real,N: nat] :
% 5.41/5.64 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 5.41/5.64 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_commutes
% 5.41/5.64 thf(fact_434_power__commutes,axiom,
% 5.41/5.64 ! [A: rat,N: nat] :
% 5.41/5.64 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 5.41/5.64 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_commutes
% 5.41/5.64 thf(fact_435_power__commutes,axiom,
% 5.41/5.64 ! [A: nat,N: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 5.41/5.64 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_commutes
% 5.41/5.64 thf(fact_436_power__commutes,axiom,
% 5.41/5.64 ! [A: int,N: nat] :
% 5.41/5.64 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 5.41/5.64 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_commutes
% 5.41/5.64 thf(fact_437_power__mult__distrib,axiom,
% 5.41/5.64 ! [A: complex,B2: complex,N: nat] :
% 5.41/5.64 ( ( power_power_complex @ ( times_times_complex @ A @ B2 ) @ N )
% 5.41/5.64 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B2 @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult_distrib
% 5.41/5.64 thf(fact_438_power__mult__distrib,axiom,
% 5.41/5.64 ! [A: real,B2: real,N: nat] :
% 5.41/5.64 ( ( power_power_real @ ( times_times_real @ A @ B2 ) @ N )
% 5.41/5.64 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B2 @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult_distrib
% 5.41/5.64 thf(fact_439_power__mult__distrib,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,N: nat] :
% 5.41/5.64 ( ( power_power_rat @ ( times_times_rat @ A @ B2 ) @ N )
% 5.41/5.64 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult_distrib
% 5.41/5.64 thf(fact_440_power__mult__distrib,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,N: nat] :
% 5.41/5.64 ( ( power_power_nat @ ( times_times_nat @ A @ B2 ) @ N )
% 5.41/5.64 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B2 @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult_distrib
% 5.41/5.64 thf(fact_441_power__mult__distrib,axiom,
% 5.41/5.64 ! [A: int,B2: int,N: nat] :
% 5.41/5.64 ( ( power_power_int @ ( times_times_int @ A @ B2 ) @ N )
% 5.41/5.64 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B2 @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult_distrib
% 5.41/5.64 thf(fact_442_power__commuting__commutes,axiom,
% 5.41/5.64 ! [X4: complex,Y3: complex,N: nat] :
% 5.41/5.64 ( ( ( times_times_complex @ X4 @ Y3 )
% 5.41/5.64 = ( times_times_complex @ Y3 @ X4 ) )
% 5.41/5.64 => ( ( times_times_complex @ ( power_power_complex @ X4 @ N ) @ Y3 )
% 5.41/5.64 = ( times_times_complex @ Y3 @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_commuting_commutes
% 5.41/5.64 thf(fact_443_power__commuting__commutes,axiom,
% 5.41/5.64 ! [X4: real,Y3: real,N: nat] :
% 5.41/5.64 ( ( ( times_times_real @ X4 @ Y3 )
% 5.41/5.64 = ( times_times_real @ Y3 @ X4 ) )
% 5.41/5.64 => ( ( times_times_real @ ( power_power_real @ X4 @ N ) @ Y3 )
% 5.41/5.64 = ( times_times_real @ Y3 @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_commuting_commutes
% 5.41/5.64 thf(fact_444_power__commuting__commutes,axiom,
% 5.41/5.64 ! [X4: rat,Y3: rat,N: nat] :
% 5.41/5.64 ( ( ( times_times_rat @ X4 @ Y3 )
% 5.41/5.64 = ( times_times_rat @ Y3 @ X4 ) )
% 5.41/5.64 => ( ( times_times_rat @ ( power_power_rat @ X4 @ N ) @ Y3 )
% 5.41/5.64 = ( times_times_rat @ Y3 @ ( power_power_rat @ X4 @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_commuting_commutes
% 5.41/5.64 thf(fact_445_power__commuting__commutes,axiom,
% 5.41/5.64 ! [X4: nat,Y3: nat,N: nat] :
% 5.41/5.64 ( ( ( times_times_nat @ X4 @ Y3 )
% 5.41/5.64 = ( times_times_nat @ Y3 @ X4 ) )
% 5.41/5.64 => ( ( times_times_nat @ ( power_power_nat @ X4 @ N ) @ Y3 )
% 5.41/5.64 = ( times_times_nat @ Y3 @ ( power_power_nat @ X4 @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_commuting_commutes
% 5.41/5.64 thf(fact_446_power__commuting__commutes,axiom,
% 5.41/5.64 ! [X4: int,Y3: int,N: nat] :
% 5.41/5.64 ( ( ( times_times_int @ X4 @ Y3 )
% 5.41/5.64 = ( times_times_int @ Y3 @ X4 ) )
% 5.41/5.64 => ( ( times_times_int @ ( power_power_int @ X4 @ N ) @ Y3 )
% 5.41/5.64 = ( times_times_int @ Y3 @ ( power_power_int @ X4 @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_commuting_commutes
% 5.41/5.64 thf(fact_447_power__mult,axiom,
% 5.41/5.64 ! [A: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 5.41/5.64 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult
% 5.41/5.64 thf(fact_448_power__mult,axiom,
% 5.41/5.64 ! [A: real,M: nat,N: nat] :
% 5.41/5.64 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 5.41/5.64 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult
% 5.41/5.64 thf(fact_449_power__mult,axiom,
% 5.41/5.64 ! [A: int,M: nat,N: nat] :
% 5.41/5.64 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 5.41/5.64 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult
% 5.41/5.64 thf(fact_450_power__mult,axiom,
% 5.41/5.64 ! [A: complex,M: nat,N: nat] :
% 5.41/5.64 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 5.41/5.64 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult
% 5.41/5.64 thf(fact_451_left__add__mult__distrib,axiom,
% 5.41/5.64 ! [I: nat,U: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_add_mult_distrib
% 5.41/5.64 thf(fact_452_div__mult2__eq,axiom,
% 5.41/5.64 ! [M: nat,N: nat,Q2: nat] :
% 5.41/5.64 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.41/5.64 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % div_mult2_eq
% 5.41/5.64 thf(fact_453_power__odd__eq,axiom,
% 5.41/5.64 ! [A: complex,N: nat] :
% 5.41/5.64 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.64 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_odd_eq
% 5.41/5.64 thf(fact_454_power__odd__eq,axiom,
% 5.41/5.64 ! [A: real,N: nat] :
% 5.41/5.64 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.64 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_odd_eq
% 5.41/5.64 thf(fact_455_power__odd__eq,axiom,
% 5.41/5.64 ! [A: rat,N: nat] :
% 5.41/5.64 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.64 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_odd_eq
% 5.41/5.64 thf(fact_456_power__odd__eq,axiom,
% 5.41/5.64 ! [A: nat,N: nat] :
% 5.41/5.64 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.64 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_odd_eq
% 5.41/5.64 thf(fact_457_power__odd__eq,axiom,
% 5.41/5.64 ! [A: int,N: nat] :
% 5.41/5.64 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.64 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_odd_eq
% 5.41/5.64 thf(fact_458_less__1__mult,axiom,
% 5.41/5.64 ! [M: real,N: real] :
% 5.41/5.64 ( ( ord_less_real @ one_one_real @ M )
% 5.41/5.64 => ( ( ord_less_real @ one_one_real @ N )
% 5.41/5.64 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_1_mult
% 5.41/5.64 thf(fact_459_less__1__mult,axiom,
% 5.41/5.64 ! [M: rat,N: rat] :
% 5.41/5.64 ( ( ord_less_rat @ one_one_rat @ M )
% 5.41/5.64 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.41/5.64 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_1_mult
% 5.41/5.64 thf(fact_460_less__1__mult,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ one_one_nat @ M )
% 5.41/5.64 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.41/5.64 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_1_mult
% 5.41/5.64 thf(fact_461_less__1__mult,axiom,
% 5.41/5.64 ! [M: int,N: int] :
% 5.41/5.64 ( ( ord_less_int @ one_one_int @ M )
% 5.41/5.64 => ( ( ord_less_int @ one_one_int @ N )
% 5.41/5.64 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_1_mult
% 5.41/5.64 thf(fact_462_eq__add__iff1,axiom,
% 5.41/5.64 ! [A: real,E: real,C: real,B2: real,D: real] :
% 5.41/5.64 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B2 ) @ E ) @ C )
% 5.41/5.64 = D ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff1
% 5.41/5.64 thf(fact_463_eq__add__iff1,axiom,
% 5.41/5.64 ! [A: rat,E: rat,C: rat,B2: rat,D: rat] :
% 5.41/5.64 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B2 ) @ E ) @ C )
% 5.41/5.64 = D ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff1
% 5.41/5.64 thf(fact_464_eq__add__iff1,axiom,
% 5.41/5.64 ! [A: int,E: int,C: int,B2: int,D: int] :
% 5.41/5.64 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B2 ) @ E ) @ C )
% 5.41/5.64 = D ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff1
% 5.41/5.64 thf(fact_465_eq__add__iff2,axiom,
% 5.41/5.64 ! [A: real,E: real,C: real,B2: real,D: real] :
% 5.41/5.64 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( C
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B2 @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff2
% 5.41/5.64 thf(fact_466_eq__add__iff2,axiom,
% 5.41/5.64 ! [A: rat,E: rat,C: rat,B2: rat,D: rat] :
% 5.41/5.64 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( C
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B2 @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff2
% 5.41/5.64 thf(fact_467_eq__add__iff2,axiom,
% 5.41/5.64 ! [A: int,E: int,C: int,B2: int,D: int] :
% 5.41/5.64 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( C
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff2
% 5.41/5.64 thf(fact_468_square__diff__square__factored,axiom,
% 5.41/5.64 ! [X4: real,Y3: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y3 @ Y3 ) )
% 5.41/5.64 = ( times_times_real @ ( plus_plus_real @ X4 @ Y3 ) @ ( minus_minus_real @ X4 @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % square_diff_square_factored
% 5.41/5.64 thf(fact_469_square__diff__square__factored,axiom,
% 5.41/5.64 ! [X4: rat,Y3: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y3 @ Y3 ) )
% 5.41/5.64 = ( times_times_rat @ ( plus_plus_rat @ X4 @ Y3 ) @ ( minus_minus_rat @ X4 @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % square_diff_square_factored
% 5.41/5.64 thf(fact_470_square__diff__square__factored,axiom,
% 5.41/5.64 ! [X4: int,Y3: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y3 @ Y3 ) )
% 5.41/5.64 = ( times_times_int @ ( plus_plus_int @ X4 @ Y3 ) @ ( minus_minus_int @ X4 @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % square_diff_square_factored
% 5.41/5.64 thf(fact_471_mult__diff__mult,axiom,
% 5.41/5.64 ! [X4: real,Y3: real,A: real,B2: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( times_times_real @ X4 @ Y3 ) @ ( times_times_real @ A @ B2 ) )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ X4 @ ( minus_minus_real @ Y3 @ B2 ) ) @ ( times_times_real @ ( minus_minus_real @ X4 @ A ) @ B2 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_diff_mult
% 5.41/5.64 thf(fact_472_mult__diff__mult,axiom,
% 5.41/5.64 ! [X4: rat,Y3: rat,A: rat,B2: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( times_times_rat @ X4 @ Y3 ) @ ( times_times_rat @ A @ B2 ) )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ X4 @ ( minus_minus_rat @ Y3 @ B2 ) ) @ ( times_times_rat @ ( minus_minus_rat @ X4 @ A ) @ B2 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_diff_mult
% 5.41/5.64 thf(fact_473_mult__diff__mult,axiom,
% 5.41/5.64 ! [X4: int,Y3: int,A: int,B2: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( times_times_int @ X4 @ Y3 ) @ ( times_times_int @ A @ B2 ) )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ X4 @ ( minus_minus_int @ Y3 @ B2 ) ) @ ( times_times_int @ ( minus_minus_int @ X4 @ A ) @ B2 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_diff_mult
% 5.41/5.64 thf(fact_474_lift__Suc__mono__less,axiom,
% 5.41/5.64 ! [F: nat > real,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_less
% 5.41/5.64 thf(fact_475_lift__Suc__mono__less,axiom,
% 5.41/5.64 ! [F: nat > rat,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_rat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_less
% 5.41/5.64 thf(fact_476_lift__Suc__mono__less,axiom,
% 5.41/5.64 ! [F: nat > num,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_num @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_less
% 5.41/5.64 thf(fact_477_lift__Suc__mono__less,axiom,
% 5.41/5.64 ! [F: nat > nat,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_nat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_less
% 5.41/5.64 thf(fact_478_lift__Suc__mono__less,axiom,
% 5.41/5.64 ! [F: nat > int,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_int @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_less
% 5.41/5.64 thf(fact_479_lift__Suc__mono__less__iff,axiom,
% 5.41/5.64 ! [F: nat > real,N: nat,M: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.41/5.64 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_less_iff
% 5.41/5.64 thf(fact_480_lift__Suc__mono__less__iff,axiom,
% 5.41/5.64 ! [F: nat > rat,N: nat,M: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_rat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.41/5.64 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_less_iff
% 5.41/5.64 thf(fact_481_lift__Suc__mono__less__iff,axiom,
% 5.41/5.64 ! [F: nat > num,N: nat,M: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_num @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.41/5.64 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_less_iff
% 5.41/5.64 thf(fact_482_lift__Suc__mono__less__iff,axiom,
% 5.41/5.64 ! [F: nat > nat,N: nat,M: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_nat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.41/5.64 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_less_iff
% 5.41/5.64 thf(fact_483_lift__Suc__mono__less__iff,axiom,
% 5.41/5.64 ! [F: nat > int,N: nat,M: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_int @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.41/5.64 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_less_iff
% 5.41/5.64 thf(fact_484_lift__Suc__mono__le,axiom,
% 5.41/5.64 ! [F: nat > set_nat,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_eq_set_nat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_le
% 5.41/5.64 thf(fact_485_lift__Suc__mono__le,axiom,
% 5.41/5.64 ! [F: nat > rat,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_eq_rat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_le
% 5.41/5.64 thf(fact_486_lift__Suc__mono__le,axiom,
% 5.41/5.64 ! [F: nat > num,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_eq_num @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_le
% 5.41/5.64 thf(fact_487_lift__Suc__mono__le,axiom,
% 5.41/5.64 ! [F: nat > nat,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_le
% 5.41/5.64 thf(fact_488_lift__Suc__mono__le,axiom,
% 5.41/5.64 ! [F: nat > int,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_eq_int @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_mono_le
% 5.41/5.64 thf(fact_489_lift__Suc__antimono__le,axiom,
% 5.41/5.64 ! [F: nat > set_nat,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_antimono_le
% 5.41/5.64 thf(fact_490_lift__Suc__antimono__le,axiom,
% 5.41/5.64 ! [F: nat > rat,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_antimono_le
% 5.41/5.64 thf(fact_491_lift__Suc__antimono__le,axiom,
% 5.41/5.64 ! [F: nat > num,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_antimono_le
% 5.41/5.64 thf(fact_492_lift__Suc__antimono__le,axiom,
% 5.41/5.64 ! [F: nat > nat,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_antimono_le
% 5.41/5.64 thf(fact_493_lift__Suc__antimono__le,axiom,
% 5.41/5.64 ! [F: nat > int,N: nat,N5: nat] :
% 5.41/5.64 ( ! [N4: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.64 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % lift_Suc_antimono_le
% 5.41/5.64 thf(fact_494_Suc__leI,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ N )
% 5.41/5.64 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_leI
% 5.41/5.64 thf(fact_495_Suc__le__eq,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.41/5.64 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_le_eq
% 5.41/5.64 thf(fact_496_dec__induct,axiom,
% 5.41/5.64 ! [I: nat,J: nat,P: nat > $o] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( P @ I )
% 5.41/5.64 => ( ! [N4: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ N4 )
% 5.41/5.64 => ( ( ord_less_nat @ N4 @ J )
% 5.41/5.64 => ( ( P @ N4 )
% 5.41/5.64 => ( P @ ( suc @ N4 ) ) ) ) )
% 5.41/5.64 => ( P @ J ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % dec_induct
% 5.41/5.64 thf(fact_497_inc__induct,axiom,
% 5.41/5.64 ! [I: nat,J: nat,P: nat > $o] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( P @ J )
% 5.41/5.64 => ( ! [N4: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ N4 )
% 5.41/5.64 => ( ( ord_less_nat @ N4 @ J )
% 5.41/5.64 => ( ( P @ ( suc @ N4 ) )
% 5.41/5.64 => ( P @ N4 ) ) ) )
% 5.41/5.64 => ( P @ I ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % inc_induct
% 5.41/5.64 thf(fact_498_Suc__le__lessD,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.41/5.64 => ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_le_lessD
% 5.41/5.64 thf(fact_499_le__less__Suc__eq,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.41/5.64 = ( N = M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_less_Suc_eq
% 5.41/5.64 thf(fact_500_less__Suc__eq__le,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.41/5.64 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_Suc_eq_le
% 5.41/5.64 thf(fact_501_less__eq__Suc__le,axiom,
% 5.41/5.64 ( ord_less_nat
% 5.41/5.64 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_eq_Suc_le
% 5.41/5.64 thf(fact_502_le__imp__less__Suc,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_imp_less_Suc
% 5.41/5.64 thf(fact_503_less__imp__Suc__add,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ N )
% 5.41/5.64 => ? [K2: nat] :
% 5.41/5.64 ( N
% 5.41/5.64 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_imp_Suc_add
% 5.41/5.64 thf(fact_504_less__iff__Suc__add,axiom,
% 5.41/5.64 ( ord_less_nat
% 5.41/5.64 = ( ^ [M6: nat,N2: nat] :
% 5.41/5.64 ? [K3: nat] :
% 5.41/5.64 ( N2
% 5.41/5.64 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_iff_Suc_add
% 5.41/5.64 thf(fact_505_less__add__Suc2,axiom,
% 5.41/5.64 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_Suc2
% 5.41/5.64 thf(fact_506_less__add__Suc1,axiom,
% 5.41/5.64 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_Suc1
% 5.41/5.64 thf(fact_507_less__natE,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ N )
% 5.41/5.64 => ~ ! [Q3: nat] :
% 5.41/5.64 ( N
% 5.41/5.64 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_natE
% 5.41/5.64 thf(fact_508_diff__less__Suc,axiom,
% 5.41/5.64 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_less_Suc
% 5.41/5.64 thf(fact_509_Suc__diff__Suc,axiom,
% 5.41/5.64 ! [N: nat,M: nat] :
% 5.41/5.64 ( ( ord_less_nat @ N @ M )
% 5.41/5.64 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.41/5.64 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_diff_Suc
% 5.41/5.64 thf(fact_510_Suc__diff__le,axiom,
% 5.41/5.64 ! [N: nat,M: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.41/5.64 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_diff_le
% 5.41/5.64 thf(fact_511_Suc__eq__plus1,axiom,
% 5.41/5.64 ( suc
% 5.41/5.64 = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_eq_plus1
% 5.41/5.64 thf(fact_512_plus__1__eq__Suc,axiom,
% 5.41/5.64 ( ( plus_plus_nat @ one_one_nat )
% 5.41/5.64 = suc ) ).
% 5.41/5.64
% 5.41/5.64 % plus_1_eq_Suc
% 5.41/5.64 thf(fact_513_Suc__eq__plus1__left,axiom,
% 5.41/5.64 ( suc
% 5.41/5.64 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_eq_plus1_left
% 5.41/5.64 thf(fact_514_diff__Suc__eq__diff__pred,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.41/5.64 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_Suc_eq_diff_pred
% 5.41/5.64 thf(fact_515_Suc__nat__number__of__add,axiom,
% 5.41/5.64 ! [V: num,N: nat] :
% 5.41/5.64 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.41/5.64 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_nat_number_of_add
% 5.41/5.64 thf(fact_516_div__nat__eqI,axiom,
% 5.41/5.64 ! [N: nat,Q2: nat,M: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 5.41/5.64 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 5.41/5.64 => ( ( divide_divide_nat @ M @ N )
% 5.41/5.64 = Q2 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % div_nat_eqI
% 5.41/5.64 thf(fact_517_ordered__ring__class_Ole__add__iff2,axiom,
% 5.41/5.64 ! [A: real,E: real,C: real,B2: real,D: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B2 @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_ring_class.le_add_iff2
% 5.41/5.64 thf(fact_518_ordered__ring__class_Ole__add__iff2,axiom,
% 5.41/5.64 ! [A: rat,E: rat,C: rat,B2: rat,D: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B2 @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_ring_class.le_add_iff2
% 5.41/5.64 thf(fact_519_ordered__ring__class_Ole__add__iff2,axiom,
% 5.41/5.64 ! [A: int,E: int,C: int,B2: int,D: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_ring_class.le_add_iff2
% 5.41/5.64 thf(fact_520_ordered__ring__class_Ole__add__iff1,axiom,
% 5.41/5.64 ! [A: real,E: real,C: real,B2: real,D: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B2 ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_ring_class.le_add_iff1
% 5.41/5.64 thf(fact_521_ordered__ring__class_Ole__add__iff1,axiom,
% 5.41/5.64 ! [A: rat,E: rat,C: rat,B2: rat,D: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B2 ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_ring_class.le_add_iff1
% 5.41/5.64 thf(fact_522_ordered__ring__class_Ole__add__iff1,axiom,
% 5.41/5.64 ! [A: int,E: int,C: int,B2: int,D: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B2 ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_ring_class.le_add_iff1
% 5.41/5.64 thf(fact_523_less__add__iff2,axiom,
% 5.41/5.64 ! [A: real,E: real,C: real,B2: real,D: real] :
% 5.41/5.64 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B2 @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_iff2
% 5.41/5.64 thf(fact_524_less__add__iff2,axiom,
% 5.41/5.64 ! [A: rat,E: rat,C: rat,B2: rat,D: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B2 @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_iff2
% 5.41/5.64 thf(fact_525_less__add__iff2,axiom,
% 5.41/5.64 ! [A: int,E: int,C: int,B2: int,D: int] :
% 5.41/5.64 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B2 @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_iff2
% 5.41/5.64 thf(fact_526_less__add__iff1,axiom,
% 5.41/5.64 ! [A: real,E: real,C: real,B2: real,D: real] :
% 5.41/5.64 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B2 ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_iff1
% 5.41/5.64 thf(fact_527_less__add__iff1,axiom,
% 5.41/5.64 ! [A: rat,E: rat,C: rat,B2: rat,D: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B2 ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_iff1
% 5.41/5.64 thf(fact_528_less__add__iff1,axiom,
% 5.41/5.64 ! [A: int,E: int,C: int,B2: int,D: int] :
% 5.41/5.64 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B2 @ E ) @ D ) )
% 5.41/5.64 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B2 ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_iff1
% 5.41/5.64 thf(fact_529_square__diff__one__factored,axiom,
% 5.41/5.64 ! [X4: complex] :
% 5.41/5.64 ( ( minus_minus_complex @ ( times_times_complex @ X4 @ X4 ) @ one_one_complex )
% 5.41/5.64 = ( times_times_complex @ ( plus_plus_complex @ X4 @ one_one_complex ) @ ( minus_minus_complex @ X4 @ one_one_complex ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % square_diff_one_factored
% 5.41/5.64 thf(fact_530_square__diff__one__factored,axiom,
% 5.41/5.64 ! [X4: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( times_times_real @ X4 @ X4 ) @ one_one_real )
% 5.41/5.64 = ( times_times_real @ ( plus_plus_real @ X4 @ one_one_real ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % square_diff_one_factored
% 5.41/5.64 thf(fact_531_square__diff__one__factored,axiom,
% 5.41/5.64 ! [X4: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( times_times_rat @ X4 @ X4 ) @ one_one_rat )
% 5.41/5.64 = ( times_times_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) @ ( minus_minus_rat @ X4 @ one_one_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % square_diff_one_factored
% 5.41/5.64 thf(fact_532_square__diff__one__factored,axiom,
% 5.41/5.64 ! [X4: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( times_times_int @ X4 @ X4 ) @ one_one_int )
% 5.41/5.64 = ( times_times_int @ ( plus_plus_int @ X4 @ one_one_int ) @ ( minus_minus_int @ X4 @ one_one_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % square_diff_one_factored
% 5.41/5.64 thf(fact_533_mult__numeral__1__right,axiom,
% 5.41/5.64 ! [A: complex] :
% 5.41/5.64 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_numeral_1_right
% 5.41/5.64 thf(fact_534_mult__numeral__1__right,axiom,
% 5.41/5.64 ! [A: real] :
% 5.41/5.64 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_numeral_1_right
% 5.41/5.64 thf(fact_535_mult__numeral__1__right,axiom,
% 5.41/5.64 ! [A: rat] :
% 5.41/5.64 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_numeral_1_right
% 5.41/5.64 thf(fact_536_mult__numeral__1__right,axiom,
% 5.41/5.64 ! [A: nat] :
% 5.41/5.64 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_numeral_1_right
% 5.41/5.64 thf(fact_537_mult__numeral__1__right,axiom,
% 5.41/5.64 ! [A: int] :
% 5.41/5.64 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_numeral_1_right
% 5.41/5.64 thf(fact_538_mult__numeral__1,axiom,
% 5.41/5.64 ! [A: complex] :
% 5.41/5.64 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_numeral_1
% 5.41/5.64 thf(fact_539_mult__numeral__1,axiom,
% 5.41/5.64 ! [A: real] :
% 5.41/5.64 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_numeral_1
% 5.41/5.64 thf(fact_540_mult__numeral__1,axiom,
% 5.41/5.64 ! [A: rat] :
% 5.41/5.64 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_numeral_1
% 5.41/5.64 thf(fact_541_mult__numeral__1,axiom,
% 5.41/5.64 ! [A: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_numeral_1
% 5.41/5.64 thf(fact_542_mult__numeral__1,axiom,
% 5.41/5.64 ! [A: int] :
% 5.41/5.64 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_numeral_1
% 5.41/5.64 thf(fact_543_left__right__inverse__power,axiom,
% 5.41/5.64 ! [X4: complex,Y3: complex,N: nat] :
% 5.41/5.64 ( ( ( times_times_complex @ X4 @ Y3 )
% 5.41/5.64 = one_one_complex )
% 5.41/5.64 => ( ( times_times_complex @ ( power_power_complex @ X4 @ N ) @ ( power_power_complex @ Y3 @ N ) )
% 5.41/5.64 = one_one_complex ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_right_inverse_power
% 5.41/5.64 thf(fact_544_left__right__inverse__power,axiom,
% 5.41/5.64 ! [X4: real,Y3: real,N: nat] :
% 5.41/5.64 ( ( ( times_times_real @ X4 @ Y3 )
% 5.41/5.64 = one_one_real )
% 5.41/5.64 => ( ( times_times_real @ ( power_power_real @ X4 @ N ) @ ( power_power_real @ Y3 @ N ) )
% 5.41/5.64 = one_one_real ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_right_inverse_power
% 5.41/5.64 thf(fact_545_left__right__inverse__power,axiom,
% 5.41/5.64 ! [X4: rat,Y3: rat,N: nat] :
% 5.41/5.64 ( ( ( times_times_rat @ X4 @ Y3 )
% 5.41/5.64 = one_one_rat )
% 5.41/5.64 => ( ( times_times_rat @ ( power_power_rat @ X4 @ N ) @ ( power_power_rat @ Y3 @ N ) )
% 5.41/5.64 = one_one_rat ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_right_inverse_power
% 5.41/5.64 thf(fact_546_left__right__inverse__power,axiom,
% 5.41/5.64 ! [X4: nat,Y3: nat,N: nat] :
% 5.41/5.64 ( ( ( times_times_nat @ X4 @ Y3 )
% 5.41/5.64 = one_one_nat )
% 5.41/5.64 => ( ( times_times_nat @ ( power_power_nat @ X4 @ N ) @ ( power_power_nat @ Y3 @ N ) )
% 5.41/5.64 = one_one_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_right_inverse_power
% 5.41/5.64 thf(fact_547_left__right__inverse__power,axiom,
% 5.41/5.64 ! [X4: int,Y3: int,N: nat] :
% 5.41/5.64 ( ( ( times_times_int @ X4 @ Y3 )
% 5.41/5.64 = one_one_int )
% 5.41/5.64 => ( ( times_times_int @ ( power_power_int @ X4 @ N ) @ ( power_power_int @ Y3 @ N ) )
% 5.41/5.64 = one_one_int ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_right_inverse_power
% 5.41/5.64 thf(fact_548_power__add,axiom,
% 5.41/5.64 ! [A: complex,M: nat,N: nat] :
% 5.41/5.64 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.64 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_add
% 5.41/5.64 thf(fact_549_power__add,axiom,
% 5.41/5.64 ! [A: real,M: nat,N: nat] :
% 5.41/5.64 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.64 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_add
% 5.41/5.64 thf(fact_550_power__add,axiom,
% 5.41/5.64 ! [A: rat,M: nat,N: nat] :
% 5.41/5.64 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.64 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_add
% 5.41/5.64 thf(fact_551_power__add,axiom,
% 5.41/5.64 ! [A: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.64 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_add
% 5.41/5.64 thf(fact_552_power__add,axiom,
% 5.41/5.64 ! [A: int,M: nat,N: nat] :
% 5.41/5.64 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.64 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_add
% 5.41/5.64 thf(fact_553_Suc__div__le__mono,axiom,
% 5.41/5.64 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_div_le_mono
% 5.41/5.64 thf(fact_554_less__mult__imp__div__less,axiom,
% 5.41/5.64 ! [M: nat,I: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 5.41/5.64 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_mult_imp_div_less
% 5.41/5.64 thf(fact_555_times__div__less__eq__dividend,axiom,
% 5.41/5.64 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.41/5.64
% 5.41/5.64 % times_div_less_eq_dividend
% 5.41/5.64 thf(fact_556_div__times__less__eq__dividend,axiom,
% 5.41/5.64 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.41/5.64
% 5.41/5.64 % div_times_less_eq_dividend
% 5.41/5.64 thf(fact_557_power__gt1__lemma,axiom,
% 5.41/5.64 ! [A: real,N: nat] :
% 5.41/5.64 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.64 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_gt1_lemma
% 5.41/5.64 thf(fact_558_power__gt1__lemma,axiom,
% 5.41/5.64 ! [A: rat,N: nat] :
% 5.41/5.64 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.64 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_gt1_lemma
% 5.41/5.64 thf(fact_559_power__gt1__lemma,axiom,
% 5.41/5.64 ! [A: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.64 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_gt1_lemma
% 5.41/5.64 thf(fact_560_power__gt1__lemma,axiom,
% 5.41/5.64 ! [A: int,N: nat] :
% 5.41/5.64 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.64 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_gt1_lemma
% 5.41/5.64 thf(fact_561_power__less__power__Suc,axiom,
% 5.41/5.64 ! [A: real,N: nat] :
% 5.41/5.64 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.64 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_less_power_Suc
% 5.41/5.64 thf(fact_562_power__less__power__Suc,axiom,
% 5.41/5.64 ! [A: rat,N: nat] :
% 5.41/5.64 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.64 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_less_power_Suc
% 5.41/5.64 thf(fact_563_power__less__power__Suc,axiom,
% 5.41/5.64 ! [A: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.64 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_less_power_Suc
% 5.41/5.64 thf(fact_564_power__less__power__Suc,axiom,
% 5.41/5.64 ! [A: int,N: nat] :
% 5.41/5.64 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.64 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_less_power_Suc
% 5.41/5.64 thf(fact_565_power__gt1,axiom,
% 5.41/5.64 ! [A: real,N: nat] :
% 5.41/5.64 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.64 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_gt1
% 5.41/5.64 thf(fact_566_power__gt1,axiom,
% 5.41/5.64 ! [A: rat,N: nat] :
% 5.41/5.64 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.64 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_gt1
% 5.41/5.64 thf(fact_567_power__gt1,axiom,
% 5.41/5.64 ! [A: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.64 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_gt1
% 5.41/5.64 thf(fact_568_power__gt1,axiom,
% 5.41/5.64 ! [A: int,N: nat] :
% 5.41/5.64 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.64 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_gt1
% 5.41/5.64 thf(fact_569_linorder__neqE__linordered__idom,axiom,
% 5.41/5.64 ! [X4: real,Y3: real] :
% 5.41/5.64 ( ( X4 != Y3 )
% 5.41/5.64 => ( ~ ( ord_less_real @ X4 @ Y3 )
% 5.41/5.64 => ( ord_less_real @ Y3 @ X4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % linorder_neqE_linordered_idom
% 5.41/5.64 thf(fact_570_linorder__neqE__linordered__idom,axiom,
% 5.41/5.64 ! [X4: rat,Y3: rat] :
% 5.41/5.64 ( ( X4 != Y3 )
% 5.41/5.64 => ( ~ ( ord_less_rat @ X4 @ Y3 )
% 5.41/5.64 => ( ord_less_rat @ Y3 @ X4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % linorder_neqE_linordered_idom
% 5.41/5.64 thf(fact_571_linorder__neqE__linordered__idom,axiom,
% 5.41/5.64 ! [X4: int,Y3: int] :
% 5.41/5.64 ( ( X4 != Y3 )
% 5.41/5.64 => ( ~ ( ord_less_int @ X4 @ Y3 )
% 5.41/5.64 => ( ord_less_int @ Y3 @ X4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % linorder_neqE_linordered_idom
% 5.41/5.64 thf(fact_572_nat__diff__add__eq2,axiom,
% 5.41/5.64 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.64 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_diff_add_eq2
% 5.41/5.64 thf(fact_573_nat__diff__add__eq1,axiom,
% 5.41/5.64 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ J @ I )
% 5.41/5.64 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.64 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_diff_add_eq1
% 5.41/5.64 thf(fact_574_nat__le__add__iff2,axiom,
% 5.41/5.64 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.64 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_le_add_iff2
% 5.41/5.64 thf(fact_575_nat__le__add__iff1,axiom,
% 5.41/5.64 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ J @ I )
% 5.41/5.64 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.64 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_le_add_iff1
% 5.41/5.64 thf(fact_576_nat__eq__add__iff2,axiom,
% 5.41/5.64 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.64 = ( M
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_eq_add_iff2
% 5.41/5.64 thf(fact_577_nat__eq__add__iff1,axiom,
% 5.41/5.64 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ J @ I )
% 5.41/5.64 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.64 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 5.41/5.64 = N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_eq_add_iff1
% 5.41/5.64 thf(fact_578_nat__neq__iff,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( M != N )
% 5.41/5.64 = ( ( ord_less_nat @ M @ N )
% 5.41/5.64 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_neq_iff
% 5.41/5.64 thf(fact_579_less__not__refl,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ~ ( ord_less_nat @ N @ N ) ).
% 5.41/5.64
% 5.41/5.64 % less_not_refl
% 5.41/5.64 thf(fact_580_less__not__refl2,axiom,
% 5.41/5.64 ! [N: nat,M: nat] :
% 5.41/5.64 ( ( ord_less_nat @ N @ M )
% 5.41/5.64 => ( M != N ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_not_refl2
% 5.41/5.64 thf(fact_581_less__not__refl3,axiom,
% 5.41/5.64 ! [S: nat,T: nat] :
% 5.41/5.64 ( ( ord_less_nat @ S @ T )
% 5.41/5.64 => ( S != T ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_not_refl3
% 5.41/5.64 thf(fact_582_less__irrefl__nat,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ~ ( ord_less_nat @ N @ N ) ).
% 5.41/5.64
% 5.41/5.64 % less_irrefl_nat
% 5.41/5.64 thf(fact_583_nat__less__induct,axiom,
% 5.41/5.64 ! [P: nat > $o,N: nat] :
% 5.41/5.64 ( ! [N4: nat] :
% 5.41/5.64 ( ! [M5: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M5 @ N4 )
% 5.41/5.64 => ( P @ M5 ) )
% 5.41/5.64 => ( P @ N4 ) )
% 5.41/5.64 => ( P @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_less_induct
% 5.41/5.64 thf(fact_584_infinite__descent,axiom,
% 5.41/5.64 ! [P: nat > $o,N: nat] :
% 5.41/5.64 ( ! [N4: nat] :
% 5.41/5.64 ( ~ ( P @ N4 )
% 5.41/5.64 => ? [M5: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M5 @ N4 )
% 5.41/5.64 & ~ ( P @ M5 ) ) )
% 5.41/5.64 => ( P @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % infinite_descent
% 5.41/5.64 thf(fact_585_linorder__neqE__nat,axiom,
% 5.41/5.64 ! [X4: nat,Y3: nat] :
% 5.41/5.64 ( ( X4 != Y3 )
% 5.41/5.64 => ( ~ ( ord_less_nat @ X4 @ Y3 )
% 5.41/5.64 => ( ord_less_nat @ Y3 @ X4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % linorder_neqE_nat
% 5.41/5.64 thf(fact_586_le__refl,axiom,
% 5.41/5.64 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.41/5.64
% 5.41/5.64 % le_refl
% 5.41/5.64 thf(fact_587_le__trans,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( ord_less_eq_nat @ J @ K )
% 5.41/5.64 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_trans
% 5.41/5.64 thf(fact_588_eq__imp__le,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( M = N )
% 5.41/5.64 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_imp_le
% 5.41/5.64 thf(fact_589_le__antisym,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( M = N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_antisym
% 5.41/5.64 thf(fact_590_nat__le__linear,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_le_linear
% 5.41/5.64 thf(fact_591_Nat_Oex__has__greatest__nat,axiom,
% 5.41/5.64 ! [P: nat > $o,K: nat,B2: nat] :
% 5.41/5.64 ( ( P @ K )
% 5.41/5.64 => ( ! [Y4: nat] :
% 5.41/5.64 ( ( P @ Y4 )
% 5.41/5.64 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 5.41/5.64 => ? [X3: nat] :
% 5.41/5.64 ( ( P @ X3 )
% 5.41/5.64 & ! [Y5: nat] :
% 5.41/5.64 ( ( P @ Y5 )
% 5.41/5.64 => ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.ex_has_greatest_nat
% 5.41/5.64 thf(fact_592_diff__commute,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.41/5.64 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_commute
% 5.41/5.64 thf(fact_593_left__add__twice,axiom,
% 5.41/5.64 ! [A: complex,B2: complex] :
% 5.41/5.64 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B2 ) )
% 5.41/5.64 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_add_twice
% 5.41/5.64 thf(fact_594_left__add__twice,axiom,
% 5.41/5.64 ! [A: real,B2: real] :
% 5.41/5.64 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B2 ) )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_add_twice
% 5.41/5.64 thf(fact_595_left__add__twice,axiom,
% 5.41/5.64 ! [A: rat,B2: rat] :
% 5.41/5.64 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B2 ) )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_add_twice
% 5.41/5.64 thf(fact_596_left__add__twice,axiom,
% 5.41/5.64 ! [A: nat,B2: nat] :
% 5.41/5.64 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_add_twice
% 5.41/5.64 thf(fact_597_left__add__twice,axiom,
% 5.41/5.64 ! [A: int,B2: int] :
% 5.41/5.64 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % left_add_twice
% 5.41/5.64 thf(fact_598_mult__2__right,axiom,
% 5.41/5.64 ! [Z: complex] :
% 5.41/5.64 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_2_right
% 5.41/5.64 thf(fact_599_mult__2__right,axiom,
% 5.41/5.64 ! [Z: real] :
% 5.41/5.64 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_2_right
% 5.41/5.64 thf(fact_600_mult__2__right,axiom,
% 5.41/5.64 ! [Z: rat] :
% 5.41/5.64 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_2_right
% 5.41/5.64 thf(fact_601_mult__2__right,axiom,
% 5.41/5.64 ! [Z: nat] :
% 5.41/5.64 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_2_right
% 5.41/5.64 thf(fact_602_mult__2__right,axiom,
% 5.41/5.64 ! [Z: int] :
% 5.41/5.64 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_2_right
% 5.41/5.64 thf(fact_603_mult__2,axiom,
% 5.41/5.64 ! [Z: complex] :
% 5.41/5.64 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.41/5.64 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_2
% 5.41/5.64 thf(fact_604_mult__2,axiom,
% 5.41/5.64 ! [Z: real] :
% 5.41/5.64 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.41/5.64 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_2
% 5.41/5.64 thf(fact_605_mult__2,axiom,
% 5.41/5.64 ! [Z: rat] :
% 5.41/5.64 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.41/5.64 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_2
% 5.41/5.64 thf(fact_606_mult__2,axiom,
% 5.41/5.64 ! [Z: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.41/5.64 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_2
% 5.41/5.64 thf(fact_607_mult__2,axiom,
% 5.41/5.64 ! [Z: int] :
% 5.41/5.64 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.41/5.64 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_2
% 5.41/5.64 thf(fact_608_power2__eq__square,axiom,
% 5.41/5.64 ! [A: complex] :
% 5.41/5.64 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( times_times_complex @ A @ A ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_eq_square
% 5.41/5.64 thf(fact_609_power2__eq__square,axiom,
% 5.41/5.64 ! [A: real] :
% 5.41/5.64 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( times_times_real @ A @ A ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_eq_square
% 5.41/5.64 thf(fact_610_power2__eq__square,axiom,
% 5.41/5.64 ! [A: rat] :
% 5.41/5.64 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( times_times_rat @ A @ A ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_eq_square
% 5.41/5.64 thf(fact_611_power2__eq__square,axiom,
% 5.41/5.64 ! [A: nat] :
% 5.41/5.64 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( times_times_nat @ A @ A ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_eq_square
% 5.41/5.64 thf(fact_612_power2__eq__square,axiom,
% 5.41/5.64 ! [A: int] :
% 5.41/5.64 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( times_times_int @ A @ A ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_eq_square
% 5.41/5.64 thf(fact_613_power4__eq__xxxx,axiom,
% 5.41/5.64 ! [X4: complex] :
% 5.41/5.64 ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.64 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 5.41/5.64
% 5.41/5.64 % power4_eq_xxxx
% 5.41/5.64 thf(fact_614_power4__eq__xxxx,axiom,
% 5.41/5.64 ! [X4: real] :
% 5.41/5.64 ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.64 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 5.41/5.64
% 5.41/5.64 % power4_eq_xxxx
% 5.41/5.64 thf(fact_615_power4__eq__xxxx,axiom,
% 5.41/5.64 ! [X4: rat] :
% 5.41/5.64 ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.64 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 5.41/5.64
% 5.41/5.64 % power4_eq_xxxx
% 5.41/5.64 thf(fact_616_power4__eq__xxxx,axiom,
% 5.41/5.64 ! [X4: nat] :
% 5.41/5.64 ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.64 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 5.41/5.64
% 5.41/5.64 % power4_eq_xxxx
% 5.41/5.64 thf(fact_617_power4__eq__xxxx,axiom,
% 5.41/5.64 ! [X4: int] :
% 5.41/5.64 ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.64 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 5.41/5.64
% 5.41/5.64 % power4_eq_xxxx
% 5.41/5.64 thf(fact_618_power__even__eq,axiom,
% 5.41/5.64 ! [A: nat,N: nat] :
% 5.41/5.64 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.64 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_even_eq
% 5.41/5.64 thf(fact_619_power__even__eq,axiom,
% 5.41/5.64 ! [A: real,N: nat] :
% 5.41/5.64 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.64 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_even_eq
% 5.41/5.64 thf(fact_620_power__even__eq,axiom,
% 5.41/5.64 ! [A: int,N: nat] :
% 5.41/5.64 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.64 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_even_eq
% 5.41/5.64 thf(fact_621_power__even__eq,axiom,
% 5.41/5.64 ! [A: complex,N: nat] :
% 5.41/5.64 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.64 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_even_eq
% 5.41/5.64 thf(fact_622_nat__less__add__iff1,axiom,
% 5.41/5.64 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ J @ I )
% 5.41/5.64 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.64 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_less_add_iff1
% 5.41/5.64 thf(fact_623_nat__less__add__iff2,axiom,
% 5.41/5.64 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.64 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_less_add_iff2
% 5.41/5.64 thf(fact_624_power2__sum,axiom,
% 5.41/5.64 ! [X4: complex,Y3: complex] :
% 5.41/5.64 ( ( power_power_complex @ ( plus_plus_complex @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_sum
% 5.41/5.64 thf(fact_625_power2__sum,axiom,
% 5.41/5.64 ! [X4: real,Y3: real] :
% 5.41/5.64 ( ( power_power_real @ ( plus_plus_real @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_sum
% 5.41/5.64 thf(fact_626_power2__sum,axiom,
% 5.41/5.64 ! [X4: rat,Y3: rat] :
% 5.41/5.64 ( ( power_power_rat @ ( plus_plus_rat @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_sum
% 5.41/5.64 thf(fact_627_power2__sum,axiom,
% 5.41/5.64 ! [X4: nat,Y3: nat] :
% 5.41/5.64 ( ( power_power_nat @ ( plus_plus_nat @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_sum
% 5.41/5.64 thf(fact_628_power2__sum,axiom,
% 5.41/5.64 ! [X4: int,Y3: int] :
% 5.41/5.64 ( ( power_power_int @ ( plus_plus_int @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_sum
% 5.41/5.64 thf(fact_629_add__diff__add,axiom,
% 5.41/5.64 ! [A: real,C: real,B2: real,D: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) )
% 5.41/5.64 = ( plus_plus_real @ ( minus_minus_real @ A @ B2 ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_add
% 5.41/5.64 thf(fact_630_add__diff__add,axiom,
% 5.41/5.64 ! [A: rat,C: rat,B2: rat,D: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ D ) )
% 5.41/5.64 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B2 ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_add
% 5.41/5.64 thf(fact_631_add__diff__add,axiom,
% 5.41/5.64 ! [A: int,C: int,B2: int,D: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) )
% 5.41/5.64 = ( plus_plus_int @ ( minus_minus_int @ A @ B2 ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_add
% 5.41/5.64 thf(fact_632_nat__less__le,axiom,
% 5.41/5.64 ( ord_less_nat
% 5.41/5.64 = ( ^ [M6: nat,N2: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.41/5.64 & ( M6 != N2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_less_le
% 5.41/5.64 thf(fact_633_less__imp__le__nat,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ N )
% 5.41/5.64 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_imp_le_nat
% 5.41/5.64 thf(fact_634_le__eq__less__or__eq,axiom,
% 5.41/5.64 ( ord_less_eq_nat
% 5.41/5.64 = ( ^ [M6: nat,N2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M6 @ N2 )
% 5.41/5.64 | ( M6 = N2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_eq_less_or_eq
% 5.41/5.64 thf(fact_635_less__or__eq__imp__le,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ( ord_less_nat @ M @ N )
% 5.41/5.64 | ( M = N ) )
% 5.41/5.64 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_or_eq_imp_le
% 5.41/5.64 thf(fact_636_le__neq__implies__less,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ( ( M != N )
% 5.41/5.64 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_neq_implies_less
% 5.41/5.64 thf(fact_637_less__mono__imp__le__mono,axiom,
% 5.41/5.64 ! [F: nat > nat,I: nat,J: nat] :
% 5.41/5.64 ( ! [I3: nat,J2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I3 @ J2 )
% 5.41/5.64 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_mono_imp_le_mono
% 5.41/5.64 thf(fact_638_add__lessD1,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.41/5.64 => ( ord_less_nat @ I @ K ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_lessD1
% 5.41/5.64 thf(fact_639_add__less__mono,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I @ J )
% 5.41/5.64 => ( ( ord_less_nat @ K @ L2 )
% 5.41/5.64 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_mono
% 5.41/5.64 thf(fact_640_not__add__less1,axiom,
% 5.41/5.64 ! [I: nat,J: nat] :
% 5.41/5.64 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 5.41/5.64
% 5.41/5.64 % not_add_less1
% 5.41/5.64 thf(fact_641_not__add__less2,axiom,
% 5.41/5.64 ! [J: nat,I: nat] :
% 5.41/5.64 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 5.41/5.64
% 5.41/5.64 % not_add_less2
% 5.41/5.64 thf(fact_642_add__less__mono1,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I @ J )
% 5.41/5.64 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_mono1
% 5.41/5.64 thf(fact_643_trans__less__add1,axiom,
% 5.41/5.64 ! [I: nat,J: nat,M: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I @ J )
% 5.41/5.64 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % trans_less_add1
% 5.41/5.64 thf(fact_644_trans__less__add2,axiom,
% 5.41/5.64 ! [I: nat,J: nat,M: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I @ J )
% 5.41/5.64 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % trans_less_add2
% 5.41/5.64 thf(fact_645_less__add__eq__less,axiom,
% 5.41/5.64 ! [K: nat,L2: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ K @ L2 )
% 5.41/5.64 => ( ( ( plus_plus_nat @ M @ L2 )
% 5.41/5.64 = ( plus_plus_nat @ K @ N ) )
% 5.41/5.64 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_eq_less
% 5.41/5.64 thf(fact_646_add__leE,axiom,
% 5.41/5.64 ! [M: nat,K: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.41/5.64 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_leE
% 5.41/5.64 thf(fact_647_le__add1,axiom,
% 5.41/5.64 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_add1
% 5.41/5.64 thf(fact_648_le__add2,axiom,
% 5.41/5.64 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_add2
% 5.41/5.64 thf(fact_649_add__leD1,axiom,
% 5.41/5.64 ! [M: nat,K: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.41/5.64 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_leD1
% 5.41/5.64 thf(fact_650_add__leD2,axiom,
% 5.41/5.64 ! [M: nat,K: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.41/5.64 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_leD2
% 5.41/5.64 thf(fact_651_le__Suc__ex,axiom,
% 5.41/5.64 ! [K: nat,L2: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ L2 )
% 5.41/5.64 => ? [N4: nat] :
% 5.41/5.64 ( L2
% 5.41/5.64 = ( plus_plus_nat @ K @ N4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_Suc_ex
% 5.41/5.64 thf(fact_652_add__le__mono,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.41/5.64 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_mono
% 5.41/5.64 thf(fact_653_add__le__mono1,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_mono1
% 5.41/5.64 thf(fact_654_trans__le__add1,axiom,
% 5.41/5.64 ! [I: nat,J: nat,M: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % trans_le_add1
% 5.41/5.64 thf(fact_655_trans__le__add2,axiom,
% 5.41/5.64 ! [I: nat,J: nat,M: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % trans_le_add2
% 5.41/5.64 thf(fact_656_nat__le__iff__add,axiom,
% 5.41/5.64 ( ord_less_eq_nat
% 5.41/5.64 = ( ^ [M6: nat,N2: nat] :
% 5.41/5.64 ? [K3: nat] :
% 5.41/5.64 ( N2
% 5.41/5.64 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_le_iff_add
% 5.41/5.64 thf(fact_657_diff__less__mono2,axiom,
% 5.41/5.64 ! [M: nat,N: nat,L2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ N )
% 5.41/5.64 => ( ( ord_less_nat @ M @ L2 )
% 5.41/5.64 => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_less_mono2
% 5.41/5.64 thf(fact_658_less__imp__diff__less,axiom,
% 5.41/5.64 ! [J: nat,K: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ J @ K )
% 5.41/5.64 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_imp_diff_less
% 5.41/5.64 thf(fact_659_eq__diff__iff,axiom,
% 5.41/5.64 ! [K: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ M )
% 5.41/5.64 => ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.64 => ( ( ( minus_minus_nat @ M @ K )
% 5.41/5.64 = ( minus_minus_nat @ N @ K ) )
% 5.41/5.64 = ( M = N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_diff_iff
% 5.41/5.64 thf(fact_660_le__diff__iff,axiom,
% 5.41/5.64 ! [K: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ M )
% 5.41/5.64 => ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.64 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.41/5.64 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_diff_iff
% 5.41/5.64 thf(fact_661_Nat_Odiff__diff__eq,axiom,
% 5.41/5.64 ! [K: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ M )
% 5.41/5.64 => ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.64 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.41/5.64 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.diff_diff_eq
% 5.41/5.64 thf(fact_662_diff__le__mono,axiom,
% 5.41/5.64 ! [M: nat,N: nat,L2: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_le_mono
% 5.41/5.64 thf(fact_663_diff__le__self,axiom,
% 5.41/5.64 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.41/5.64
% 5.41/5.64 % diff_le_self
% 5.41/5.64 thf(fact_664_le__diff__iff_H,axiom,
% 5.41/5.64 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ C )
% 5.41/5.64 => ( ( ord_less_eq_nat @ B2 @ C )
% 5.41/5.64 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B2 ) )
% 5.41/5.64 = ( ord_less_eq_nat @ B2 @ A ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_diff_iff'
% 5.41/5.64 thf(fact_665_diff__le__mono2,axiom,
% 5.41/5.64 ! [M: nat,N: nat,L2: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_le_mono2
% 5.41/5.64 thf(fact_666_power2__diff,axiom,
% 5.41/5.64 ! [X4: complex,Y3: complex] :
% 5.41/5.64 ( ( power_power_complex @ ( minus_minus_complex @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_diff
% 5.41/5.64 thf(fact_667_power2__diff,axiom,
% 5.41/5.64 ! [X4: real,Y3: real] :
% 5.41/5.64 ( ( power_power_real @ ( minus_minus_real @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_diff
% 5.41/5.64 thf(fact_668_power2__diff,axiom,
% 5.41/5.64 ! [X4: rat,Y3: rat] :
% 5.41/5.64 ( ( power_power_rat @ ( minus_minus_rat @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_diff
% 5.41/5.64 thf(fact_669_power2__diff,axiom,
% 5.41/5.64 ! [X4: int,Y3: int] :
% 5.41/5.64 ( ( power_power_int @ ( minus_minus_int @ X4 @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.64 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power2_diff
% 5.41/5.64 thf(fact_670_Nat_Odiff__cancel,axiom,
% 5.41/5.64 ! [K: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.41/5.64 = ( minus_minus_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.diff_cancel
% 5.41/5.64 thf(fact_671_diff__cancel2,axiom,
% 5.41/5.64 ! [M: nat,K: nat,N: nat] :
% 5.41/5.64 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.41/5.64 = ( minus_minus_nat @ M @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_cancel2
% 5.41/5.64 thf(fact_672_diff__add__inverse,axiom,
% 5.41/5.64 ! [N: nat,M: nat] :
% 5.41/5.64 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.41/5.64 = M ) ).
% 5.41/5.64
% 5.41/5.64 % diff_add_inverse
% 5.41/5.64 thf(fact_673_diff__add__inverse2,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.41/5.64 = M ) ).
% 5.41/5.64
% 5.41/5.64 % diff_add_inverse2
% 5.41/5.64 thf(fact_674_add__le__add__imp__diff__le,axiom,
% 5.41/5.64 ! [I: real,K: real,N: real,J: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.41/5.64 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.41/5.64 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_add_imp_diff_le
% 5.41/5.64 thf(fact_675_add__le__add__imp__diff__le,axiom,
% 5.41/5.64 ! [I: rat,K: rat,N: rat,J: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.41/5.64 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.41/5.64 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_add_imp_diff_le
% 5.41/5.64 thf(fact_676_add__le__add__imp__diff__le,axiom,
% 5.41/5.64 ! [I: nat,K: nat,N: nat,J: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.41/5.64 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_add_imp_diff_le
% 5.41/5.64 thf(fact_677_add__le__add__imp__diff__le,axiom,
% 5.41/5.64 ! [I: int,K: int,N: int,J: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.41/5.64 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.41/5.64 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_add_imp_diff_le
% 5.41/5.64 thf(fact_678_add__le__imp__le__diff,axiom,
% 5.41/5.64 ! [I: real,K: real,N: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.41/5.64 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_imp_le_diff
% 5.41/5.64 thf(fact_679_add__le__imp__le__diff,axiom,
% 5.41/5.64 ! [I: rat,K: rat,N: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.41/5.64 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_imp_le_diff
% 5.41/5.64 thf(fact_680_add__le__imp__le__diff,axiom,
% 5.41/5.64 ! [I: nat,K: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.41/5.64 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_imp_le_diff
% 5.41/5.64 thf(fact_681_add__le__imp__le__diff,axiom,
% 5.41/5.64 ! [I: int,K: int,N: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.41/5.64 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_imp_le_diff
% 5.41/5.64 thf(fact_682_add__mono1,axiom,
% 5.41/5.64 ! [A: real,B2: real] :
% 5.41/5.64 ( ( ord_less_real @ A @ B2 )
% 5.41/5.64 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B2 @ one_one_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_mono1
% 5.41/5.64 thf(fact_683_add__mono1,axiom,
% 5.41/5.64 ! [A: rat,B2: rat] :
% 5.41/5.64 ( ( ord_less_rat @ A @ B2 )
% 5.41/5.64 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B2 @ one_one_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_mono1
% 5.41/5.64 thf(fact_684_add__mono1,axiom,
% 5.41/5.64 ! [A: nat,B2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ A @ B2 )
% 5.41/5.64 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B2 @ one_one_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_mono1
% 5.41/5.64 thf(fact_685_add__mono1,axiom,
% 5.41/5.64 ! [A: int,B2: int] :
% 5.41/5.64 ( ( ord_less_int @ A @ B2 )
% 5.41/5.64 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B2 @ one_one_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_mono1
% 5.41/5.64 thf(fact_686_less__add__one,axiom,
% 5.41/5.64 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_one
% 5.41/5.64 thf(fact_687_less__add__one,axiom,
% 5.41/5.64 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_one
% 5.41/5.64 thf(fact_688_less__add__one,axiom,
% 5.41/5.64 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_one
% 5.41/5.64 thf(fact_689_less__add__one,axiom,
% 5.41/5.64 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_add_one
% 5.41/5.64 thf(fact_690_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.41/5.64 ! [A: real,B2: real] :
% 5.41/5.64 ( ~ ( ord_less_real @ A @ B2 )
% 5.41/5.64 => ( ( plus_plus_real @ B2 @ ( minus_minus_real @ A @ B2 ) )
% 5.41/5.64 = A ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_semidom_class.add_diff_inverse
% 5.41/5.64 thf(fact_691_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.41/5.64 ! [A: rat,B2: rat] :
% 5.41/5.64 ( ~ ( ord_less_rat @ A @ B2 )
% 5.41/5.64 => ( ( plus_plus_rat @ B2 @ ( minus_minus_rat @ A @ B2 ) )
% 5.41/5.64 = A ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_semidom_class.add_diff_inverse
% 5.41/5.64 thf(fact_692_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.41/5.64 ! [A: nat,B2: nat] :
% 5.41/5.64 ( ~ ( ord_less_nat @ A @ B2 )
% 5.41/5.64 => ( ( plus_plus_nat @ B2 @ ( minus_minus_nat @ A @ B2 ) )
% 5.41/5.64 = A ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_semidom_class.add_diff_inverse
% 5.41/5.64 thf(fact_693_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.41/5.64 ! [A: int,B2: int] :
% 5.41/5.64 ( ~ ( ord_less_int @ A @ B2 )
% 5.41/5.64 => ( ( plus_plus_int @ B2 @ ( minus_minus_int @ A @ B2 ) )
% 5.41/5.64 = A ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_semidom_class.add_diff_inverse
% 5.41/5.64 thf(fact_694_mono__nat__linear__lb,axiom,
% 5.41/5.64 ! [F: nat > nat,M: nat,K: nat] :
% 5.41/5.64 ( ! [M4: nat,N4: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M4 @ N4 )
% 5.41/5.64 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N4 ) ) )
% 5.41/5.64 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mono_nat_linear_lb
% 5.41/5.64 thf(fact_695_less__diff__iff,axiom,
% 5.41/5.64 ! [K: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ M )
% 5.41/5.64 => ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.64 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.41/5.64 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_diff_iff
% 5.41/5.64 thf(fact_696_diff__less__mono,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_nat @ A @ B2 )
% 5.41/5.64 => ( ( ord_less_eq_nat @ C @ A )
% 5.41/5.64 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B2 @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_less_mono
% 5.41/5.64 thf(fact_697_add__diff__inverse__nat,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ~ ( ord_less_nat @ M @ N )
% 5.41/5.64 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.64 = M ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_inverse_nat
% 5.41/5.64 thf(fact_698_less__diff__conv,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.41/5.64 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_diff_conv
% 5.41/5.64 thf(fact_699_Nat_Ole__imp__diff__is__add,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( ( minus_minus_nat @ J @ I )
% 5.41/5.64 = K )
% 5.41/5.64 = ( J
% 5.41/5.64 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.le_imp_diff_is_add
% 5.41/5.64 thf(fact_700_Nat_Odiff__add__assoc2,axiom,
% 5.41/5.64 ! [K: nat,J: nat,I: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.64 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 5.41/5.64 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.diff_add_assoc2
% 5.41/5.64 thf(fact_701_Nat_Odiff__add__assoc,axiom,
% 5.41/5.64 ! [K: nat,J: nat,I: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.64 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.41/5.64 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.diff_add_assoc
% 5.41/5.64 thf(fact_702_Nat_Ole__diff__conv2,axiom,
% 5.41/5.64 ! [K: nat,J: nat,I: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.64 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.41/5.64 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.le_diff_conv2
% 5.41/5.64 thf(fact_703_le__diff__conv,axiom,
% 5.41/5.64 ! [J: nat,K: nat,I: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.41/5.64 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_diff_conv
% 5.41/5.64 thf(fact_704_less__diff__conv2,axiom,
% 5.41/5.64 ! [K: nat,J: nat,I: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.64 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.41/5.64 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_diff_conv2
% 5.41/5.64 thf(fact_705_field__sum__of__halves,axiom,
% 5.41/5.64 ! [X4: real] :
% 5.41/5.64 ( ( plus_plus_real @ ( divide_divide_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.64 = X4 ) ).
% 5.41/5.64
% 5.41/5.64 % field_sum_of_halves
% 5.41/5.64 thf(fact_706_field__sum__of__halves,axiom,
% 5.41/5.64 ! [X4: rat] :
% 5.41/5.64 ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.41/5.64 = X4 ) ).
% 5.41/5.64
% 5.41/5.64 % field_sum_of_halves
% 5.41/5.64 thf(fact_707__092_060open_062res_A_061_A2_A_094_A_Ideg_Adiv_A2_J_A_K_Asc_A_L_Aminy_092_060close_062,axiom,
% 5.41/5.64 ( res
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc ) @ miny ) ) ).
% 5.41/5.64
% 5.41/5.64 % \<open>res = 2 ^ (deg div 2) * sc + miny\<close>
% 5.41/5.64 thf(fact_708_sum__squares__bound,axiom,
% 5.41/5.64 ! [X4: real,Y3: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % sum_squares_bound
% 5.41/5.64 thf(fact_709_sum__squares__bound,axiom,
% 5.41/5.64 ! [X4: rat,Y3: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) @ Y3 ) @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % sum_squares_bound
% 5.41/5.64 thf(fact_710_enat__ord__number_I1_J,axiom,
% 5.41/5.64 ! [M: num,N: num] :
% 5.41/5.64 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.41/5.64 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % enat_ord_number(1)
% 5.41/5.64 thf(fact_711_enat__ord__number_I2_J,axiom,
% 5.41/5.64 ! [M: num,N: num] :
% 5.41/5.64 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.41/5.64 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % enat_ord_number(2)
% 5.41/5.64 thf(fact_712_double__not__eq__Suc__double,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.41/5.64 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % double_not_eq_Suc_double
% 5.41/5.64 thf(fact_713_Suc__double__not__eq__double,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.64 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % Suc_double_not_eq_double
% 5.41/5.64 thf(fact_714_add__diff__cancel,axiom,
% 5.41/5.64 ! [A: real,B2: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ B2 )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel
% 5.41/5.64 thf(fact_715_add__diff__cancel,axiom,
% 5.41/5.64 ! [A: rat,B2: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B2 ) @ B2 )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel
% 5.41/5.64 thf(fact_716_add__diff__cancel,axiom,
% 5.41/5.64 ! [A: int,B2: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel
% 5.41/5.64 thf(fact_717_diff__add__cancel,axiom,
% 5.41/5.64 ! [A: real,B2: real] :
% 5.41/5.64 ( ( plus_plus_real @ ( minus_minus_real @ A @ B2 ) @ B2 )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % diff_add_cancel
% 5.41/5.64 thf(fact_718_diff__add__cancel,axiom,
% 5.41/5.64 ! [A: rat,B2: rat] :
% 5.41/5.64 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B2 ) @ B2 )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % diff_add_cancel
% 5.41/5.64 thf(fact_719_diff__add__cancel,axiom,
% 5.41/5.64 ! [A: int,B2: int] :
% 5.41/5.64 ( ( plus_plus_int @ ( minus_minus_int @ A @ B2 ) @ B2 )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % diff_add_cancel
% 5.41/5.64 thf(fact_720_add__diff__cancel__left,axiom,
% 5.41/5.64 ! [C: real,A: real,B2: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) )
% 5.41/5.64 = ( minus_minus_real @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_left
% 5.41/5.64 thf(fact_721_add__diff__cancel__left,axiom,
% 5.41/5.64 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B2 ) )
% 5.41/5.64 = ( minus_minus_rat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_left
% 5.41/5.64 thf(fact_722_add__diff__cancel__left,axiom,
% 5.41/5.64 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.64 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 5.41/5.64 = ( minus_minus_nat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_left
% 5.41/5.64 thf(fact_723_add__diff__cancel__left,axiom,
% 5.41/5.64 ! [C: int,A: int,B2: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 5.41/5.64 = ( minus_minus_int @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_left
% 5.41/5.64 thf(fact_724_add__diff__cancel__left_H,axiom,
% 5.41/5.64 ! [A: real,B2: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ A )
% 5.41/5.64 = B2 ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_left'
% 5.41/5.64 thf(fact_725_add__diff__cancel__left_H,axiom,
% 5.41/5.64 ! [A: rat,B2: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B2 ) @ A )
% 5.41/5.64 = B2 ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_left'
% 5.41/5.64 thf(fact_726_add__diff__cancel__left_H,axiom,
% 5.41/5.64 ! [A: nat,B2: nat] :
% 5.41/5.64 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B2 ) @ A )
% 5.41/5.64 = B2 ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_left'
% 5.41/5.64 thf(fact_727_add__diff__cancel__left_H,axiom,
% 5.41/5.64 ! [A: int,B2: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( plus_plus_int @ A @ B2 ) @ A )
% 5.41/5.64 = B2 ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_left'
% 5.41/5.64 thf(fact_728_add__diff__cancel__right,axiom,
% 5.41/5.64 ! [A: real,C: real,B2: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_real @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_right
% 5.41/5.64 thf(fact_729_add__diff__cancel__right,axiom,
% 5.41/5.64 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_rat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_right
% 5.41/5.64 thf(fact_730_add__diff__cancel__right,axiom,
% 5.41/5.64 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.64 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_nat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_right
% 5.41/5.64 thf(fact_731_add__diff__cancel__right,axiom,
% 5.41/5.64 ! [A: int,C: int,B2: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 5.41/5.64 = ( minus_minus_int @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_right
% 5.41/5.64 thf(fact_732_add__diff__cancel__right_H,axiom,
% 5.41/5.64 ! [A: real,B2: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ B2 )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_right'
% 5.41/5.64 thf(fact_733_add__diff__cancel__right_H,axiom,
% 5.41/5.64 ! [A: rat,B2: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B2 ) @ B2 )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_right'
% 5.41/5.64 thf(fact_734_add__diff__cancel__right_H,axiom,
% 5.41/5.64 ! [A: nat,B2: nat] :
% 5.41/5.64 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_right'
% 5.41/5.64 thf(fact_735_add__diff__cancel__right_H,axiom,
% 5.41/5.64 ! [A: int,B2: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_cancel_right'
% 5.41/5.64 thf(fact_736_add__right__cancel,axiom,
% 5.41/5.64 ! [B2: real,A: real,C: real] :
% 5.41/5.64 ( ( ( plus_plus_real @ B2 @ A )
% 5.41/5.64 = ( plus_plus_real @ C @ A ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_right_cancel
% 5.41/5.64 thf(fact_737_add__right__cancel,axiom,
% 5.41/5.64 ! [B2: rat,A: rat,C: rat] :
% 5.41/5.64 ( ( ( plus_plus_rat @ B2 @ A )
% 5.41/5.64 = ( plus_plus_rat @ C @ A ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_right_cancel
% 5.41/5.64 thf(fact_738_add__right__cancel,axiom,
% 5.41/5.64 ! [B2: nat,A: nat,C: nat] :
% 5.41/5.64 ( ( ( plus_plus_nat @ B2 @ A )
% 5.41/5.64 = ( plus_plus_nat @ C @ A ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_right_cancel
% 5.41/5.64 thf(fact_739_add__right__cancel,axiom,
% 5.41/5.64 ! [B2: int,A: int,C: int] :
% 5.41/5.64 ( ( ( plus_plus_int @ B2 @ A )
% 5.41/5.64 = ( plus_plus_int @ C @ A ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_right_cancel
% 5.41/5.64 thf(fact_740_add__left__cancel,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( ( plus_plus_real @ A @ B2 )
% 5.41/5.64 = ( plus_plus_real @ A @ C ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_left_cancel
% 5.41/5.64 thf(fact_741_add__left__cancel,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( ( plus_plus_rat @ A @ B2 )
% 5.41/5.64 = ( plus_plus_rat @ A @ C ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_left_cancel
% 5.41/5.64 thf(fact_742_add__left__cancel,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( ( plus_plus_nat @ A @ B2 )
% 5.41/5.64 = ( plus_plus_nat @ A @ C ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_left_cancel
% 5.41/5.64 thf(fact_743_add__left__cancel,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( ( plus_plus_int @ A @ B2 )
% 5.41/5.64 = ( plus_plus_int @ A @ C ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_left_cancel
% 5.41/5.64 thf(fact_744_add__le__cancel__right,axiom,
% 5.41/5.64 ! [A: real,C: real,B2: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) )
% 5.41/5.64 = ( ord_less_eq_real @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_cancel_right
% 5.41/5.64 thf(fact_745_add__le__cancel__right,axiom,
% 5.41/5.64 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ C ) )
% 5.41/5.64 = ( ord_less_eq_rat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_cancel_right
% 5.41/5.64 thf(fact_746_add__le__cancel__right,axiom,
% 5.41/5.64 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 5.41/5.64 = ( ord_less_eq_nat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_cancel_right
% 5.41/5.64 thf(fact_747_add__le__cancel__right,axiom,
% 5.41/5.64 ! [A: int,C: int,B2: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 5.41/5.64 = ( ord_less_eq_int @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_cancel_right
% 5.41/5.64 thf(fact_748_add__le__cancel__left,axiom,
% 5.41/5.64 ! [C: real,A: real,B2: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) )
% 5.41/5.64 = ( ord_less_eq_real @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_cancel_left
% 5.41/5.64 thf(fact_749_add__le__cancel__left,axiom,
% 5.41/5.64 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B2 ) )
% 5.41/5.64 = ( ord_less_eq_rat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_cancel_left
% 5.41/5.64 thf(fact_750_add__le__cancel__left,axiom,
% 5.41/5.64 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 5.41/5.64 = ( ord_less_eq_nat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_cancel_left
% 5.41/5.64 thf(fact_751_add__le__cancel__left,axiom,
% 5.41/5.64 ! [C: int,A: int,B2: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 5.41/5.64 = ( ord_less_eq_int @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_cancel_left
% 5.41/5.64 thf(fact_752_add__less__cancel__right,axiom,
% 5.41/5.64 ! [A: real,C: real,B2: real] :
% 5.41/5.64 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) )
% 5.41/5.64 = ( ord_less_real @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_cancel_right
% 5.41/5.64 thf(fact_753_add__less__cancel__right,axiom,
% 5.41/5.64 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ C ) )
% 5.41/5.64 = ( ord_less_rat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_cancel_right
% 5.41/5.64 thf(fact_754_add__less__cancel__right,axiom,
% 5.41/5.64 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 5.41/5.64 = ( ord_less_nat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_cancel_right
% 5.41/5.64 thf(fact_755_add__less__cancel__right,axiom,
% 5.41/5.64 ! [A: int,C: int,B2: int] :
% 5.41/5.64 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 5.41/5.64 = ( ord_less_int @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_cancel_right
% 5.41/5.64 thf(fact_756_add__less__cancel__left,axiom,
% 5.41/5.64 ! [C: real,A: real,B2: real] :
% 5.41/5.64 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) )
% 5.41/5.64 = ( ord_less_real @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_cancel_left
% 5.41/5.64 thf(fact_757_add__less__cancel__left,axiom,
% 5.41/5.64 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B2 ) )
% 5.41/5.64 = ( ord_less_rat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_cancel_left
% 5.41/5.64 thf(fact_758_add__less__cancel__left,axiom,
% 5.41/5.64 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 5.41/5.64 = ( ord_less_nat @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_cancel_left
% 5.41/5.64 thf(fact_759_add__less__cancel__left,axiom,
% 5.41/5.64 ! [C: int,A: int,B2: int] :
% 5.41/5.64 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 5.41/5.64 = ( ord_less_int @ A @ B2 ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_cancel_left
% 5.41/5.64 thf(fact_760_mult__1,axiom,
% 5.41/5.64 ! [A: complex] :
% 5.41/5.64 ( ( times_times_complex @ one_one_complex @ A )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_1
% 5.41/5.64 thf(fact_761_mult__1,axiom,
% 5.41/5.64 ! [A: real] :
% 5.41/5.64 ( ( times_times_real @ one_one_real @ A )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_1
% 5.41/5.64 thf(fact_762_mult__1,axiom,
% 5.41/5.64 ! [A: rat] :
% 5.41/5.64 ( ( times_times_rat @ one_one_rat @ A )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_1
% 5.41/5.64 thf(fact_763_mult__1,axiom,
% 5.41/5.64 ! [A: nat] :
% 5.41/5.64 ( ( times_times_nat @ one_one_nat @ A )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_1
% 5.41/5.64 thf(fact_764_mult__1,axiom,
% 5.41/5.64 ! [A: int] :
% 5.41/5.64 ( ( times_times_int @ one_one_int @ A )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult_1
% 5.41/5.64 thf(fact_765_mult_Oright__neutral,axiom,
% 5.41/5.64 ! [A: complex] :
% 5.41/5.64 ( ( times_times_complex @ A @ one_one_complex )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult.right_neutral
% 5.41/5.64 thf(fact_766_mult_Oright__neutral,axiom,
% 5.41/5.64 ! [A: real] :
% 5.41/5.64 ( ( times_times_real @ A @ one_one_real )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult.right_neutral
% 5.41/5.64 thf(fact_767_mult_Oright__neutral,axiom,
% 5.41/5.64 ! [A: rat] :
% 5.41/5.64 ( ( times_times_rat @ A @ one_one_rat )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult.right_neutral
% 5.41/5.64 thf(fact_768_mult_Oright__neutral,axiom,
% 5.41/5.64 ! [A: nat] :
% 5.41/5.64 ( ( times_times_nat @ A @ one_one_nat )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult.right_neutral
% 5.41/5.64 thf(fact_769_mult_Oright__neutral,axiom,
% 5.41/5.64 ! [A: int] :
% 5.41/5.64 ( ( times_times_int @ A @ one_one_int )
% 5.41/5.64 = A ) ).
% 5.41/5.64
% 5.41/5.64 % mult.right_neutral
% 5.41/5.64 thf(fact_770_semiring__norm_I13_J,axiom,
% 5.41/5.64 ! [M: num,N: num] :
% 5.41/5.64 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.64 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % semiring_norm(13)
% 5.41/5.64 thf(fact_771_semiring__norm_I12_J,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ( ( times_times_num @ one @ N )
% 5.41/5.64 = N ) ).
% 5.41/5.64
% 5.41/5.64 % semiring_norm(12)
% 5.41/5.64 thf(fact_772_semiring__norm_I11_J,axiom,
% 5.41/5.64 ! [M: num] :
% 5.41/5.64 ( ( times_times_num @ M @ one )
% 5.41/5.64 = M ) ).
% 5.41/5.64
% 5.41/5.64 % semiring_norm(11)
% 5.41/5.64 thf(fact_773_num__double,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.41/5.64 = ( bit0 @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % num_double
% 5.41/5.64 thf(fact_774_power__mult__numeral,axiom,
% 5.41/5.64 ! [A: nat,M: num,N: num] :
% 5.41/5.64 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.64 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult_numeral
% 5.41/5.64 thf(fact_775_power__mult__numeral,axiom,
% 5.41/5.64 ! [A: real,M: num,N: num] :
% 5.41/5.64 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.64 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult_numeral
% 5.41/5.64 thf(fact_776_power__mult__numeral,axiom,
% 5.41/5.64 ! [A: int,M: num,N: num] :
% 5.41/5.64 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.64 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult_numeral
% 5.41/5.64 thf(fact_777_power__mult__numeral,axiom,
% 5.41/5.64 ! [A: complex,M: num,N: num] :
% 5.41/5.64 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.64 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mult_numeral
% 5.41/5.64 thf(fact_778_complete__real,axiom,
% 5.41/5.64 ! [S2: set_real] :
% 5.41/5.64 ( ? [X5: real] : ( member_real @ X5 @ S2 )
% 5.41/5.64 => ( ? [Z3: real] :
% 5.41/5.64 ! [X3: real] :
% 5.41/5.64 ( ( member_real @ X3 @ S2 )
% 5.41/5.64 => ( ord_less_eq_real @ X3 @ Z3 ) )
% 5.41/5.64 => ? [Y4: real] :
% 5.41/5.64 ( ! [X5: real] :
% 5.41/5.64 ( ( member_real @ X5 @ S2 )
% 5.41/5.64 => ( ord_less_eq_real @ X5 @ Y4 ) )
% 5.41/5.64 & ! [Z3: real] :
% 5.41/5.64 ( ! [X3: real] :
% 5.41/5.64 ( ( member_real @ X3 @ S2 )
% 5.41/5.64 => ( ord_less_eq_real @ X3 @ Z3 ) )
% 5.41/5.64 => ( ord_less_eq_real @ Y4 @ Z3 ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % complete_real
% 5.41/5.64 thf(fact_779_real__arch__pow,axiom,
% 5.41/5.64 ! [X4: real,Y3: real] :
% 5.41/5.64 ( ( ord_less_real @ one_one_real @ X4 )
% 5.41/5.64 => ? [N4: nat] : ( ord_less_real @ Y3 @ ( power_power_real @ X4 @ N4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % real_arch_pow
% 5.41/5.64 thf(fact_780_less__eq__real__def,axiom,
% 5.41/5.64 ( ord_less_eq_real
% 5.41/5.64 = ( ^ [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_real @ X @ Y )
% 5.41/5.64 | ( X = Y ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_eq_real_def
% 5.41/5.64 thf(fact_781_add__diff__assoc__enat,axiom,
% 5.41/5.64 ! [Z: extended_enat,Y3: extended_enat,X4: extended_enat] :
% 5.41/5.64 ( ( ord_le2932123472753598470d_enat @ Z @ Y3 )
% 5.41/5.64 => ( ( plus_p3455044024723400733d_enat @ X4 @ ( minus_3235023915231533773d_enat @ Y3 @ Z ) )
% 5.41/5.64 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X4 @ Y3 ) @ Z ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_assoc_enat
% 5.41/5.64 thf(fact_782_enat__less__induct,axiom,
% 5.41/5.64 ! [P: extended_enat > $o,N: extended_enat] :
% 5.41/5.64 ( ! [N4: extended_enat] :
% 5.41/5.64 ( ! [M5: extended_enat] :
% 5.41/5.64 ( ( ord_le72135733267957522d_enat @ M5 @ N4 )
% 5.41/5.64 => ( P @ M5 ) )
% 5.41/5.64 => ( P @ N4 ) )
% 5.41/5.64 => ( P @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % enat_less_induct
% 5.41/5.64 thf(fact_783_four__x__squared,axiom,
% 5.41/5.64 ! [X4: real] :
% 5.41/5.64 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.64 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % four_x_squared
% 5.41/5.64 thf(fact_784_L2__set__mult__ineq__lemma,axiom,
% 5.41/5.64 ! [A: real,C: real,B2: 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 @ B2 @ 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 @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % L2_set_mult_ineq_lemma
% 5.41/5.64 thf(fact_785_div__mult2__numeral__eq,axiom,
% 5.41/5.64 ! [A: nat,K: num,L2: num] :
% 5.41/5.64 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.64 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % div_mult2_numeral_eq
% 5.41/5.64 thf(fact_786_div__mult2__numeral__eq,axiom,
% 5.41/5.64 ! [A: int,K: num,L2: num] :
% 5.41/5.64 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 5.41/5.64 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % div_mult2_numeral_eq
% 5.41/5.64 thf(fact_787_mult_Oleft__commute,axiom,
% 5.41/5.64 ! [B2: real,A: real,C: real] :
% 5.41/5.64 ( ( times_times_real @ B2 @ ( times_times_real @ A @ C ) )
% 5.41/5.64 = ( times_times_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.left_commute
% 5.41/5.64 thf(fact_788_mult_Oleft__commute,axiom,
% 5.41/5.64 ! [B2: rat,A: rat,C: rat] :
% 5.41/5.64 ( ( times_times_rat @ B2 @ ( times_times_rat @ A @ C ) )
% 5.41/5.64 = ( times_times_rat @ A @ ( times_times_rat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.left_commute
% 5.41/5.64 thf(fact_789_mult_Oleft__commute,axiom,
% 5.41/5.64 ! [B2: nat,A: nat,C: nat] :
% 5.41/5.64 ( ( times_times_nat @ B2 @ ( times_times_nat @ A @ C ) )
% 5.41/5.64 = ( times_times_nat @ A @ ( times_times_nat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.left_commute
% 5.41/5.64 thf(fact_790_mult_Oleft__commute,axiom,
% 5.41/5.64 ! [B2: int,A: int,C: int] :
% 5.41/5.64 ( ( times_times_int @ B2 @ ( times_times_int @ A @ C ) )
% 5.41/5.64 = ( times_times_int @ A @ ( times_times_int @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.left_commute
% 5.41/5.64 thf(fact_791_mult_Ocommute,axiom,
% 5.41/5.64 ( times_times_real
% 5.41/5.64 = ( ^ [A4: real,B3: real] : ( times_times_real @ B3 @ A4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.commute
% 5.41/5.64 thf(fact_792_mult_Ocommute,axiom,
% 5.41/5.64 ( times_times_rat
% 5.41/5.64 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ B3 @ A4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.commute
% 5.41/5.64 thf(fact_793_mult_Ocommute,axiom,
% 5.41/5.64 ( times_times_nat
% 5.41/5.64 = ( ^ [A4: nat,B3: nat] : ( times_times_nat @ B3 @ A4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.commute
% 5.41/5.64 thf(fact_794_mult_Ocommute,axiom,
% 5.41/5.64 ( times_times_int
% 5.41/5.64 = ( ^ [A4: int,B3: int] : ( times_times_int @ B3 @ A4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.commute
% 5.41/5.64 thf(fact_795_mult_Oassoc,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( times_times_real @ ( times_times_real @ A @ B2 ) @ C )
% 5.41/5.64 = ( times_times_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.assoc
% 5.41/5.64 thf(fact_796_mult_Oassoc,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( times_times_rat @ ( times_times_rat @ A @ B2 ) @ C )
% 5.41/5.64 = ( times_times_rat @ A @ ( times_times_rat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.assoc
% 5.41/5.64 thf(fact_797_mult_Oassoc,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 5.41/5.64 = ( times_times_nat @ A @ ( times_times_nat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.assoc
% 5.41/5.64 thf(fact_798_mult_Oassoc,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( times_times_int @ ( times_times_int @ A @ B2 ) @ C )
% 5.41/5.64 = ( times_times_int @ A @ ( times_times_int @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult.assoc
% 5.41/5.64 thf(fact_799_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( times_times_real @ ( times_times_real @ A @ B2 ) @ C )
% 5.41/5.64 = ( times_times_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ab_semigroup_mult_class.mult_ac(1)
% 5.41/5.64 thf(fact_800_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( times_times_rat @ ( times_times_rat @ A @ B2 ) @ C )
% 5.41/5.64 = ( times_times_rat @ A @ ( times_times_rat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ab_semigroup_mult_class.mult_ac(1)
% 5.41/5.64 thf(fact_801_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( times_times_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 5.41/5.64 = ( times_times_nat @ A @ ( times_times_nat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ab_semigroup_mult_class.mult_ac(1)
% 5.41/5.64 thf(fact_802_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( times_times_int @ ( times_times_int @ A @ B2 ) @ C )
% 5.41/5.64 = ( times_times_int @ A @ ( times_times_int @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ab_semigroup_mult_class.mult_ac(1)
% 5.41/5.64 thf(fact_803_one__reorient,axiom,
% 5.41/5.64 ! [X4: complex] :
% 5.41/5.64 ( ( one_one_complex = X4 )
% 5.41/5.64 = ( X4 = one_one_complex ) ) ).
% 5.41/5.64
% 5.41/5.64 % one_reorient
% 5.41/5.64 thf(fact_804_one__reorient,axiom,
% 5.41/5.64 ! [X4: real] :
% 5.41/5.64 ( ( one_one_real = X4 )
% 5.41/5.64 = ( X4 = one_one_real ) ) ).
% 5.41/5.64
% 5.41/5.64 % one_reorient
% 5.41/5.64 thf(fact_805_one__reorient,axiom,
% 5.41/5.64 ! [X4: rat] :
% 5.41/5.64 ( ( one_one_rat = X4 )
% 5.41/5.64 = ( X4 = one_one_rat ) ) ).
% 5.41/5.64
% 5.41/5.64 % one_reorient
% 5.41/5.64 thf(fact_806_one__reorient,axiom,
% 5.41/5.64 ! [X4: nat] :
% 5.41/5.64 ( ( one_one_nat = X4 )
% 5.41/5.64 = ( X4 = one_one_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % one_reorient
% 5.41/5.64 thf(fact_807_one__reorient,axiom,
% 5.41/5.64 ! [X4: int] :
% 5.41/5.64 ( ( one_one_int = X4 )
% 5.41/5.64 = ( X4 = one_one_int ) ) ).
% 5.41/5.64
% 5.41/5.64 % one_reorient
% 5.41/5.64 thf(fact_808_add__right__imp__eq,axiom,
% 5.41/5.64 ! [B2: real,A: real,C: real] :
% 5.41/5.64 ( ( ( plus_plus_real @ B2 @ A )
% 5.41/5.64 = ( plus_plus_real @ C @ A ) )
% 5.41/5.64 => ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_right_imp_eq
% 5.41/5.64 thf(fact_809_add__right__imp__eq,axiom,
% 5.41/5.64 ! [B2: rat,A: rat,C: rat] :
% 5.41/5.64 ( ( ( plus_plus_rat @ B2 @ A )
% 5.41/5.64 = ( plus_plus_rat @ C @ A ) )
% 5.41/5.64 => ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_right_imp_eq
% 5.41/5.64 thf(fact_810_add__right__imp__eq,axiom,
% 5.41/5.64 ! [B2: nat,A: nat,C: nat] :
% 5.41/5.64 ( ( ( plus_plus_nat @ B2 @ A )
% 5.41/5.64 = ( plus_plus_nat @ C @ A ) )
% 5.41/5.64 => ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_right_imp_eq
% 5.41/5.64 thf(fact_811_add__right__imp__eq,axiom,
% 5.41/5.64 ! [B2: int,A: int,C: int] :
% 5.41/5.64 ( ( ( plus_plus_int @ B2 @ A )
% 5.41/5.64 = ( plus_plus_int @ C @ A ) )
% 5.41/5.64 => ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_right_imp_eq
% 5.41/5.64 thf(fact_812_add__left__imp__eq,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( ( plus_plus_real @ A @ B2 )
% 5.41/5.64 = ( plus_plus_real @ A @ C ) )
% 5.41/5.64 => ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_left_imp_eq
% 5.41/5.64 thf(fact_813_add__left__imp__eq,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( ( plus_plus_rat @ A @ B2 )
% 5.41/5.64 = ( plus_plus_rat @ A @ C ) )
% 5.41/5.64 => ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_left_imp_eq
% 5.41/5.64 thf(fact_814_add__left__imp__eq,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( ( plus_plus_nat @ A @ B2 )
% 5.41/5.64 = ( plus_plus_nat @ A @ C ) )
% 5.41/5.64 => ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_left_imp_eq
% 5.41/5.64 thf(fact_815_add__left__imp__eq,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( ( plus_plus_int @ A @ B2 )
% 5.41/5.64 = ( plus_plus_int @ A @ C ) )
% 5.41/5.64 => ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_left_imp_eq
% 5.41/5.64 thf(fact_816_add_Oleft__commute,axiom,
% 5.41/5.64 ! [B2: real,A: real,C: real] :
% 5.41/5.64 ( ( plus_plus_real @ B2 @ ( plus_plus_real @ A @ C ) )
% 5.41/5.64 = ( plus_plus_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.left_commute
% 5.41/5.64 thf(fact_817_add_Oleft__commute,axiom,
% 5.41/5.64 ! [B2: rat,A: rat,C: rat] :
% 5.41/5.64 ( ( plus_plus_rat @ B2 @ ( plus_plus_rat @ A @ C ) )
% 5.41/5.64 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.left_commute
% 5.41/5.64 thf(fact_818_add_Oleft__commute,axiom,
% 5.41/5.64 ! [B2: nat,A: nat,C: nat] :
% 5.41/5.64 ( ( plus_plus_nat @ B2 @ ( plus_plus_nat @ A @ C ) )
% 5.41/5.64 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.left_commute
% 5.41/5.64 thf(fact_819_add_Oleft__commute,axiom,
% 5.41/5.64 ! [B2: int,A: int,C: int] :
% 5.41/5.64 ( ( plus_plus_int @ B2 @ ( plus_plus_int @ A @ C ) )
% 5.41/5.64 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.left_commute
% 5.41/5.64 thf(fact_820_add_Ocommute,axiom,
% 5.41/5.64 ( plus_plus_real
% 5.41/5.64 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ B3 @ A4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.commute
% 5.41/5.64 thf(fact_821_add_Ocommute,axiom,
% 5.41/5.64 ( plus_plus_rat
% 5.41/5.64 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ B3 @ A4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.commute
% 5.41/5.64 thf(fact_822_add_Ocommute,axiom,
% 5.41/5.64 ( plus_plus_nat
% 5.41/5.64 = ( ^ [A4: nat,B3: nat] : ( plus_plus_nat @ B3 @ A4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.commute
% 5.41/5.64 thf(fact_823_add_Ocommute,axiom,
% 5.41/5.64 ( plus_plus_int
% 5.41/5.64 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ B3 @ A4 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.commute
% 5.41/5.64 thf(fact_824_add_Oright__cancel,axiom,
% 5.41/5.64 ! [B2: real,A: real,C: real] :
% 5.41/5.64 ( ( ( plus_plus_real @ B2 @ A )
% 5.41/5.64 = ( plus_plus_real @ C @ A ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.right_cancel
% 5.41/5.64 thf(fact_825_add_Oright__cancel,axiom,
% 5.41/5.64 ! [B2: rat,A: rat,C: rat] :
% 5.41/5.64 ( ( ( plus_plus_rat @ B2 @ A )
% 5.41/5.64 = ( plus_plus_rat @ C @ A ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.right_cancel
% 5.41/5.64 thf(fact_826_add_Oright__cancel,axiom,
% 5.41/5.64 ! [B2: int,A: int,C: int] :
% 5.41/5.64 ( ( ( plus_plus_int @ B2 @ A )
% 5.41/5.64 = ( plus_plus_int @ C @ A ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.right_cancel
% 5.41/5.64 thf(fact_827_add_Oleft__cancel,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( ( plus_plus_real @ A @ B2 )
% 5.41/5.64 = ( plus_plus_real @ A @ C ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.left_cancel
% 5.41/5.64 thf(fact_828_add_Oleft__cancel,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( ( plus_plus_rat @ A @ B2 )
% 5.41/5.64 = ( plus_plus_rat @ A @ C ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.left_cancel
% 5.41/5.64 thf(fact_829_add_Oleft__cancel,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( ( plus_plus_int @ A @ B2 )
% 5.41/5.64 = ( plus_plus_int @ A @ C ) )
% 5.41/5.64 = ( B2 = C ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.left_cancel
% 5.41/5.64 thf(fact_830_add_Oassoc,axiom,
% 5.41/5.64 ! [A: real,B2: real,C: real] :
% 5.41/5.64 ( ( plus_plus_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.assoc
% 5.41/5.64 thf(fact_831_add_Oassoc,axiom,
% 5.41/5.64 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.64 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.assoc
% 5.41/5.64 thf(fact_832_add_Oassoc,axiom,
% 5.41/5.64 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.64 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.assoc
% 5.41/5.64 thf(fact_833_add_Oassoc,axiom,
% 5.41/5.64 ! [A: int,B2: int,C: int] :
% 5.41/5.64 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.41/5.64 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add.assoc
% 5.41/5.64 thf(fact_834_group__cancel_Oadd2,axiom,
% 5.41/5.64 ! [B4: real,K: real,B2: real,A: real] :
% 5.41/5.64 ( ( B4
% 5.41/5.64 = ( plus_plus_real @ K @ B2 ) )
% 5.41/5.64 => ( ( plus_plus_real @ A @ B4 )
% 5.41/5.64 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % group_cancel.add2
% 5.41/5.64 thf(fact_835_group__cancel_Oadd2,axiom,
% 5.41/5.64 ! [B4: rat,K: rat,B2: rat,A: rat] :
% 5.41/5.64 ( ( B4
% 5.41/5.64 = ( plus_plus_rat @ K @ B2 ) )
% 5.41/5.64 => ( ( plus_plus_rat @ A @ B4 )
% 5.41/5.64 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % group_cancel.add2
% 5.41/5.64 thf(fact_836_group__cancel_Oadd2,axiom,
% 5.41/5.64 ! [B4: nat,K: nat,B2: nat,A: nat] :
% 5.41/5.64 ( ( B4
% 5.41/5.64 = ( plus_plus_nat @ K @ B2 ) )
% 5.41/5.64 => ( ( plus_plus_nat @ A @ B4 )
% 5.41/5.64 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % group_cancel.add2
% 5.41/5.64 thf(fact_837_group__cancel_Oadd2,axiom,
% 5.41/5.64 ! [B4: int,K: int,B2: int,A: int] :
% 5.41/5.65 ( ( B4
% 5.41/5.65 = ( plus_plus_int @ K @ B2 ) )
% 5.41/5.65 => ( ( plus_plus_int @ A @ B4 )
% 5.41/5.65 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % group_cancel.add2
% 5.41/5.65 thf(fact_838_group__cancel_Oadd1,axiom,
% 5.41/5.65 ! [A3: real,K: real,A: real,B2: real] :
% 5.41/5.65 ( ( A3
% 5.41/5.65 = ( plus_plus_real @ K @ A ) )
% 5.41/5.65 => ( ( plus_plus_real @ A3 @ B2 )
% 5.41/5.65 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % group_cancel.add1
% 5.41/5.65 thf(fact_839_group__cancel_Oadd1,axiom,
% 5.41/5.65 ! [A3: rat,K: rat,A: rat,B2: rat] :
% 5.41/5.65 ( ( A3
% 5.41/5.65 = ( plus_plus_rat @ K @ A ) )
% 5.41/5.65 => ( ( plus_plus_rat @ A3 @ B2 )
% 5.41/5.65 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % group_cancel.add1
% 5.41/5.65 thf(fact_840_group__cancel_Oadd1,axiom,
% 5.41/5.65 ! [A3: nat,K: nat,A: nat,B2: nat] :
% 5.41/5.65 ( ( A3
% 5.41/5.65 = ( plus_plus_nat @ K @ A ) )
% 5.41/5.65 => ( ( plus_plus_nat @ A3 @ B2 )
% 5.41/5.65 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % group_cancel.add1
% 5.41/5.65 thf(fact_841_group__cancel_Oadd1,axiom,
% 5.41/5.65 ! [A3: int,K: int,A: int,B2: int] :
% 5.41/5.65 ( ( A3
% 5.41/5.65 = ( plus_plus_int @ K @ A ) )
% 5.41/5.65 => ( ( plus_plus_int @ A3 @ B2 )
% 5.41/5.65 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % group_cancel.add1
% 5.41/5.65 thf(fact_842_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.41/5.65 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ( plus_plus_real @ I @ K )
% 5.41/5.65 = ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(4)
% 5.41/5.65 thf(fact_843_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.41/5.65 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ( plus_plus_rat @ I @ K )
% 5.41/5.65 = ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(4)
% 5.41/5.65 thf(fact_844_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ( plus_plus_nat @ I @ K )
% 5.41/5.65 = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(4)
% 5.41/5.65 thf(fact_845_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.41/5.65 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ( plus_plus_int @ I @ K )
% 5.41/5.65 = ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(4)
% 5.41/5.65 thf(fact_846_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( plus_plus_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ab_semigroup_add_class.add_ac(1)
% 5.41/5.65 thf(fact_847_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ab_semigroup_add_class.add_ac(1)
% 5.41/5.65 thf(fact_848_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ab_semigroup_add_class.add_ac(1)
% 5.41/5.65 thf(fact_849_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ab_semigroup_add_class.add_ac(1)
% 5.41/5.65 thf(fact_850_diff__right__commute,axiom,
% 5.41/5.65 ! [A: real,C: real,B2: real] :
% 5.41/5.65 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B2 )
% 5.41/5.65 = ( minus_minus_real @ ( minus_minus_real @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_right_commute
% 5.41/5.65 thf(fact_851_diff__right__commute,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.65 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B2 )
% 5.41/5.65 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_right_commute
% 5.41/5.65 thf(fact_852_diff__right__commute,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.65 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B2 )
% 5.41/5.65 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_right_commute
% 5.41/5.65 thf(fact_853_diff__right__commute,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B2 )
% 5.41/5.65 = ( minus_minus_int @ ( minus_minus_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_right_commute
% 5.41/5.65 thf(fact_854_diff__eq__diff__eq,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real,D: real] :
% 5.41/5.65 ( ( ( minus_minus_real @ A @ B2 )
% 5.41/5.65 = ( minus_minus_real @ C @ D ) )
% 5.41/5.65 => ( ( A = B2 )
% 5.41/5.65 = ( C = D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_diff_eq
% 5.41/5.65 thf(fact_855_diff__eq__diff__eq,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ( minus_minus_rat @ A @ B2 )
% 5.41/5.65 = ( minus_minus_rat @ C @ D ) )
% 5.41/5.65 => ( ( A = B2 )
% 5.41/5.65 = ( C = D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_diff_eq
% 5.41/5.65 thf(fact_856_diff__eq__diff__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int,D: int] :
% 5.41/5.65 ( ( ( minus_minus_int @ A @ B2 )
% 5.41/5.65 = ( minus_minus_int @ C @ D ) )
% 5.41/5.65 => ( ( A = B2 )
% 5.41/5.65 = ( C = D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_diff_eq
% 5.41/5.65 thf(fact_857_add__le__imp__le__right,axiom,
% 5.41/5.65 ! [A: real,C: real,B2: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) )
% 5.41/5.65 => ( ord_less_eq_real @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_imp_le_right
% 5.41/5.65 thf(fact_858_add__le__imp__le__right,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ C ) )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_imp_le_right
% 5.41/5.65 thf(fact_859_add__le__imp__le__right,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 5.41/5.65 => ( ord_less_eq_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_imp_le_right
% 5.41/5.65 thf(fact_860_add__le__imp__le__right,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 5.41/5.65 => ( ord_less_eq_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_imp_le_right
% 5.41/5.65 thf(fact_861_add__le__imp__le__left,axiom,
% 5.41/5.65 ! [C: real,A: real,B2: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) )
% 5.41/5.65 => ( ord_less_eq_real @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_imp_le_left
% 5.41/5.65 thf(fact_862_add__le__imp__le__left,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B2 ) )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_imp_le_left
% 5.41/5.65 thf(fact_863_add__le__imp__le__left,axiom,
% 5.41/5.65 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 5.41/5.65 => ( ord_less_eq_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_imp_le_left
% 5.41/5.65 thf(fact_864_add__le__imp__le__left,axiom,
% 5.41/5.65 ! [C: int,A: int,B2: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 5.41/5.65 => ( ord_less_eq_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_imp_le_left
% 5.41/5.65 thf(fact_865_le__iff__add,axiom,
% 5.41/5.65 ( ord_less_eq_nat
% 5.41/5.65 = ( ^ [A4: nat,B3: nat] :
% 5.41/5.65 ? [C2: nat] :
% 5.41/5.65 ( B3
% 5.41/5.65 = ( plus_plus_nat @ A4 @ C2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_iff_add
% 5.41/5.65 thf(fact_866_add__right__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_right_mono
% 5.41/5.65 thf(fact_867_add__right__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_right_mono
% 5.41/5.65 thf(fact_868_add__right__mono,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_right_mono
% 5.41/5.65 thf(fact_869_add__right__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_right_mono
% 5.41/5.65 thf(fact_870_less__eqE,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ~ ! [C3: nat] :
% 5.41/5.65 ( B2
% 5.41/5.65 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_eqE
% 5.41/5.65 thf(fact_871_add__left__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_left_mono
% 5.41/5.65 thf(fact_872_add__left__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_left_mono
% 5.41/5.65 thf(fact_873_add__left__mono,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_left_mono
% 5.41/5.65 thf(fact_874_add__left__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_left_mono
% 5.41/5.65 thf(fact_875_add__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real,D: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_real @ C @ D )
% 5.41/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono
% 5.41/5.65 thf(fact_876_add__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_rat @ C @ D )
% 5.41/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono
% 5.41/5.65 thf(fact_877_add__mono,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_nat @ C @ D )
% 5.41/5.65 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono
% 5.41/5.65 thf(fact_878_add__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int,D: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_int @ C @ D )
% 5.41/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono
% 5.41/5.65 thf(fact_879_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.41/5.65 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.65 ( ( ( ord_less_eq_real @ I @ J )
% 5.41/5.65 & ( ord_less_eq_real @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(1)
% 5.41/5.65 thf(fact_880_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.41/5.65 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.65 ( ( ( ord_less_eq_rat @ I @ J )
% 5.41/5.65 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(1)
% 5.41/5.65 thf(fact_881_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.65 ( ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.65 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(1)
% 5.41/5.65 thf(fact_882_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.41/5.65 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.65 ( ( ( ord_less_eq_int @ I @ J )
% 5.41/5.65 & ( ord_less_eq_int @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(1)
% 5.41/5.65 thf(fact_883_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.41/5.65 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( ord_less_eq_real @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(2)
% 5.41/5.65 thf(fact_884_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.41/5.65 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(2)
% 5.41/5.65 thf(fact_885_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(2)
% 5.41/5.65 thf(fact_886_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.41/5.65 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( ord_less_eq_int @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(2)
% 5.41/5.65 thf(fact_887_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.41/5.65 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.65 ( ( ( ord_less_eq_real @ I @ J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(3)
% 5.41/5.65 thf(fact_888_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.41/5.65 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.65 ( ( ( ord_less_eq_rat @ I @ J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(3)
% 5.41/5.65 thf(fact_889_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.65 ( ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(3)
% 5.41/5.65 thf(fact_890_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.41/5.65 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.65 ( ( ( ord_less_eq_int @ I @ J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_semiring(3)
% 5.41/5.65 thf(fact_891_diff__eq__diff__less__eq,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real,D: real] :
% 5.41/5.65 ( ( ( minus_minus_real @ A @ B2 )
% 5.41/5.65 = ( minus_minus_real @ C @ D ) )
% 5.41/5.65 => ( ( ord_less_eq_real @ A @ B2 )
% 5.41/5.65 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_diff_less_eq
% 5.41/5.65 thf(fact_892_diff__eq__diff__less__eq,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ( minus_minus_rat @ A @ B2 )
% 5.41/5.65 = ( minus_minus_rat @ C @ D ) )
% 5.41/5.65 => ( ( ord_less_eq_rat @ A @ B2 )
% 5.41/5.65 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_diff_less_eq
% 5.41/5.65 thf(fact_893_diff__eq__diff__less__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int,D: int] :
% 5.41/5.65 ( ( ( minus_minus_int @ A @ B2 )
% 5.41/5.65 = ( minus_minus_int @ C @ D ) )
% 5.41/5.65 => ( ( ord_less_eq_int @ A @ B2 )
% 5.41/5.65 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_diff_less_eq
% 5.41/5.65 thf(fact_894_diff__right__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_right_mono
% 5.41/5.65 thf(fact_895_diff__right__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_right_mono
% 5.41/5.65 thf(fact_896_diff__right__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_right_mono
% 5.41/5.65 thf(fact_897_diff__left__mono,axiom,
% 5.41/5.65 ! [B2: real,A: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ B2 @ A )
% 5.41/5.65 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_left_mono
% 5.41/5.65 thf(fact_898_diff__left__mono,axiom,
% 5.41/5.65 ! [B2: rat,A: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ B2 @ A )
% 5.41/5.65 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_left_mono
% 5.41/5.65 thf(fact_899_diff__left__mono,axiom,
% 5.41/5.65 ! [B2: int,A: int,C: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ B2 @ A )
% 5.41/5.65 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_left_mono
% 5.41/5.65 thf(fact_900_diff__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,D: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_real @ D @ C )
% 5.41/5.65 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_mono
% 5.41/5.65 thf(fact_901_diff__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,D: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_rat @ D @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_mono
% 5.41/5.65 thf(fact_902_diff__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,D: int,C: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_int @ D @ C )
% 5.41/5.65 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_mono
% 5.41/5.65 thf(fact_903_add__less__imp__less__right,axiom,
% 5.41/5.65 ! [A: real,C: real,B2: real] :
% 5.41/5.65 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) )
% 5.41/5.65 => ( ord_less_real @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_imp_less_right
% 5.41/5.65 thf(fact_904_add__less__imp__less__right,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ C ) )
% 5.41/5.65 => ( ord_less_rat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_imp_less_right
% 5.41/5.65 thf(fact_905_add__less__imp__less__right,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.65 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 5.41/5.65 => ( ord_less_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_imp_less_right
% 5.41/5.65 thf(fact_906_add__less__imp__less__right,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 5.41/5.65 => ( ord_less_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_imp_less_right
% 5.41/5.65 thf(fact_907_add__less__imp__less__left,axiom,
% 5.41/5.65 ! [C: real,A: real,B2: real] :
% 5.41/5.65 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) )
% 5.41/5.65 => ( ord_less_real @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_imp_less_left
% 5.41/5.65 thf(fact_908_add__less__imp__less__left,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B2 ) )
% 5.41/5.65 => ( ord_less_rat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_imp_less_left
% 5.41/5.65 thf(fact_909_add__less__imp__less__left,axiom,
% 5.41/5.65 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.65 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 5.41/5.65 => ( ord_less_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_imp_less_left
% 5.41/5.65 thf(fact_910_add__less__imp__less__left,axiom,
% 5.41/5.65 ! [C: int,A: int,B2: int] :
% 5.41/5.65 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 5.41/5.65 => ( ord_less_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_imp_less_left
% 5.41/5.65 thf(fact_911_add__strict__right__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B2 )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_right_mono
% 5.41/5.65 thf(fact_912_add__strict__right__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B2 )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_right_mono
% 5.41/5.65 thf(fact_913_add__strict__right__mono,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_nat @ A @ B2 )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_right_mono
% 5.41/5.65 thf(fact_914_add__strict__right__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ B2 )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_right_mono
% 5.41/5.65 thf(fact_915_add__strict__left__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B2 )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_left_mono
% 5.41/5.65 thf(fact_916_add__strict__left__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B2 )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_left_mono
% 5.41/5.65 thf(fact_917_add__strict__left__mono,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_nat @ A @ B2 )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_left_mono
% 5.41/5.65 thf(fact_918_add__strict__left__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ B2 )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_left_mono
% 5.41/5.65 thf(fact_919_add__strict__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real,D: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_real @ C @ D )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_mono
% 5.41/5.65 thf(fact_920_add__strict__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_rat @ C @ D )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_mono
% 5.41/5.65 thf(fact_921_add__strict__mono,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.41/5.65 ( ( ord_less_nat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_nat @ C @ D )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_mono
% 5.41/5.65 thf(fact_922_add__strict__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int,D: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_int @ C @ D )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_mono
% 5.41/5.65 thf(fact_923_add__mono__thms__linordered__field_I1_J,axiom,
% 5.41/5.65 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.65 ( ( ( ord_less_real @ I @ J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(1)
% 5.41/5.65 thf(fact_924_add__mono__thms__linordered__field_I1_J,axiom,
% 5.41/5.65 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.65 ( ( ( ord_less_rat @ I @ J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(1)
% 5.41/5.65 thf(fact_925_add__mono__thms__linordered__field_I1_J,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.65 ( ( ( ord_less_nat @ I @ J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(1)
% 5.41/5.65 thf(fact_926_add__mono__thms__linordered__field_I1_J,axiom,
% 5.41/5.65 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.65 ( ( ( ord_less_int @ I @ J )
% 5.41/5.65 & ( K = L2 ) )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(1)
% 5.41/5.65 thf(fact_927_add__mono__thms__linordered__field_I2_J,axiom,
% 5.41/5.65 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( ord_less_real @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(2)
% 5.41/5.65 thf(fact_928_add__mono__thms__linordered__field_I2_J,axiom,
% 5.41/5.65 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( ord_less_rat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(2)
% 5.41/5.65 thf(fact_929_add__mono__thms__linordered__field_I2_J,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( ord_less_nat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(2)
% 5.41/5.65 thf(fact_930_add__mono__thms__linordered__field_I2_J,axiom,
% 5.41/5.65 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.65 ( ( ( I = J )
% 5.41/5.65 & ( ord_less_int @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(2)
% 5.41/5.65 thf(fact_931_add__mono__thms__linordered__field_I5_J,axiom,
% 5.41/5.65 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.65 ( ( ( ord_less_real @ I @ J )
% 5.41/5.65 & ( ord_less_real @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(5)
% 5.41/5.65 thf(fact_932_add__mono__thms__linordered__field_I5_J,axiom,
% 5.41/5.65 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.65 ( ( ( ord_less_rat @ I @ J )
% 5.41/5.65 & ( ord_less_rat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(5)
% 5.41/5.65 thf(fact_933_add__mono__thms__linordered__field_I5_J,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.65 ( ( ( ord_less_nat @ I @ J )
% 5.41/5.65 & ( ord_less_nat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(5)
% 5.41/5.65 thf(fact_934_add__mono__thms__linordered__field_I5_J,axiom,
% 5.41/5.65 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.65 ( ( ( ord_less_int @ I @ J )
% 5.41/5.65 & ( ord_less_int @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(5)
% 5.41/5.65 thf(fact_935_diff__strict__right__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B2 )
% 5.41/5.65 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_strict_right_mono
% 5.41/5.65 thf(fact_936_diff__strict__right__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B2 )
% 5.41/5.65 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_strict_right_mono
% 5.41/5.65 thf(fact_937_diff__strict__right__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ B2 )
% 5.41/5.65 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_strict_right_mono
% 5.41/5.65 thf(fact_938_diff__strict__left__mono,axiom,
% 5.41/5.65 ! [B2: real,A: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ B2 @ A )
% 5.41/5.65 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_strict_left_mono
% 5.41/5.65 thf(fact_939_diff__strict__left__mono,axiom,
% 5.41/5.65 ! [B2: rat,A: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ B2 @ A )
% 5.41/5.65 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_strict_left_mono
% 5.41/5.65 thf(fact_940_diff__strict__left__mono,axiom,
% 5.41/5.65 ! [B2: int,A: int,C: int] :
% 5.41/5.65 ( ( ord_less_int @ B2 @ A )
% 5.41/5.65 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_strict_left_mono
% 5.41/5.65 thf(fact_941_diff__eq__diff__less,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real,D: real] :
% 5.41/5.65 ( ( ( minus_minus_real @ A @ B2 )
% 5.41/5.65 = ( minus_minus_real @ C @ D ) )
% 5.41/5.65 => ( ( ord_less_real @ A @ B2 )
% 5.41/5.65 = ( ord_less_real @ C @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_diff_less
% 5.41/5.65 thf(fact_942_diff__eq__diff__less,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ( minus_minus_rat @ A @ B2 )
% 5.41/5.65 = ( minus_minus_rat @ C @ D ) )
% 5.41/5.65 => ( ( ord_less_rat @ A @ B2 )
% 5.41/5.65 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_diff_less
% 5.41/5.65 thf(fact_943_diff__eq__diff__less,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int,D: int] :
% 5.41/5.65 ( ( ( minus_minus_int @ A @ B2 )
% 5.41/5.65 = ( minus_minus_int @ C @ D ) )
% 5.41/5.65 => ( ( ord_less_int @ A @ B2 )
% 5.41/5.65 = ( ord_less_int @ C @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_diff_less
% 5.41/5.65 thf(fact_944_diff__strict__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,D: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_real @ D @ C )
% 5.41/5.65 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_strict_mono
% 5.41/5.65 thf(fact_945_diff__strict__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,D: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_rat @ D @ C )
% 5.41/5.65 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_strict_mono
% 5.41/5.65 thf(fact_946_diff__strict__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,D: int,C: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_int @ D @ C )
% 5.41/5.65 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_strict_mono
% 5.41/5.65 thf(fact_947_mult_Ocomm__neutral,axiom,
% 5.41/5.65 ! [A: complex] :
% 5.41/5.65 ( ( times_times_complex @ A @ one_one_complex )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult.comm_neutral
% 5.41/5.65 thf(fact_948_mult_Ocomm__neutral,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ( ( times_times_real @ A @ one_one_real )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult.comm_neutral
% 5.41/5.65 thf(fact_949_mult_Ocomm__neutral,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ( ( times_times_rat @ A @ one_one_rat )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult.comm_neutral
% 5.41/5.65 thf(fact_950_mult_Ocomm__neutral,axiom,
% 5.41/5.65 ! [A: nat] :
% 5.41/5.65 ( ( times_times_nat @ A @ one_one_nat )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult.comm_neutral
% 5.41/5.65 thf(fact_951_mult_Ocomm__neutral,axiom,
% 5.41/5.65 ! [A: int] :
% 5.41/5.65 ( ( times_times_int @ A @ one_one_int )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult.comm_neutral
% 5.41/5.65 thf(fact_952_comm__monoid__mult__class_Omult__1,axiom,
% 5.41/5.65 ! [A: complex] :
% 5.41/5.65 ( ( times_times_complex @ one_one_complex @ A )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % comm_monoid_mult_class.mult_1
% 5.41/5.65 thf(fact_953_comm__monoid__mult__class_Omult__1,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ( ( times_times_real @ one_one_real @ A )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % comm_monoid_mult_class.mult_1
% 5.41/5.65 thf(fact_954_comm__monoid__mult__class_Omult__1,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ( ( times_times_rat @ one_one_rat @ A )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % comm_monoid_mult_class.mult_1
% 5.41/5.65 thf(fact_955_comm__monoid__mult__class_Omult__1,axiom,
% 5.41/5.65 ! [A: nat] :
% 5.41/5.65 ( ( times_times_nat @ one_one_nat @ A )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % comm_monoid_mult_class.mult_1
% 5.41/5.65 thf(fact_956_comm__monoid__mult__class_Omult__1,axiom,
% 5.41/5.65 ! [A: int] :
% 5.41/5.65 ( ( times_times_int @ one_one_int @ A )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % comm_monoid_mult_class.mult_1
% 5.41/5.65 thf(fact_957_diff__diff__eq,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( minus_minus_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 5.41/5.65 = ( minus_minus_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_diff_eq
% 5.41/5.65 thf(fact_958_diff__diff__eq,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B2 ) @ C )
% 5.41/5.65 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_diff_eq
% 5.41/5.65 thf(fact_959_diff__diff__eq,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B2 ) @ C )
% 5.41/5.65 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_diff_eq
% 5.41/5.65 thf(fact_960_diff__diff__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( minus_minus_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 5.41/5.65 = ( minus_minus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_diff_eq
% 5.41/5.65 thf(fact_961_add__implies__diff,axiom,
% 5.41/5.65 ! [C: real,B2: real,A: real] :
% 5.41/5.65 ( ( ( plus_plus_real @ C @ B2 )
% 5.41/5.65 = A )
% 5.41/5.65 => ( C
% 5.41/5.65 = ( minus_minus_real @ A @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_implies_diff
% 5.41/5.65 thf(fact_962_add__implies__diff,axiom,
% 5.41/5.65 ! [C: rat,B2: rat,A: rat] :
% 5.41/5.65 ( ( ( plus_plus_rat @ C @ B2 )
% 5.41/5.65 = A )
% 5.41/5.65 => ( C
% 5.41/5.65 = ( minus_minus_rat @ A @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_implies_diff
% 5.41/5.65 thf(fact_963_add__implies__diff,axiom,
% 5.41/5.65 ! [C: nat,B2: nat,A: nat] :
% 5.41/5.65 ( ( ( plus_plus_nat @ C @ B2 )
% 5.41/5.65 = A )
% 5.41/5.65 => ( C
% 5.41/5.65 = ( minus_minus_nat @ A @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_implies_diff
% 5.41/5.65 thf(fact_964_add__implies__diff,axiom,
% 5.41/5.65 ! [C: int,B2: int,A: int] :
% 5.41/5.65 ( ( ( plus_plus_int @ C @ B2 )
% 5.41/5.65 = A )
% 5.41/5.65 => ( C
% 5.41/5.65 = ( minus_minus_int @ A @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_implies_diff
% 5.41/5.65 thf(fact_965_diff__add__eq__diff__diff__swap,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( minus_minus_real @ A @ ( plus_plus_real @ B2 @ C ) )
% 5.41/5.65 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_add_eq_diff_diff_swap
% 5.41/5.65 thf(fact_966_diff__add__eq__diff__diff__swap,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B2 @ C ) )
% 5.41/5.65 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_add_eq_diff_diff_swap
% 5.41/5.65 thf(fact_967_diff__add__eq__diff__diff__swap,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( minus_minus_int @ A @ ( plus_plus_int @ B2 @ C ) )
% 5.41/5.65 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_add_eq_diff_diff_swap
% 5.41/5.65 thf(fact_968_diff__add__eq,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( plus_plus_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 5.41/5.65 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_add_eq
% 5.41/5.65 thf(fact_969_diff__add__eq,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B2 ) @ C )
% 5.41/5.65 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_add_eq
% 5.41/5.65 thf(fact_970_diff__add__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 5.41/5.65 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_add_eq
% 5.41/5.65 thf(fact_971_diff__diff__eq2,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( minus_minus_real @ A @ ( minus_minus_real @ B2 @ C ) )
% 5.41/5.65 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_diff_eq2
% 5.41/5.65 thf(fact_972_diff__diff__eq2,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B2 @ C ) )
% 5.41/5.65 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_diff_eq2
% 5.41/5.65 thf(fact_973_diff__diff__eq2,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( minus_minus_int @ A @ ( minus_minus_int @ B2 @ C ) )
% 5.41/5.65 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_diff_eq2
% 5.41/5.65 thf(fact_974_add__diff__eq,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( plus_plus_real @ A @ ( minus_minus_real @ B2 @ C ) )
% 5.41/5.65 = ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_diff_eq
% 5.41/5.65 thf(fact_975_add__diff__eq,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B2 @ C ) )
% 5.41/5.65 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_diff_eq
% 5.41/5.65 thf(fact_976_add__diff__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( plus_plus_int @ A @ ( minus_minus_int @ B2 @ C ) )
% 5.41/5.65 = ( minus_minus_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_diff_eq
% 5.41/5.65 thf(fact_977_eq__diff__eq,axiom,
% 5.41/5.65 ! [A: real,C: real,B2: real] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( minus_minus_real @ C @ B2 ) )
% 5.41/5.65 = ( ( plus_plus_real @ A @ B2 )
% 5.41/5.65 = C ) ) ).
% 5.41/5.65
% 5.41/5.65 % eq_diff_eq
% 5.41/5.65 thf(fact_978_eq__diff__eq,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( minus_minus_rat @ C @ B2 ) )
% 5.41/5.65 = ( ( plus_plus_rat @ A @ B2 )
% 5.41/5.65 = C ) ) ).
% 5.41/5.65
% 5.41/5.65 % eq_diff_eq
% 5.41/5.65 thf(fact_979_eq__diff__eq,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( minus_minus_int @ C @ B2 ) )
% 5.41/5.65 = ( ( plus_plus_int @ A @ B2 )
% 5.41/5.65 = C ) ) ).
% 5.41/5.65
% 5.41/5.65 % eq_diff_eq
% 5.41/5.65 thf(fact_980_diff__eq__eq,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( ( minus_minus_real @ A @ B2 )
% 5.41/5.65 = C )
% 5.41/5.65 = ( A
% 5.41/5.65 = ( plus_plus_real @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_eq
% 5.41/5.65 thf(fact_981_diff__eq__eq,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( ( minus_minus_rat @ A @ B2 )
% 5.41/5.65 = C )
% 5.41/5.65 = ( A
% 5.41/5.65 = ( plus_plus_rat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_eq
% 5.41/5.65 thf(fact_982_diff__eq__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( ( minus_minus_int @ A @ B2 )
% 5.41/5.65 = C )
% 5.41/5.65 = ( A
% 5.41/5.65 = ( plus_plus_int @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_eq_eq
% 5.41/5.65 thf(fact_983_group__cancel_Osub1,axiom,
% 5.41/5.65 ! [A3: real,K: real,A: real,B2: real] :
% 5.41/5.65 ( ( A3
% 5.41/5.65 = ( plus_plus_real @ K @ A ) )
% 5.41/5.65 => ( ( minus_minus_real @ A3 @ B2 )
% 5.41/5.65 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % group_cancel.sub1
% 5.41/5.65 thf(fact_984_group__cancel_Osub1,axiom,
% 5.41/5.65 ! [A3: rat,K: rat,A: rat,B2: rat] :
% 5.41/5.65 ( ( A3
% 5.41/5.65 = ( plus_plus_rat @ K @ A ) )
% 5.41/5.65 => ( ( minus_minus_rat @ A3 @ B2 )
% 5.41/5.65 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % group_cancel.sub1
% 5.41/5.65 thf(fact_985_group__cancel_Osub1,axiom,
% 5.41/5.65 ! [A3: int,K: int,A: int,B2: int] :
% 5.41/5.65 ( ( A3
% 5.41/5.65 = ( plus_plus_int @ K @ A ) )
% 5.41/5.65 => ( ( minus_minus_int @ A3 @ B2 )
% 5.41/5.65 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % group_cancel.sub1
% 5.41/5.65 thf(fact_986_add__less__le__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real,D: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_real @ C @ D )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_le_mono
% 5.41/5.65 thf(fact_987_add__less__le__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_rat @ C @ D )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_le_mono
% 5.41/5.65 thf(fact_988_add__less__le__mono,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.41/5.65 ( ( ord_less_nat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_nat @ C @ D )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_le_mono
% 5.41/5.65 thf(fact_989_add__less__le__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int,D: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_int @ C @ D )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_less_le_mono
% 5.41/5.65 thf(fact_990_add__le__less__mono,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real,D: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_real @ C @ D )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_less_mono
% 5.41/5.65 thf(fact_991_add__le__less__mono,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_rat @ C @ D )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_less_mono
% 5.41/5.65 thf(fact_992_add__le__less__mono,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_nat @ C @ D )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_less_mono
% 5.41/5.65 thf(fact_993_add__le__less__mono,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int,D: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_int @ C @ D )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_le_less_mono
% 5.41/5.65 thf(fact_994_add__mono__thms__linordered__field_I3_J,axiom,
% 5.41/5.65 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.65 ( ( ( ord_less_real @ I @ J )
% 5.41/5.65 & ( ord_less_eq_real @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(3)
% 5.41/5.65 thf(fact_995_add__mono__thms__linordered__field_I3_J,axiom,
% 5.41/5.65 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.65 ( ( ( ord_less_rat @ I @ J )
% 5.41/5.65 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(3)
% 5.41/5.65 thf(fact_996_add__mono__thms__linordered__field_I3_J,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.65 ( ( ( ord_less_nat @ I @ J )
% 5.41/5.65 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(3)
% 5.41/5.65 thf(fact_997_add__mono__thms__linordered__field_I3_J,axiom,
% 5.41/5.65 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.65 ( ( ( ord_less_int @ I @ J )
% 5.41/5.65 & ( ord_less_eq_int @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(3)
% 5.41/5.65 thf(fact_998_add__mono__thms__linordered__field_I4_J,axiom,
% 5.41/5.65 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.65 ( ( ( ord_less_eq_real @ I @ J )
% 5.41/5.65 & ( ord_less_real @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(4)
% 5.41/5.65 thf(fact_999_add__mono__thms__linordered__field_I4_J,axiom,
% 5.41/5.65 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.65 ( ( ( ord_less_eq_rat @ I @ J )
% 5.41/5.65 & ( ord_less_rat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(4)
% 5.41/5.65 thf(fact_1000_add__mono__thms__linordered__field_I4_J,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.65 ( ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.65 & ( ord_less_nat @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(4)
% 5.41/5.65 thf(fact_1001_add__mono__thms__linordered__field_I4_J,axiom,
% 5.41/5.65 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.65 ( ( ( ord_less_eq_int @ I @ J )
% 5.41/5.65 & ( ord_less_int @ K @ L2 ) )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_mono_thms_linordered_field(4)
% 5.41/5.65 thf(fact_1002_diff__le__eq,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 5.41/5.65 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_le_eq
% 5.41/5.65 thf(fact_1003_diff__le__eq,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B2 ) @ C )
% 5.41/5.65 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_le_eq
% 5.41/5.65 thf(fact_1004_diff__le__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 5.41/5.65 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_le_eq
% 5.41/5.65 thf(fact_1005_le__diff__eq,axiom,
% 5.41/5.65 ! [A: real,C: real,B2: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B2 ) )
% 5.41/5.65 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_diff_eq
% 5.41/5.65 thf(fact_1006_le__diff__eq,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B2 ) )
% 5.41/5.65 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_diff_eq
% 5.41/5.65 thf(fact_1007_le__diff__eq,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B2 ) )
% 5.41/5.65 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_diff_eq
% 5.41/5.65 thf(fact_1008_diff__add,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A ) @ A )
% 5.41/5.65 = B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_add
% 5.41/5.65 thf(fact_1009_le__add__diff,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C ) @ A ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_add_diff
% 5.41/5.65 thf(fact_1010_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B2 @ A ) )
% 5.41/5.65 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.41/5.65 thf(fact_1011_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B2 @ A ) )
% 5.41/5.65 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B2 ) @ A ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.41/5.65 thf(fact_1012_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B2 ) @ A )
% 5.41/5.65 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B2 @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.41/5.65 thf(fact_1013_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A ) @ C )
% 5.41/5.65 = ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C ) @ A ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.41/5.65 thf(fact_1014_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( minus_minus_nat @ ( plus_plus_nat @ B2 @ C ) @ A )
% 5.41/5.65 = ( plus_plus_nat @ ( minus_minus_nat @ B2 @ A ) @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.41/5.65 thf(fact_1015_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B2 @ A ) )
% 5.41/5.65 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.41/5.65 thf(fact_1016_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B2 @ A ) )
% 5.41/5.65 = B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.41/5.65 thf(fact_1017_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_nat @ A @ B2 )
% 5.41/5.65 => ( ( ( minus_minus_nat @ B2 @ A )
% 5.41/5.65 = C )
% 5.41/5.65 = ( B2
% 5.41/5.65 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.41/5.65 thf(fact_1018_diff__less__eq,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 5.41/5.65 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_less_eq
% 5.41/5.65 thf(fact_1019_diff__less__eq,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B2 ) @ C )
% 5.41/5.65 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_less_eq
% 5.41/5.65 thf(fact_1020_diff__less__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( ord_less_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 5.41/5.65 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_less_eq
% 5.41/5.65 thf(fact_1021_less__diff__eq,axiom,
% 5.41/5.65 ! [A: real,C: real,B2: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B2 ) )
% 5.41/5.65 = ( ord_less_real @ ( plus_plus_real @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_diff_eq
% 5.41/5.65 thf(fact_1022_less__diff__eq,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B2 ) )
% 5.41/5.65 = ( ord_less_rat @ ( plus_plus_rat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_diff_eq
% 5.41/5.65 thf(fact_1023_less__diff__eq,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B2 ) )
% 5.41/5.65 = ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_diff_eq
% 5.41/5.65 thf(fact_1024_real__average__minus__second,axiom,
% 5.41/5.65 ! [B2: real,A: real] :
% 5.41/5.65 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B2 @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.41/5.65 = ( divide_divide_real @ ( minus_minus_real @ B2 @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % real_average_minus_second
% 5.41/5.65 thf(fact_1025_real__average__minus__first,axiom,
% 5.41/5.65 ! [A: real,B2: real] :
% 5.41/5.65 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.41/5.65 = ( divide_divide_real @ ( minus_minus_real @ B2 @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % real_average_minus_first
% 5.41/5.65 thf(fact_1026_times__divide__eq__left,axiom,
% 5.41/5.65 ! [B2: complex,C: complex,A: complex] :
% 5.41/5.65 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B2 @ C ) @ A )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( times_times_complex @ B2 @ A ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % times_divide_eq_left
% 5.41/5.65 thf(fact_1027_times__divide__eq__left,axiom,
% 5.41/5.65 ! [B2: real,C: real,A: real] :
% 5.41/5.65 ( ( times_times_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 5.41/5.65 = ( divide_divide_real @ ( times_times_real @ B2 @ A ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % times_divide_eq_left
% 5.41/5.65 thf(fact_1028_times__divide__eq__left,axiom,
% 5.41/5.65 ! [B2: rat,C: rat,A: rat] :
% 5.41/5.65 ( ( times_times_rat @ ( divide_divide_rat @ B2 @ C ) @ A )
% 5.41/5.65 = ( divide_divide_rat @ ( times_times_rat @ B2 @ A ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % times_divide_eq_left
% 5.41/5.65 thf(fact_1029_divide__divide__eq__left,axiom,
% 5.41/5.65 ! [A: complex,B2: complex,C: complex] :
% 5.41/5.65 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B2 ) @ C )
% 5.41/5.65 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_eq_left
% 5.41/5.65 thf(fact_1030_divide__divide__eq__left,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( divide_divide_real @ ( divide_divide_real @ A @ B2 ) @ C )
% 5.41/5.65 = ( divide_divide_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_eq_left
% 5.41/5.65 thf(fact_1031_divide__divide__eq__left,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B2 ) @ C )
% 5.41/5.65 = ( divide_divide_rat @ A @ ( times_times_rat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_eq_left
% 5.41/5.65 thf(fact_1032_divide__divide__eq__right,axiom,
% 5.41/5.65 ! [A: complex,B2: complex,C: complex] :
% 5.41/5.65 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B2 @ C ) )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_eq_right
% 5.41/5.65 thf(fact_1033_divide__divide__eq__right,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( divide_divide_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 5.41/5.65 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_eq_right
% 5.41/5.65 thf(fact_1034_divide__divide__eq__right,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B2 @ C ) )
% 5.41/5.65 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_eq_right
% 5.41/5.65 thf(fact_1035_times__divide__eq__right,axiom,
% 5.41/5.65 ! [A: complex,B2: complex,C: complex] :
% 5.41/5.65 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B2 @ C ) )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % times_divide_eq_right
% 5.41/5.65 thf(fact_1036_times__divide__eq__right,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( times_times_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 5.41/5.65 = ( divide_divide_real @ ( times_times_real @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % times_divide_eq_right
% 5.41/5.65 thf(fact_1037_times__divide__eq__right,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( times_times_rat @ A @ ( divide_divide_rat @ B2 @ C ) )
% 5.41/5.65 = ( divide_divide_rat @ ( times_times_rat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % times_divide_eq_right
% 5.41/5.65 thf(fact_1038_less__half__sum,axiom,
% 5.41/5.65 ! [A: real,B2: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B2 )
% 5.41/5.65 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B2 ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_half_sum
% 5.41/5.65 thf(fact_1039_less__half__sum,axiom,
% 5.41/5.65 ! [A: rat,B2: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B2 )
% 5.41/5.65 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B2 ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_half_sum
% 5.41/5.65 thf(fact_1040_gt__half__sum,axiom,
% 5.41/5.65 ! [A: real,B2: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B2 )
% 5.41/5.65 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B2 ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % gt_half_sum
% 5.41/5.65 thf(fact_1041_gt__half__sum,axiom,
% 5.41/5.65 ! [A: rat,B2: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B2 )
% 5.41/5.65 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B2 ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % gt_half_sum
% 5.41/5.65 thf(fact_1042_discrete,axiom,
% 5.41/5.65 ( ord_less_nat
% 5.41/5.65 = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % discrete
% 5.41/5.65 thf(fact_1043_discrete,axiom,
% 5.41/5.65 ( ord_less_int
% 5.41/5.65 = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % discrete
% 5.41/5.65 thf(fact_1044_low__def,axiom,
% 5.41/5.65 ( vEBT_VEBT_low
% 5.41/5.65 = ( ^ [X: nat,N2: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % low_def
% 5.41/5.65 thf(fact_1045_zdiv__numeral__Bit0,axiom,
% 5.41/5.65 ! [V: num,W: num] :
% 5.41/5.65 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.41/5.65 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % zdiv_numeral_Bit0
% 5.41/5.65 thf(fact_1046_mod__mod__trivial,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B2 ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mod_trivial
% 5.41/5.65 thf(fact_1047_mod__mod__trivial,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B2 ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mod_trivial
% 5.41/5.65 thf(fact_1048_mod__mod__trivial,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B2 ) @ B2 )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mod_trivial
% 5.41/5.65 thf(fact_1049_mod__add__self2,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_self2
% 5.41/5.65 thf(fact_1050_mod__add__self2,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_self2
% 5.41/5.65 thf(fact_1051_mod__add__self2,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) @ B2 )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_self2
% 5.41/5.65 thf(fact_1052_mod__add__self1,axiom,
% 5.41/5.65 ! [B2: nat,A: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_self1
% 5.41/5.65 thf(fact_1053_mod__add__self1,axiom,
% 5.41/5.65 ! [B2: int,A: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_self1
% 5.41/5.65 thf(fact_1054_mod__add__self1,axiom,
% 5.41/5.65 ! [B2: code_integer,A: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B2 @ A ) @ B2 )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_self1
% 5.41/5.65 thf(fact_1055_minus__mod__self2,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B2 ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mod_self2
% 5.41/5.65 thf(fact_1056_minus__mod__self2,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B2 ) @ B2 )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mod_self2
% 5.41/5.65 thf(fact_1057_real__divide__square__eq,axiom,
% 5.41/5.65 ! [R2: real,A: real] :
% 5.41/5.65 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 5.41/5.65 = ( divide_divide_real @ A @ R2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % real_divide_square_eq
% 5.41/5.65 thf(fact_1058_mod__less,axiom,
% 5.41/5.65 ! [M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ M @ N )
% 5.41/5.65 => ( ( modulo_modulo_nat @ M @ N )
% 5.41/5.65 = M ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_less
% 5.41/5.65 thf(fact_1059_mod__mult__self4,axiom,
% 5.41/5.65 ! [B2: nat,C: nat,A: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B2 @ C ) @ A ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self4
% 5.41/5.65 thf(fact_1060_mod__mult__self4,axiom,
% 5.41/5.65 ! [B2: int,C: int,A: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B2 @ C ) @ A ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self4
% 5.41/5.65 thf(fact_1061_mod__mult__self4,axiom,
% 5.41/5.65 ! [B2: code_integer,C: code_integer,A: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ C ) @ A ) @ B2 )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self4
% 5.41/5.65 thf(fact_1062_mod__mult__self3,axiom,
% 5.41/5.65 ! [C: nat,B2: nat,A: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B2 ) @ A ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self3
% 5.41/5.65 thf(fact_1063_mod__mult__self3,axiom,
% 5.41/5.65 ! [C: int,B2: int,A: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B2 ) @ A ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self3
% 5.41/5.65 thf(fact_1064_mod__mult__self3,axiom,
% 5.41/5.65 ! [C: code_integer,B2: code_integer,A: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B2 ) @ A ) @ B2 )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self3
% 5.41/5.65 thf(fact_1065_mod__mult__self2,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B2 @ C ) ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self2
% 5.41/5.65 thf(fact_1066_mod__mult__self2,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B2 @ C ) ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self2
% 5.41/5.65 thf(fact_1067_mod__mult__self2,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B2 @ C ) ) @ B2 )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self2
% 5.41/5.65 thf(fact_1068_mod__mult__self1,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B2 ) ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self1
% 5.41/5.65 thf(fact_1069_mod__mult__self1,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B2 ) ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self1
% 5.41/5.65 thf(fact_1070_mod__mult__self1,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B2 ) ) @ B2 )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_self1
% 5.41/5.65 thf(fact_1071_Suc__mod__mult__self1,axiom,
% 5.41/5.65 ! [M: nat,K: nat,N: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.41/5.65 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.65
% 5.41/5.65 % Suc_mod_mult_self1
% 5.41/5.65 thf(fact_1072_Suc__mod__mult__self2,axiom,
% 5.41/5.65 ! [M: nat,N: nat,K: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.41/5.65 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.65
% 5.41/5.65 % Suc_mod_mult_self2
% 5.41/5.65 thf(fact_1073_Suc__mod__mult__self3,axiom,
% 5.41/5.65 ! [K: nat,N: nat,M: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.41/5.65 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.65
% 5.41/5.65 % Suc_mod_mult_self3
% 5.41/5.65 thf(fact_1074_Suc__mod__mult__self4,axiom,
% 5.41/5.65 ! [N: nat,K: nat,M: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.41/5.65 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.65
% 5.41/5.65 % Suc_mod_mult_self4
% 5.41/5.65 thf(fact_1075_bits__one__mod__two__eq__one,axiom,
% 5.41/5.65 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = one_one_nat ) ).
% 5.41/5.65
% 5.41/5.65 % bits_one_mod_two_eq_one
% 5.41/5.65 thf(fact_1076_bits__one__mod__two__eq__one,axiom,
% 5.41/5.65 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.65 = one_one_int ) ).
% 5.41/5.65
% 5.41/5.65 % bits_one_mod_two_eq_one
% 5.41/5.65 thf(fact_1077_bits__one__mod__two__eq__one,axiom,
% 5.41/5.65 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.65 = one_one_Code_integer ) ).
% 5.41/5.65
% 5.41/5.65 % bits_one_mod_two_eq_one
% 5.41/5.65 thf(fact_1078_one__mod__two__eq__one,axiom,
% 5.41/5.65 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = one_one_nat ) ).
% 5.41/5.65
% 5.41/5.65 % one_mod_two_eq_one
% 5.41/5.65 thf(fact_1079_one__mod__two__eq__one,axiom,
% 5.41/5.65 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.65 = one_one_int ) ).
% 5.41/5.65
% 5.41/5.65 % one_mod_two_eq_one
% 5.41/5.65 thf(fact_1080_one__mod__two__eq__one,axiom,
% 5.41/5.65 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.65 = one_one_Code_integer ) ).
% 5.41/5.65
% 5.41/5.65 % one_mod_two_eq_one
% 5.41/5.65 thf(fact_1081_mod2__Suc__Suc,axiom,
% 5.41/5.65 ! [M: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod2_Suc_Suc
% 5.41/5.65 thf(fact_1082_Suc__times__numeral__mod__eq,axiom,
% 5.41/5.65 ! [K: num,N: nat] :
% 5.41/5.65 ( ( ( numeral_numeral_nat @ K )
% 5.41/5.65 != one_one_nat )
% 5.41/5.65 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.41/5.65 = one_one_nat ) ) ).
% 5.41/5.65
% 5.41/5.65 % Suc_times_numeral_mod_eq
% 5.41/5.65 thf(fact_1083_mod__mult__right__eq,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_right_eq
% 5.41/5.65 thf(fact_1084_mod__mult__right__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( times_times_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_right_eq
% 5.41/5.65 thf(fact_1085_mod__mult__right__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_right_eq
% 5.41/5.65 thf(fact_1086_mod__mult__left__eq,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B2 ) @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_left_eq
% 5.41/5.65 thf(fact_1087_mod__mult__left__eq,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B2 ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( times_times_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_left_eq
% 5.41/5.65 thf(fact_1088_mod__mult__left__eq,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B2 ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_left_eq
% 5.41/5.65 thf(fact_1089_mult__mod__right,axiom,
% 5.41/5.65 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.65 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B2 ) )
% 5.41/5.65 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_mod_right
% 5.41/5.65 thf(fact_1090_mult__mod__right,axiom,
% 5.41/5.65 ! [C: int,A: int,B2: int] :
% 5.41/5.65 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B2 ) )
% 5.41/5.65 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_mod_right
% 5.41/5.65 thf(fact_1091_mult__mod__right,axiom,
% 5.41/5.65 ! [C: code_integer,A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B2 ) )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_mod_right
% 5.41/5.65 thf(fact_1092_mod__mult__mult2,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) )
% 5.41/5.65 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_mult2
% 5.41/5.65 thf(fact_1093_mod__mult__mult2,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 5.41/5.65 = ( times_times_int @ ( modulo_modulo_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_mult2
% 5.41/5.65 thf(fact_1094_mod__mult__mult2,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 5.41/5.65 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_mult2
% 5.41/5.65 thf(fact_1095_mod__mult__cong,axiom,
% 5.41/5.65 ! [A: nat,C: nat,A2: nat,B2: nat,B: nat] :
% 5.41/5.65 ( ( ( modulo_modulo_nat @ A @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ A2 @ C ) )
% 5.41/5.65 => ( ( ( modulo_modulo_nat @ B2 @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ B @ C ) )
% 5.41/5.65 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B ) @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_cong
% 5.41/5.65 thf(fact_1096_mod__mult__cong,axiom,
% 5.41/5.65 ! [A: int,C: int,A2: int,B2: int,B: int] :
% 5.41/5.65 ( ( ( modulo_modulo_int @ A @ C )
% 5.41/5.65 = ( modulo_modulo_int @ A2 @ C ) )
% 5.41/5.65 => ( ( ( modulo_modulo_int @ B2 @ C )
% 5.41/5.65 = ( modulo_modulo_int @ B @ C ) )
% 5.41/5.65 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B2 ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( times_times_int @ A2 @ B ) @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_cong
% 5.41/5.65 thf(fact_1097_mod__mult__cong,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,A2: code_integer,B2: code_integer,B: code_integer] :
% 5.41/5.65 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A2 @ C ) )
% 5.41/5.65 => ( ( ( modulo364778990260209775nteger @ B2 @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.41/5.65 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B2 ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_cong
% 5.41/5.65 thf(fact_1098_mod__mult__eq,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_eq
% 5.41/5.65 thf(fact_1099_mod__mult__eq,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( times_times_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_eq
% 5.41/5.65 thf(fact_1100_mod__mult__eq,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_eq
% 5.41/5.65 thf(fact_1101_mod__add__right__eq,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_right_eq
% 5.41/5.65 thf(fact_1102_mod__add__right__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_right_eq
% 5.41/5.65 thf(fact_1103_mod__add__right__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_right_eq
% 5.41/5.65 thf(fact_1104_mod__add__left__eq,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B2 ) @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_left_eq
% 5.41/5.65 thf(fact_1105_mod__add__left__eq,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B2 ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_left_eq
% 5.41/5.65 thf(fact_1106_mod__add__left__eq,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B2 ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_left_eq
% 5.41/5.65 thf(fact_1107_mod__add__cong,axiom,
% 5.41/5.65 ! [A: nat,C: nat,A2: nat,B2: nat,B: nat] :
% 5.41/5.65 ( ( ( modulo_modulo_nat @ A @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ A2 @ C ) )
% 5.41/5.65 => ( ( ( modulo_modulo_nat @ B2 @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ B @ C ) )
% 5.41/5.65 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ B ) @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_cong
% 5.41/5.65 thf(fact_1108_mod__add__cong,axiom,
% 5.41/5.65 ! [A: int,C: int,A2: int,B2: int,B: int] :
% 5.41/5.65 ( ( ( modulo_modulo_int @ A @ C )
% 5.41/5.65 = ( modulo_modulo_int @ A2 @ C ) )
% 5.41/5.65 => ( ( ( modulo_modulo_int @ B2 @ C )
% 5.41/5.65 = ( modulo_modulo_int @ B @ C ) )
% 5.41/5.65 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( plus_plus_int @ A2 @ B ) @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_cong
% 5.41/5.65 thf(fact_1109_mod__add__cong,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,A2: code_integer,B2: code_integer,B: code_integer] :
% 5.41/5.65 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A2 @ C ) )
% 5.41/5.65 => ( ( ( modulo364778990260209775nteger @ B2 @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.41/5.65 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_cong
% 5.41/5.65 thf(fact_1110_mod__add__eq,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_eq
% 5.41/5.65 thf(fact_1111_mod__add__eq,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_eq
% 5.41/5.65 thf(fact_1112_mod__add__eq,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_add_eq
% 5.41/5.65 thf(fact_1113_mod__diff__right__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_diff_right_eq
% 5.41/5.65 thf(fact_1114_mod__diff__right__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_diff_right_eq
% 5.41/5.65 thf(fact_1115_mod__diff__left__eq,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B2 ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_diff_left_eq
% 5.41/5.65 thf(fact_1116_mod__diff__left__eq,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B2 ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_diff_left_eq
% 5.41/5.65 thf(fact_1117_mod__diff__cong,axiom,
% 5.41/5.65 ! [A: int,C: int,A2: int,B2: int,B: int] :
% 5.41/5.65 ( ( ( modulo_modulo_int @ A @ C )
% 5.41/5.65 = ( modulo_modulo_int @ A2 @ C ) )
% 5.41/5.65 => ( ( ( modulo_modulo_int @ B2 @ C )
% 5.41/5.65 = ( modulo_modulo_int @ B @ C ) )
% 5.41/5.65 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( minus_minus_int @ A2 @ B ) @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_diff_cong
% 5.41/5.65 thf(fact_1118_mod__diff__cong,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,A2: code_integer,B2: code_integer,B: code_integer] :
% 5.41/5.65 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A2 @ C ) )
% 5.41/5.65 => ( ( ( modulo364778990260209775nteger @ B2 @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.41/5.65 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B2 ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_diff_cong
% 5.41/5.65 thf(fact_1119_mod__diff__eq,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_diff_eq
% 5.41/5.65 thf(fact_1120_mod__diff__eq,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B2 @ C ) ) @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B2 ) @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_diff_eq
% 5.41/5.65 thf(fact_1121_power__mod,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,N: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B2 ) @ N ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_mod
% 5.41/5.65 thf(fact_1122_power__mod,axiom,
% 5.41/5.65 ! [A: int,B2: int,N: nat] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B2 ) @ N ) @ B2 )
% 5.41/5.65 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_mod
% 5.41/5.65 thf(fact_1123_power__mod,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer,N: nat] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B2 ) @ N ) @ B2 )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_mod
% 5.41/5.65 thf(fact_1124_mod__Suc__Suc__eq,axiom,
% 5.41/5.65 ! [M: nat,N: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.41/5.65 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_Suc_Suc_eq
% 5.41/5.65 thf(fact_1125_mod__Suc__eq,axiom,
% 5.41/5.65 ! [M: nat,N: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.41/5.65 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_Suc_eq
% 5.41/5.65 thf(fact_1126_mod__less__eq__dividend,axiom,
% 5.41/5.65 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.41/5.65
% 5.41/5.65 % mod_less_eq_dividend
% 5.41/5.65 thf(fact_1127_cong__exp__iff__simps_I9_J,axiom,
% 5.41/5.65 ! [M: num,Q2: num,N: num] :
% 5.41/5.65 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.65 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.65 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.41/5.65 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(9)
% 5.41/5.65 thf(fact_1128_cong__exp__iff__simps_I9_J,axiom,
% 5.41/5.65 ! [M: num,Q2: num,N: num] :
% 5.41/5.65 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.65 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.65 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.41/5.65 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(9)
% 5.41/5.65 thf(fact_1129_cong__exp__iff__simps_I9_J,axiom,
% 5.41/5.65 ! [M: num,Q2: num,N: num] :
% 5.41/5.65 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.65 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(9)
% 5.41/5.65 thf(fact_1130_cong__exp__iff__simps_I4_J,axiom,
% 5.41/5.65 ! [M: num,N: num] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.41/5.65 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(4)
% 5.41/5.65 thf(fact_1131_cong__exp__iff__simps_I4_J,axiom,
% 5.41/5.65 ! [M: num,N: num] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.41/5.65 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(4)
% 5.41/5.65 thf(fact_1132_cong__exp__iff__simps_I4_J,axiom,
% 5.41/5.65 ! [M: num,N: num] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.41/5.65 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(4)
% 5.41/5.65 thf(fact_1133_mod__geq,axiom,
% 5.41/5.65 ! [M: nat,N: nat] :
% 5.41/5.65 ( ~ ( ord_less_nat @ M @ N )
% 5.41/5.65 => ( ( modulo_modulo_nat @ M @ N )
% 5.41/5.65 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_geq
% 5.41/5.65 thf(fact_1134_nat__mod__eq__iff,axiom,
% 5.41/5.65 ! [X4: nat,N: nat,Y3: nat] :
% 5.41/5.65 ( ( ( modulo_modulo_nat @ X4 @ N )
% 5.41/5.65 = ( modulo_modulo_nat @ Y3 @ N ) )
% 5.41/5.65 = ( ? [Q1: nat,Q22: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ X4 @ ( times_times_nat @ N @ Q1 ) )
% 5.41/5.65 = ( plus_plus_nat @ Y3 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_mod_eq_iff
% 5.41/5.65 thf(fact_1135_cong__exp__iff__simps_I6_J,axiom,
% 5.41/5.65 ! [Q2: num,N: num] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.65 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(6)
% 5.41/5.65 thf(fact_1136_cong__exp__iff__simps_I6_J,axiom,
% 5.41/5.65 ! [Q2: num,N: num] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.65 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(6)
% 5.41/5.65 thf(fact_1137_cong__exp__iff__simps_I6_J,axiom,
% 5.41/5.65 ! [Q2: num,N: num] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.65 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(6)
% 5.41/5.65 thf(fact_1138_cong__exp__iff__simps_I8_J,axiom,
% 5.41/5.65 ! [M: num,Q2: num] :
% 5.41/5.65 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.65 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(8)
% 5.41/5.65 thf(fact_1139_cong__exp__iff__simps_I8_J,axiom,
% 5.41/5.65 ! [M: num,Q2: num] :
% 5.41/5.65 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.65 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(8)
% 5.41/5.65 thf(fact_1140_cong__exp__iff__simps_I8_J,axiom,
% 5.41/5.65 ! [M: num,Q2: num] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.65 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % cong_exp_iff_simps(8)
% 5.41/5.65 thf(fact_1141_mod__eqE,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( ( modulo_modulo_int @ A @ C )
% 5.41/5.65 = ( modulo_modulo_int @ B2 @ C ) )
% 5.41/5.65 => ~ ! [D3: int] :
% 5.41/5.65 ( B2
% 5.41/5.65 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_eqE
% 5.41/5.65 thf(fact_1142_mod__eqE,axiom,
% 5.41/5.65 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.41/5.65 = ( modulo364778990260209775nteger @ B2 @ C ) )
% 5.41/5.65 => ~ ! [D3: code_integer] :
% 5.41/5.65 ( B2
% 5.41/5.65 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_eqE
% 5.41/5.65 thf(fact_1143_div__add1__eq,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B2 @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B2 @ C ) ) @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_add1_eq
% 5.41/5.65 thf(fact_1144_div__add1__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( divide_divide_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B2 @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B2 @ C ) ) @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_add1_eq
% 5.41/5.65 thf(fact_1145_div__add1__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.65 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B2 @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B2 @ C ) ) @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_add1_eq
% 5.41/5.65 thf(fact_1146_mod__induct,axiom,
% 5.41/5.65 ! [P: nat > $o,N: nat,P2: nat,M: nat] :
% 5.41/5.65 ( ( P @ N )
% 5.41/5.65 => ( ( ord_less_nat @ N @ P2 )
% 5.41/5.65 => ( ( ord_less_nat @ M @ P2 )
% 5.41/5.65 => ( ! [N4: nat] :
% 5.41/5.65 ( ( ord_less_nat @ N4 @ P2 )
% 5.41/5.65 => ( ( P @ N4 )
% 5.41/5.65 => ( P @ ( modulo_modulo_nat @ ( suc @ N4 ) @ P2 ) ) ) )
% 5.41/5.65 => ( P @ M ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_induct
% 5.41/5.65 thf(fact_1147_mod__Suc__le__divisor,axiom,
% 5.41/5.65 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.41/5.65
% 5.41/5.65 % mod_Suc_le_divisor
% 5.41/5.65 thf(fact_1148_nat__mod__eq__lemma,axiom,
% 5.41/5.65 ! [X4: nat,N: nat,Y3: nat] :
% 5.41/5.65 ( ( ( modulo_modulo_nat @ X4 @ N )
% 5.41/5.65 = ( modulo_modulo_nat @ Y3 @ N ) )
% 5.41/5.65 => ( ( ord_less_eq_nat @ Y3 @ X4 )
% 5.41/5.65 => ? [Q3: nat] :
% 5.41/5.65 ( X4
% 5.41/5.65 = ( plus_plus_nat @ Y3 @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_mod_eq_lemma
% 5.41/5.65 thf(fact_1149_mod__eq__nat2E,axiom,
% 5.41/5.65 ! [M: nat,Q2: nat,N: nat] :
% 5.41/5.65 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.41/5.65 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.41/5.65 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.65 => ~ ! [S3: nat] :
% 5.41/5.65 ( N
% 5.41/5.65 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_eq_nat2E
% 5.41/5.65 thf(fact_1150_mod__eq__nat1E,axiom,
% 5.41/5.65 ! [M: nat,Q2: nat,N: nat] :
% 5.41/5.65 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.41/5.65 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.41/5.65 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.65 => ~ ! [S3: nat] :
% 5.41/5.65 ( M
% 5.41/5.65 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_eq_nat1E
% 5.41/5.65 thf(fact_1151_mod__if,axiom,
% 5.41/5.65 ( modulo_modulo_nat
% 5.41/5.65 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N2 ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_if
% 5.41/5.65 thf(fact_1152_le__mod__geq,axiom,
% 5.41/5.65 ! [N: nat,M: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.65 => ( ( modulo_modulo_nat @ M @ N )
% 5.41/5.65 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_mod_geq
% 5.41/5.65 thf(fact_1153_mult__div__mod__eq,axiom,
% 5.41/5.65 ! [B2: nat,A: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A @ B2 ) ) @ ( modulo_modulo_nat @ A @ B2 ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult_div_mod_eq
% 5.41/5.65 thf(fact_1154_mult__div__mod__eq,axiom,
% 5.41/5.65 ! [B2: int,A: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( times_times_int @ B2 @ ( divide_divide_int @ A @ B2 ) ) @ ( modulo_modulo_int @ A @ B2 ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult_div_mod_eq
% 5.41/5.65 thf(fact_1155_mult__div__mod__eq,axiom,
% 5.41/5.65 ! [B2: code_integer,A: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A @ B2 ) ) @ ( modulo364778990260209775nteger @ A @ B2 ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult_div_mod_eq
% 5.41/5.65 thf(fact_1156_mod__mult__div__eq,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B2 ) @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A @ B2 ) ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_div_eq
% 5.41/5.65 thf(fact_1157_mod__mult__div__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B2 ) @ ( times_times_int @ B2 @ ( divide_divide_int @ A @ B2 ) ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_div_eq
% 5.41/5.65 thf(fact_1158_mod__mult__div__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B2 ) @ ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A @ B2 ) ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_div_eq
% 5.41/5.65 thf(fact_1159_mod__div__mult__eq,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B2 ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_mult_eq
% 5.41/5.65 thf(fact_1160_mod__div__mult__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B2 ) @ ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_mult_eq
% 5.41/5.65 thf(fact_1161_mod__div__mult__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B2 ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ B2 ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_mult_eq
% 5.41/5.65 thf(fact_1162_div__mult__mod__eq,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) @ ( modulo_modulo_nat @ A @ B2 ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult_mod_eq
% 5.41/5.65 thf(fact_1163_div__mult__mod__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) @ ( modulo_modulo_int @ A @ B2 ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult_mod_eq
% 5.41/5.65 thf(fact_1164_div__mult__mod__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ B2 ) @ ( modulo364778990260209775nteger @ A @ B2 ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult_mod_eq
% 5.41/5.65 thf(fact_1165_mod__div__decomp,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( A
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) @ ( modulo_modulo_nat @ A @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_decomp
% 5.41/5.65 thf(fact_1166_mod__div__decomp,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( A
% 5.41/5.65 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) @ ( modulo_modulo_int @ A @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_decomp
% 5.41/5.65 thf(fact_1167_mod__div__decomp,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( A
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ B2 ) @ ( modulo364778990260209775nteger @ A @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_decomp
% 5.41/5.65 thf(fact_1168_cancel__div__mod__rules_I1_J,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) @ ( modulo_modulo_nat @ A @ B2 ) ) @ C )
% 5.41/5.65 = ( plus_plus_nat @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(1)
% 5.41/5.65 thf(fact_1169_cancel__div__mod__rules_I1_J,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) @ ( modulo_modulo_int @ A @ B2 ) ) @ C )
% 5.41/5.65 = ( plus_plus_int @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(1)
% 5.41/5.65 thf(fact_1170_cancel__div__mod__rules_I1_J,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ B2 ) @ ( modulo364778990260209775nteger @ A @ B2 ) ) @ C )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(1)
% 5.41/5.65 thf(fact_1171_cancel__div__mod__rules_I2_J,axiom,
% 5.41/5.65 ! [B2: nat,A: nat,C: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A @ B2 ) ) @ ( modulo_modulo_nat @ A @ B2 ) ) @ C )
% 5.41/5.65 = ( plus_plus_nat @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(2)
% 5.41/5.65 thf(fact_1172_cancel__div__mod__rules_I2_J,axiom,
% 5.41/5.65 ! [B2: int,A: int,C: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B2 @ ( divide_divide_int @ A @ B2 ) ) @ ( modulo_modulo_int @ A @ B2 ) ) @ C )
% 5.41/5.65 = ( plus_plus_int @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(2)
% 5.41/5.65 thf(fact_1173_cancel__div__mod__rules_I2_J,axiom,
% 5.41/5.65 ! [B2: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A @ B2 ) ) @ ( modulo364778990260209775nteger @ A @ B2 ) ) @ C )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(2)
% 5.41/5.65 thf(fact_1174_div__mult1__eq,axiom,
% 5.41/5.65 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.65 ( ( divide_divide_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B2 @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B2 @ C ) ) @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult1_eq
% 5.41/5.65 thf(fact_1175_div__mult1__eq,axiom,
% 5.41/5.65 ! [A: int,B2: int,C: int] :
% 5.41/5.65 ( ( divide_divide_int @ ( times_times_int @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B2 @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B2 @ C ) ) @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult1_eq
% 5.41/5.65 thf(fact_1176_div__mult1__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.65 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B2 @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B2 @ C ) ) @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult1_eq
% 5.41/5.65 thf(fact_1177_minus__mult__div__eq__mod,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( minus_minus_nat @ A @ ( times_times_nat @ B2 @ ( divide_divide_nat @ A @ B2 ) ) )
% 5.41/5.65 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mult_div_eq_mod
% 5.41/5.65 thf(fact_1178_minus__mult__div__eq__mod,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( minus_minus_int @ A @ ( times_times_int @ B2 @ ( divide_divide_int @ A @ B2 ) ) )
% 5.41/5.65 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mult_div_eq_mod
% 5.41/5.65 thf(fact_1179_minus__mult__div__eq__mod,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A @ B2 ) ) )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mult_div_eq_mod
% 5.41/5.65 thf(fact_1180_minus__mod__eq__mult__div,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B2 ) )
% 5.41/5.65 = ( times_times_nat @ B2 @ ( divide_divide_nat @ A @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mod_eq_mult_div
% 5.41/5.65 thf(fact_1181_minus__mod__eq__mult__div,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B2 ) )
% 5.41/5.65 = ( times_times_int @ B2 @ ( divide_divide_int @ A @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mod_eq_mult_div
% 5.41/5.65 thf(fact_1182_minus__mod__eq__mult__div,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B2 ) )
% 5.41/5.65 = ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ A @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mod_eq_mult_div
% 5.41/5.65 thf(fact_1183_minus__mod__eq__div__mult,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B2 ) )
% 5.41/5.65 = ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mod_eq_div_mult
% 5.41/5.65 thf(fact_1184_minus__mod__eq__div__mult,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B2 ) )
% 5.41/5.65 = ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mod_eq_div_mult
% 5.41/5.65 thf(fact_1185_minus__mod__eq__div__mult,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B2 ) )
% 5.41/5.65 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_mod_eq_div_mult
% 5.41/5.65 thf(fact_1186_minus__div__mult__eq__mod,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ B2 ) )
% 5.41/5.65 = ( modulo_modulo_nat @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_div_mult_eq_mod
% 5.41/5.65 thf(fact_1187_minus__div__mult__eq__mod,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ B2 ) )
% 5.41/5.65 = ( modulo_modulo_int @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_div_mult_eq_mod
% 5.41/5.65 thf(fact_1188_minus__div__mult__eq__mod,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ B2 ) )
% 5.41/5.65 = ( modulo364778990260209775nteger @ A @ B2 ) ) ).
% 5.41/5.65
% 5.41/5.65 % minus_div_mult_eq_mod
% 5.41/5.65 thf(fact_1189_mod__mult2__eq,axiom,
% 5.41/5.65 ! [M: nat,N: nat,Q2: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult2_eq
% 5.41/5.65 thf(fact_1190_div__mod__decomp,axiom,
% 5.41/5.65 ! [A3: nat,N: nat] :
% 5.41/5.65 ( A3
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A3 @ N ) @ N ) @ ( modulo_modulo_nat @ A3 @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_mod_decomp
% 5.41/5.65 thf(fact_1191_modulo__nat__def,axiom,
% 5.41/5.65 ( modulo_modulo_nat
% 5.41/5.65 = ( ^ [M6: nat,N2: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % modulo_nat_def
% 5.41/5.65 thf(fact_1192_linordered__field__no__lb,axiom,
% 5.41/5.65 ! [X5: real] :
% 5.41/5.65 ? [Y4: real] : ( ord_less_real @ Y4 @ X5 ) ).
% 5.41/5.65
% 5.41/5.65 % linordered_field_no_lb
% 5.41/5.65 thf(fact_1193_linordered__field__no__lb,axiom,
% 5.41/5.65 ! [X5: rat] :
% 5.41/5.65 ? [Y4: rat] : ( ord_less_rat @ Y4 @ X5 ) ).
% 5.41/5.65
% 5.41/5.65 % linordered_field_no_lb
% 5.41/5.65 thf(fact_1194_linordered__field__no__ub,axiom,
% 5.41/5.65 ! [X5: real] :
% 5.41/5.65 ? [X_1: real] : ( ord_less_real @ X5 @ X_1 ) ).
% 5.41/5.65
% 5.41/5.65 % linordered_field_no_ub
% 5.41/5.65 thf(fact_1195_linordered__field__no__ub,axiom,
% 5.41/5.65 ! [X5: rat] :
% 5.41/5.65 ? [X_1: rat] : ( ord_less_rat @ X5 @ X_1 ) ).
% 5.41/5.65
% 5.41/5.65 % linordered_field_no_ub
% 5.41/5.65 thf(fact_1196_bounded__Max__nat,axiom,
% 5.41/5.65 ! [P: nat > $o,X4: nat,M7: nat] :
% 5.41/5.65 ( ( P @ X4 )
% 5.41/5.65 => ( ! [X3: nat] :
% 5.41/5.65 ( ( P @ X3 )
% 5.41/5.65 => ( ord_less_eq_nat @ X3 @ M7 ) )
% 5.41/5.65 => ~ ! [M4: nat] :
% 5.41/5.65 ( ( P @ M4 )
% 5.41/5.65 => ~ ! [X5: nat] :
% 5.41/5.65 ( ( P @ X5 )
% 5.41/5.65 => ( ord_less_eq_nat @ X5 @ M4 ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % bounded_Max_nat
% 5.41/5.65 thf(fact_1197_div__exp__mod__exp__eq,axiom,
% 5.41/5.65 ! [A: nat,N: nat,M: nat] :
% 5.41/5.65 ( ( 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 ) )
% 5.41/5.65 = ( 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 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_exp_mod_exp_eq
% 5.41/5.65 thf(fact_1198_div__exp__mod__exp__eq,axiom,
% 5.41/5.65 ! [A: int,N: nat,M: nat] :
% 5.41/5.65 ( ( 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 ) )
% 5.41/5.65 = ( 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 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_exp_mod_exp_eq
% 5.41/5.65 thf(fact_1199_div__exp__mod__exp__eq,axiom,
% 5.41/5.65 ! [A: code_integer,N: nat,M: nat] :
% 5.41/5.65 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.65 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_exp_mod_exp_eq
% 5.41/5.65 thf(fact_1200_mult__exp__mod__exp__eq,axiom,
% 5.41/5.65 ! [M: nat,N: nat,A: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.65 => ( ( 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 ) )
% 5.41/5.65 = ( 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 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_exp_mod_exp_eq
% 5.41/5.65 thf(fact_1201_mult__exp__mod__exp__eq,axiom,
% 5.41/5.65 ! [M: nat,N: nat,A: int] :
% 5.41/5.65 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.65 => ( ( 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 ) )
% 5.41/5.65 = ( 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 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_exp_mod_exp_eq
% 5.41/5.65 thf(fact_1202_mult__exp__mod__exp__eq,axiom,
% 5.41/5.65 ! [M: nat,N: nat,A: code_integer] :
% 5.41/5.65 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.65 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.65 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_exp_mod_exp_eq
% 5.41/5.65 thf(fact_1203_divide__divide__eq__left_H,axiom,
% 5.41/5.65 ! [A: complex,B2: complex,C: complex] :
% 5.41/5.65 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B2 ) @ C )
% 5.41/5.65 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_eq_left'
% 5.41/5.65 thf(fact_1204_divide__divide__eq__left_H,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( divide_divide_real @ ( divide_divide_real @ A @ B2 ) @ C )
% 5.41/5.65 = ( divide_divide_real @ A @ ( times_times_real @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_eq_left'
% 5.41/5.65 thf(fact_1205_divide__divide__eq__left_H,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B2 ) @ C )
% 5.41/5.65 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_eq_left'
% 5.41/5.65 thf(fact_1206_divide__divide__times__eq,axiom,
% 5.41/5.65 ! [X4: complex,Y3: complex,Z: complex,W: complex] :
% 5.41/5.65 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X4 @ Y3 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( times_times_complex @ X4 @ W ) @ ( times_times_complex @ Y3 @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_times_eq
% 5.41/5.65 thf(fact_1207_divide__divide__times__eq,axiom,
% 5.41/5.65 ! [X4: real,Y3: real,Z: real,W: real] :
% 5.41/5.65 ( ( divide_divide_real @ ( divide_divide_real @ X4 @ Y3 ) @ ( divide_divide_real @ Z @ W ) )
% 5.41/5.65 = ( divide_divide_real @ ( times_times_real @ X4 @ W ) @ ( times_times_real @ Y3 @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_times_eq
% 5.41/5.65 thf(fact_1208_divide__divide__times__eq,axiom,
% 5.41/5.65 ! [X4: rat,Y3: rat,Z: rat,W: rat] :
% 5.41/5.65 ( ( divide_divide_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.41/5.65 = ( divide_divide_rat @ ( times_times_rat @ X4 @ W ) @ ( times_times_rat @ Y3 @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_divide_times_eq
% 5.41/5.65 thf(fact_1209_times__divide__times__eq,axiom,
% 5.41/5.65 ! [X4: complex,Y3: complex,Z: complex,W: complex] :
% 5.41/5.65 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X4 @ Y3 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ Y3 @ W ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % times_divide_times_eq
% 5.41/5.65 thf(fact_1210_times__divide__times__eq,axiom,
% 5.41/5.65 ! [X4: real,Y3: real,Z: real,W: real] :
% 5.41/5.65 ( ( times_times_real @ ( divide_divide_real @ X4 @ Y3 ) @ ( divide_divide_real @ Z @ W ) )
% 5.41/5.65 = ( divide_divide_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y3 @ W ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % times_divide_times_eq
% 5.41/5.65 thf(fact_1211_times__divide__times__eq,axiom,
% 5.41/5.65 ! [X4: rat,Y3: rat,Z: rat,W: rat] :
% 5.41/5.65 ( ( times_times_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.41/5.65 = ( divide_divide_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ Y3 @ W ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % times_divide_times_eq
% 5.41/5.65 thf(fact_1212_add__divide__distrib,axiom,
% 5.41/5.65 ! [A: complex,B2: complex,C: complex] :
% 5.41/5.65 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_distrib
% 5.41/5.65 thf(fact_1213_add__divide__distrib,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( divide_divide_real @ ( plus_plus_real @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_distrib
% 5.41/5.65 thf(fact_1214_add__divide__distrib,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B2 ) @ C )
% 5.41/5.65 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_distrib
% 5.41/5.65 thf(fact_1215_diff__divide__distrib,axiom,
% 5.41/5.65 ! [A: complex,B2: complex,C: complex] :
% 5.41/5.65 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B2 ) @ C )
% 5.41/5.65 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_divide_distrib
% 5.41/5.65 thf(fact_1216_diff__divide__distrib,axiom,
% 5.41/5.65 ! [A: real,B2: real,C: real] :
% 5.41/5.65 ( ( divide_divide_real @ ( minus_minus_real @ A @ B2 ) @ C )
% 5.41/5.65 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_divide_distrib
% 5.41/5.65 thf(fact_1217_diff__divide__distrib,axiom,
% 5.41/5.65 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.65 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B2 ) @ C )
% 5.41/5.65 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B2 @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_divide_distrib
% 5.41/5.65 thf(fact_1218_unset__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: code_integer] :
% 5.41/5.65 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % unset_bit_Suc
% 5.41/5.65 thf(fact_1219_unset__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: int] :
% 5.41/5.65 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.41/5.65 = ( 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 ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % unset_bit_Suc
% 5.41/5.65 thf(fact_1220_unset__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: nat] :
% 5.41/5.65 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.41/5.65 = ( 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 ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % unset_bit_Suc
% 5.41/5.65 thf(fact_1221_flip__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: code_integer] :
% 5.41/5.65 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % flip_bit_Suc
% 5.41/5.65 thf(fact_1222_flip__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: int] :
% 5.41/5.65 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.41/5.65 = ( 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 ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % flip_bit_Suc
% 5.41/5.65 thf(fact_1223_flip__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: nat] :
% 5.41/5.65 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.41/5.65 = ( 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 ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % flip_bit_Suc
% 5.41/5.65 thf(fact_1224_set__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: code_integer] :
% 5.41/5.65 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % set_bit_Suc
% 5.41/5.65 thf(fact_1225_set__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: int] :
% 5.41/5.65 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.41/5.65 = ( 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 ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % set_bit_Suc
% 5.41/5.65 thf(fact_1226_set__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: nat] :
% 5.41/5.65 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.41/5.65 = ( 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 ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % set_bit_Suc
% 5.41/5.65 thf(fact_1227_dbl__simps_I3_J,axiom,
% 5.41/5.65 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.41/5.65 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % dbl_simps(3)
% 5.41/5.65 thf(fact_1228_dbl__simps_I3_J,axiom,
% 5.41/5.65 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.41/5.65 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % dbl_simps(3)
% 5.41/5.65 thf(fact_1229_dbl__simps_I3_J,axiom,
% 5.41/5.65 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.41/5.65 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % dbl_simps(3)
% 5.41/5.65 thf(fact_1230_dbl__simps_I3_J,axiom,
% 5.41/5.65 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.41/5.65 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % dbl_simps(3)
% 5.41/5.65 thf(fact_1231_divmod__digit__1_I1_J,axiom,
% 5.41/5.65 ! [A: code_integer,B2: code_integer] :
% 5.41/5.65 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.65 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.41/5.65 => ( ( ord_le3102999989581377725nteger @ B2 @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.41/5.65 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) @ one_one_Code_integer )
% 5.41/5.65 = ( divide6298287555418463151nteger @ A @ B2 ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divmod_digit_1(1)
% 5.41/5.65 thf(fact_1232_divmod__digit__1_I1_J,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_nat @ B2 @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.41/5.65 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) @ one_one_nat )
% 5.41/5.65 = ( divide_divide_nat @ A @ B2 ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divmod_digit_1(1)
% 5.41/5.65 thf(fact_1233_divmod__digit__1_I1_J,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.41/5.65 => ( ( ord_less_eq_int @ B2 @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.41/5.65 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) @ one_one_int )
% 5.41/5.65 = ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divmod_digit_1(1)
% 5.41/5.65 thf(fact_1234_signed__take__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: code_integer] :
% 5.41/5.65 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % signed_take_bit_Suc
% 5.41/5.65 thf(fact_1235_signed__take__bit__Suc,axiom,
% 5.41/5.65 ! [N: nat,A: int] :
% 5.41/5.65 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.41/5.65 = ( 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 ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % signed_take_bit_Suc
% 5.41/5.65 thf(fact_1236_power__numeral,axiom,
% 5.41/5.65 ! [K: num,L2: num] :
% 5.41/5.65 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.65 = ( numera6690914467698888265omplex @ ( pow @ K @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_numeral
% 5.41/5.65 thf(fact_1237_power__numeral,axiom,
% 5.41/5.65 ! [K: num,L2: num] :
% 5.41/5.65 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.65 = ( numeral_numeral_real @ ( pow @ K @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_numeral
% 5.41/5.65 thf(fact_1238_power__numeral,axiom,
% 5.41/5.65 ! [K: num,L2: num] :
% 5.41/5.65 ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.65 = ( numeral_numeral_rat @ ( pow @ K @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_numeral
% 5.41/5.65 thf(fact_1239_power__numeral,axiom,
% 5.41/5.65 ! [K: num,L2: num] :
% 5.41/5.65 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.65 = ( numeral_numeral_nat @ ( pow @ K @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_numeral
% 5.41/5.65 thf(fact_1240_power__numeral,axiom,
% 5.41/5.65 ! [K: num,L2: num] :
% 5.41/5.65 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.65 = ( numeral_numeral_int @ ( pow @ K @ L2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_numeral
% 5.41/5.65 thf(fact_1241_arith__geo__mean,axiom,
% 5.41/5.65 ! [U: real,X4: real,Y3: real] :
% 5.41/5.65 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( times_times_real @ X4 @ Y3 ) )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.41/5.65 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % arith_geo_mean
% 5.41/5.65 thf(fact_1242_arith__geo__mean,axiom,
% 5.41/5.65 ! [U: rat,X4: rat,Y3: rat] :
% 5.41/5.65 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( times_times_rat @ X4 @ Y3 ) )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.41/5.65 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X4 @ Y3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % arith_geo_mean
% 5.41/5.65 thf(fact_1243_odd__two__times__div__two__nat,axiom,
% 5.41/5.65 ! [N: nat] :
% 5.41/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.65 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % odd_two_times_div_two_nat
% 5.41/5.65 thf(fact_1244_less__nat__zero__code,axiom,
% 5.41/5.65 ! [N: nat] :
% 5.41/5.65 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.41/5.65
% 5.41/5.65 % less_nat_zero_code
% 5.41/5.65 thf(fact_1245_neq0__conv,axiom,
% 5.41/5.65 ! [N: nat] :
% 5.41/5.65 ( ( N != zero_zero_nat )
% 5.41/5.65 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.65
% 5.41/5.65 % neq0_conv
% 5.41/5.65 thf(fact_1246_bot__nat__0_Onot__eq__extremum,axiom,
% 5.41/5.65 ! [A: nat] :
% 5.41/5.65 ( ( A != zero_zero_nat )
% 5.41/5.65 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.41/5.65
% 5.41/5.65 % bot_nat_0.not_eq_extremum
% 5.41/5.65 thf(fact_1247_le0,axiom,
% 5.41/5.65 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.41/5.65
% 5.41/5.65 % le0
% 5.41/5.65 thf(fact_1248_bot__nat__0_Oextremum,axiom,
% 5.41/5.65 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.41/5.65
% 5.41/5.65 % bot_nat_0.extremum
% 5.41/5.65 thf(fact_1249_Nat_Oadd__0__right,axiom,
% 5.41/5.65 ! [M: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.41/5.65 = M ) ).
% 5.41/5.65
% 5.41/5.65 % Nat.add_0_right
% 5.41/5.65 thf(fact_1250_add__is__0,axiom,
% 5.41/5.65 ! [M: nat,N: nat] :
% 5.41/5.65 ( ( ( plus_plus_nat @ M @ N )
% 5.41/5.65 = zero_zero_nat )
% 5.41/5.65 = ( ( M = zero_zero_nat )
% 5.41/5.65 & ( N = zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_is_0
% 5.41/5.65 thf(fact_1251_diff__self__eq__0,axiom,
% 5.41/5.65 ! [M: nat] :
% 5.41/5.65 ( ( minus_minus_nat @ M @ M )
% 5.41/5.65 = zero_zero_nat ) ).
% 5.41/5.65
% 5.41/5.65 % diff_self_eq_0
% 5.41/5.65 thf(fact_1252_diff__0__eq__0,axiom,
% 5.41/5.65 ! [N: nat] :
% 5.41/5.65 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.41/5.65 = zero_zero_nat ) ).
% 5.41/5.65
% 5.41/5.65 % diff_0_eq_0
% 5.41/5.65 thf(fact_1253_mult__cancel2,axiom,
% 5.41/5.65 ! [M: nat,K: nat,N: nat] :
% 5.41/5.65 ( ( ( times_times_nat @ M @ K )
% 5.41/5.65 = ( times_times_nat @ N @ K ) )
% 5.41/5.65 = ( ( M = N )
% 5.41/5.65 | ( K = zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_cancel2
% 5.41/5.65 thf(fact_1254_mult__cancel1,axiom,
% 5.41/5.65 ! [K: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ( times_times_nat @ K @ M )
% 5.41/5.65 = ( times_times_nat @ K @ N ) )
% 5.41/5.65 = ( ( M = N )
% 5.41/5.65 | ( K = zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_cancel1
% 5.41/5.65 thf(fact_1255_mult__0__right,axiom,
% 5.41/5.65 ! [M: nat] :
% 5.41/5.65 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.41/5.65 = zero_zero_nat ) ).
% 5.41/5.65
% 5.41/5.65 % mult_0_right
% 5.41/5.65 thf(fact_1256_mult__is__0,axiom,
% 5.41/5.65 ! [M: nat,N: nat] :
% 5.41/5.65 ( ( ( times_times_nat @ M @ N )
% 5.41/5.65 = zero_zero_nat )
% 5.41/5.65 = ( ( M = zero_zero_nat )
% 5.41/5.65 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_is_0
% 5.41/5.65 thf(fact_1257_div__pos__pos__trivial,axiom,
% 5.41/5.65 ! [K: int,L2: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.65 => ( ( ord_less_int @ K @ L2 )
% 5.41/5.65 => ( ( divide_divide_int @ K @ L2 )
% 5.41/5.65 = zero_zero_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_pos_pos_trivial
% 5.41/5.65 thf(fact_1258_div__neg__neg__trivial,axiom,
% 5.41/5.65 ! [K: int,L2: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.41/5.65 => ( ( ord_less_int @ L2 @ K )
% 5.41/5.65 => ( ( divide_divide_int @ K @ L2 )
% 5.41/5.65 = zero_zero_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_neg_neg_trivial
% 5.41/5.65 thf(fact_1259_i0__less,axiom,
% 5.41/5.65 ! [N: extended_enat] :
% 5.41/5.65 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.41/5.65 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.41/5.65
% 5.41/5.65 % i0_less
% 5.41/5.65 thf(fact_1260_idiff__0,axiom,
% 5.41/5.65 ! [N: extended_enat] :
% 5.41/5.65 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.41/5.65 = zero_z5237406670263579293d_enat ) ).
% 5.41/5.65
% 5.41/5.65 % idiff_0
% 5.41/5.65 thf(fact_1261_idiff__0__right,axiom,
% 5.41/5.65 ! [N: extended_enat] :
% 5.41/5.65 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.41/5.65 = N ) ).
% 5.41/5.65
% 5.41/5.65 % idiff_0_right
% 5.41/5.65 thf(fact_1262_le__zero__eq,axiom,
% 5.41/5.65 ! [N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.41/5.65 = ( N = zero_zero_nat ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_zero_eq
% 5.41/5.65 thf(fact_1263_not__gr__zero,axiom,
% 5.41/5.65 ! [N: nat] :
% 5.41/5.65 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.41/5.65 = ( N = zero_zero_nat ) ) ).
% 5.41/5.65
% 5.41/5.65 % not_gr_zero
% 5.41/5.65 thf(fact_1264_mult__cancel__right,axiom,
% 5.41/5.65 ! [A: real,C: real,B2: real] :
% 5.41/5.65 ( ( ( times_times_real @ A @ C )
% 5.41/5.65 = ( times_times_real @ B2 @ C ) )
% 5.41/5.65 = ( ( C = zero_zero_real )
% 5.41/5.65 | ( A = B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_cancel_right
% 5.41/5.65 thf(fact_1265_mult__cancel__right,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.65 ( ( ( times_times_rat @ A @ C )
% 5.41/5.65 = ( times_times_rat @ B2 @ C ) )
% 5.41/5.65 = ( ( C = zero_zero_rat )
% 5.41/5.65 | ( A = B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_cancel_right
% 5.41/5.65 thf(fact_1266_mult__cancel__right,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.65 ( ( ( times_times_nat @ A @ C )
% 5.41/5.65 = ( times_times_nat @ B2 @ C ) )
% 5.41/5.65 = ( ( C = zero_zero_nat )
% 5.41/5.65 | ( A = B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_cancel_right
% 5.41/5.65 thf(fact_1267_mult__cancel__right,axiom,
% 5.41/5.65 ! [A: int,C: int,B2: int] :
% 5.41/5.65 ( ( ( times_times_int @ A @ C )
% 5.41/5.65 = ( times_times_int @ B2 @ C ) )
% 5.41/5.65 = ( ( C = zero_zero_int )
% 5.41/5.65 | ( A = B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_cancel_right
% 5.41/5.65 thf(fact_1268_mult__cancel__left,axiom,
% 5.41/5.65 ! [C: real,A: real,B2: real] :
% 5.41/5.65 ( ( ( times_times_real @ C @ A )
% 5.41/5.65 = ( times_times_real @ C @ B2 ) )
% 5.41/5.65 = ( ( C = zero_zero_real )
% 5.41/5.65 | ( A = B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_cancel_left
% 5.41/5.65 thf(fact_1269_mult__cancel__left,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.65 ( ( ( times_times_rat @ C @ A )
% 5.41/5.65 = ( times_times_rat @ C @ B2 ) )
% 5.41/5.65 = ( ( C = zero_zero_rat )
% 5.41/5.65 | ( A = B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_cancel_left
% 5.41/5.65 thf(fact_1270_mult__cancel__left,axiom,
% 5.41/5.65 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.65 ( ( ( times_times_nat @ C @ A )
% 5.41/5.65 = ( times_times_nat @ C @ B2 ) )
% 5.41/5.65 = ( ( C = zero_zero_nat )
% 5.41/5.65 | ( A = B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_cancel_left
% 5.41/5.65 thf(fact_1271_mult__cancel__left,axiom,
% 5.41/5.65 ! [C: int,A: int,B2: int] :
% 5.41/5.65 ( ( ( times_times_int @ C @ A )
% 5.41/5.65 = ( times_times_int @ C @ B2 ) )
% 5.41/5.65 = ( ( C = zero_zero_int )
% 5.41/5.65 | ( A = B2 ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_cancel_left
% 5.41/5.65 thf(fact_1272_mult__eq__0__iff,axiom,
% 5.41/5.65 ! [A: real,B2: real] :
% 5.41/5.65 ( ( ( times_times_real @ A @ B2 )
% 5.41/5.65 = zero_zero_real )
% 5.41/5.65 = ( ( A = zero_zero_real )
% 5.41/5.65 | ( B2 = zero_zero_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_eq_0_iff
% 5.41/5.65 thf(fact_1273_mult__eq__0__iff,axiom,
% 5.41/5.65 ! [A: rat,B2: rat] :
% 5.41/5.65 ( ( ( times_times_rat @ A @ B2 )
% 5.41/5.65 = zero_zero_rat )
% 5.41/5.65 = ( ( A = zero_zero_rat )
% 5.41/5.65 | ( B2 = zero_zero_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_eq_0_iff
% 5.41/5.65 thf(fact_1274_mult__eq__0__iff,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( ( times_times_nat @ A @ B2 )
% 5.41/5.65 = zero_zero_nat )
% 5.41/5.65 = ( ( A = zero_zero_nat )
% 5.41/5.65 | ( B2 = zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_eq_0_iff
% 5.41/5.65 thf(fact_1275_mult__eq__0__iff,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( ( times_times_int @ A @ B2 )
% 5.41/5.65 = zero_zero_int )
% 5.41/5.65 = ( ( A = zero_zero_int )
% 5.41/5.65 | ( B2 = zero_zero_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_eq_0_iff
% 5.41/5.65 thf(fact_1276_mult__zero__right,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ( ( times_times_real @ A @ zero_zero_real )
% 5.41/5.65 = zero_zero_real ) ).
% 5.41/5.65
% 5.41/5.65 % mult_zero_right
% 5.41/5.65 thf(fact_1277_mult__zero__right,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.41/5.65 = zero_zero_rat ) ).
% 5.41/5.65
% 5.41/5.65 % mult_zero_right
% 5.41/5.65 thf(fact_1278_mult__zero__right,axiom,
% 5.41/5.65 ! [A: nat] :
% 5.41/5.65 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.41/5.65 = zero_zero_nat ) ).
% 5.41/5.65
% 5.41/5.65 % mult_zero_right
% 5.41/5.65 thf(fact_1279_mult__zero__right,axiom,
% 5.41/5.65 ! [A: int] :
% 5.41/5.65 ( ( times_times_int @ A @ zero_zero_int )
% 5.41/5.65 = zero_zero_int ) ).
% 5.41/5.65
% 5.41/5.65 % mult_zero_right
% 5.41/5.65 thf(fact_1280_mult__zero__left,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ( ( times_times_real @ zero_zero_real @ A )
% 5.41/5.65 = zero_zero_real ) ).
% 5.41/5.65
% 5.41/5.65 % mult_zero_left
% 5.41/5.65 thf(fact_1281_mult__zero__left,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.41/5.65 = zero_zero_rat ) ).
% 5.41/5.65
% 5.41/5.65 % mult_zero_left
% 5.41/5.65 thf(fact_1282_mult__zero__left,axiom,
% 5.41/5.65 ! [A: nat] :
% 5.41/5.65 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.41/5.65 = zero_zero_nat ) ).
% 5.41/5.65
% 5.41/5.65 % mult_zero_left
% 5.41/5.65 thf(fact_1283_mult__zero__left,axiom,
% 5.41/5.65 ! [A: int] :
% 5.41/5.65 ( ( times_times_int @ zero_zero_int @ A )
% 5.41/5.65 = zero_zero_int ) ).
% 5.41/5.65
% 5.41/5.65 % mult_zero_left
% 5.41/5.65 thf(fact_1284_add__0,axiom,
% 5.41/5.65 ! [A: literal] :
% 5.41/5.65 ( ( plus_plus_literal @ zero_zero_literal @ A )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % add_0
% 5.41/5.65 thf(fact_1285_add__0,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % add_0
% 5.41/5.65 thf(fact_1286_add__0,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % add_0
% 5.41/5.65 thf(fact_1287_add__0,axiom,
% 5.41/5.65 ! [A: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % add_0
% 5.41/5.65 thf(fact_1288_add__0,axiom,
% 5.41/5.65 ! [A: int] :
% 5.41/5.65 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % add_0
% 5.41/5.65 thf(fact_1289_zero__eq__add__iff__both__eq__0,axiom,
% 5.41/5.65 ! [X4: nat,Y3: nat] :
% 5.41/5.65 ( ( zero_zero_nat
% 5.41/5.65 = ( plus_plus_nat @ X4 @ Y3 ) )
% 5.41/5.65 = ( ( X4 = zero_zero_nat )
% 5.41/5.65 & ( Y3 = zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % zero_eq_add_iff_both_eq_0
% 5.41/5.65 thf(fact_1290_add__eq__0__iff__both__eq__0,axiom,
% 5.41/5.65 ! [X4: nat,Y3: nat] :
% 5.41/5.65 ( ( ( plus_plus_nat @ X4 @ Y3 )
% 5.41/5.65 = zero_zero_nat )
% 5.41/5.65 = ( ( X4 = zero_zero_nat )
% 5.41/5.65 & ( Y3 = zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_eq_0_iff_both_eq_0
% 5.41/5.65 thf(fact_1291_add__cancel__right__right,axiom,
% 5.41/5.65 ! [A: real,B2: real] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( plus_plus_real @ A @ B2 ) )
% 5.41/5.65 = ( B2 = zero_zero_real ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_right_right
% 5.41/5.65 thf(fact_1292_add__cancel__right__right,axiom,
% 5.41/5.65 ! [A: rat,B2: rat] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( plus_plus_rat @ A @ B2 ) )
% 5.41/5.65 = ( B2 = zero_zero_rat ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_right_right
% 5.41/5.65 thf(fact_1293_add__cancel__right__right,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( plus_plus_nat @ A @ B2 ) )
% 5.41/5.65 = ( B2 = zero_zero_nat ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_right_right
% 5.41/5.65 thf(fact_1294_add__cancel__right__right,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( plus_plus_int @ A @ B2 ) )
% 5.41/5.65 = ( B2 = zero_zero_int ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_right_right
% 5.41/5.65 thf(fact_1295_add__cancel__right__left,axiom,
% 5.41/5.65 ! [A: real,B2: real] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( plus_plus_real @ B2 @ A ) )
% 5.41/5.65 = ( B2 = zero_zero_real ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_right_left
% 5.41/5.65 thf(fact_1296_add__cancel__right__left,axiom,
% 5.41/5.65 ! [A: rat,B2: rat] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( plus_plus_rat @ B2 @ A ) )
% 5.41/5.65 = ( B2 = zero_zero_rat ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_right_left
% 5.41/5.65 thf(fact_1297_add__cancel__right__left,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( plus_plus_nat @ B2 @ A ) )
% 5.41/5.65 = ( B2 = zero_zero_nat ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_right_left
% 5.41/5.65 thf(fact_1298_add__cancel__right__left,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( A
% 5.41/5.65 = ( plus_plus_int @ B2 @ A ) )
% 5.41/5.65 = ( B2 = zero_zero_int ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_right_left
% 5.41/5.65 thf(fact_1299_add__cancel__left__right,axiom,
% 5.41/5.65 ! [A: real,B2: real] :
% 5.41/5.65 ( ( ( plus_plus_real @ A @ B2 )
% 5.41/5.65 = A )
% 5.41/5.65 = ( B2 = zero_zero_real ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_left_right
% 5.41/5.65 thf(fact_1300_add__cancel__left__right,axiom,
% 5.41/5.65 ! [A: rat,B2: rat] :
% 5.41/5.65 ( ( ( plus_plus_rat @ A @ B2 )
% 5.41/5.65 = A )
% 5.41/5.65 = ( B2 = zero_zero_rat ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_left_right
% 5.41/5.65 thf(fact_1301_add__cancel__left__right,axiom,
% 5.41/5.65 ! [A: nat,B2: nat] :
% 5.41/5.65 ( ( ( plus_plus_nat @ A @ B2 )
% 5.41/5.65 = A )
% 5.41/5.65 = ( B2 = zero_zero_nat ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_left_right
% 5.41/5.65 thf(fact_1302_add__cancel__left__right,axiom,
% 5.41/5.65 ! [A: int,B2: int] :
% 5.41/5.65 ( ( ( plus_plus_int @ A @ B2 )
% 5.41/5.65 = A )
% 5.41/5.65 = ( B2 = zero_zero_int ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_left_right
% 5.41/5.65 thf(fact_1303_add__cancel__left__left,axiom,
% 5.41/5.65 ! [B2: real,A: real] :
% 5.41/5.65 ( ( ( plus_plus_real @ B2 @ A )
% 5.41/5.65 = A )
% 5.41/5.65 = ( B2 = zero_zero_real ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_left_left
% 5.41/5.65 thf(fact_1304_add__cancel__left__left,axiom,
% 5.41/5.65 ! [B2: rat,A: rat] :
% 5.41/5.65 ( ( ( plus_plus_rat @ B2 @ A )
% 5.41/5.65 = A )
% 5.41/5.65 = ( B2 = zero_zero_rat ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_left_left
% 5.41/5.65 thf(fact_1305_add__cancel__left__left,axiom,
% 5.41/5.65 ! [B2: nat,A: nat] :
% 5.41/5.65 ( ( ( plus_plus_nat @ B2 @ A )
% 5.41/5.65 = A )
% 5.41/5.65 = ( B2 = zero_zero_nat ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_left_left
% 5.41/5.65 thf(fact_1306_add__cancel__left__left,axiom,
% 5.41/5.65 ! [B2: int,A: int] :
% 5.41/5.65 ( ( ( plus_plus_int @ B2 @ A )
% 5.41/5.65 = A )
% 5.41/5.65 = ( B2 = zero_zero_int ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_cancel_left_left
% 5.41/5.65 thf(fact_1307_double__zero__sym,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ( ( zero_zero_real
% 5.41/5.65 = ( plus_plus_real @ A @ A ) )
% 5.41/5.65 = ( A = zero_zero_real ) ) ).
% 5.41/5.65
% 5.41/5.65 % double_zero_sym
% 5.41/5.65 thf(fact_1308_double__zero__sym,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ( ( zero_zero_rat
% 5.41/5.65 = ( plus_plus_rat @ A @ A ) )
% 5.41/5.65 = ( A = zero_zero_rat ) ) ).
% 5.41/5.65
% 5.41/5.65 % double_zero_sym
% 5.41/5.65 thf(fact_1309_double__zero__sym,axiom,
% 5.41/5.65 ! [A: int] :
% 5.41/5.65 ( ( zero_zero_int
% 5.41/5.65 = ( plus_plus_int @ A @ A ) )
% 5.41/5.65 = ( A = zero_zero_int ) ) ).
% 5.41/5.65
% 5.41/5.65 % double_zero_sym
% 5.41/5.65 thf(fact_1310_add_Oright__neutral,axiom,
% 5.41/5.65 ! [A: literal] :
% 5.41/5.65 ( ( plus_plus_literal @ A @ zero_zero_literal )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % add.right_neutral
% 5.41/5.65 thf(fact_1311_add_Oright__neutral,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % add.right_neutral
% 5.41/5.65 thf(fact_1312_add_Oright__neutral,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % add.right_neutral
% 5.41/5.65 thf(fact_1313_add_Oright__neutral,axiom,
% 5.41/5.65 ! [A: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % add.right_neutral
% 5.41/5.66 thf(fact_1314_add_Oright__neutral,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % add.right_neutral
% 5.41/5.66 thf(fact_1315_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( minus_minus_real @ A @ A )
% 5.41/5.66 = zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % cancel_comm_monoid_add_class.diff_cancel
% 5.41/5.66 thf(fact_1316_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( minus_minus_rat @ A @ A )
% 5.41/5.66 = zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % cancel_comm_monoid_add_class.diff_cancel
% 5.41/5.66 thf(fact_1317_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( minus_minus_nat @ A @ A )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % cancel_comm_monoid_add_class.diff_cancel
% 5.41/5.66 thf(fact_1318_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( minus_minus_int @ A @ A )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % cancel_comm_monoid_add_class.diff_cancel
% 5.41/5.66 thf(fact_1319_diff__zero,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % diff_zero
% 5.41/5.66 thf(fact_1320_diff__zero,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % diff_zero
% 5.41/5.66 thf(fact_1321_diff__zero,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % diff_zero
% 5.41/5.66 thf(fact_1322_diff__zero,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % diff_zero
% 5.41/5.66 thf(fact_1323_zero__diff,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % zero_diff
% 5.41/5.66 thf(fact_1324_diff__0__right,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % diff_0_right
% 5.41/5.66 thf(fact_1325_diff__0__right,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % diff_0_right
% 5.41/5.66 thf(fact_1326_diff__0__right,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % diff_0_right
% 5.41/5.66 thf(fact_1327_diff__self,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( minus_minus_real @ A @ A )
% 5.41/5.66 = zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % diff_self
% 5.41/5.66 thf(fact_1328_diff__self,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( minus_minus_rat @ A @ A )
% 5.41/5.66 = zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % diff_self
% 5.41/5.66 thf(fact_1329_diff__self,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( minus_minus_int @ A @ A )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % diff_self
% 5.41/5.66 thf(fact_1330_div__0,axiom,
% 5.41/5.66 ! [A: complex] :
% 5.41/5.66 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.41/5.66 = zero_zero_complex ) ).
% 5.41/5.66
% 5.41/5.66 % div_0
% 5.41/5.66 thf(fact_1331_div__0,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.41/5.66 = zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % div_0
% 5.41/5.66 thf(fact_1332_div__0,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.41/5.66 = zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % div_0
% 5.41/5.66 thf(fact_1333_div__0,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % div_0
% 5.41/5.66 thf(fact_1334_div__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % div_0
% 5.41/5.66 thf(fact_1335_div__by__0,axiom,
% 5.41/5.66 ! [A: complex] :
% 5.41/5.66 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.41/5.66 = zero_zero_complex ) ).
% 5.41/5.66
% 5.41/5.66 % div_by_0
% 5.41/5.66 thf(fact_1336_div__by__0,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.41/5.66 = zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % div_by_0
% 5.41/5.66 thf(fact_1337_div__by__0,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.41/5.66 = zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % div_by_0
% 5.41/5.66 thf(fact_1338_div__by__0,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % div_by_0
% 5.41/5.66 thf(fact_1339_div__by__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % div_by_0
% 5.41/5.66 thf(fact_1340_bits__div__0,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % bits_div_0
% 5.41/5.66 thf(fact_1341_bits__div__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % bits_div_0
% 5.41/5.66 thf(fact_1342_bits__div__by__0,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % bits_div_by_0
% 5.41/5.66 thf(fact_1343_bits__div__by__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % bits_div_by_0
% 5.41/5.66 thf(fact_1344_divide__eq__0__iff,axiom,
% 5.41/5.66 ! [A: complex,B2: complex] :
% 5.41/5.66 ( ( ( divide1717551699836669952omplex @ A @ B2 )
% 5.41/5.66 = zero_zero_complex )
% 5.41/5.66 = ( ( A = zero_zero_complex )
% 5.41/5.66 | ( B2 = zero_zero_complex ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_0_iff
% 5.41/5.66 thf(fact_1345_divide__eq__0__iff,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ( divide_divide_real @ A @ B2 )
% 5.41/5.66 = zero_zero_real )
% 5.41/5.66 = ( ( A = zero_zero_real )
% 5.41/5.66 | ( B2 = zero_zero_real ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_0_iff
% 5.41/5.66 thf(fact_1346_divide__eq__0__iff,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ( divide_divide_rat @ A @ B2 )
% 5.41/5.66 = zero_zero_rat )
% 5.41/5.66 = ( ( A = zero_zero_rat )
% 5.41/5.66 | ( B2 = zero_zero_rat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_0_iff
% 5.41/5.66 thf(fact_1347_divide__cancel__left,axiom,
% 5.41/5.66 ! [C: complex,A: complex,B2: complex] :
% 5.41/5.66 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.41/5.66 = ( divide1717551699836669952omplex @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_zero_complex )
% 5.41/5.66 | ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_cancel_left
% 5.41/5.66 thf(fact_1348_divide__cancel__left,axiom,
% 5.41/5.66 ! [C: real,A: real,B2: real] :
% 5.41/5.66 ( ( ( divide_divide_real @ C @ A )
% 5.41/5.66 = ( divide_divide_real @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_zero_real )
% 5.41/5.66 | ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_cancel_left
% 5.41/5.66 thf(fact_1349_divide__cancel__left,axiom,
% 5.41/5.66 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.66 ( ( ( divide_divide_rat @ C @ A )
% 5.41/5.66 = ( divide_divide_rat @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_zero_rat )
% 5.41/5.66 | ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_cancel_left
% 5.41/5.66 thf(fact_1350_divide__cancel__right,axiom,
% 5.41/5.66 ! [A: complex,C: complex,B2: complex] :
% 5.41/5.66 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.41/5.66 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_zero_complex )
% 5.41/5.66 | ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_cancel_right
% 5.41/5.66 thf(fact_1351_divide__cancel__right,axiom,
% 5.41/5.66 ! [A: real,C: real,B2: real] :
% 5.41/5.66 ( ( ( divide_divide_real @ A @ C )
% 5.41/5.66 = ( divide_divide_real @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_zero_real )
% 5.41/5.66 | ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_cancel_right
% 5.41/5.66 thf(fact_1352_divide__cancel__right,axiom,
% 5.41/5.66 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.66 ( ( ( divide_divide_rat @ A @ C )
% 5.41/5.66 = ( divide_divide_rat @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_zero_rat )
% 5.41/5.66 | ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_cancel_right
% 5.41/5.66 thf(fact_1353_division__ring__divide__zero,axiom,
% 5.41/5.66 ! [A: complex] :
% 5.41/5.66 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.41/5.66 = zero_zero_complex ) ).
% 5.41/5.66
% 5.41/5.66 % division_ring_divide_zero
% 5.41/5.66 thf(fact_1354_division__ring__divide__zero,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.41/5.66 = zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % division_ring_divide_zero
% 5.41/5.66 thf(fact_1355_division__ring__divide__zero,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.41/5.66 = zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % division_ring_divide_zero
% 5.41/5.66 thf(fact_1356_dvd__0__right,axiom,
% 5.41/5.66 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_0_right
% 5.41/5.66 thf(fact_1357_dvd__0__right,axiom,
% 5.41/5.66 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_0_right
% 5.41/5.66 thf(fact_1358_dvd__0__right,axiom,
% 5.41/5.66 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_0_right
% 5.41/5.66 thf(fact_1359_dvd__0__right,axiom,
% 5.41/5.66 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_0_right
% 5.41/5.66 thf(fact_1360_dvd__0__right,axiom,
% 5.41/5.66 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_0_right
% 5.41/5.66 thf(fact_1361_dvd__0__left__iff,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.41/5.66 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_0_left_iff
% 5.41/5.66 thf(fact_1362_dvd__0__left__iff,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.41/5.66 = ( A = zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_0_left_iff
% 5.41/5.66 thf(fact_1363_dvd__0__left__iff,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.41/5.66 = ( A = zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_0_left_iff
% 5.41/5.66 thf(fact_1364_dvd__0__left__iff,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.41/5.66 = ( A = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_0_left_iff
% 5.41/5.66 thf(fact_1365_dvd__0__left__iff,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.41/5.66 = ( A = zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_0_left_iff
% 5.41/5.66 thf(fact_1366_dvd__add__triv__right__iff,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B2 @ A ) )
% 5.41/5.66 = ( dvd_dvd_Code_integer @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_triv_right_iff
% 5.41/5.66 thf(fact_1367_dvd__add__triv__right__iff,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B2 @ A ) )
% 5.41/5.66 = ( dvd_dvd_real @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_triv_right_iff
% 5.41/5.66 thf(fact_1368_dvd__add__triv__right__iff,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B2 @ A ) )
% 5.41/5.66 = ( dvd_dvd_rat @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_triv_right_iff
% 5.41/5.66 thf(fact_1369_dvd__add__triv__right__iff,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B2 @ A ) )
% 5.41/5.66 = ( dvd_dvd_nat @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_triv_right_iff
% 5.41/5.66 thf(fact_1370_dvd__add__triv__right__iff,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B2 @ A ) )
% 5.41/5.66 = ( dvd_dvd_int @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_triv_right_iff
% 5.41/5.66 thf(fact_1371_dvd__add__triv__left__iff,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_Code_integer @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_triv_left_iff
% 5.41/5.66 thf(fact_1372_dvd__add__triv__left__iff,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_real @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_triv_left_iff
% 5.41/5.66 thf(fact_1373_dvd__add__triv__left__iff,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_rat @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_triv_left_iff
% 5.41/5.66 thf(fact_1374_dvd__add__triv__left__iff,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_nat @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_triv_left_iff
% 5.41/5.66 thf(fact_1375_dvd__add__triv__left__iff,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_int @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_triv_left_iff
% 5.41/5.66 thf(fact_1376_power__Suc0__right,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % power_Suc0_right
% 5.41/5.66 thf(fact_1377_power__Suc0__right,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % power_Suc0_right
% 5.41/5.66 thf(fact_1378_power__Suc0__right,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % power_Suc0_right
% 5.41/5.66 thf(fact_1379_power__Suc0__right,axiom,
% 5.41/5.66 ! [A: complex] :
% 5.41/5.66 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % power_Suc0_right
% 5.41/5.66 thf(fact_1380_mod__0,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % mod_0
% 5.41/5.66 thf(fact_1381_mod__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % mod_0
% 5.41/5.66 thf(fact_1382_mod__0,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ).
% 5.41/5.66
% 5.41/5.66 % mod_0
% 5.41/5.66 thf(fact_1383_mod__by__0,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % mod_by_0
% 5.41/5.66 thf(fact_1384_mod__by__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % mod_by_0
% 5.41/5.66 thf(fact_1385_mod__by__0,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % mod_by_0
% 5.41/5.66 thf(fact_1386_mod__self,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ A @ A )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % mod_self
% 5.41/5.66 thf(fact_1387_mod__self,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( modulo_modulo_int @ A @ A )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % mod_self
% 5.41/5.66 thf(fact_1388_mod__self,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( modulo364778990260209775nteger @ A @ A )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ).
% 5.41/5.66
% 5.41/5.66 % mod_self
% 5.41/5.66 thf(fact_1389_bits__mod__0,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % bits_mod_0
% 5.41/5.66 thf(fact_1390_bits__mod__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % bits_mod_0
% 5.41/5.66 thf(fact_1391_bits__mod__0,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ).
% 5.41/5.66
% 5.41/5.66 % bits_mod_0
% 5.41/5.66 thf(fact_1392_div__dvd__div,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.41/5.66 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.41/5.66 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B2 @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.41/5.66 = ( dvd_dvd_Code_integer @ B2 @ C ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_dvd_div
% 5.41/5.66 thf(fact_1393_div__dvd__div,axiom,
% 5.41/5.66 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ B2 )
% 5.41/5.66 => ( ( dvd_dvd_nat @ A @ C )
% 5.41/5.66 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B2 @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.41/5.66 = ( dvd_dvd_nat @ B2 @ C ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_dvd_div
% 5.41/5.66 thf(fact_1394_div__dvd__div,axiom,
% 5.41/5.66 ! [A: int,B2: int,C: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ B2 )
% 5.41/5.66 => ( ( dvd_dvd_int @ A @ C )
% 5.41/5.66 => ( ( dvd_dvd_int @ ( divide_divide_int @ B2 @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.41/5.66 = ( dvd_dvd_int @ B2 @ C ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_dvd_div
% 5.41/5.66 thf(fact_1395_zero__less__Suc,axiom,
% 5.41/5.66 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_Suc
% 5.41/5.66 thf(fact_1396_less__Suc0,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = ( N = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_Suc0
% 5.41/5.66 thf(fact_1397_add__gr__0,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.66 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.66 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_gr_0
% 5.41/5.66 thf(fact_1398_one__eq__mult__iff,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ( suc @ zero_zero_nat )
% 5.41/5.66 = ( times_times_nat @ M @ N ) )
% 5.41/5.66 = ( ( M
% 5.41/5.66 = ( suc @ zero_zero_nat ) )
% 5.41/5.66 & ( N
% 5.41/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % one_eq_mult_iff
% 5.41/5.66 thf(fact_1399_mult__eq__1__iff,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ( times_times_nat @ M @ N )
% 5.41/5.66 = ( suc @ zero_zero_nat ) )
% 5.41/5.66 = ( ( M
% 5.41/5.66 = ( suc @ zero_zero_nat ) )
% 5.41/5.66 & ( N
% 5.41/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_eq_1_iff
% 5.41/5.66 thf(fact_1400_div__by__Suc__0,axiom,
% 5.41/5.66 ! [M: nat] :
% 5.41/5.66 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = M ) ).
% 5.41/5.66
% 5.41/5.66 % div_by_Suc_0
% 5.41/5.66 thf(fact_1401_zero__less__diff,axiom,
% 5.41/5.66 ! [N: nat,M: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.41/5.66 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_diff
% 5.41/5.66 thf(fact_1402_nat__mult__less__cancel__disj,axiom,
% 5.41/5.66 ! [K: nat,M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.66 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.66 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_mult_less_cancel_disj
% 5.41/5.66 thf(fact_1403_nat__0__less__mult__iff,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.41/5.66 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_0_less_mult_iff
% 5.41/5.66 thf(fact_1404_mult__less__cancel2,axiom,
% 5.41/5.66 ! [M: nat,K: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.41/5.66 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.66 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_less_cancel2
% 5.41/5.66 thf(fact_1405_div__less,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ M @ N )
% 5.41/5.66 => ( ( divide_divide_nat @ M @ N )
% 5.41/5.66 = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_less
% 5.41/5.66 thf(fact_1406_not__real__square__gt__zero,axiom,
% 5.41/5.66 ! [X4: real] :
% 5.41/5.66 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X4 @ X4 ) ) )
% 5.41/5.66 = ( X4 = zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_real_square_gt_zero
% 5.41/5.66 thf(fact_1407_diff__is__0__eq,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ( minus_minus_nat @ M @ N )
% 5.41/5.66 = zero_zero_nat )
% 5.41/5.66 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_is_0_eq
% 5.41/5.66 thf(fact_1408_diff__is__0__eq_H,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.66 => ( ( minus_minus_nat @ M @ N )
% 5.41/5.66 = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_is_0_eq'
% 5.41/5.66 thf(fact_1409_dvd__1__iff__1,axiom,
% 5.41/5.66 ! [M: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = ( M
% 5.41/5.66 = ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_1_iff_1
% 5.41/5.66 thf(fact_1410_dvd__1__left,axiom,
% 5.41/5.66 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_1_left
% 5.41/5.66 thf(fact_1411_less__one,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ N @ one_one_nat )
% 5.41/5.66 = ( N = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_one
% 5.41/5.66 thf(fact_1412_power__Suc__0,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.66 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_Suc_0
% 5.41/5.66 thf(fact_1413_nat__power__eq__Suc__0__iff,axiom,
% 5.41/5.66 ! [X4: nat,M: nat] :
% 5.41/5.66 ( ( ( power_power_nat @ X4 @ M )
% 5.41/5.66 = ( suc @ zero_zero_nat ) )
% 5.41/5.66 = ( ( M = zero_zero_nat )
% 5.41/5.66 | ( X4
% 5.41/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_power_eq_Suc_0_iff
% 5.41/5.66 thf(fact_1414_nat__zero__less__power__iff,axiom,
% 5.41/5.66 ! [X4: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X4 @ N ) )
% 5.41/5.66 = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.41/5.66 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_zero_less_power_iff
% 5.41/5.66 thf(fact_1415_nat__mult__div__cancel__disj,axiom,
% 5.41/5.66 ! [K: nat,M: nat,N: nat] :
% 5.41/5.66 ( ( ( K = zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.66 = zero_zero_nat ) )
% 5.41/5.66 & ( ( K != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.66 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_mult_div_cancel_disj
% 5.41/5.66 thf(fact_1416_mod__by__Suc__0,axiom,
% 5.41/5.66 ! [M: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % mod_by_Suc_0
% 5.41/5.66 thf(fact_1417_nat__mult__dvd__cancel__disj,axiom,
% 5.41/5.66 ! [K: nat,M: nat,N: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.66 = ( ( K = zero_zero_nat )
% 5.41/5.66 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_mult_dvd_cancel_disj
% 5.41/5.66 thf(fact_1418_nat__dvd__1__iff__1,axiom,
% 5.41/5.66 ! [M: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.41/5.66 = ( M = one_one_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_dvd_1_iff_1
% 5.41/5.66 thf(fact_1419_signed__take__bit__of__0,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % signed_take_bit_of_0
% 5.41/5.66 thf(fact_1420_dbl__simps_I2_J,axiom,
% 5.41/5.66 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.41/5.66 = zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % dbl_simps(2)
% 5.41/5.66 thf(fact_1421_dbl__simps_I2_J,axiom,
% 5.41/5.66 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.41/5.66 = zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % dbl_simps(2)
% 5.41/5.66 thf(fact_1422_dbl__simps_I2_J,axiom,
% 5.41/5.66 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % dbl_simps(2)
% 5.41/5.66 thf(fact_1423_add__le__same__cancel1,axiom,
% 5.41/5.66 ! [B2: real,A: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ ( plus_plus_real @ B2 @ A ) @ B2 )
% 5.41/5.66 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_le_same_cancel1
% 5.41/5.66 thf(fact_1424_add__le__same__cancel1,axiom,
% 5.41/5.66 ! [B2: rat,A: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B2 @ A ) @ B2 )
% 5.41/5.66 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_le_same_cancel1
% 5.41/5.66 thf(fact_1425_add__le__same__cancel1,axiom,
% 5.41/5.66 ! [B2: nat,A: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 5.41/5.66 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_le_same_cancel1
% 5.41/5.66 thf(fact_1426_add__le__same__cancel1,axiom,
% 5.41/5.66 ! [B2: int,A: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 5.41/5.66 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_le_same_cancel1
% 5.41/5.66 thf(fact_1427_add__le__same__cancel2,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B2 ) @ B2 )
% 5.41/5.66 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_le_same_cancel2
% 5.41/5.66 thf(fact_1428_add__le__same__cancel2,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B2 ) @ B2 )
% 5.41/5.66 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_le_same_cancel2
% 5.41/5.66 thf(fact_1429_add__le__same__cancel2,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 5.41/5.66 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_le_same_cancel2
% 5.41/5.66 thf(fact_1430_add__le__same__cancel2,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 5.41/5.66 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_le_same_cancel2
% 5.41/5.66 thf(fact_1431_le__add__same__cancel1,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_add_same_cancel1
% 5.41/5.66 thf(fact_1432_le__add__same__cancel1,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_add_same_cancel1
% 5.41/5.66 thf(fact_1433_le__add__same__cancel1,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_add_same_cancel1
% 5.41/5.66 thf(fact_1434_le__add__same__cancel1,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_add_same_cancel1
% 5.41/5.66 thf(fact_1435_le__add__same__cancel2,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_add_same_cancel2
% 5.41/5.66 thf(fact_1436_le__add__same__cancel2,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_add_same_cancel2
% 5.41/5.66 thf(fact_1437_le__add__same__cancel2,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_add_same_cancel2
% 5.41/5.66 thf(fact_1438_le__add__same__cancel2,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_add_same_cancel2
% 5.41/5.66 thf(fact_1439_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.41/5.66 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % double_add_le_zero_iff_single_add_le_zero
% 5.41/5.66 thf(fact_1440_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.41/5.66 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % double_add_le_zero_iff_single_add_le_zero
% 5.41/5.66 thf(fact_1441_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.41/5.66 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % double_add_le_zero_iff_single_add_le_zero
% 5.41/5.66 thf(fact_1442_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.41/5.66 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_le_double_add_iff_zero_le_single_add
% 5.41/5.66 thf(fact_1443_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.41/5.66 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_le_double_add_iff_zero_le_single_add
% 5.41/5.66 thf(fact_1444_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.41/5.66 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_le_double_add_iff_zero_le_single_add
% 5.41/5.66 thf(fact_1445_diff__ge__0__iff__ge,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_eq_real @ B2 @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_ge_0_iff_ge
% 5.41/5.66 thf(fact_1446_diff__ge__0__iff__ge,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_eq_rat @ B2 @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_ge_0_iff_ge
% 5.41/5.66 thf(fact_1447_diff__ge__0__iff__ge,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_eq_int @ B2 @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_ge_0_iff_ge
% 5.41/5.66 thf(fact_1448_add__less__same__cancel1,axiom,
% 5.41/5.66 ! [B2: real,A: real] :
% 5.41/5.66 ( ( ord_less_real @ ( plus_plus_real @ B2 @ A ) @ B2 )
% 5.41/5.66 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_less_same_cancel1
% 5.41/5.66 thf(fact_1449_add__less__same__cancel1,axiom,
% 5.41/5.66 ! [B2: rat,A: rat] :
% 5.41/5.66 ( ( ord_less_rat @ ( plus_plus_rat @ B2 @ A ) @ B2 )
% 5.41/5.66 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_less_same_cancel1
% 5.41/5.66 thf(fact_1450_add__less__same__cancel1,axiom,
% 5.41/5.66 ! [B2: nat,A: nat] :
% 5.41/5.66 ( ( ord_less_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 5.41/5.66 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_less_same_cancel1
% 5.41/5.66 thf(fact_1451_add__less__same__cancel1,axiom,
% 5.41/5.66 ! [B2: int,A: int] :
% 5.41/5.66 ( ( ord_less_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 5.41/5.66 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_less_same_cancel1
% 5.41/5.66 thf(fact_1452_add__less__same__cancel2,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ ( plus_plus_real @ A @ B2 ) @ B2 )
% 5.41/5.66 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_less_same_cancel2
% 5.41/5.66 thf(fact_1453_add__less__same__cancel2,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B2 ) @ B2 )
% 5.41/5.66 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_less_same_cancel2
% 5.41/5.66 thf(fact_1454_add__less__same__cancel2,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 5.41/5.66 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_less_same_cancel2
% 5.41/5.66 thf(fact_1455_add__less__same__cancel2,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 5.41/5.66 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_less_same_cancel2
% 5.41/5.66 thf(fact_1456_less__add__same__cancel1,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_real @ zero_zero_real @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_add_same_cancel1
% 5.41/5.66 thf(fact_1457_less__add__same__cancel1,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_rat @ zero_zero_rat @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_add_same_cancel1
% 5.41/5.66 thf(fact_1458_less__add__same__cancel1,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_add_same_cancel1
% 5.41/5.66 thf(fact_1459_less__add__same__cancel1,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_add_same_cancel1
% 5.41/5.66 thf(fact_1460_less__add__same__cancel2,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ A @ ( plus_plus_real @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_real @ zero_zero_real @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_add_same_cancel2
% 5.41/5.66 thf(fact_1461_less__add__same__cancel2,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_rat @ zero_zero_rat @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_add_same_cancel2
% 5.41/5.66 thf(fact_1462_less__add__same__cancel2,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_add_same_cancel2
% 5.41/5.66 thf(fact_1463_less__add__same__cancel2,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( ord_less_int @ A @ ( plus_plus_int @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_add_same_cancel2
% 5.41/5.66 thf(fact_1464_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.41/5.66 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % double_add_less_zero_iff_single_add_less_zero
% 5.41/5.66 thf(fact_1465_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.41/5.66 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % double_add_less_zero_iff_single_add_less_zero
% 5.41/5.66 thf(fact_1466_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.41/5.66 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % double_add_less_zero_iff_single_add_less_zero
% 5.41/5.66 thf(fact_1467_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.41/5.66 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_double_add_iff_zero_less_single_add
% 5.41/5.66 thf(fact_1468_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.41/5.66 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_double_add_iff_zero_less_single_add
% 5.41/5.66 thf(fact_1469_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.41/5.66 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_double_add_iff_zero_less_single_add
% 5.41/5.66 thf(fact_1470_diff__gt__0__iff__gt,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_real @ B2 @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_gt_0_iff_gt
% 5.41/5.66 thf(fact_1471_diff__gt__0__iff__gt,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_rat @ B2 @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_gt_0_iff_gt
% 5.41/5.66 thf(fact_1472_diff__gt__0__iff__gt,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B2 ) )
% 5.41/5.66 = ( ord_less_int @ B2 @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_gt_0_iff_gt
% 5.41/5.66 thf(fact_1473_mult__cancel__left1,axiom,
% 5.41/5.66 ! [C: complex,B2: complex] :
% 5.41/5.66 ( ( C
% 5.41/5.66 = ( times_times_complex @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_zero_complex )
% 5.41/5.66 | ( B2 = one_one_complex ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_left1
% 5.41/5.66 thf(fact_1474_mult__cancel__left1,axiom,
% 5.41/5.66 ! [C: real,B2: real] :
% 5.41/5.66 ( ( C
% 5.41/5.66 = ( times_times_real @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_zero_real )
% 5.41/5.66 | ( B2 = one_one_real ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_left1
% 5.41/5.66 thf(fact_1475_mult__cancel__left1,axiom,
% 5.41/5.66 ! [C: rat,B2: rat] :
% 5.41/5.66 ( ( C
% 5.41/5.66 = ( times_times_rat @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_zero_rat )
% 5.41/5.66 | ( B2 = one_one_rat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_left1
% 5.41/5.66 thf(fact_1476_mult__cancel__left1,axiom,
% 5.41/5.66 ! [C: int,B2: int] :
% 5.41/5.66 ( ( C
% 5.41/5.66 = ( times_times_int @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_zero_int )
% 5.41/5.66 | ( B2 = one_one_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_left1
% 5.41/5.66 thf(fact_1477_mult__cancel__left2,axiom,
% 5.41/5.66 ! [C: complex,A: complex] :
% 5.41/5.66 ( ( ( times_times_complex @ C @ A )
% 5.41/5.66 = C )
% 5.41/5.66 = ( ( C = zero_zero_complex )
% 5.41/5.66 | ( A = one_one_complex ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_left2
% 5.41/5.66 thf(fact_1478_mult__cancel__left2,axiom,
% 5.41/5.66 ! [C: real,A: real] :
% 5.41/5.66 ( ( ( times_times_real @ C @ A )
% 5.41/5.66 = C )
% 5.41/5.66 = ( ( C = zero_zero_real )
% 5.41/5.66 | ( A = one_one_real ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_left2
% 5.41/5.66 thf(fact_1479_mult__cancel__left2,axiom,
% 5.41/5.66 ! [C: rat,A: rat] :
% 5.41/5.66 ( ( ( times_times_rat @ C @ A )
% 5.41/5.66 = C )
% 5.41/5.66 = ( ( C = zero_zero_rat )
% 5.41/5.66 | ( A = one_one_rat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_left2
% 5.41/5.66 thf(fact_1480_mult__cancel__left2,axiom,
% 5.41/5.66 ! [C: int,A: int] :
% 5.41/5.66 ( ( ( times_times_int @ C @ A )
% 5.41/5.66 = C )
% 5.41/5.66 = ( ( C = zero_zero_int )
% 5.41/5.66 | ( A = one_one_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_left2
% 5.41/5.66 thf(fact_1481_mult__cancel__right1,axiom,
% 5.41/5.66 ! [C: complex,B2: complex] :
% 5.41/5.66 ( ( C
% 5.41/5.66 = ( times_times_complex @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_zero_complex )
% 5.41/5.66 | ( B2 = one_one_complex ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_right1
% 5.41/5.66 thf(fact_1482_mult__cancel__right1,axiom,
% 5.41/5.66 ! [C: real,B2: real] :
% 5.41/5.66 ( ( C
% 5.41/5.66 = ( times_times_real @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_zero_real )
% 5.41/5.66 | ( B2 = one_one_real ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_right1
% 5.41/5.66 thf(fact_1483_mult__cancel__right1,axiom,
% 5.41/5.66 ! [C: rat,B2: rat] :
% 5.41/5.66 ( ( C
% 5.41/5.66 = ( times_times_rat @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_zero_rat )
% 5.41/5.66 | ( B2 = one_one_rat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_right1
% 5.41/5.66 thf(fact_1484_mult__cancel__right1,axiom,
% 5.41/5.66 ! [C: int,B2: int] :
% 5.41/5.66 ( ( C
% 5.41/5.66 = ( times_times_int @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_zero_int )
% 5.41/5.66 | ( B2 = one_one_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_right1
% 5.41/5.66 thf(fact_1485_mult__cancel__right2,axiom,
% 5.41/5.66 ! [A: complex,C: complex] :
% 5.41/5.66 ( ( ( times_times_complex @ A @ C )
% 5.41/5.66 = C )
% 5.41/5.66 = ( ( C = zero_zero_complex )
% 5.41/5.66 | ( A = one_one_complex ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_right2
% 5.41/5.66 thf(fact_1486_mult__cancel__right2,axiom,
% 5.41/5.66 ! [A: real,C: real] :
% 5.41/5.66 ( ( ( times_times_real @ A @ C )
% 5.41/5.66 = C )
% 5.41/5.66 = ( ( C = zero_zero_real )
% 5.41/5.66 | ( A = one_one_real ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_right2
% 5.41/5.66 thf(fact_1487_mult__cancel__right2,axiom,
% 5.41/5.66 ! [A: rat,C: rat] :
% 5.41/5.66 ( ( ( times_times_rat @ A @ C )
% 5.41/5.66 = C )
% 5.41/5.66 = ( ( C = zero_zero_rat )
% 5.41/5.66 | ( A = one_one_rat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_right2
% 5.41/5.66 thf(fact_1488_mult__cancel__right2,axiom,
% 5.41/5.66 ! [A: int,C: int] :
% 5.41/5.66 ( ( ( times_times_int @ A @ C )
% 5.41/5.66 = C )
% 5.41/5.66 = ( ( C = zero_zero_int )
% 5.41/5.66 | ( A = one_one_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_cancel_right2
% 5.41/5.66 thf(fact_1489_sum__squares__eq__zero__iff,axiom,
% 5.41/5.66 ! [X4: real,Y3: real] :
% 5.41/5.66 ( ( ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y3 @ Y3 ) )
% 5.41/5.66 = zero_zero_real )
% 5.41/5.66 = ( ( X4 = zero_zero_real )
% 5.41/5.66 & ( Y3 = zero_zero_real ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_squares_eq_zero_iff
% 5.41/5.66 thf(fact_1490_sum__squares__eq__zero__iff,axiom,
% 5.41/5.66 ! [X4: rat,Y3: rat] :
% 5.41/5.66 ( ( ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y3 @ Y3 ) )
% 5.41/5.66 = zero_zero_rat )
% 5.41/5.66 = ( ( X4 = zero_zero_rat )
% 5.41/5.66 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_squares_eq_zero_iff
% 5.41/5.66 thf(fact_1491_sum__squares__eq__zero__iff,axiom,
% 5.41/5.66 ! [X4: int,Y3: int] :
% 5.41/5.66 ( ( ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y3 @ Y3 ) )
% 5.41/5.66 = zero_zero_int )
% 5.41/5.66 = ( ( X4 = zero_zero_int )
% 5.41/5.66 & ( Y3 = zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_squares_eq_zero_iff
% 5.41/5.66 thf(fact_1492_div__mult__mult1__if,axiom,
% 5.41/5.66 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.66 ( ( ( C = zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) )
% 5.41/5.66 = zero_zero_nat ) )
% 5.41/5.66 & ( ( C != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) )
% 5.41/5.66 = ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_mult1_if
% 5.41/5.66 thf(fact_1493_div__mult__mult1__if,axiom,
% 5.41/5.66 ! [C: int,A: int,B2: int] :
% 5.41/5.66 ( ( ( C = zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.41/5.66 = zero_zero_int ) )
% 5.41/5.66 & ( ( C != zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.41/5.66 = ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_mult1_if
% 5.41/5.66 thf(fact_1494_div__mult__mult2,axiom,
% 5.41/5.66 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.66 ( ( C != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) )
% 5.41/5.66 = ( divide_divide_nat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_mult2
% 5.41/5.66 thf(fact_1495_div__mult__mult2,axiom,
% 5.41/5.66 ! [C: int,A: int,B2: int] :
% 5.41/5.66 ( ( C != zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 5.41/5.66 = ( divide_divide_int @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_mult2
% 5.41/5.66 thf(fact_1496_div__mult__mult1,axiom,
% 5.41/5.66 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.66 ( ( C != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) )
% 5.41/5.66 = ( divide_divide_nat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_mult1
% 5.41/5.66 thf(fact_1497_div__mult__mult1,axiom,
% 5.41/5.66 ! [C: int,A: int,B2: int] :
% 5.41/5.66 ( ( C != zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.41/5.66 = ( divide_divide_int @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_mult1
% 5.41/5.66 thf(fact_1498_nonzero__mult__div__cancel__left,axiom,
% 5.41/5.66 ! [A: complex,B2: complex] :
% 5.41/5.66 ( ( A != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B2 ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_div_cancel_left
% 5.41/5.66 thf(fact_1499_nonzero__mult__div__cancel__left,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( A != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ ( times_times_real @ A @ B2 ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_div_cancel_left
% 5.41/5.66 thf(fact_1500_nonzero__mult__div__cancel__left,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( A != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B2 ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_div_cancel_left
% 5.41/5.66 thf(fact_1501_nonzero__mult__div__cancel__left,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( A != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B2 ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_div_cancel_left
% 5.41/5.66 thf(fact_1502_nonzero__mult__div__cancel__left,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( A != zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ ( times_times_int @ A @ B2 ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_div_cancel_left
% 5.41/5.66 thf(fact_1503_nonzero__mult__div__cancel__right,axiom,
% 5.41/5.66 ! [B2: complex,A: complex] :
% 5.41/5.66 ( ( B2 != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B2 ) @ B2 )
% 5.41/5.66 = A ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_div_cancel_right
% 5.41/5.66 thf(fact_1504_nonzero__mult__div__cancel__right,axiom,
% 5.41/5.66 ! [B2: real,A: real] :
% 5.41/5.66 ( ( B2 != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ ( times_times_real @ A @ B2 ) @ B2 )
% 5.41/5.66 = A ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_div_cancel_right
% 5.41/5.66 thf(fact_1505_nonzero__mult__div__cancel__right,axiom,
% 5.41/5.66 ! [B2: rat,A: rat] :
% 5.41/5.66 ( ( B2 != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B2 ) @ B2 )
% 5.41/5.66 = A ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_div_cancel_right
% 5.41/5.66 thf(fact_1506_nonzero__mult__div__cancel__right,axiom,
% 5.41/5.66 ! [B2: nat,A: nat] :
% 5.41/5.66 ( ( B2 != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B2 ) @ B2 )
% 5.41/5.66 = A ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_div_cancel_right
% 5.41/5.66 thf(fact_1507_nonzero__mult__div__cancel__right,axiom,
% 5.41/5.66 ! [B2: int,A: int] :
% 5.41/5.66 ( ( B2 != zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ ( times_times_int @ A @ B2 ) @ B2 )
% 5.41/5.66 = A ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_div_cancel_right
% 5.41/5.66 thf(fact_1508_mult__divide__mult__cancel__left__if,axiom,
% 5.41/5.66 ! [C: complex,A: complex,B2: complex] :
% 5.41/5.66 ( ( ( C = zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B2 ) )
% 5.41/5.66 = zero_zero_complex ) )
% 5.41/5.66 & ( ( C != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B2 ) )
% 5.41/5.66 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_divide_mult_cancel_left_if
% 5.41/5.66 thf(fact_1509_mult__divide__mult__cancel__left__if,axiom,
% 5.41/5.66 ! [C: real,A: real,B2: real] :
% 5.41/5.66 ( ( ( C = zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.41/5.66 = zero_zero_real ) )
% 5.41/5.66 & ( ( C != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.41/5.66 = ( divide_divide_real @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_divide_mult_cancel_left_if
% 5.41/5.66 thf(fact_1510_mult__divide__mult__cancel__left__if,axiom,
% 5.41/5.66 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.66 ( ( ( C = zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.41/5.66 = zero_zero_rat ) )
% 5.41/5.66 & ( ( C != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.41/5.66 = ( divide_divide_rat @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_divide_mult_cancel_left_if
% 5.41/5.66 thf(fact_1511_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.41/5.66 ! [C: complex,A: complex,B2: complex] :
% 5.41/5.66 ( ( C != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B2 ) )
% 5.41/5.66 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_left
% 5.41/5.66 thf(fact_1512_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.41/5.66 ! [C: real,A: real,B2: real] :
% 5.41/5.66 ( ( C != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.41/5.66 = ( divide_divide_real @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_left
% 5.41/5.66 thf(fact_1513_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.41/5.66 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.66 ( ( C != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.41/5.66 = ( divide_divide_rat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_left
% 5.41/5.66 thf(fact_1514_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.41/5.66 ! [C: complex,A: complex,B2: complex] :
% 5.41/5.66 ( ( C != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B2 @ C ) )
% 5.41/5.66 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_left2
% 5.41/5.66 thf(fact_1515_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.41/5.66 ! [C: real,A: real,B2: real] :
% 5.41/5.66 ( ( C != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B2 @ C ) )
% 5.41/5.66 = ( divide_divide_real @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_left2
% 5.41/5.66 thf(fact_1516_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.41/5.66 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.66 ( ( C != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B2 @ C ) )
% 5.41/5.66 = ( divide_divide_rat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_left2
% 5.41/5.66 thf(fact_1517_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.41/5.66 ! [C: complex,A: complex,B2: complex] :
% 5.41/5.66 ( ( C != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B2 @ C ) )
% 5.41/5.66 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_right
% 5.41/5.66 thf(fact_1518_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.41/5.66 ! [C: real,A: real,B2: real] :
% 5.41/5.66 ( ( C != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 5.41/5.66 = ( divide_divide_real @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_right
% 5.41/5.66 thf(fact_1519_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.41/5.66 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.66 ( ( C != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) )
% 5.41/5.66 = ( divide_divide_rat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_right
% 5.41/5.66 thf(fact_1520_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.41/5.66 ! [C: complex,A: complex,B2: complex] :
% 5.41/5.66 ( ( C != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B2 ) )
% 5.41/5.66 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_right2
% 5.41/5.66 thf(fact_1521_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.41/5.66 ! [C: real,A: real,B2: real] :
% 5.41/5.66 ( ( C != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B2 ) )
% 5.41/5.66 = ( divide_divide_real @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_right2
% 5.41/5.66 thf(fact_1522_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.41/5.66 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.66 ( ( C != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B2 ) )
% 5.41/5.66 = ( divide_divide_rat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_mult_divide_mult_cancel_right2
% 5.41/5.66 thf(fact_1523_diff__numeral__special_I9_J,axiom,
% 5.41/5.66 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.41/5.66 = zero_zero_complex ) ).
% 5.41/5.66
% 5.41/5.66 % diff_numeral_special(9)
% 5.41/5.66 thf(fact_1524_diff__numeral__special_I9_J,axiom,
% 5.41/5.66 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.41/5.66 = zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % diff_numeral_special(9)
% 5.41/5.66 thf(fact_1525_diff__numeral__special_I9_J,axiom,
% 5.41/5.66 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.41/5.66 = zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % diff_numeral_special(9)
% 5.41/5.66 thf(fact_1526_diff__numeral__special_I9_J,axiom,
% 5.41/5.66 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % diff_numeral_special(9)
% 5.41/5.66 thf(fact_1527_diff__add__zero,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % diff_add_zero
% 5.41/5.66 thf(fact_1528_div__self,axiom,
% 5.41/5.66 ! [A: complex] :
% 5.41/5.66 ( ( A != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.41/5.66 = one_one_complex ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_self
% 5.41/5.66 thf(fact_1529_div__self,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( A != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ A @ A )
% 5.41/5.66 = one_one_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_self
% 5.41/5.66 thf(fact_1530_div__self,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( A != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ A @ A )
% 5.41/5.66 = one_one_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_self
% 5.41/5.66 thf(fact_1531_div__self,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( A != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ A @ A )
% 5.41/5.66 = one_one_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_self
% 5.41/5.66 thf(fact_1532_div__self,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( A != zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ A @ A )
% 5.41/5.66 = one_one_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_self
% 5.41/5.66 thf(fact_1533_divide__eq__1__iff,axiom,
% 5.41/5.66 ! [A: complex,B2: complex] :
% 5.41/5.66 ( ( ( divide1717551699836669952omplex @ A @ B2 )
% 5.41/5.66 = one_one_complex )
% 5.41/5.66 = ( ( B2 != zero_zero_complex )
% 5.41/5.66 & ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_1_iff
% 5.41/5.66 thf(fact_1534_divide__eq__1__iff,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ( divide_divide_real @ A @ B2 )
% 5.41/5.66 = one_one_real )
% 5.41/5.66 = ( ( B2 != zero_zero_real )
% 5.41/5.66 & ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_1_iff
% 5.41/5.66 thf(fact_1535_divide__eq__1__iff,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ( divide_divide_rat @ A @ B2 )
% 5.41/5.66 = one_one_rat )
% 5.41/5.66 = ( ( B2 != zero_zero_rat )
% 5.41/5.66 & ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_1_iff
% 5.41/5.66 thf(fact_1536_one__eq__divide__iff,axiom,
% 5.41/5.66 ! [A: complex,B2: complex] :
% 5.41/5.66 ( ( one_one_complex
% 5.41/5.66 = ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.41/5.66 = ( ( B2 != zero_zero_complex )
% 5.41/5.66 & ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % one_eq_divide_iff
% 5.41/5.66 thf(fact_1537_one__eq__divide__iff,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( one_one_real
% 5.41/5.66 = ( divide_divide_real @ A @ B2 ) )
% 5.41/5.66 = ( ( B2 != zero_zero_real )
% 5.41/5.66 & ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % one_eq_divide_iff
% 5.41/5.66 thf(fact_1538_one__eq__divide__iff,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( one_one_rat
% 5.41/5.66 = ( divide_divide_rat @ A @ B2 ) )
% 5.41/5.66 = ( ( B2 != zero_zero_rat )
% 5.41/5.66 & ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % one_eq_divide_iff
% 5.41/5.66 thf(fact_1539_divide__self,axiom,
% 5.41/5.66 ! [A: complex] :
% 5.41/5.66 ( ( A != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.41/5.66 = one_one_complex ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_self
% 5.41/5.66 thf(fact_1540_divide__self,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( A != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ A @ A )
% 5.41/5.66 = one_one_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_self
% 5.41/5.66 thf(fact_1541_divide__self,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( A != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ A @ A )
% 5.41/5.66 = one_one_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_self
% 5.41/5.66 thf(fact_1542_divide__self__if,axiom,
% 5.41/5.66 ! [A: complex] :
% 5.41/5.66 ( ( ( A = zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.41/5.66 = zero_zero_complex ) )
% 5.41/5.66 & ( ( A != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.41/5.66 = one_one_complex ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_self_if
% 5.41/5.66 thf(fact_1543_divide__self__if,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ( A = zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ A @ A )
% 5.41/5.66 = zero_zero_real ) )
% 5.41/5.66 & ( ( A != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ A @ A )
% 5.41/5.66 = one_one_real ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_self_if
% 5.41/5.66 thf(fact_1544_divide__self__if,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ( A = zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ A @ A )
% 5.41/5.66 = zero_zero_rat ) )
% 5.41/5.66 & ( ( A != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ A @ A )
% 5.41/5.66 = one_one_rat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_self_if
% 5.41/5.66 thf(fact_1545_divide__eq__eq__1,axiom,
% 5.41/5.66 ! [B2: real,A: real] :
% 5.41/5.66 ( ( ( divide_divide_real @ B2 @ A )
% 5.41/5.66 = one_one_real )
% 5.41/5.66 = ( ( A != zero_zero_real )
% 5.41/5.66 & ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_eq_1
% 5.41/5.66 thf(fact_1546_divide__eq__eq__1,axiom,
% 5.41/5.66 ! [B2: rat,A: rat] :
% 5.41/5.66 ( ( ( divide_divide_rat @ B2 @ A )
% 5.41/5.66 = one_one_rat )
% 5.41/5.66 = ( ( A != zero_zero_rat )
% 5.41/5.66 & ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_eq_1
% 5.41/5.66 thf(fact_1547_eq__divide__eq__1,axiom,
% 5.41/5.66 ! [B2: real,A: real] :
% 5.41/5.66 ( ( one_one_real
% 5.41/5.66 = ( divide_divide_real @ B2 @ A ) )
% 5.41/5.66 = ( ( A != zero_zero_real )
% 5.41/5.66 & ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % eq_divide_eq_1
% 5.41/5.66 thf(fact_1548_eq__divide__eq__1,axiom,
% 5.41/5.66 ! [B2: rat,A: rat] :
% 5.41/5.66 ( ( one_one_rat
% 5.41/5.66 = ( divide_divide_rat @ B2 @ A ) )
% 5.41/5.66 = ( ( A != zero_zero_rat )
% 5.41/5.66 & ( A = B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % eq_divide_eq_1
% 5.41/5.66 thf(fact_1549_one__divide__eq__0__iff,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.41/5.66 = zero_zero_real )
% 5.41/5.66 = ( A = zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % one_divide_eq_0_iff
% 5.41/5.66 thf(fact_1550_one__divide__eq__0__iff,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.41/5.66 = zero_zero_rat )
% 5.41/5.66 = ( A = zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % one_divide_eq_0_iff
% 5.41/5.66 thf(fact_1551_zero__eq__1__divide__iff,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( zero_zero_real
% 5.41/5.66 = ( divide_divide_real @ one_one_real @ A ) )
% 5.41/5.66 = ( A = zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_eq_1_divide_iff
% 5.41/5.66 thf(fact_1552_zero__eq__1__divide__iff,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( zero_zero_rat
% 5.41/5.66 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.41/5.66 = ( A = zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_eq_1_divide_iff
% 5.41/5.66 thf(fact_1553_dvd__times__right__cancel__iff,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.66 ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.66 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B2 @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.41/5.66 = ( dvd_dvd_Code_integer @ B2 @ C ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_times_right_cancel_iff
% 5.41/5.66 thf(fact_1554_dvd__times__right__cancel__iff,axiom,
% 5.41/5.66 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.66 ( ( A != zero_zero_nat )
% 5.41/5.66 => ( ( dvd_dvd_nat @ ( times_times_nat @ B2 @ A ) @ ( times_times_nat @ C @ A ) )
% 5.41/5.66 = ( dvd_dvd_nat @ B2 @ C ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_times_right_cancel_iff
% 5.41/5.66 thf(fact_1555_dvd__times__right__cancel__iff,axiom,
% 5.41/5.66 ! [A: int,B2: int,C: int] :
% 5.41/5.66 ( ( A != zero_zero_int )
% 5.41/5.66 => ( ( dvd_dvd_int @ ( times_times_int @ B2 @ A ) @ ( times_times_int @ C @ A ) )
% 5.41/5.66 = ( dvd_dvd_int @ B2 @ C ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_times_right_cancel_iff
% 5.41/5.66 thf(fact_1556_dvd__times__left__cancel__iff,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.66 ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.66 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B2 ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.41/5.66 = ( dvd_dvd_Code_integer @ B2 @ C ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_times_left_cancel_iff
% 5.41/5.66 thf(fact_1557_dvd__times__left__cancel__iff,axiom,
% 5.41/5.66 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.66 ( ( A != zero_zero_nat )
% 5.41/5.66 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ ( times_times_nat @ A @ C ) )
% 5.41/5.66 = ( dvd_dvd_nat @ B2 @ C ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_times_left_cancel_iff
% 5.41/5.66 thf(fact_1558_dvd__times__left__cancel__iff,axiom,
% 5.41/5.66 ! [A: int,B2: int,C: int] :
% 5.41/5.66 ( ( A != zero_zero_int )
% 5.41/5.66 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ ( times_times_int @ A @ C ) )
% 5.41/5.66 = ( dvd_dvd_int @ B2 @ C ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_times_left_cancel_iff
% 5.41/5.66 thf(fact_1559_dvd__mult__cancel__right,axiom,
% 5.41/5.66 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_z3403309356797280102nteger )
% 5.41/5.66 | ( dvd_dvd_Code_integer @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_cancel_right
% 5.41/5.66 thf(fact_1560_dvd__mult__cancel__right,axiom,
% 5.41/5.66 ! [A: real,C: real,B2: real] :
% 5.41/5.66 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_zero_real )
% 5.41/5.66 | ( dvd_dvd_real @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_cancel_right
% 5.41/5.66 thf(fact_1561_dvd__mult__cancel__right,axiom,
% 5.41/5.66 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.66 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_zero_rat )
% 5.41/5.66 | ( dvd_dvd_rat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_cancel_right
% 5.41/5.66 thf(fact_1562_dvd__mult__cancel__right,axiom,
% 5.41/5.66 ! [A: int,C: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 5.41/5.66 = ( ( C = zero_zero_int )
% 5.41/5.66 | ( dvd_dvd_int @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_cancel_right
% 5.41/5.66 thf(fact_1563_dvd__mult__cancel__left,axiom,
% 5.41/5.66 ! [C: code_integer,A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_z3403309356797280102nteger )
% 5.41/5.66 | ( dvd_dvd_Code_integer @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_cancel_left
% 5.41/5.66 thf(fact_1564_dvd__mult__cancel__left,axiom,
% 5.41/5.66 ! [C: real,A: real,B2: real] :
% 5.41/5.66 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_zero_real )
% 5.41/5.66 | ( dvd_dvd_real @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_cancel_left
% 5.41/5.66 thf(fact_1565_dvd__mult__cancel__left,axiom,
% 5.41/5.66 ! [C: rat,A: rat,B2: rat] :
% 5.41/5.66 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_zero_rat )
% 5.41/5.66 | ( dvd_dvd_rat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_cancel_left
% 5.41/5.66 thf(fact_1566_dvd__mult__cancel__left,axiom,
% 5.41/5.66 ! [C: int,A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.41/5.66 = ( ( C = zero_zero_int )
% 5.41/5.66 | ( dvd_dvd_int @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_cancel_left
% 5.41/5.66 thf(fact_1567_power__0__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.41/5.66 = zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % power_0_Suc
% 5.41/5.66 thf(fact_1568_power__0__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % power_0_Suc
% 5.41/5.66 thf(fact_1569_power__0__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.41/5.66 = zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % power_0_Suc
% 5.41/5.66 thf(fact_1570_power__0__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % power_0_Suc
% 5.41/5.66 thf(fact_1571_power__0__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.41/5.66 = zero_zero_complex ) ).
% 5.41/5.66
% 5.41/5.66 % power_0_Suc
% 5.41/5.66 thf(fact_1572_power__zero__numeral,axiom,
% 5.41/5.66 ! [K: num] :
% 5.41/5.66 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.41/5.66 = zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % power_zero_numeral
% 5.41/5.66 thf(fact_1573_power__zero__numeral,axiom,
% 5.41/5.66 ! [K: num] :
% 5.41/5.66 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % power_zero_numeral
% 5.41/5.66 thf(fact_1574_power__zero__numeral,axiom,
% 5.41/5.66 ! [K: num] :
% 5.41/5.66 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.41/5.66 = zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % power_zero_numeral
% 5.41/5.66 thf(fact_1575_power__zero__numeral,axiom,
% 5.41/5.66 ! [K: num] :
% 5.41/5.66 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % power_zero_numeral
% 5.41/5.66 thf(fact_1576_power__zero__numeral,axiom,
% 5.41/5.66 ! [K: num] :
% 5.41/5.66 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.41/5.66 = zero_zero_complex ) ).
% 5.41/5.66
% 5.41/5.66 % power_zero_numeral
% 5.41/5.66 thf(fact_1577_power__eq__0__iff,axiom,
% 5.41/5.66 ! [A: rat,N: nat] :
% 5.41/5.66 ( ( ( power_power_rat @ A @ N )
% 5.41/5.66 = zero_zero_rat )
% 5.41/5.66 = ( ( A = zero_zero_rat )
% 5.41/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_eq_0_iff
% 5.41/5.66 thf(fact_1578_power__eq__0__iff,axiom,
% 5.41/5.66 ! [A: nat,N: nat] :
% 5.41/5.66 ( ( ( power_power_nat @ A @ N )
% 5.41/5.66 = zero_zero_nat )
% 5.41/5.66 = ( ( A = zero_zero_nat )
% 5.41/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_eq_0_iff
% 5.41/5.66 thf(fact_1579_power__eq__0__iff,axiom,
% 5.41/5.66 ! [A: real,N: nat] :
% 5.41/5.66 ( ( ( power_power_real @ A @ N )
% 5.41/5.66 = zero_zero_real )
% 5.41/5.66 = ( ( A = zero_zero_real )
% 5.41/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_eq_0_iff
% 5.41/5.66 thf(fact_1580_power__eq__0__iff,axiom,
% 5.41/5.66 ! [A: int,N: nat] :
% 5.41/5.66 ( ( ( power_power_int @ A @ N )
% 5.41/5.66 = zero_zero_int )
% 5.41/5.66 = ( ( A = zero_zero_int )
% 5.41/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_eq_0_iff
% 5.41/5.66 thf(fact_1581_power__eq__0__iff,axiom,
% 5.41/5.66 ! [A: complex,N: nat] :
% 5.41/5.66 ( ( ( power_power_complex @ A @ N )
% 5.41/5.66 = zero_zero_complex )
% 5.41/5.66 = ( ( A = zero_zero_complex )
% 5.41/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_eq_0_iff
% 5.41/5.66 thf(fact_1582_unit__prod,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.66 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.41/5.66 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B2 ) @ one_one_Code_integer ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_prod
% 5.41/5.66 thf(fact_1583_unit__prod,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.66 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.41/5.66 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ one_one_nat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_prod
% 5.41/5.66 thf(fact_1584_unit__prod,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.66 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.41/5.66 => ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ one_one_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_prod
% 5.41/5.66 thf(fact_1585_dvd__add__times__triv__left__iff,axiom,
% 5.41/5.66 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_Code_integer @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_times_triv_left_iff
% 5.41/5.66 thf(fact_1586_dvd__add__times__triv__left__iff,axiom,
% 5.41/5.66 ! [A: real,C: real,B2: real] :
% 5.41/5.66 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_real @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_times_triv_left_iff
% 5.41/5.66 thf(fact_1587_dvd__add__times__triv__left__iff,axiom,
% 5.41/5.66 ! [A: rat,C: rat,B2: rat] :
% 5.41/5.66 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_rat @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_times_triv_left_iff
% 5.41/5.66 thf(fact_1588_dvd__add__times__triv__left__iff,axiom,
% 5.41/5.66 ! [A: nat,C: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_nat @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_times_triv_left_iff
% 5.41/5.66 thf(fact_1589_dvd__add__times__triv__left__iff,axiom,
% 5.41/5.66 ! [A: int,C: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_int @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_times_triv_left_iff
% 5.41/5.66 thf(fact_1590_dvd__add__times__triv__right__iff,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B2 @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.41/5.66 = ( dvd_dvd_Code_integer @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_times_triv_right_iff
% 5.41/5.66 thf(fact_1591_dvd__add__times__triv__right__iff,axiom,
% 5.41/5.66 ! [A: real,B2: real,C: real] :
% 5.41/5.66 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B2 @ ( times_times_real @ C @ A ) ) )
% 5.41/5.66 = ( dvd_dvd_real @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_times_triv_right_iff
% 5.41/5.66 thf(fact_1592_dvd__add__times__triv__right__iff,axiom,
% 5.41/5.66 ! [A: rat,B2: rat,C: rat] :
% 5.41/5.66 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B2 @ ( times_times_rat @ C @ A ) ) )
% 5.41/5.66 = ( dvd_dvd_rat @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_times_triv_right_iff
% 5.41/5.66 thf(fact_1593_dvd__add__times__triv__right__iff,axiom,
% 5.41/5.66 ! [A: nat,B2: nat,C: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B2 @ ( times_times_nat @ C @ A ) ) )
% 5.41/5.66 = ( dvd_dvd_nat @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_times_triv_right_iff
% 5.41/5.66 thf(fact_1594_dvd__add__times__triv__right__iff,axiom,
% 5.41/5.66 ! [A: int,B2: int,C: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B2 @ ( times_times_int @ C @ A ) ) )
% 5.41/5.66 = ( dvd_dvd_int @ A @ B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_add_times_triv_right_iff
% 5.41/5.66 thf(fact_1595_mod__mult__self1__is__0,axiom,
% 5.41/5.66 ! [B2: nat,A: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ ( times_times_nat @ B2 @ A ) @ B2 )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % mod_mult_self1_is_0
% 5.41/5.66 thf(fact_1596_mod__mult__self1__is__0,axiom,
% 5.41/5.66 ! [B2: int,A: int] :
% 5.41/5.66 ( ( modulo_modulo_int @ ( times_times_int @ B2 @ A ) @ B2 )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % mod_mult_self1_is_0
% 5.41/5.66 thf(fact_1597_mod__mult__self1__is__0,axiom,
% 5.41/5.66 ! [B2: code_integer,A: code_integer] :
% 5.41/5.66 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B2 @ A ) @ B2 )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ).
% 5.41/5.66
% 5.41/5.66 % mod_mult_self1_is_0
% 5.41/5.66 thf(fact_1598_mod__mult__self2__is__0,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B2 ) @ B2 )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % mod_mult_self2_is_0
% 5.41/5.66 thf(fact_1599_mod__mult__self2__is__0,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( modulo_modulo_int @ ( times_times_int @ A @ B2 ) @ B2 )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % mod_mult_self2_is_0
% 5.41/5.66 thf(fact_1600_mod__mult__self2__is__0,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B2 ) @ B2 )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ).
% 5.41/5.66
% 5.41/5.66 % mod_mult_self2_is_0
% 5.41/5.66 thf(fact_1601_dvd__div__mult__self,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.41/5.66 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B2 @ A ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_div_mult_self
% 5.41/5.66 thf(fact_1602_dvd__div__mult__self,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ B2 )
% 5.41/5.66 => ( ( times_times_nat @ ( divide_divide_nat @ B2 @ A ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_div_mult_self
% 5.41/5.66 thf(fact_1603_dvd__div__mult__self,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ B2 )
% 5.41/5.66 => ( ( times_times_int @ ( divide_divide_int @ B2 @ A ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_div_mult_self
% 5.41/5.66 thf(fact_1604_dvd__mult__div__cancel,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.41/5.66 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B2 @ A ) )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_div_cancel
% 5.41/5.66 thf(fact_1605_dvd__mult__div__cancel,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ B2 )
% 5.41/5.66 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B2 @ A ) )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_div_cancel
% 5.41/5.66 thf(fact_1606_dvd__mult__div__cancel,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ B2 )
% 5.41/5.66 => ( ( times_times_int @ A @ ( divide_divide_int @ B2 @ A ) )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_mult_div_cancel
% 5.41/5.66 thf(fact_1607_mod__by__1,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % mod_by_1
% 5.41/5.66 thf(fact_1608_mod__by__1,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % mod_by_1
% 5.41/5.66 thf(fact_1609_mod__by__1,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ).
% 5.41/5.66
% 5.41/5.66 % mod_by_1
% 5.41/5.66 thf(fact_1610_bits__mod__by__1,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % bits_mod_by_1
% 5.41/5.66 thf(fact_1611_bits__mod__by__1,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % bits_mod_by_1
% 5.41/5.66 thf(fact_1612_bits__mod__by__1,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ).
% 5.41/5.66
% 5.41/5.66 % bits_mod_by_1
% 5.41/5.66 thf(fact_1613_unit__div,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.66 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.41/5.66 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B2 ) @ one_one_Code_integer ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div
% 5.41/5.66 thf(fact_1614_unit__div,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.66 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.41/5.66 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B2 ) @ one_one_nat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div
% 5.41/5.66 thf(fact_1615_unit__div,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.66 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.41/5.66 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B2 ) @ one_one_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div
% 5.41/5.66 thf(fact_1616_unit__div__1__unit,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.66 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div_1_unit
% 5.41/5.66 thf(fact_1617_unit__div__1__unit,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.66 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div_1_unit
% 5.41/5.66 thf(fact_1618_unit__div__1__unit,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.66 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div_1_unit
% 5.41/5.66 thf(fact_1619_unit__div__1__div__1,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.66 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.41/5.66 = A ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div_1_div_1
% 5.41/5.66 thf(fact_1620_unit__div__1__div__1,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.41/5.66 = A ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div_1_div_1
% 5.41/5.66 thf(fact_1621_unit__div__1__div__1,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.66 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.41/5.66 = A ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div_1_div_1
% 5.41/5.66 thf(fact_1622_div__add,axiom,
% 5.41/5.66 ! [C: code_integer,A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.41/5.66 => ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.41/5.66 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) @ C )
% 5.41/5.66 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B2 @ C ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_add
% 5.41/5.66 thf(fact_1623_div__add,axiom,
% 5.41/5.66 ! [C: nat,A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ C @ A )
% 5.41/5.66 => ( ( dvd_dvd_nat @ C @ B2 )
% 5.41/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 5.41/5.66 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B2 @ C ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_add
% 5.41/5.66 thf(fact_1624_div__add,axiom,
% 5.41/5.66 ! [C: int,A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ C @ A )
% 5.41/5.66 => ( ( dvd_dvd_int @ C @ B2 )
% 5.41/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.41/5.66 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B2 @ C ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_add
% 5.41/5.66 thf(fact_1625_div__diff,axiom,
% 5.41/5.66 ! [C: code_integer,A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.41/5.66 => ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.41/5.66 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B2 ) @ C )
% 5.41/5.66 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B2 @ C ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_diff
% 5.41/5.66 thf(fact_1626_div__diff,axiom,
% 5.41/5.66 ! [C: int,A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ C @ A )
% 5.41/5.66 => ( ( dvd_dvd_int @ C @ B2 )
% 5.41/5.66 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B2 ) @ C )
% 5.41/5.66 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B2 @ C ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_diff
% 5.41/5.66 thf(fact_1627_mod__div__trivial,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B2 ) @ B2 )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % mod_div_trivial
% 5.41/5.66 thf(fact_1628_mod__div__trivial,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B2 ) @ B2 )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % mod_div_trivial
% 5.41/5.66 thf(fact_1629_mod__div__trivial,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B2 ) @ B2 )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ).
% 5.41/5.66
% 5.41/5.66 % mod_div_trivial
% 5.41/5.66 thf(fact_1630_bits__mod__div__trivial,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B2 ) @ B2 )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % bits_mod_div_trivial
% 5.41/5.66 thf(fact_1631_bits__mod__div__trivial,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B2 ) @ B2 )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % bits_mod_div_trivial
% 5.41/5.66 thf(fact_1632_bits__mod__div__trivial,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B2 ) @ B2 )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ).
% 5.41/5.66
% 5.41/5.66 % bits_mod_div_trivial
% 5.41/5.66 thf(fact_1633_zmod__numeral__Bit0,axiom,
% 5.41/5.66 ! [V: num,W: num] :
% 5.41/5.66 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.41/5.66 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zmod_numeral_Bit0
% 5.41/5.66 thf(fact_1634_dvd__imp__mod__0,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ B2 )
% 5.41/5.66 => ( ( modulo_modulo_nat @ B2 @ A )
% 5.41/5.66 = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_imp_mod_0
% 5.41/5.66 thf(fact_1635_dvd__imp__mod__0,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ B2 )
% 5.41/5.66 => ( ( modulo_modulo_int @ B2 @ A )
% 5.41/5.66 = zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_imp_mod_0
% 5.41/5.66 thf(fact_1636_dvd__imp__mod__0,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.41/5.66 => ( ( modulo364778990260209775nteger @ B2 @ A )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.66
% 5.41/5.66 % dvd_imp_mod_0
% 5.41/5.66 thf(fact_1637_Suc__pred,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.41/5.66 = N ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_pred
% 5.41/5.66 thf(fact_1638_one__le__mult__iff,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.41/5.66 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.41/5.66 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % one_le_mult_iff
% 5.41/5.66 thf(fact_1639_nat__mult__le__cancel__disj,axiom,
% 5.41/5.66 ! [K: nat,M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.66 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.66 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_mult_le_cancel_disj
% 5.41/5.66 thf(fact_1640_mult__le__cancel2,axiom,
% 5.41/5.66 ! [M: nat,K: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.41/5.66 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.66 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_le_cancel2
% 5.41/5.66 thf(fact_1641_div__mult__self1__is__m,axiom,
% 5.41/5.66 ! [N: nat,M: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.41/5.66 = M ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_self1_is_m
% 5.41/5.66 thf(fact_1642_div__mult__self__is__m,axiom,
% 5.41/5.66 ! [N: nat,M: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.41/5.66 = M ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_self_is_m
% 5.41/5.66 thf(fact_1643_signed__take__bit__Suc__1,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.41/5.66 = one_one_int ) ).
% 5.41/5.66
% 5.41/5.66 % signed_take_bit_Suc_1
% 5.41/5.66 thf(fact_1644_signed__take__bit__numeral__of__1,axiom,
% 5.41/5.66 ! [K: num] :
% 5.41/5.66 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.41/5.66 = one_one_int ) ).
% 5.41/5.66
% 5.41/5.66 % signed_take_bit_numeral_of_1
% 5.41/5.66 thf(fact_1645_dbl__simps_I5_J,axiom,
% 5.41/5.66 ! [K: num] :
% 5.41/5.66 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.41/5.66 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dbl_simps(5)
% 5.41/5.66 thf(fact_1646_dbl__simps_I5_J,axiom,
% 5.41/5.66 ! [K: num] :
% 5.41/5.66 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.41/5.66 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dbl_simps(5)
% 5.41/5.66 thf(fact_1647_dbl__simps_I5_J,axiom,
% 5.41/5.66 ! [K: num] :
% 5.41/5.66 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.41/5.66 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dbl_simps(5)
% 5.41/5.66 thf(fact_1648_dbl__simps_I5_J,axiom,
% 5.41/5.66 ! [K: num] :
% 5.41/5.66 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.41/5.66 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % dbl_simps(5)
% 5.41/5.66 thf(fact_1649_zero__le__divide__1__iff,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.41/5.66 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_le_divide_1_iff
% 5.41/5.66 thf(fact_1650_zero__le__divide__1__iff,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.41/5.66 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_le_divide_1_iff
% 5.41/5.66 thf(fact_1651_divide__le__0__1__iff,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.41/5.66 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_le_0_1_iff
% 5.41/5.66 thf(fact_1652_divide__le__0__1__iff,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.41/5.66 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_le_0_1_iff
% 5.41/5.66 thf(fact_1653_zero__less__divide__1__iff,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.41/5.66 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_divide_1_iff
% 5.41/5.66 thf(fact_1654_zero__less__divide__1__iff,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.41/5.66 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_divide_1_iff
% 5.41/5.66 thf(fact_1655_less__divide__eq__1__pos,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.66 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_real @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_divide_eq_1_pos
% 5.41/5.66 thf(fact_1656_less__divide__eq__1__pos,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.66 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_rat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_divide_eq_1_pos
% 5.41/5.66 thf(fact_1657_less__divide__eq__1__neg,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.66 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_real @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_divide_eq_1_neg
% 5.41/5.66 thf(fact_1658_less__divide__eq__1__neg,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.66 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_rat @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_divide_eq_1_neg
% 5.41/5.66 thf(fact_1659_divide__less__eq__1__pos,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.66 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 5.41/5.66 = ( ord_less_real @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_less_eq_1_pos
% 5.41/5.66 thf(fact_1660_divide__less__eq__1__pos,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.66 => ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ A ) @ one_one_rat )
% 5.41/5.66 = ( ord_less_rat @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_less_eq_1_pos
% 5.41/5.66 thf(fact_1661_divide__less__eq__1__neg,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.66 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 5.41/5.66 = ( ord_less_real @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_less_eq_1_neg
% 5.41/5.66 thf(fact_1662_divide__less__eq__1__neg,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.66 => ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ A ) @ one_one_rat )
% 5.41/5.66 = ( ord_less_rat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_less_eq_1_neg
% 5.41/5.66 thf(fact_1663_divide__less__0__1__iff,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.41/5.66 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_less_0_1_iff
% 5.41/5.66 thf(fact_1664_divide__less__0__1__iff,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.41/5.66 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_less_0_1_iff
% 5.41/5.66 thf(fact_1665_divide__eq__eq__numeral1_I1_J,axiom,
% 5.41/5.66 ! [B2: complex,W: num,A: complex] :
% 5.41/5.66 ( ( ( divide1717551699836669952omplex @ B2 @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.66 = A )
% 5.41/5.66 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.41/5.66 != zero_zero_complex )
% 5.41/5.66 => ( B2
% 5.41/5.66 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.41/5.66 & ( ( ( numera6690914467698888265omplex @ W )
% 5.41/5.66 = zero_zero_complex )
% 5.41/5.66 => ( A = zero_zero_complex ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_eq_numeral1(1)
% 5.41/5.66 thf(fact_1666_divide__eq__eq__numeral1_I1_J,axiom,
% 5.41/5.66 ! [B2: real,W: num,A: real] :
% 5.41/5.66 ( ( ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) )
% 5.41/5.66 = A )
% 5.41/5.66 = ( ( ( ( numeral_numeral_real @ W )
% 5.41/5.66 != zero_zero_real )
% 5.41/5.66 => ( B2
% 5.41/5.66 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.41/5.66 & ( ( ( numeral_numeral_real @ W )
% 5.41/5.66 = zero_zero_real )
% 5.41/5.66 => ( A = zero_zero_real ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_eq_numeral1(1)
% 5.41/5.66 thf(fact_1667_divide__eq__eq__numeral1_I1_J,axiom,
% 5.41/5.66 ! [B2: rat,W: num,A: rat] :
% 5.41/5.66 ( ( ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) )
% 5.41/5.66 = A )
% 5.41/5.66 = ( ( ( ( numeral_numeral_rat @ W )
% 5.41/5.66 != zero_zero_rat )
% 5.41/5.66 => ( B2
% 5.41/5.66 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.41/5.66 & ( ( ( numeral_numeral_rat @ W )
% 5.41/5.66 = zero_zero_rat )
% 5.41/5.66 => ( A = zero_zero_rat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_eq_eq_numeral1(1)
% 5.41/5.66 thf(fact_1668_eq__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.66 ! [A: complex,B2: complex,W: num] :
% 5.41/5.66 ( ( A
% 5.41/5.66 = ( divide1717551699836669952omplex @ B2 @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.66 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.41/5.66 != zero_zero_complex )
% 5.41/5.66 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.66 = B2 ) )
% 5.41/5.66 & ( ( ( numera6690914467698888265omplex @ W )
% 5.41/5.66 = zero_zero_complex )
% 5.41/5.66 => ( A = zero_zero_complex ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % eq_divide_eq_numeral1(1)
% 5.41/5.66 thf(fact_1669_eq__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.66 ! [A: real,B2: real,W: num] :
% 5.41/5.66 ( ( A
% 5.41/5.66 = ( divide_divide_real @ B2 @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.66 = ( ( ( ( numeral_numeral_real @ W )
% 5.41/5.66 != zero_zero_real )
% 5.41/5.66 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.41/5.66 = B2 ) )
% 5.41/5.66 & ( ( ( numeral_numeral_real @ W )
% 5.41/5.66 = zero_zero_real )
% 5.41/5.66 => ( A = zero_zero_real ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % eq_divide_eq_numeral1(1)
% 5.41/5.66 thf(fact_1670_eq__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.66 ! [A: rat,B2: rat,W: num] :
% 5.41/5.66 ( ( A
% 5.41/5.66 = ( divide_divide_rat @ B2 @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.66 = ( ( ( ( numeral_numeral_rat @ W )
% 5.41/5.66 != zero_zero_rat )
% 5.41/5.66 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.41/5.66 = B2 ) )
% 5.41/5.66 & ( ( ( numeral_numeral_rat @ W )
% 5.41/5.66 = zero_zero_rat )
% 5.41/5.66 => ( A = zero_zero_rat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % eq_divide_eq_numeral1(1)
% 5.41/5.66 thf(fact_1671_nonzero__divide__mult__cancel__left,axiom,
% 5.41/5.66 ! [A: complex,B2: complex] :
% 5.41/5.66 ( ( A != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B2 ) )
% 5.41/5.66 = ( divide1717551699836669952omplex @ one_one_complex @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_divide_mult_cancel_left
% 5.41/5.66 thf(fact_1672_nonzero__divide__mult__cancel__left,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( A != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B2 ) )
% 5.41/5.66 = ( divide_divide_real @ one_one_real @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_divide_mult_cancel_left
% 5.41/5.66 thf(fact_1673_nonzero__divide__mult__cancel__left,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( A != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B2 ) )
% 5.41/5.66 = ( divide_divide_rat @ one_one_rat @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_divide_mult_cancel_left
% 5.41/5.66 thf(fact_1674_nonzero__divide__mult__cancel__right,axiom,
% 5.41/5.66 ! [B2: complex,A: complex] :
% 5.41/5.66 ( ( B2 != zero_zero_complex )
% 5.41/5.66 => ( ( divide1717551699836669952omplex @ B2 @ ( times_times_complex @ A @ B2 ) )
% 5.41/5.66 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_divide_mult_cancel_right
% 5.41/5.66 thf(fact_1675_nonzero__divide__mult__cancel__right,axiom,
% 5.41/5.66 ! [B2: real,A: real] :
% 5.41/5.66 ( ( B2 != zero_zero_real )
% 5.41/5.66 => ( ( divide_divide_real @ B2 @ ( times_times_real @ A @ B2 ) )
% 5.41/5.66 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_divide_mult_cancel_right
% 5.41/5.66 thf(fact_1676_nonzero__divide__mult__cancel__right,axiom,
% 5.41/5.66 ! [B2: rat,A: rat] :
% 5.41/5.66 ( ( B2 != zero_zero_rat )
% 5.41/5.66 => ( ( divide_divide_rat @ B2 @ ( times_times_rat @ A @ B2 ) )
% 5.41/5.66 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonzero_divide_mult_cancel_right
% 5.41/5.66 thf(fact_1677_div__mult__self1,axiom,
% 5.41/5.66 ! [B2: nat,A: nat,C: nat] :
% 5.41/5.66 ( ( B2 != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B2 ) ) @ B2 )
% 5.41/5.66 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_self1
% 5.41/5.66 thf(fact_1678_div__mult__self1,axiom,
% 5.41/5.66 ! [B2: int,A: int,C: int] :
% 5.41/5.66 ( ( B2 != zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B2 ) ) @ B2 )
% 5.41/5.66 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_self1
% 5.41/5.66 thf(fact_1679_div__mult__self2,axiom,
% 5.41/5.66 ! [B2: nat,A: nat,C: nat] :
% 5.41/5.66 ( ( B2 != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B2 @ C ) ) @ B2 )
% 5.41/5.66 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_self2
% 5.41/5.66 thf(fact_1680_div__mult__self2,axiom,
% 5.41/5.66 ! [B2: int,A: int,C: int] :
% 5.41/5.66 ( ( B2 != zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B2 @ C ) ) @ B2 )
% 5.41/5.66 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_self2
% 5.41/5.66 thf(fact_1681_div__mult__self3,axiom,
% 5.41/5.66 ! [B2: nat,C: nat,A: nat] :
% 5.41/5.66 ( ( B2 != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B2 ) @ A ) @ B2 )
% 5.41/5.66 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_self3
% 5.41/5.66 thf(fact_1682_div__mult__self3,axiom,
% 5.41/5.66 ! [B2: int,C: int,A: int] :
% 5.41/5.66 ( ( B2 != zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B2 ) @ A ) @ B2 )
% 5.41/5.66 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_self3
% 5.41/5.66 thf(fact_1683_div__mult__self4,axiom,
% 5.41/5.66 ! [B2: nat,C: nat,A: nat] :
% 5.41/5.66 ( ( B2 != zero_zero_nat )
% 5.41/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B2 @ C ) @ A ) @ B2 )
% 5.41/5.66 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_self4
% 5.41/5.66 thf(fact_1684_div__mult__self4,axiom,
% 5.41/5.66 ! [B2: int,C: int,A: int] :
% 5.41/5.66 ( ( B2 != zero_zero_int )
% 5.41/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B2 @ C ) @ A ) @ B2 )
% 5.41/5.66 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_mult_self4
% 5.41/5.66 thf(fact_1685_power__mono__iff,axiom,
% 5.41/5.66 ! [A: real,B2: real,N: nat] :
% 5.41/5.66 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.41/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_eq_real @ A @ B2 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_mono_iff
% 5.41/5.66 thf(fact_1686_power__mono__iff,axiom,
% 5.41/5.66 ! [A: rat,B2: rat,N: nat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.41/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_eq_rat @ A @ B2 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_mono_iff
% 5.41/5.66 thf(fact_1687_power__mono__iff,axiom,
% 5.41/5.66 ! [A: nat,B2: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.66 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.41/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_eq_nat @ A @ B2 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_mono_iff
% 5.41/5.66 thf(fact_1688_power__mono__iff,axiom,
% 5.41/5.66 ! [A: int,B2: int,N: nat] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.41/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_eq_int @ A @ B2 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_mono_iff
% 5.41/5.66 thf(fact_1689_unit__mult__div__div,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.66 => ( ( times_3573771949741848930nteger @ B2 @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.41/5.66 = ( divide6298287555418463151nteger @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_mult_div_div
% 5.41/5.66 thf(fact_1690_unit__mult__div__div,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.66 => ( ( times_times_nat @ B2 @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.41/5.66 = ( divide_divide_nat @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_mult_div_div
% 5.41/5.66 thf(fact_1691_unit__mult__div__div,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.66 => ( ( times_times_int @ B2 @ ( divide_divide_int @ one_one_int @ A ) )
% 5.41/5.66 = ( divide_divide_int @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_mult_div_div
% 5.41/5.66 thf(fact_1692_unit__div__mult__self,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.66 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B2 @ A ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div_mult_self
% 5.41/5.66 thf(fact_1693_unit__div__mult__self,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.66 => ( ( times_times_nat @ ( divide_divide_nat @ B2 @ A ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div_mult_self
% 5.41/5.66 thf(fact_1694_unit__div__mult__self,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.66 => ( ( times_times_int @ ( divide_divide_int @ B2 @ A ) @ A )
% 5.41/5.66 = B2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % unit_div_mult_self
% 5.41/5.66 thf(fact_1695_signed__take__bit__Suc__bit0,axiom,
% 5.41/5.66 ! [N: nat,K: num] :
% 5.41/5.66 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.41/5.66 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % signed_take_bit_Suc_bit0
% 5.41/5.66 thf(fact_1696_Suc__diff__1,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.41/5.66 = N ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_diff_1
% 5.41/5.66 thf(fact_1697_half__negative__int__iff,axiom,
% 5.41/5.66 ! [K: int] :
% 5.41/5.66 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.41/5.66 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % half_negative_int_iff
% 5.41/5.66 thf(fact_1698_half__nonnegative__int__iff,axiom,
% 5.41/5.66 ! [K: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.41/5.66
% 5.41/5.66 % half_nonnegative_int_iff
% 5.41/5.66 thf(fact_1699_le__divide__eq__1__pos,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.66 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_divide_eq_1_pos
% 5.41/5.66 thf(fact_1700_le__divide__eq__1__pos,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.66 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_eq_rat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_divide_eq_1_pos
% 5.41/5.66 thf(fact_1701_le__divide__eq__1__neg,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.66 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_eq_real @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_divide_eq_1_neg
% 5.41/5.66 thf(fact_1702_le__divide__eq__1__neg,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.66 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A ) )
% 5.41/5.66 = ( ord_less_eq_rat @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_divide_eq_1_neg
% 5.41/5.66 thf(fact_1703_divide__le__eq__1__pos,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.66 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 5.41/5.66 = ( ord_less_eq_real @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_le_eq_1_pos
% 5.41/5.66 thf(fact_1704_divide__le__eq__1__pos,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.66 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ A ) @ one_one_rat )
% 5.41/5.66 = ( ord_less_eq_rat @ B2 @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_le_eq_1_pos
% 5.41/5.66 thf(fact_1705_divide__le__eq__1__neg,axiom,
% 5.41/5.66 ! [A: real,B2: real] :
% 5.41/5.66 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.66 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 5.41/5.66 = ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_le_eq_1_neg
% 5.41/5.66 thf(fact_1706_divide__le__eq__1__neg,axiom,
% 5.41/5.66 ! [A: rat,B2: rat] :
% 5.41/5.66 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.66 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ A ) @ one_one_rat )
% 5.41/5.66 = ( ord_less_eq_rat @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divide_le_eq_1_neg
% 5.41/5.66 thf(fact_1707_power__strict__decreasing__iff,axiom,
% 5.41/5.66 ! [B2: real,M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.41/5.66 => ( ( ord_less_real @ B2 @ one_one_real )
% 5.41/5.66 => ( ( ord_less_real @ ( power_power_real @ B2 @ M ) @ ( power_power_real @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_strict_decreasing_iff
% 5.41/5.66 thf(fact_1708_power__strict__decreasing__iff,axiom,
% 5.41/5.66 ! [B2: rat,M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.41/5.66 => ( ( ord_less_rat @ B2 @ one_one_rat )
% 5.41/5.66 => ( ( ord_less_rat @ ( power_power_rat @ B2 @ M ) @ ( power_power_rat @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_strict_decreasing_iff
% 5.41/5.66 thf(fact_1709_power__strict__decreasing__iff,axiom,
% 5.41/5.66 ! [B2: nat,M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.41/5.66 => ( ( ord_less_nat @ B2 @ one_one_nat )
% 5.41/5.66 => ( ( ord_less_nat @ ( power_power_nat @ B2 @ M ) @ ( power_power_nat @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_strict_decreasing_iff
% 5.41/5.66 thf(fact_1710_power__strict__decreasing__iff,axiom,
% 5.41/5.66 ! [B2: int,M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.41/5.66 => ( ( ord_less_int @ B2 @ one_one_int )
% 5.41/5.66 => ( ( ord_less_int @ ( power_power_int @ B2 @ M ) @ ( power_power_int @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_strict_decreasing_iff
% 5.41/5.66 thf(fact_1711_even__mult__iff,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B2 ) )
% 5.41/5.66 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.66 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_mult_iff
% 5.41/5.66 thf(fact_1712_even__mult__iff,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B2 ) )
% 5.41/5.66 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.66 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_mult_iff
% 5.41/5.66 thf(fact_1713_even__mult__iff,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B2 ) )
% 5.41/5.66 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.66 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_mult_iff
% 5.41/5.66 thf(fact_1714_zero__eq__power2,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_rat )
% 5.41/5.66 = ( A = zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_eq_power2
% 5.41/5.66 thf(fact_1715_zero__eq__power2,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_nat )
% 5.41/5.66 = ( A = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_eq_power2
% 5.41/5.66 thf(fact_1716_zero__eq__power2,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_real )
% 5.41/5.66 = ( A = zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_eq_power2
% 5.41/5.66 thf(fact_1717_zero__eq__power2,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_int )
% 5.41/5.66 = ( A = zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_eq_power2
% 5.41/5.66 thf(fact_1718_zero__eq__power2,axiom,
% 5.41/5.66 ! [A: complex] :
% 5.41/5.66 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_complex )
% 5.41/5.66 = ( A = zero_zero_complex ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_eq_power2
% 5.41/5.66 thf(fact_1719_odd__add,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B2 ) ) )
% 5.41/5.66 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.66 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % odd_add
% 5.41/5.66 thf(fact_1720_odd__add,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B2 ) ) )
% 5.41/5.66 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.66 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % odd_add
% 5.41/5.66 thf(fact_1721_odd__add,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B2 ) ) )
% 5.41/5.66 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.66 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % odd_add
% 5.41/5.66 thf(fact_1722_even__add,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B2 ) )
% 5.41/5.66 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.66 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_add
% 5.41/5.66 thf(fact_1723_even__add,axiom,
% 5.41/5.66 ! [A: nat,B2: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B2 ) )
% 5.41/5.66 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.66 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_add
% 5.41/5.66 thf(fact_1724_even__add,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B2 ) )
% 5.41/5.66 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.66 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_add
% 5.41/5.66 thf(fact_1725_even__mod__2__iff,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_mod_2_iff
% 5.41/5.66 thf(fact_1726_even__mod__2__iff,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_mod_2_iff
% 5.41/5.66 thf(fact_1727_even__mod__2__iff,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_mod_2_iff
% 5.41/5.66 thf(fact_1728_even__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.41/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_Suc
% 5.41/5.66 thf(fact_1729_even__Suc__Suc__iff,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.41/5.66 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_Suc_Suc_iff
% 5.41/5.66 thf(fact_1730_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 != ( suc @ zero_zero_nat ) )
% 5.41/5.66 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod2_eq_Suc_0_eq_0
% 5.41/5.66 thf(fact_1731_add__self__mod__2,axiom,
% 5.41/5.66 ! [M: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % add_self_mod_2
% 5.41/5.66 thf(fact_1732_one__div__two__eq__zero,axiom,
% 5.41/5.66 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % one_div_two_eq_zero
% 5.41/5.66 thf(fact_1733_one__div__two__eq__zero,axiom,
% 5.41/5.66 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % one_div_two_eq_zero
% 5.41/5.66 thf(fact_1734_bits__1__div__2,axiom,
% 5.41/5.66 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % bits_1_div_2
% 5.41/5.66 thf(fact_1735_bits__1__div__2,axiom,
% 5.41/5.66 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % bits_1_div_2
% 5.41/5.66 thf(fact_1736_power__decreasing__iff,axiom,
% 5.41/5.66 ! [B2: real,M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.41/5.66 => ( ( ord_less_real @ B2 @ one_one_real )
% 5.41/5.66 => ( ( ord_less_eq_real @ ( power_power_real @ B2 @ M ) @ ( power_power_real @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_decreasing_iff
% 5.41/5.66 thf(fact_1737_power__decreasing__iff,axiom,
% 5.41/5.66 ! [B2: rat,M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.41/5.66 => ( ( ord_less_rat @ B2 @ one_one_rat )
% 5.41/5.66 => ( ( ord_less_eq_rat @ ( power_power_rat @ B2 @ M ) @ ( power_power_rat @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_decreasing_iff
% 5.41/5.66 thf(fact_1738_power__decreasing__iff,axiom,
% 5.41/5.66 ! [B2: nat,M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.41/5.66 => ( ( ord_less_nat @ B2 @ one_one_nat )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ M ) @ ( power_power_nat @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_decreasing_iff
% 5.41/5.66 thf(fact_1739_power__decreasing__iff,axiom,
% 5.41/5.66 ! [B2: int,M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.41/5.66 => ( ( ord_less_int @ B2 @ one_one_int )
% 5.41/5.66 => ( ( ord_less_eq_int @ ( power_power_int @ B2 @ M ) @ ( power_power_int @ B2 @ N ) )
% 5.41/5.66 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_decreasing_iff
% 5.41/5.66 thf(fact_1740_power2__less__eq__zero__iff,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.41/5.66 = ( A = zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_less_eq_zero_iff
% 5.41/5.66 thf(fact_1741_power2__less__eq__zero__iff,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.41/5.66 = ( A = zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_less_eq_zero_iff
% 5.41/5.66 thf(fact_1742_power2__less__eq__zero__iff,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.41/5.66 = ( A = zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_less_eq_zero_iff
% 5.41/5.66 thf(fact_1743_power2__eq__iff__nonneg,axiom,
% 5.41/5.66 ! [X4: real,Y3: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.41/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.41/5.66 => ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( X4 = Y3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_eq_iff_nonneg
% 5.41/5.66 thf(fact_1744_power2__eq__iff__nonneg,axiom,
% 5.41/5.66 ! [X4: rat,Y3: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.41/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.41/5.66 => ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( X4 = Y3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_eq_iff_nonneg
% 5.41/5.66 thf(fact_1745_power2__eq__iff__nonneg,axiom,
% 5.41/5.66 ! [X4: nat,Y3: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 5.41/5.66 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.41/5.66 => ( ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( X4 = Y3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_eq_iff_nonneg
% 5.41/5.66 thf(fact_1746_power2__eq__iff__nonneg,axiom,
% 5.41/5.66 ! [X4: int,Y3: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.41/5.66 => ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( X4 = Y3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_eq_iff_nonneg
% 5.41/5.66 thf(fact_1747_zero__less__power2,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( A != zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_power2
% 5.41/5.66 thf(fact_1748_zero__less__power2,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( A != zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_power2
% 5.41/5.66 thf(fact_1749_zero__less__power2,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = ( A != zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_power2
% 5.41/5.66 thf(fact_1750_sum__power2__eq__zero__iff,axiom,
% 5.41/5.66 ! [X4: rat,Y3: rat] :
% 5.41/5.66 ( ( ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = zero_zero_rat )
% 5.41/5.66 = ( ( X4 = zero_zero_rat )
% 5.41/5.66 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_eq_zero_iff
% 5.41/5.66 thf(fact_1751_sum__power2__eq__zero__iff,axiom,
% 5.41/5.66 ! [X4: real,Y3: real] :
% 5.41/5.66 ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = zero_zero_real )
% 5.41/5.66 = ( ( X4 = zero_zero_real )
% 5.41/5.66 & ( Y3 = zero_zero_real ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_eq_zero_iff
% 5.41/5.66 thf(fact_1752_sum__power2__eq__zero__iff,axiom,
% 5.41/5.66 ! [X4: int,Y3: int] :
% 5.41/5.66 ( ( ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = zero_zero_int )
% 5.41/5.66 = ( ( X4 = zero_zero_int )
% 5.41/5.66 & ( Y3 = zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_eq_zero_iff
% 5.41/5.66 thf(fact_1753_even__plus__one__iff,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.41/5.66 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_plus_one_iff
% 5.41/5.66 thf(fact_1754_even__plus__one__iff,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.41/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_plus_one_iff
% 5.41/5.66 thf(fact_1755_even__plus__one__iff,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.41/5.66 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_plus_one_iff
% 5.41/5.66 thf(fact_1756_even__diff,axiom,
% 5.41/5.66 ! [A: code_integer,B2: code_integer] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_diff
% 5.41/5.66 thf(fact_1757_even__diff,axiom,
% 5.41/5.66 ! [A: int,B2: int] :
% 5.41/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B2 ) )
% 5.41/5.66 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_diff
% 5.41/5.66 thf(fact_1758_not__mod__2__eq__0__eq__1,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 != zero_zero_nat )
% 5.41/5.66 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = one_one_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_0_eq_1
% 5.41/5.66 thf(fact_1759_not__mod__2__eq__0__eq__1,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.66 != zero_zero_int )
% 5.41/5.66 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.66 = one_one_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_0_eq_1
% 5.41/5.66 thf(fact_1760_not__mod__2__eq__0__eq__1,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.66 != zero_z3403309356797280102nteger )
% 5.41/5.66 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.66 = one_one_Code_integer ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_0_eq_1
% 5.41/5.66 thf(fact_1761_not__mod__2__eq__1__eq__0,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 != one_one_nat )
% 5.41/5.66 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_1_eq_0
% 5.41/5.66 thf(fact_1762_not__mod__2__eq__1__eq__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.66 != one_one_int )
% 5.41/5.66 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_1_eq_0
% 5.41/5.66 thf(fact_1763_not__mod__2__eq__1__eq__0,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.66 != one_one_Code_integer )
% 5.41/5.66 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_1_eq_0
% 5.41/5.66 thf(fact_1764_even__power,axiom,
% 5.41/5.66 ! [A: code_integer,N: nat] :
% 5.41/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.41/5.66 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_power
% 5.41/5.66 thf(fact_1765_even__power,axiom,
% 5.41/5.66 ! [A: nat,N: nat] :
% 5.41/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.41/5.66 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % even_power
% 5.41/5.67 thf(fact_1766_even__power,axiom,
% 5.41/5.67 ! [A: int,N: nat] :
% 5.41/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.41/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % even_power
% 5.41/5.67 thf(fact_1767_odd__Suc__minus__one,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.67 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.41/5.67 = N ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_Suc_minus_one
% 5.41/5.67 thf(fact_1768_odd__Suc__div__two,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.67 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_Suc_div_two
% 5.41/5.67 thf(fact_1769_even__Suc__div__two,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.67 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % even_Suc_div_two
% 5.41/5.67 thf(fact_1770_mod2__gr__0,axiom,
% 5.41/5.67 ! [M: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.67 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.67 = one_one_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % mod2_gr_0
% 5.41/5.67 thf(fact_1771_unset__bit__0,axiom,
% 5.41/5.67 ! [A: int] :
% 5.41/5.67 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.41/5.67 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % unset_bit_0
% 5.41/5.67 thf(fact_1772_unset__bit__0,axiom,
% 5.41/5.67 ! [A: nat] :
% 5.41/5.67 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.41/5.67 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % unset_bit_0
% 5.41/5.67 thf(fact_1773_odd__succ__div__two,axiom,
% 5.41/5.67 ! [A: code_integer] :
% 5.41/5.67 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_succ_div_two
% 5.41/5.67 thf(fact_1774_odd__succ__div__two,axiom,
% 5.41/5.67 ! [A: nat] :
% 5.41/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_succ_div_two
% 5.41/5.67 thf(fact_1775_odd__succ__div__two,axiom,
% 5.41/5.67 ! [A: int] :
% 5.41/5.67 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_succ_div_two
% 5.41/5.67 thf(fact_1776_even__succ__div__two,axiom,
% 5.41/5.67 ! [A: code_integer] :
% 5.41/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % even_succ_div_two
% 5.41/5.67 thf(fact_1777_even__succ__div__two,axiom,
% 5.41/5.67 ! [A: nat] :
% 5.41/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % even_succ_div_two
% 5.41/5.67 thf(fact_1778_even__succ__div__two,axiom,
% 5.41/5.67 ! [A: int] :
% 5.41/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % even_succ_div_two
% 5.41/5.67 thf(fact_1779_even__succ__div__2,axiom,
% 5.41/5.67 ! [A: code_integer] :
% 5.41/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % even_succ_div_2
% 5.41/5.67 thf(fact_1780_even__succ__div__2,axiom,
% 5.41/5.67 ! [A: nat] :
% 5.41/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % even_succ_div_2
% 5.41/5.67 thf(fact_1781_even__succ__div__2,axiom,
% 5.41/5.67 ! [A: int] :
% 5.41/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % even_succ_div_2
% 5.41/5.67 thf(fact_1782_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.41/5.67 = ( N = zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % semiring_parity_class.even_mask_iff
% 5.41/5.67 thf(fact_1783_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.41/5.67 = ( N = zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % semiring_parity_class.even_mask_iff
% 5.41/5.67 thf(fact_1784_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.41/5.67 = ( N = zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % semiring_parity_class.even_mask_iff
% 5.41/5.67 thf(fact_1785_zero__le__power__eq__numeral,axiom,
% 5.41/5.67 ! [A: real,W: num] :
% 5.41/5.67 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % zero_le_power_eq_numeral
% 5.41/5.67 thf(fact_1786_zero__le__power__eq__numeral,axiom,
% 5.41/5.67 ! [A: rat,W: num] :
% 5.41/5.67 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % zero_le_power_eq_numeral
% 5.41/5.67 thf(fact_1787_zero__le__power__eq__numeral,axiom,
% 5.41/5.67 ! [A: int,W: num] :
% 5.41/5.67 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % zero_le_power_eq_numeral
% 5.41/5.67 thf(fact_1788_zero__less__power__eq__numeral,axiom,
% 5.41/5.67 ! [A: real,W: num] :
% 5.41/5.67 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.67 = ( ( ( numeral_numeral_nat @ W )
% 5.41/5.67 = zero_zero_nat )
% 5.41/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( A != zero_zero_real ) )
% 5.41/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % zero_less_power_eq_numeral
% 5.41/5.67 thf(fact_1789_zero__less__power__eq__numeral,axiom,
% 5.41/5.67 ! [A: rat,W: num] :
% 5.41/5.67 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.67 = ( ( ( numeral_numeral_nat @ W )
% 5.41/5.67 = zero_zero_nat )
% 5.41/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( A != zero_zero_rat ) )
% 5.41/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % zero_less_power_eq_numeral
% 5.41/5.67 thf(fact_1790_zero__less__power__eq__numeral,axiom,
% 5.41/5.67 ! [A: int,W: num] :
% 5.41/5.67 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.67 = ( ( ( numeral_numeral_nat @ W )
% 5.41/5.67 = zero_zero_nat )
% 5.41/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( A != zero_zero_int ) )
% 5.41/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % zero_less_power_eq_numeral
% 5.41/5.67 thf(fact_1791_power__less__zero__eq,axiom,
% 5.41/5.67 ! [A: real,N: nat] :
% 5.41/5.67 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.41/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.67 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_less_zero_eq
% 5.41/5.67 thf(fact_1792_power__less__zero__eq,axiom,
% 5.41/5.67 ! [A: rat,N: nat] :
% 5.41/5.67 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.41/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.67 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_less_zero_eq
% 5.41/5.67 thf(fact_1793_power__less__zero__eq,axiom,
% 5.41/5.67 ! [A: int,N: nat] :
% 5.41/5.67 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.41/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.67 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_less_zero_eq
% 5.41/5.67 thf(fact_1794_power__less__zero__eq__numeral,axiom,
% 5.41/5.67 ! [A: real,W: num] :
% 5.41/5.67 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.41/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_less_zero_eq_numeral
% 5.41/5.67 thf(fact_1795_power__less__zero__eq__numeral,axiom,
% 5.41/5.67 ! [A: rat,W: num] :
% 5.41/5.67 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.41/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_less_zero_eq_numeral
% 5.41/5.67 thf(fact_1796_power__less__zero__eq__numeral,axiom,
% 5.41/5.67 ! [A: int,W: num] :
% 5.41/5.67 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.41/5.67 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.67 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_less_zero_eq_numeral
% 5.41/5.67 thf(fact_1797_even__diff__nat,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.67 = ( ( ord_less_nat @ M @ N )
% 5.41/5.67 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % even_diff_nat
% 5.41/5.67 thf(fact_1798_odd__two__times__div__two__succ,axiom,
% 5.41/5.67 ! [A: code_integer] :
% 5.41/5.67 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.41/5.67 = A ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_two_times_div_two_succ
% 5.41/5.67 thf(fact_1799_odd__two__times__div__two__succ,axiom,
% 5.41/5.67 ! [A: nat] :
% 5.41/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.41/5.67 = A ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_two_times_div_two_succ
% 5.41/5.67 thf(fact_1800_odd__two__times__div__two__succ,axiom,
% 5.41/5.67 ! [A: int] :
% 5.41/5.67 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.67 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.41/5.67 = A ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_two_times_div_two_succ
% 5.46/5.67 thf(fact_1801_power__le__zero__eq__numeral,axiom,
% 5.46/5.67 ! [A: real,W: num] :
% 5.46/5.67 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq_numeral
% 5.46/5.67 thf(fact_1802_power__le__zero__eq__numeral,axiom,
% 5.46/5.67 ! [A: rat,W: num] :
% 5.46/5.67 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq_numeral
% 5.46/5.67 thf(fact_1803_power__le__zero__eq__numeral,axiom,
% 5.46/5.67 ! [A: int,W: num] :
% 5.46/5.67 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.67 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq_numeral
% 5.46/5.67 thf(fact_1804_set__bit__0,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.46/5.67 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_bit_0
% 5.46/5.67 thf(fact_1805_set__bit__0,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.46/5.67 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % set_bit_0
% 5.46/5.67 thf(fact_1806_even__succ__div__exp,axiom,
% 5.46/5.67 ! [A: code_integer,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_exp
% 5.46/5.67 thf(fact_1807_even__succ__div__exp,axiom,
% 5.46/5.67 ! [A: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_exp
% 5.46/5.67 thf(fact_1808_even__succ__div__exp,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_div_exp
% 5.46/5.67 thf(fact_1809_even__succ__mod__exp,axiom,
% 5.46/5.67 ! [A: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_mod_exp
% 5.46/5.67 thf(fact_1810_even__succ__mod__exp,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_mod_exp
% 5.46/5.67 thf(fact_1811_even__succ__mod__exp,axiom,
% 5.46/5.67 ! [A: code_integer,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.67 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_succ_mod_exp
% 5.46/5.67 thf(fact_1812_split__zdiv,axiom,
% 5.46/5.67 ! [P: int > $o,N: int,K: int] :
% 5.46/5.67 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.46/5.67 = ( ( ( K = zero_zero_int )
% 5.46/5.67 => ( P @ zero_zero_int ) )
% 5.46/5.67 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.67 => ! [I2: int,J3: int] :
% 5.46/5.67 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.46/5.67 & ( ord_less_int @ J3 @ K )
% 5.46/5.67 & ( N
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.46/5.67 => ( P @ I2 ) ) )
% 5.46/5.67 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.67 => ! [I2: int,J3: int] :
% 5.46/5.67 ( ( ( ord_less_int @ K @ J3 )
% 5.46/5.67 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.46/5.67 & ( N
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.46/5.67 => ( P @ I2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % split_zdiv
% 5.46/5.67 thf(fact_1813_div__pos__geq,axiom,
% 5.46/5.67 ! [L2: int,K: int] :
% 5.46/5.67 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.67 => ( ( ord_less_eq_int @ L2 @ K )
% 5.46/5.67 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.67 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_pos_geq
% 5.46/5.67 thf(fact_1814_int__div__neg__eq,axiom,
% 5.46/5.67 ! [A: int,B2: int,Q2: int,R2: int] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ B2 @ Q2 ) @ R2 ) )
% 5.46/5.67 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.46/5.67 => ( ( ord_less_int @ B2 @ R2 )
% 5.46/5.67 => ( ( divide_divide_int @ A @ B2 )
% 5.46/5.67 = Q2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % int_div_neg_eq
% 5.46/5.67 thf(fact_1815_int__div__pos__eq,axiom,
% 5.46/5.67 ! [A: int,B2: int,Q2: int,R2: int] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ B2 @ Q2 ) @ R2 ) )
% 5.46/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.46/5.67 => ( ( ord_less_int @ R2 @ B2 )
% 5.46/5.67 => ( ( divide_divide_int @ A @ B2 )
% 5.46/5.67 = Q2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % int_div_pos_eq
% 5.46/5.67 thf(fact_1816_div__mod__decomp__int,axiom,
% 5.46/5.67 ! [A3: int,N: int] :
% 5.46/5.67 ( A3
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A3 @ N ) @ N ) @ ( modulo_modulo_int @ A3 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_mod_decomp_int
% 5.46/5.67 thf(fact_1817_split__neg__lemma,axiom,
% 5.46/5.67 ! [K: int,P: int > int > $o,N: int] :
% 5.46/5.67 ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.67 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.46/5.67 = ( ! [I2: int,J3: int] :
% 5.46/5.67 ( ( ( ord_less_int @ K @ J3 )
% 5.46/5.67 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.46/5.67 & ( N
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.46/5.67 => ( P @ I2 @ J3 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % split_neg_lemma
% 5.46/5.67 thf(fact_1818_split__pos__lemma,axiom,
% 5.46/5.67 ! [K: int,P: int > int > $o,N: int] :
% 5.46/5.67 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.67 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.46/5.67 = ( ! [I2: int,J3: int] :
% 5.46/5.67 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.46/5.67 & ( ord_less_int @ J3 @ K )
% 5.46/5.67 & ( N
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.46/5.67 => ( P @ I2 @ J3 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % split_pos_lemma
% 5.46/5.67 thf(fact_1819_int__div__less__self,axiom,
% 5.46/5.67 ! [X4: int,K: int] :
% 5.46/5.67 ( ( ord_less_int @ zero_zero_int @ X4 )
% 5.46/5.67 => ( ( ord_less_int @ one_one_int @ K )
% 5.46/5.67 => ( ord_less_int @ ( divide_divide_int @ X4 @ K ) @ X4 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % int_div_less_self
% 5.46/5.67 thf(fact_1820_verit__le__mono__div__int,axiom,
% 5.46/5.67 ! [A3: int,B4: int,N: int] :
% 5.46/5.67 ( ( ord_less_int @ A3 @ B4 )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.46/5.67 => ( ord_less_eq_int
% 5.46/5.67 @ ( plus_plus_int @ ( divide_divide_int @ A3 @ N )
% 5.46/5.67 @ ( if_int
% 5.46/5.67 @ ( ( modulo_modulo_int @ B4 @ N )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 @ one_one_int
% 5.46/5.67 @ zero_zero_int ) )
% 5.46/5.67 @ ( divide_divide_int @ B4 @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % verit_le_mono_div_int
% 5.46/5.67 thf(fact_1821_zdiv__zmult2__eq,axiom,
% 5.46/5.67 ! [C: int,A: int,B2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ C ) )
% 5.46/5.67 = ( divide_divide_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zdiv_zmult2_eq
% 5.46/5.67 thf(fact_1822_zmod__zmult2__eq,axiom,
% 5.46/5.67 ! [C: int,A: int,B2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.67 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B2 @ C ) )
% 5.46/5.67 = ( plus_plus_int @ ( times_times_int @ B2 @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) @ ( modulo_modulo_int @ A @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zmod_zmult2_eq
% 5.46/5.67 thf(fact_1823_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B2 ) )
% 5.46/5.67 = ( ( ord_less_eq_int @ B2 @ A )
% 5.46/5.67 & ( ord_less_int @ zero_zero_int @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nonneg1_imp_zdiv_pos_iff
% 5.46/5.67 thf(fact_1824_pos__imp__zdiv__nonneg__iff,axiom,
% 5.46/5.67 ! [B2: int,A: int] :
% 5.46/5.67 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B2 ) )
% 5.46/5.67 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pos_imp_zdiv_nonneg_iff
% 5.46/5.67 thf(fact_1825_neg__imp__zdiv__nonneg__iff,axiom,
% 5.46/5.67 ! [B2: int,A: int] :
% 5.46/5.67 ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.46/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B2 ) )
% 5.46/5.67 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_imp_zdiv_nonneg_iff
% 5.46/5.67 thf(fact_1826_pos__imp__zdiv__pos__iff,axiom,
% 5.46/5.67 ! [K: int,I: int] :
% 5.46/5.67 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.46/5.67 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pos_imp_zdiv_pos_iff
% 5.46/5.67 thf(fact_1827_pos__imp__zdiv__neg__iff,axiom,
% 5.46/5.67 ! [B2: int,A: int] :
% 5.46/5.67 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.67 => ( ( ord_less_int @ ( divide_divide_int @ A @ B2 ) @ zero_zero_int )
% 5.46/5.67 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pos_imp_zdiv_neg_iff
% 5.46/5.67 thf(fact_1828_neg__imp__zdiv__neg__iff,axiom,
% 5.46/5.67 ! [B2: int,A: int] :
% 5.46/5.67 ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.46/5.67 => ( ( ord_less_int @ ( divide_divide_int @ A @ B2 ) @ zero_zero_int )
% 5.46/5.67 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_imp_zdiv_neg_iff
% 5.46/5.67 thf(fact_1829_div__nonpos__pos__le0,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.67 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_nonpos_pos_le0
% 5.46/5.67 thf(fact_1830_div__nonneg__neg__le0,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.67 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.46/5.67 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_nonneg_neg_le0
% 5.46/5.67 thf(fact_1831_div__neg__pos__less0,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.67 => ( ord_less_int @ ( divide_divide_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_neg_pos_less0
% 5.46/5.67 thf(fact_1832_div__positive__int,axiom,
% 5.46/5.67 ! [L2: int,K: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ L2 @ K )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.67 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_positive_int
% 5.46/5.67 thf(fact_1833_div__int__pos__iff,axiom,
% 5.46/5.67 ! [K: int,L2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 5.46/5.67 = ( ( K = zero_zero_int )
% 5.46/5.67 | ( L2 = zero_zero_int )
% 5.46/5.67 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.67 & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 5.46/5.67 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.67 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_int_pos_iff
% 5.46/5.67 thf(fact_1834_zdiv__mono2__neg,axiom,
% 5.46/5.67 ! [A: int,B: int,B2: int] :
% 5.46/5.67 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.67 => ( ( ord_less_eq_int @ B @ B2 )
% 5.46/5.67 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zdiv_mono2_neg
% 5.46/5.67 thf(fact_1835_zdiv__mono1__neg,axiom,
% 5.46/5.67 ! [A: int,A2: int,B2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ A @ A2 )
% 5.46/5.67 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.46/5.67 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B2 ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zdiv_mono1_neg
% 5.46/5.67 thf(fact_1836_zdiv__eq__0__iff,axiom,
% 5.46/5.67 ! [I: int,K: int] :
% 5.46/5.67 ( ( ( divide_divide_int @ I @ K )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 = ( ( K = zero_zero_int )
% 5.46/5.67 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.46/5.67 & ( ord_less_int @ I @ K ) )
% 5.46/5.67 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.46/5.67 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zdiv_eq_0_iff
% 5.46/5.67 thf(fact_1837_zdiv__mono__strict,axiom,
% 5.46/5.67 ! [A3: int,B4: int,N: int] :
% 5.46/5.67 ( ( ord_less_int @ A3 @ B4 )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.46/5.67 => ( ( ( modulo_modulo_int @ A3 @ N )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 => ( ( ( modulo_modulo_int @ B4 @ N )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 => ( ord_less_int @ ( divide_divide_int @ A3 @ N ) @ ( divide_divide_int @ B4 @ N ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zdiv_mono_strict
% 5.46/5.67 thf(fact_1838_zdiv__mono2,axiom,
% 5.46/5.67 ! [A: int,B: int,B2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.67 => ( ( ord_less_eq_int @ B @ B2 )
% 5.46/5.67 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zdiv_mono2
% 5.46/5.67 thf(fact_1839_zdiv__mono1,axiom,
% 5.46/5.67 ! [A: int,A2: int,B2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ A @ A2 )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.67 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A2 @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zdiv_mono1
% 5.46/5.67 thf(fact_1840_dvd__field__iff,axiom,
% 5.46/5.67 ( dvd_dvd_real
% 5.46/5.67 = ( ^ [A4: real,B3: real] :
% 5.46/5.67 ( ( A4 = zero_zero_real )
% 5.46/5.67 => ( B3 = zero_zero_real ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_field_iff
% 5.46/5.67 thf(fact_1841_dvd__field__iff,axiom,
% 5.46/5.67 ( dvd_dvd_rat
% 5.46/5.67 = ( ^ [A4: rat,B3: rat] :
% 5.46/5.67 ( ( A4 = zero_zero_rat )
% 5.46/5.67 => ( B3 = zero_zero_rat ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_field_iff
% 5.46/5.67 thf(fact_1842_dvd__refl,axiom,
% 5.46/5.67 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_refl
% 5.46/5.67 thf(fact_1843_dvd__refl,axiom,
% 5.46/5.67 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_refl
% 5.46/5.67 thf(fact_1844_dvd__refl,axiom,
% 5.46/5.67 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_refl
% 5.46/5.67 thf(fact_1845_dvd__trans,axiom,
% 5.46/5.67 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B2 @ C )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_trans
% 5.46/5.67 thf(fact_1846_dvd__trans,axiom,
% 5.46/5.67 ! [A: int,B2: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_int @ B2 @ C )
% 5.46/5.67 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_trans
% 5.46/5.67 thf(fact_1847_dvd__trans,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B2 @ C )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_trans
% 5.46/5.67 thf(fact_1848_dvd__0__left,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.46/5.67 => ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_1849_dvd__0__left,axiom,
% 5.46/5.67 ! [A: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.46/5.67 => ( A = zero_zero_real ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_1850_dvd__0__left,axiom,
% 5.46/5.67 ! [A: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.46/5.67 => ( A = zero_zero_rat ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_1851_dvd__0__left,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.46/5.67 => ( A = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_1852_dvd__0__left,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.46/5.67 => ( A = zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_0_left
% 5.46/5.67 thf(fact_1853_dvd__antisym,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ M @ N )
% 5.46/5.67 => ( ( dvd_dvd_nat @ N @ M )
% 5.46/5.67 => ( M = N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_antisym
% 5.46/5.67 thf(fact_1854_zero__reorient,axiom,
% 5.46/5.67 ! [X4: literal] :
% 5.46/5.67 ( ( zero_zero_literal = X4 )
% 5.46/5.67 = ( X4 = zero_zero_literal ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_reorient
% 5.46/5.67 thf(fact_1855_zero__reorient,axiom,
% 5.46/5.67 ! [X4: real] :
% 5.46/5.67 ( ( zero_zero_real = X4 )
% 5.46/5.67 = ( X4 = zero_zero_real ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_reorient
% 5.46/5.67 thf(fact_1856_zero__reorient,axiom,
% 5.46/5.67 ! [X4: rat] :
% 5.46/5.67 ( ( zero_zero_rat = X4 )
% 5.46/5.67 = ( X4 = zero_zero_rat ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_reorient
% 5.46/5.67 thf(fact_1857_zero__reorient,axiom,
% 5.46/5.67 ! [X4: nat] :
% 5.46/5.67 ( ( zero_zero_nat = X4 )
% 5.46/5.67 = ( X4 = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_reorient
% 5.46/5.67 thf(fact_1858_zero__reorient,axiom,
% 5.46/5.67 ! [X4: int] :
% 5.46/5.67 ( ( zero_zero_int = X4 )
% 5.46/5.67 = ( X4 = zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_reorient
% 5.46/5.67 thf(fact_1859_not__is__unit__0,axiom,
% 5.46/5.67 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.46/5.67
% 5.46/5.67 % not_is_unit_0
% 5.46/5.67 thf(fact_1860_not__is__unit__0,axiom,
% 5.46/5.67 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.46/5.67
% 5.46/5.67 % not_is_unit_0
% 5.46/5.67 thf(fact_1861_not__is__unit__0,axiom,
% 5.46/5.67 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.46/5.67
% 5.46/5.67 % not_is_unit_0
% 5.46/5.67 thf(fact_1862_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B2: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B2 @ A )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ A @ B2 )
% 5.46/5.67 = zero_z3403309356797280102nteger )
% 5.46/5.67 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_1863_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B2: complex,A: complex] :
% 5.46/5.67 ( ( dvd_dvd_complex @ B2 @ A )
% 5.46/5.67 => ( ( ( divide1717551699836669952omplex @ A @ B2 )
% 5.46/5.67 = zero_zero_complex )
% 5.46/5.67 = ( A = zero_zero_complex ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_1864_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B2: real,A: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ B2 @ A )
% 5.46/5.67 => ( ( ( divide_divide_real @ A @ B2 )
% 5.46/5.67 = zero_zero_real )
% 5.46/5.67 = ( A = zero_zero_real ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_1865_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B2: rat,A: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ B2 @ A )
% 5.46/5.67 => ( ( ( divide_divide_rat @ A @ B2 )
% 5.46/5.67 = zero_zero_rat )
% 5.46/5.67 = ( A = zero_zero_rat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_1866_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B2: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B2 @ A )
% 5.46/5.67 => ( ( ( divide_divide_nat @ A @ B2 )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 = ( A = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_1867_dvd__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B2: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.67 => ( ( ( divide_divide_int @ A @ B2 )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 = ( A = zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_0_iff
% 5.46/5.67 thf(fact_1868_nat__dvd__not__less,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.67 => ( ( ord_less_nat @ M @ N )
% 5.46/5.67 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_dvd_not_less
% 5.46/5.67 thf(fact_1869_mod__0__imp__dvd,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] :
% 5.46/5.67 ( ( ( modulo_modulo_nat @ A @ B2 )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 => ( dvd_dvd_nat @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_0_imp_dvd
% 5.46/5.67 thf(fact_1870_mod__0__imp__dvd,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 => ( dvd_dvd_int @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_0_imp_dvd
% 5.46/5.67 thf(fact_1871_mod__0__imp__dvd,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( ( modulo364778990260209775nteger @ A @ B2 )
% 5.46/5.67 = zero_z3403309356797280102nteger )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_0_imp_dvd
% 5.46/5.67 thf(fact_1872_dvd__eq__mod__eq__0,axiom,
% 5.46/5.67 ( dvd_dvd_nat
% 5.46/5.67 = ( ^ [A4: nat,B3: nat] :
% 5.46/5.67 ( ( modulo_modulo_nat @ B3 @ A4 )
% 5.46/5.67 = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_eq_mod_eq_0
% 5.46/5.67 thf(fact_1873_dvd__eq__mod__eq__0,axiom,
% 5.46/5.67 ( dvd_dvd_int
% 5.46/5.67 = ( ^ [A4: int,B3: int] :
% 5.46/5.67 ( ( modulo_modulo_int @ B3 @ A4 )
% 5.46/5.67 = zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_eq_mod_eq_0
% 5.46/5.67 thf(fact_1874_dvd__eq__mod__eq__0,axiom,
% 5.46/5.67 ( dvd_dvd_Code_integer
% 5.46/5.67 = ( ^ [A4: code_integer,B3: code_integer] :
% 5.46/5.67 ( ( modulo364778990260209775nteger @ B3 @ A4 )
% 5.46/5.67 = zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_eq_mod_eq_0
% 5.46/5.67 thf(fact_1875_mod__eq__0__iff__dvd,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] :
% 5.46/5.67 ( ( ( modulo_modulo_nat @ A @ B2 )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 = ( dvd_dvd_nat @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_eq_0_iff_dvd
% 5.46/5.67 thf(fact_1876_mod__eq__0__iff__dvd,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 = ( dvd_dvd_int @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_eq_0_iff_dvd
% 5.46/5.67 thf(fact_1877_mod__eq__0__iff__dvd,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( ( modulo364778990260209775nteger @ A @ B2 )
% 5.46/5.67 = zero_z3403309356797280102nteger )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_eq_0_iff_dvd
% 5.46/5.67 thf(fact_1878_list__decode_Ocases,axiom,
% 5.46/5.67 ! [X4: nat] :
% 5.46/5.67 ( ( X4 != zero_zero_nat )
% 5.46/5.67 => ~ ! [N4: nat] :
% 5.46/5.67 ( X4
% 5.46/5.67 != ( suc @ N4 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % list_decode.cases
% 5.46/5.67 thf(fact_1879_pos__zmod__mult__2,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.67 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.67 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B2 @ A ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % pos_zmod_mult_2
% 5.46/5.67 thf(fact_1880_neg__zmod__mult__2,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.67 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.67 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B2 @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % neg_zmod_mult_2
% 5.46/5.67 thf(fact_1881_unit__dvdE,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ! [C3: code_integer] :
% 5.46/5.67 ( B2
% 5.46/5.67 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_dvdE
% 5.46/5.67 thf(fact_1882_unit__dvdE,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ~ ( ( A != zero_zero_nat )
% 5.46/5.67 => ! [C3: nat] :
% 5.46/5.67 ( B2
% 5.46/5.67 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_dvdE
% 5.46/5.67 thf(fact_1883_unit__dvdE,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ~ ( ( A != zero_zero_int )
% 5.46/5.67 => ! [C3: int] :
% 5.46/5.67 ( B2
% 5.46/5.67 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_dvdE
% 5.46/5.67 thf(fact_1884_dvd__div__eq__mult,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.67 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ B2 @ A )
% 5.46/5.67 = C )
% 5.46/5.67 = ( B2
% 5.46/5.67 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_mult
% 5.46/5.67 thf(fact_1885_dvd__div__eq__mult,axiom,
% 5.46/5.67 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ B2 )
% 5.46/5.67 => ( ( ( divide_divide_nat @ B2 @ A )
% 5.46/5.67 = C )
% 5.46/5.67 = ( B2
% 5.46/5.67 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_mult
% 5.46/5.67 thf(fact_1886_dvd__div__eq__mult,axiom,
% 5.46/5.67 ! [A: int,B2: int,C: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ B2 )
% 5.46/5.67 => ( ( ( divide_divide_int @ B2 @ A )
% 5.46/5.67 = C )
% 5.46/5.67 = ( B2
% 5.46/5.67 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_mult
% 5.46/5.67 thf(fact_1887_div__dvd__iff__mult,axiom,
% 5.46/5.67 ! [B2: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( B2 != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B2 @ A )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B2 ) @ C )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_dvd_iff_mult
% 5.46/5.67 thf(fact_1888_div__dvd__iff__mult,axiom,
% 5.46/5.67 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.67 ( ( B2 != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B2 @ A )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B2 ) @ C )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_dvd_iff_mult
% 5.46/5.67 thf(fact_1889_div__dvd__iff__mult,axiom,
% 5.46/5.67 ! [B2: int,A: int,C: int] :
% 5.46/5.67 ( ( B2 != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B2 ) @ C )
% 5.46/5.67 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_dvd_iff_mult
% 5.46/5.67 thf(fact_1890_dvd__div__iff__mult,axiom,
% 5.46/5.67 ! [C: code_integer,B2: code_integer,A: code_integer] :
% 5.46/5.67 ( ( C != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_iff_mult
% 5.46/5.67 thf(fact_1891_dvd__div__iff__mult,axiom,
% 5.46/5.67 ! [C: nat,B2: nat,A: nat] :
% 5.46/5.67 ( ( C != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_iff_mult
% 5.46/5.67 thf(fact_1892_dvd__div__iff__mult,axiom,
% 5.46/5.67 ! [C: int,B2: int,A: int] :
% 5.46/5.67 ( ( C != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_iff_mult
% 5.46/5.67 thf(fact_1893_dvd__div__div__eq__mult,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B2: code_integer,D: code_integer] :
% 5.46/5.67 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( C != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ B2 @ A )
% 5.46/5.67 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.46/5.67 = ( ( times_3573771949741848930nteger @ B2 @ C )
% 5.46/5.67 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_div_eq_mult
% 5.46/5.67 thf(fact_1894_dvd__div__div__eq__mult,axiom,
% 5.46/5.67 ! [A: nat,C: nat,B2: nat,D: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( C != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ D )
% 5.46/5.67 => ( ( ( divide_divide_nat @ B2 @ A )
% 5.46/5.67 = ( divide_divide_nat @ D @ C ) )
% 5.46/5.67 = ( ( times_times_nat @ B2 @ C )
% 5.46/5.67 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_div_eq_mult
% 5.46/5.67 thf(fact_1895_dvd__div__div__eq__mult,axiom,
% 5.46/5.67 ! [A: int,C: int,B2: int,D: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( C != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ D )
% 5.46/5.67 => ( ( ( divide_divide_int @ B2 @ A )
% 5.46/5.67 = ( divide_divide_int @ D @ C ) )
% 5.46/5.67 = ( ( times_times_int @ B2 @ C )
% 5.46/5.67 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_div_eq_mult
% 5.46/5.67 thf(fact_1896_unit__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B2: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ A @ B2 )
% 5.46/5.67 = zero_z3403309356797280102nteger )
% 5.46/5.67 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_eq_0_iff
% 5.46/5.67 thf(fact_1897_unit__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B2: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.67 => ( ( ( divide_divide_nat @ A @ B2 )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 = ( A = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_eq_0_iff
% 5.46/5.67 thf(fact_1898_unit__div__eq__0__iff,axiom,
% 5.46/5.67 ! [B2: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.67 => ( ( ( divide_divide_int @ A @ B2 )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 = ( A = zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_div_eq_0_iff
% 5.46/5.67 thf(fact_1899_is__unit__power__iff,axiom,
% 5.46/5.67 ! [A: code_integer,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_power_iff
% 5.46/5.67 thf(fact_1900_is__unit__power__iff,axiom,
% 5.46/5.67 ! [A: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.46/5.67 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_power_iff
% 5.46/5.67 thf(fact_1901_is__unit__power__iff,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.46/5.67 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_power_iff
% 5.46/5.67 thf(fact_1902_unit__imp__mod__eq__0,axiom,
% 5.46/5.67 ! [B2: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.67 => ( ( modulo_modulo_nat @ A @ B2 )
% 5.46/5.67 = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_mod_eq_0
% 5.46/5.67 thf(fact_1903_unit__imp__mod__eq__0,axiom,
% 5.46/5.67 ! [B2: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.67 => ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.67 = zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_mod_eq_0
% 5.46/5.67 thf(fact_1904_unit__imp__mod__eq__0,axiom,
% 5.46/5.67 ! [B2: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ A @ B2 )
% 5.46/5.67 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_mod_eq_0
% 5.46/5.67 thf(fact_1905_dvd__imp__le,axiom,
% 5.46/5.67 ! [K: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ K @ N )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_imp_le
% 5.46/5.67 thf(fact_1906_nat__mult__dvd__cancel1,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.67 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_mult_dvd_cancel1
% 5.46/5.67 thf(fact_1907_dvd__mult__cancel,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.67 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel
% 5.46/5.67 thf(fact_1908_power__0__left,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ( N = zero_zero_nat )
% 5.46/5.67 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.46/5.67 = one_one_rat ) )
% 5.46/5.67 & ( ( N != zero_zero_nat )
% 5.46/5.67 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.46/5.67 = zero_zero_rat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_0_left
% 5.46/5.67 thf(fact_1909_power__0__left,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ( N = zero_zero_nat )
% 5.46/5.67 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.46/5.67 = one_one_nat ) )
% 5.46/5.67 & ( ( N != zero_zero_nat )
% 5.46/5.67 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.46/5.67 = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_0_left
% 5.46/5.67 thf(fact_1910_power__0__left,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ( N = zero_zero_nat )
% 5.46/5.67 => ( ( power_power_real @ zero_zero_real @ N )
% 5.46/5.67 = one_one_real ) )
% 5.46/5.67 & ( ( N != zero_zero_nat )
% 5.46/5.67 => ( ( power_power_real @ zero_zero_real @ N )
% 5.46/5.67 = zero_zero_real ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_0_left
% 5.46/5.67 thf(fact_1911_power__0__left,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ( N = zero_zero_nat )
% 5.46/5.67 => ( ( power_power_int @ zero_zero_int @ N )
% 5.46/5.67 = one_one_int ) )
% 5.46/5.67 & ( ( N != zero_zero_nat )
% 5.46/5.67 => ( ( power_power_int @ zero_zero_int @ N )
% 5.46/5.67 = zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_0_left
% 5.46/5.67 thf(fact_1912_power__0__left,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ( N = zero_zero_nat )
% 5.46/5.67 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.46/5.67 = one_one_complex ) )
% 5.46/5.67 & ( ( N != zero_zero_nat )
% 5.46/5.67 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.46/5.67 = zero_zero_complex ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_0_left
% 5.46/5.67 thf(fact_1913_zero__power,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.46/5.67 = zero_zero_rat ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_power
% 5.46/5.67 thf(fact_1914_zero__power,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.46/5.67 = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_power
% 5.46/5.67 thf(fact_1915_zero__power,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( power_power_real @ zero_zero_real @ N )
% 5.46/5.67 = zero_zero_real ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_power
% 5.46/5.67 thf(fact_1916_zero__power,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( power_power_int @ zero_zero_int @ N )
% 5.46/5.67 = zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_power
% 5.46/5.67 thf(fact_1917_zero__power,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.46/5.67 = zero_zero_complex ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_power
% 5.46/5.67 thf(fact_1918_mod__greater__zero__iff__not__dvd,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.67 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_greater_zero_iff_not_dvd
% 5.46/5.67 thf(fact_1919_even__set__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 & ( M != zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_set_bit_iff
% 5.46/5.67 thf(fact_1920_even__set__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 & ( M != zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_set_bit_iff
% 5.46/5.67 thf(fact_1921_even__set__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 & ( M != zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_set_bit_iff
% 5.46/5.67 thf(fact_1922_even__flip__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 != ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_flip_bit_iff
% 5.46/5.67 thf(fact_1923_even__flip__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 != ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_flip_bit_iff
% 5.46/5.67 thf(fact_1924_even__flip__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 != ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_flip_bit_iff
% 5.46/5.67 thf(fact_1925_even__unset__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 | ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_unset_bit_iff
% 5.46/5.67 thf(fact_1926_even__unset__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 | ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_unset_bit_iff
% 5.46/5.67 thf(fact_1927_even__unset__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 | ( M = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_unset_bit_iff
% 5.46/5.67 thf(fact_1928_dvd__triv__right,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_right
% 5.46/5.67 thf(fact_1929_dvd__triv__right,axiom,
% 5.46/5.67 ! [A: real,B2: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_right
% 5.46/5.67 thf(fact_1930_dvd__triv__right,axiom,
% 5.46/5.67 ! [A: rat,B2: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_right
% 5.46/5.67 thf(fact_1931_dvd__triv__right,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_right
% 5.46/5.67 thf(fact_1932_dvd__triv__right,axiom,
% 5.46/5.67 ! [A: int,B2: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_right
% 5.46/5.67 thf(fact_1933_dvd__mult__right,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B2 ) @ C )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ B2 @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_right
% 5.46/5.67 thf(fact_1934_dvd__mult__right,axiom,
% 5.46/5.67 ! [A: real,B2: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ ( times_times_real @ A @ B2 ) @ C )
% 5.46/5.67 => ( dvd_dvd_real @ B2 @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_right
% 5.46/5.67 thf(fact_1935_dvd__mult__right,axiom,
% 5.46/5.67 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B2 ) @ C )
% 5.46/5.67 => ( dvd_dvd_rat @ B2 @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_right
% 5.46/5.67 thf(fact_1936_dvd__mult__right,axiom,
% 5.46/5.67 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 5.46/5.67 => ( dvd_dvd_nat @ B2 @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_right
% 5.46/5.67 thf(fact_1937_dvd__mult__right,axiom,
% 5.46/5.67 ! [A: int,B2: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ C )
% 5.46/5.67 => ( dvd_dvd_int @ B2 @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_right
% 5.46/5.67 thf(fact_1938_mult__dvd__mono,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer,C: code_integer,D: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B2 @ D ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_dvd_mono
% 5.46/5.67 thf(fact_1939_mult__dvd__mono,axiom,
% 5.46/5.67 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_real @ C @ D )
% 5.46/5.67 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_dvd_mono
% 5.46/5.67 thf(fact_1940_mult__dvd__mono,axiom,
% 5.46/5.67 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_rat @ C @ D )
% 5.46/5.67 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ D ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_dvd_mono
% 5.46/5.67 thf(fact_1941_mult__dvd__mono,axiom,
% 5.46/5.67 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ D )
% 5.46/5.67 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_dvd_mono
% 5.46/5.67 thf(fact_1942_mult__dvd__mono,axiom,
% 5.46/5.67 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ D )
% 5.46/5.67 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_dvd_mono
% 5.46/5.67 thf(fact_1943_dvd__triv__left,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_left
% 5.46/5.67 thf(fact_1944_dvd__triv__left,axiom,
% 5.46/5.67 ! [A: real,B2: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_left
% 5.46/5.67 thf(fact_1945_dvd__triv__left,axiom,
% 5.46/5.67 ! [A: rat,B2: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_left
% 5.46/5.67 thf(fact_1946_dvd__triv__left,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_left
% 5.46/5.67 thf(fact_1947_dvd__triv__left,axiom,
% 5.46/5.67 ! [A: int,B2: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_triv_left
% 5.46/5.67 thf(fact_1948_dvd__mult__left,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B2 ) @ C )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_left
% 5.46/5.67 thf(fact_1949_dvd__mult__left,axiom,
% 5.46/5.67 ! [A: real,B2: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ ( times_times_real @ A @ B2 ) @ C )
% 5.46/5.67 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_left
% 5.46/5.67 thf(fact_1950_dvd__mult__left,axiom,
% 5.46/5.67 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B2 ) @ C )
% 5.46/5.67 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_left
% 5.46/5.67 thf(fact_1951_dvd__mult__left,axiom,
% 5.46/5.67 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_left
% 5.46/5.67 thf(fact_1952_dvd__mult__left,axiom,
% 5.46/5.67 ! [A: int,B2: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ C )
% 5.46/5.67 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_left
% 5.46/5.67 thf(fact_1953_dvd__mult2,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult2
% 5.46/5.67 thf(fact_1954_dvd__mult2,axiom,
% 5.46/5.67 ! [A: real,B2: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ B2 )
% 5.46/5.67 => ( dvd_dvd_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult2
% 5.46/5.67 thf(fact_1955_dvd__mult2,axiom,
% 5.46/5.67 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ B2 )
% 5.46/5.67 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult2
% 5.46/5.67 thf(fact_1956_dvd__mult2,axiom,
% 5.46/5.67 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B2 )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult2
% 5.46/5.67 thf(fact_1957_dvd__mult2,axiom,
% 5.46/5.67 ! [A: int,B2: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B2 )
% 5.46/5.67 => ( dvd_dvd_int @ A @ ( times_times_int @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult2
% 5.46/5.67 thf(fact_1958_dvd__mult,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult
% 5.46/5.67 thf(fact_1959_dvd__mult,axiom,
% 5.46/5.67 ! [A: real,C: real,B2: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ C )
% 5.46/5.67 => ( dvd_dvd_real @ A @ ( times_times_real @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult
% 5.46/5.67 thf(fact_1960_dvd__mult,axiom,
% 5.46/5.67 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ C )
% 5.46/5.67 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult
% 5.46/5.67 thf(fact_1961_dvd__mult,axiom,
% 5.46/5.67 ! [A: nat,C: nat,B2: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ C )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult
% 5.46/5.67 thf(fact_1962_dvd__mult,axiom,
% 5.46/5.67 ! [A: int,C: int,B2: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ C )
% 5.46/5.67 => ( dvd_dvd_int @ A @ ( times_times_int @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult
% 5.46/5.67 thf(fact_1963_dvd__def,axiom,
% 5.46/5.67 ( dvd_dvd_Code_integer
% 5.46/5.67 = ( ^ [B3: code_integer,A4: code_integer] :
% 5.46/5.67 ? [K3: code_integer] :
% 5.46/5.67 ( A4
% 5.46/5.67 = ( times_3573771949741848930nteger @ B3 @ K3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_def
% 5.46/5.67 thf(fact_1964_dvd__def,axiom,
% 5.46/5.67 ( dvd_dvd_real
% 5.46/5.67 = ( ^ [B3: real,A4: real] :
% 5.46/5.67 ? [K3: real] :
% 5.46/5.67 ( A4
% 5.46/5.67 = ( times_times_real @ B3 @ K3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_def
% 5.46/5.67 thf(fact_1965_dvd__def,axiom,
% 5.46/5.67 ( dvd_dvd_rat
% 5.46/5.67 = ( ^ [B3: rat,A4: rat] :
% 5.46/5.67 ? [K3: rat] :
% 5.46/5.67 ( A4
% 5.46/5.67 = ( times_times_rat @ B3 @ K3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_def
% 5.46/5.67 thf(fact_1966_dvd__def,axiom,
% 5.46/5.67 ( dvd_dvd_nat
% 5.46/5.67 = ( ^ [B3: nat,A4: nat] :
% 5.46/5.67 ? [K3: nat] :
% 5.46/5.67 ( A4
% 5.46/5.67 = ( times_times_nat @ B3 @ K3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_def
% 5.46/5.67 thf(fact_1967_dvd__def,axiom,
% 5.46/5.67 ( dvd_dvd_int
% 5.46/5.67 = ( ^ [B3: int,A4: int] :
% 5.46/5.67 ? [K3: int] :
% 5.46/5.67 ( A4
% 5.46/5.67 = ( times_times_int @ B3 @ K3 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_def
% 5.46/5.67 thf(fact_1968_dvdI,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer,K: code_integer] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_3573771949741848930nteger @ B2 @ K ) )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdI
% 5.46/5.67 thf(fact_1969_dvdI,axiom,
% 5.46/5.67 ! [A: real,B2: real,K: real] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_times_real @ B2 @ K ) )
% 5.46/5.67 => ( dvd_dvd_real @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdI
% 5.46/5.67 thf(fact_1970_dvdI,axiom,
% 5.46/5.67 ! [A: rat,B2: rat,K: rat] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_times_rat @ B2 @ K ) )
% 5.46/5.67 => ( dvd_dvd_rat @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdI
% 5.46/5.67 thf(fact_1971_dvdI,axiom,
% 5.46/5.67 ! [A: nat,B2: nat,K: nat] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_times_nat @ B2 @ K ) )
% 5.46/5.67 => ( dvd_dvd_nat @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdI
% 5.46/5.67 thf(fact_1972_dvdI,axiom,
% 5.46/5.67 ! [A: int,B2: int,K: int] :
% 5.46/5.67 ( ( A
% 5.46/5.67 = ( times_times_int @ B2 @ K ) )
% 5.46/5.67 => ( dvd_dvd_int @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdI
% 5.46/5.67 thf(fact_1973_dvdE,axiom,
% 5.46/5.67 ! [B2: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B2 @ A )
% 5.46/5.67 => ~ ! [K2: code_integer] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_3573771949741848930nteger @ B2 @ K2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdE
% 5.46/5.67 thf(fact_1974_dvdE,axiom,
% 5.46/5.67 ! [B2: real,A: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ B2 @ A )
% 5.46/5.67 => ~ ! [K2: real] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_times_real @ B2 @ K2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdE
% 5.46/5.67 thf(fact_1975_dvdE,axiom,
% 5.46/5.67 ! [B2: rat,A: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ B2 @ A )
% 5.46/5.67 => ~ ! [K2: rat] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_times_rat @ B2 @ K2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdE
% 5.46/5.67 thf(fact_1976_dvdE,axiom,
% 5.46/5.67 ! [B2: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B2 @ A )
% 5.46/5.67 => ~ ! [K2: nat] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_times_nat @ B2 @ K2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdE
% 5.46/5.67 thf(fact_1977_dvdE,axiom,
% 5.46/5.67 ! [B2: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.67 => ~ ! [K2: int] :
% 5.46/5.67 ( A
% 5.46/5.67 != ( times_times_int @ B2 @ K2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvdE
% 5.46/5.67 thf(fact_1978_dvd__unit__imp__unit,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_unit_imp_unit
% 5.46/5.67 thf(fact_1979_dvd__unit__imp__unit,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_unit_imp_unit
% 5.46/5.67 thf(fact_1980_dvd__unit__imp__unit,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.67 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_unit_imp_unit
% 5.46/5.67 thf(fact_1981_unit__imp__dvd,axiom,
% 5.46/5.67 ! [B2: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_dvd
% 5.46/5.67 thf(fact_1982_unit__imp__dvd,axiom,
% 5.46/5.67 ! [B2: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.67 => ( dvd_dvd_nat @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_dvd
% 5.46/5.67 thf(fact_1983_unit__imp__dvd,axiom,
% 5.46/5.67 ! [B2: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.67 => ( dvd_dvd_int @ B2 @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % unit_imp_dvd
% 5.46/5.67 thf(fact_1984_one__dvd,axiom,
% 5.46/5.67 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_1985_one__dvd,axiom,
% 5.46/5.67 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_1986_one__dvd,axiom,
% 5.46/5.67 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_1987_one__dvd,axiom,
% 5.46/5.67 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_1988_one__dvd,axiom,
% 5.46/5.67 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_1989_one__dvd,axiom,
% 5.46/5.67 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.46/5.67
% 5.46/5.67 % one_dvd
% 5.46/5.67 thf(fact_1990_dvd__add__right__iff,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_right_iff
% 5.46/5.67 thf(fact_1991_dvd__add__right__iff,axiom,
% 5.46/5.67 ! [A: real,B2: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_right_iff
% 5.46/5.67 thf(fact_1992_dvd__add__right__iff,axiom,
% 5.46/5.67 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_right_iff
% 5.46/5.67 thf(fact_1993_dvd__add__right__iff,axiom,
% 5.46/5.67 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_right_iff
% 5.46/5.67 thf(fact_1994_dvd__add__right__iff,axiom,
% 5.46/5.67 ! [A: int,B2: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_right_iff
% 5.46/5.67 thf(fact_1995_dvd__add__left__iff,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_left_iff
% 5.46/5.67 thf(fact_1996_dvd__add__left__iff,axiom,
% 5.46/5.67 ! [A: real,C: real,B2: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_real @ A @ B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_left_iff
% 5.46/5.67 thf(fact_1997_dvd__add__left__iff,axiom,
% 5.46/5.67 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_rat @ A @ B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_left_iff
% 5.46/5.67 thf(fact_1998_dvd__add__left__iff,axiom,
% 5.46/5.67 ! [A: nat,C: nat,B2: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_nat @ A @ B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_left_iff
% 5.46/5.67 thf(fact_1999_dvd__add__left__iff,axiom,
% 5.46/5.67 ! [A: int,C: int,B2: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ C )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B2 @ C ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add_left_iff
% 5.46/5.67 thf(fact_2000_dvd__add,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B2 @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add
% 5.46/5.67 thf(fact_2001_dvd__add,axiom,
% 5.46/5.67 ! [A: real,B2: real,C: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_real @ A @ C )
% 5.46/5.67 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B2 @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add
% 5.46/5.67 thf(fact_2002_dvd__add,axiom,
% 5.46/5.67 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_rat @ A @ C )
% 5.46/5.67 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B2 @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add
% 5.46/5.67 thf(fact_2003_dvd__add,axiom,
% 5.46/5.67 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ A @ C )
% 5.46/5.67 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add
% 5.46/5.67 thf(fact_2004_dvd__add,axiom,
% 5.46/5.67 ! [A: int,B2: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_int @ A @ C )
% 5.46/5.67 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_add
% 5.46/5.67 thf(fact_2005_dvd__diff__commute,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B2 ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff_commute
% 5.46/5.67 thf(fact_2006_dvd__diff__commute,axiom,
% 5.46/5.67 ! [A: int,C: int,B2: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B2 ) )
% 5.46/5.67 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B2 @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff_commute
% 5.46/5.67 thf(fact_2007_dvd__diff,axiom,
% 5.46/5.67 ! [X4: code_integer,Y3: code_integer,Z: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ X4 @ Y3 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ X4 @ Z )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ X4 @ ( minus_8373710615458151222nteger @ Y3 @ Z ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff
% 5.46/5.67 thf(fact_2008_dvd__diff,axiom,
% 5.46/5.67 ! [X4: real,Y3: real,Z: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ X4 @ Y3 )
% 5.46/5.67 => ( ( dvd_dvd_real @ X4 @ Z )
% 5.46/5.67 => ( dvd_dvd_real @ X4 @ ( minus_minus_real @ Y3 @ Z ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff
% 5.46/5.67 thf(fact_2009_dvd__diff,axiom,
% 5.46/5.67 ! [X4: rat,Y3: rat,Z: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ X4 @ Y3 )
% 5.46/5.67 => ( ( dvd_dvd_rat @ X4 @ Z )
% 5.46/5.67 => ( dvd_dvd_rat @ X4 @ ( minus_minus_rat @ Y3 @ Z ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff
% 5.46/5.67 thf(fact_2010_dvd__diff,axiom,
% 5.46/5.67 ! [X4: int,Y3: int,Z: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ X4 @ Y3 )
% 5.46/5.67 => ( ( dvd_dvd_int @ X4 @ Z )
% 5.46/5.67 => ( dvd_dvd_int @ X4 @ ( minus_minus_int @ Y3 @ Z ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff
% 5.46/5.67 thf(fact_2011_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: code_integer,A: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.46/5.67 = ( divide6298287555418463151nteger @ B2 @ C ) )
% 5.46/5.67 = ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_2012_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: complex,A: complex,B2: complex] :
% 5.46/5.67 ( ( dvd_dvd_complex @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_complex @ C @ B2 )
% 5.46/5.67 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.46/5.67 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 5.46/5.67 = ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_2013_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: real,A: real,B2: real] :
% 5.46/5.67 ( ( dvd_dvd_real @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_real @ C @ B2 )
% 5.46/5.67 => ( ( ( divide_divide_real @ A @ C )
% 5.46/5.67 = ( divide_divide_real @ B2 @ C ) )
% 5.46/5.67 = ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_2014_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.67 ( ( dvd_dvd_rat @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_rat @ C @ B2 )
% 5.46/5.67 => ( ( ( divide_divide_rat @ A @ C )
% 5.46/5.67 = ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.67 = ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_2015_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ B2 )
% 5.46/5.67 => ( ( ( divide_divide_nat @ A @ C )
% 5.46/5.67 = ( divide_divide_nat @ B2 @ C ) )
% 5.46/5.67 = ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_2016_dvd__div__eq__iff,axiom,
% 5.46/5.67 ! [C: int,A: int,B2: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ B2 )
% 5.46/5.67 => ( ( ( divide_divide_int @ A @ C )
% 5.46/5.67 = ( divide_divide_int @ B2 @ C ) )
% 5.46/5.67 = ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_iff
% 5.46/5.67 thf(fact_2017_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.46/5.67 = ( divide6298287555418463151nteger @ B2 @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.46/5.67 => ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_2018_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: complex,C: complex,B2: complex] :
% 5.46/5.67 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.46/5.67 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_complex @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_complex @ C @ B2 )
% 5.46/5.67 => ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_2019_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: real,C: real,B2: real] :
% 5.46/5.67 ( ( ( divide_divide_real @ A @ C )
% 5.46/5.67 = ( divide_divide_real @ B2 @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_real @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_real @ C @ B2 )
% 5.46/5.67 => ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_2020_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.67 ( ( ( divide_divide_rat @ A @ C )
% 5.46/5.67 = ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_rat @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_rat @ C @ B2 )
% 5.46/5.67 => ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_2021_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: nat,C: nat,B2: nat] :
% 5.46/5.67 ( ( ( divide_divide_nat @ A @ C )
% 5.46/5.67 = ( divide_divide_nat @ B2 @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ B2 )
% 5.46/5.67 => ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_2022_dvd__div__eq__cancel,axiom,
% 5.46/5.67 ! [A: int,C: int,B2: int] :
% 5.46/5.67 ( ( ( divide_divide_int @ A @ C )
% 5.46/5.67 = ( divide_divide_int @ B2 @ C ) )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ A )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ B2 )
% 5.46/5.67 => ( A = B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_div_eq_cancel
% 5.46/5.67 thf(fact_2023_div__div__div__same,axiom,
% 5.46/5.67 ! [D: code_integer,B2: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ D @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B2 @ A )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B2 @ D ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ A @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_div_div_same
% 5.46/5.67 thf(fact_2024_div__div__div__same,axiom,
% 5.46/5.67 ! [D: nat,B2: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ D @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B2 @ A )
% 5.46/5.67 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B2 @ D ) )
% 5.46/5.67 = ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_div_div_same
% 5.46/5.67 thf(fact_2025_div__div__div__same,axiom,
% 5.46/5.67 ! [D: int,B2: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ D @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.67 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B2 @ D ) )
% 5.46/5.67 = ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % div_div_div_same
% 5.46/5.67 thf(fact_2026_dvd__power__same,axiom,
% 5.46/5.67 ! [X4: code_integer,Y3: code_integer,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ X4 @ Y3 )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ N ) @ ( power_8256067586552552935nteger @ Y3 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_same
% 5.46/5.67 thf(fact_2027_dvd__power__same,axiom,
% 5.46/5.67 ! [X4: nat,Y3: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ X4 @ Y3 )
% 5.46/5.67 => ( dvd_dvd_nat @ ( power_power_nat @ X4 @ N ) @ ( power_power_nat @ Y3 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_same
% 5.46/5.67 thf(fact_2028_dvd__power__same,axiom,
% 5.46/5.67 ! [X4: real,Y3: real,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_real @ X4 @ Y3 )
% 5.46/5.67 => ( dvd_dvd_real @ ( power_power_real @ X4 @ N ) @ ( power_power_real @ Y3 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_same
% 5.46/5.67 thf(fact_2029_dvd__power__same,axiom,
% 5.46/5.67 ! [X4: int,Y3: int,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_int @ X4 @ Y3 )
% 5.46/5.67 => ( dvd_dvd_int @ ( power_power_int @ X4 @ N ) @ ( power_power_int @ Y3 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_same
% 5.46/5.67 thf(fact_2030_dvd__power__same,axiom,
% 5.46/5.67 ! [X4: complex,Y3: complex,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_complex @ X4 @ Y3 )
% 5.46/5.67 => ( dvd_dvd_complex @ ( power_power_complex @ X4 @ N ) @ ( power_power_complex @ Y3 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_same
% 5.46/5.67 thf(fact_2031_dvd__mod__iff,axiom,
% 5.46/5.67 ! [C: nat,B2: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B2 ) )
% 5.46/5.67 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_iff
% 5.46/5.67 thf(fact_2032_dvd__mod__iff,axiom,
% 5.46/5.67 ! [C: int,B2: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B2 ) )
% 5.46/5.67 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_iff
% 5.46/5.67 thf(fact_2033_dvd__mod__iff,axiom,
% 5.46/5.67 ! [C: code_integer,B2: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B2 ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_iff
% 5.46/5.67 thf(fact_2034_dvd__mod__imp__dvd,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B2 ) )
% 5.46/5.67 => ( ( dvd_dvd_nat @ C @ B2 )
% 5.46/5.67 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_imp_dvd
% 5.46/5.67 thf(fact_2035_dvd__mod__imp__dvd,axiom,
% 5.46/5.67 ! [C: int,A: int,B2: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B2 ) )
% 5.46/5.67 => ( ( dvd_dvd_int @ C @ B2 )
% 5.46/5.67 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_imp_dvd
% 5.46/5.67 thf(fact_2036_dvd__mod__imp__dvd,axiom,
% 5.46/5.67 ! [C: code_integer,A: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B2 ) )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod_imp_dvd
% 5.46/5.67 thf(fact_2037_dvd__mod,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ K @ M )
% 5.46/5.67 => ( ( dvd_dvd_nat @ K @ N )
% 5.46/5.67 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod
% 5.46/5.67 thf(fact_2038_dvd__mod,axiom,
% 5.46/5.67 ! [K: int,M: int,N: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ K @ M )
% 5.46/5.67 => ( ( dvd_dvd_int @ K @ N )
% 5.46/5.67 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod
% 5.46/5.67 thf(fact_2039_dvd__mod,axiom,
% 5.46/5.67 ! [K: code_integer,M: code_integer,N: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ K @ N )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mod
% 5.46/5.67 thf(fact_2040_mod__mod__cancel,axiom,
% 5.46/5.67 ! [C: nat,B2: nat,A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ C @ B2 )
% 5.46/5.67 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B2 ) @ C )
% 5.46/5.67 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_mod_cancel
% 5.46/5.67 thf(fact_2041_mod__mod__cancel,axiom,
% 5.46/5.67 ! [C: int,B2: int,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ C @ B2 )
% 5.46/5.67 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B2 ) @ C )
% 5.46/5.67 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_mod_cancel
% 5.46/5.67 thf(fact_2042_mod__mod__cancel,axiom,
% 5.46/5.67 ! [C: code_integer,B2: code_integer,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.46/5.67 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B2 ) @ C )
% 5.46/5.67 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mod_mod_cancel
% 5.46/5.67 thf(fact_2043_dvd__diff__nat,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ K @ M )
% 5.46/5.67 => ( ( dvd_dvd_nat @ K @ N )
% 5.46/5.67 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_diff_nat
% 5.46/5.67 thf(fact_2044_zero__le,axiom,
% 5.46/5.67 ! [X4: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X4 ) ).
% 5.46/5.67
% 5.46/5.67 % zero_le
% 5.46/5.67 thf(fact_2045_le__numeral__extra_I3_J,axiom,
% 5.46/5.67 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.46/5.67
% 5.46/5.67 % le_numeral_extra(3)
% 5.46/5.67 thf(fact_2046_le__numeral__extra_I3_J,axiom,
% 5.46/5.67 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.46/5.67
% 5.46/5.67 % le_numeral_extra(3)
% 5.46/5.67 thf(fact_2047_le__numeral__extra_I3_J,axiom,
% 5.46/5.67 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.46/5.67
% 5.46/5.67 % le_numeral_extra(3)
% 5.46/5.67 thf(fact_2048_le__numeral__extra_I3_J,axiom,
% 5.46/5.67 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.46/5.67
% 5.46/5.67 % le_numeral_extra(3)
% 5.46/5.67 thf(fact_2049_zero__less__iff__neq__zero,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 = ( N != zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_less_iff_neq_zero
% 5.46/5.67 thf(fact_2050_gr__implies__not__zero,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ M @ N )
% 5.46/5.67 => ( N != zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % gr_implies_not_zero
% 5.46/5.67 thf(fact_2051_not__less__zero,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.46/5.67
% 5.46/5.67 % not_less_zero
% 5.46/5.67 thf(fact_2052_gr__zeroI,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( N != zero_zero_nat )
% 5.46/5.67 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % gr_zeroI
% 5.46/5.67 thf(fact_2053_less__numeral__extra_I3_J,axiom,
% 5.46/5.67 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.46/5.67
% 5.46/5.67 % less_numeral_extra(3)
% 5.46/5.67 thf(fact_2054_less__numeral__extra_I3_J,axiom,
% 5.46/5.67 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.46/5.67
% 5.46/5.67 % less_numeral_extra(3)
% 5.46/5.67 thf(fact_2055_less__numeral__extra_I3_J,axiom,
% 5.46/5.67 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.46/5.67
% 5.46/5.67 % less_numeral_extra(3)
% 5.46/5.67 thf(fact_2056_less__numeral__extra_I3_J,axiom,
% 5.46/5.67 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.46/5.67
% 5.46/5.67 % less_numeral_extra(3)
% 5.46/5.67 thf(fact_2057_field__lbound__gt__zero,axiom,
% 5.46/5.67 ! [D1: real,D22: real] :
% 5.46/5.67 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.46/5.67 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.46/5.67 => ? [E2: real] :
% 5.46/5.67 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.46/5.67 & ( ord_less_real @ E2 @ D1 )
% 5.46/5.67 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % field_lbound_gt_zero
% 5.46/5.67 thf(fact_2058_field__lbound__gt__zero,axiom,
% 5.46/5.67 ! [D1: rat,D22: rat] :
% 5.46/5.67 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.46/5.67 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.46/5.67 => ? [E2: rat] :
% 5.46/5.67 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.46/5.67 & ( ord_less_rat @ E2 @ D1 )
% 5.46/5.67 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % field_lbound_gt_zero
% 5.46/5.67 thf(fact_2059_zero__neq__numeral,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( zero_zero_complex
% 5.46/5.67 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_neq_numeral
% 5.46/5.67 thf(fact_2060_zero__neq__numeral,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( zero_zero_real
% 5.46/5.67 != ( numeral_numeral_real @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_neq_numeral
% 5.46/5.67 thf(fact_2061_zero__neq__numeral,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( zero_zero_rat
% 5.46/5.67 != ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_neq_numeral
% 5.46/5.67 thf(fact_2062_zero__neq__numeral,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( zero_zero_nat
% 5.46/5.67 != ( numeral_numeral_nat @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_neq_numeral
% 5.46/5.67 thf(fact_2063_zero__neq__numeral,axiom,
% 5.46/5.67 ! [N: num] :
% 5.46/5.67 ( zero_zero_int
% 5.46/5.67 != ( numeral_numeral_int @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_neq_numeral
% 5.46/5.67 thf(fact_2064_mult__right__cancel,axiom,
% 5.46/5.67 ! [C: real,A: real,B2: real] :
% 5.46/5.67 ( ( C != zero_zero_real )
% 5.46/5.67 => ( ( ( times_times_real @ A @ C )
% 5.46/5.67 = ( times_times_real @ B2 @ C ) )
% 5.46/5.67 = ( A = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_right_cancel
% 5.46/5.67 thf(fact_2065_mult__right__cancel,axiom,
% 5.46/5.67 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.67 ( ( C != zero_zero_rat )
% 5.46/5.67 => ( ( ( times_times_rat @ A @ C )
% 5.46/5.67 = ( times_times_rat @ B2 @ C ) )
% 5.46/5.67 = ( A = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_right_cancel
% 5.46/5.67 thf(fact_2066_mult__right__cancel,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.67 ( ( C != zero_zero_nat )
% 5.46/5.67 => ( ( ( times_times_nat @ A @ C )
% 5.46/5.67 = ( times_times_nat @ B2 @ C ) )
% 5.46/5.67 = ( A = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_right_cancel
% 5.46/5.67 thf(fact_2067_mult__right__cancel,axiom,
% 5.46/5.67 ! [C: int,A: int,B2: int] :
% 5.46/5.67 ( ( C != zero_zero_int )
% 5.46/5.67 => ( ( ( times_times_int @ A @ C )
% 5.46/5.67 = ( times_times_int @ B2 @ C ) )
% 5.46/5.67 = ( A = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_right_cancel
% 5.46/5.67 thf(fact_2068_mult__left__cancel,axiom,
% 5.46/5.67 ! [C: real,A: real,B2: real] :
% 5.46/5.67 ( ( C != zero_zero_real )
% 5.46/5.67 => ( ( ( times_times_real @ C @ A )
% 5.46/5.67 = ( times_times_real @ C @ B2 ) )
% 5.46/5.67 = ( A = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_left_cancel
% 5.46/5.67 thf(fact_2069_mult__left__cancel,axiom,
% 5.46/5.67 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.67 ( ( C != zero_zero_rat )
% 5.46/5.67 => ( ( ( times_times_rat @ C @ A )
% 5.46/5.67 = ( times_times_rat @ C @ B2 ) )
% 5.46/5.67 = ( A = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_left_cancel
% 5.46/5.67 thf(fact_2070_mult__left__cancel,axiom,
% 5.46/5.67 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.67 ( ( C != zero_zero_nat )
% 5.46/5.67 => ( ( ( times_times_nat @ C @ A )
% 5.46/5.67 = ( times_times_nat @ C @ B2 ) )
% 5.46/5.67 = ( A = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_left_cancel
% 5.46/5.67 thf(fact_2071_mult__left__cancel,axiom,
% 5.46/5.67 ! [C: int,A: int,B2: int] :
% 5.46/5.67 ( ( C != zero_zero_int )
% 5.46/5.67 => ( ( ( times_times_int @ C @ A )
% 5.46/5.67 = ( times_times_int @ C @ B2 ) )
% 5.46/5.67 = ( A = B2 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_left_cancel
% 5.46/5.67 thf(fact_2072_no__zero__divisors,axiom,
% 5.46/5.67 ! [A: real,B2: real] :
% 5.46/5.67 ( ( A != zero_zero_real )
% 5.46/5.67 => ( ( B2 != zero_zero_real )
% 5.46/5.67 => ( ( times_times_real @ A @ B2 )
% 5.46/5.67 != zero_zero_real ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % no_zero_divisors
% 5.46/5.67 thf(fact_2073_no__zero__divisors,axiom,
% 5.46/5.67 ! [A: rat,B2: rat] :
% 5.46/5.67 ( ( A != zero_zero_rat )
% 5.46/5.67 => ( ( B2 != zero_zero_rat )
% 5.46/5.67 => ( ( times_times_rat @ A @ B2 )
% 5.46/5.67 != zero_zero_rat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % no_zero_divisors
% 5.46/5.67 thf(fact_2074_no__zero__divisors,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( B2 != zero_zero_nat )
% 5.46/5.67 => ( ( times_times_nat @ A @ B2 )
% 5.46/5.67 != zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % no_zero_divisors
% 5.46/5.67 thf(fact_2075_no__zero__divisors,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( B2 != zero_zero_int )
% 5.46/5.67 => ( ( times_times_int @ A @ B2 )
% 5.46/5.67 != zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % no_zero_divisors
% 5.46/5.67 thf(fact_2076_divisors__zero,axiom,
% 5.46/5.67 ! [A: real,B2: real] :
% 5.46/5.67 ( ( ( times_times_real @ A @ B2 )
% 5.46/5.67 = zero_zero_real )
% 5.46/5.67 => ( ( A = zero_zero_real )
% 5.46/5.67 | ( B2 = zero_zero_real ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divisors_zero
% 5.46/5.67 thf(fact_2077_divisors__zero,axiom,
% 5.46/5.67 ! [A: rat,B2: rat] :
% 5.46/5.67 ( ( ( times_times_rat @ A @ B2 )
% 5.46/5.67 = zero_zero_rat )
% 5.46/5.67 => ( ( A = zero_zero_rat )
% 5.46/5.67 | ( B2 = zero_zero_rat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divisors_zero
% 5.46/5.67 thf(fact_2078_divisors__zero,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] :
% 5.46/5.67 ( ( ( times_times_nat @ A @ B2 )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 => ( ( A = zero_zero_nat )
% 5.46/5.67 | ( B2 = zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divisors_zero
% 5.46/5.67 thf(fact_2079_divisors__zero,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( ( times_times_int @ A @ B2 )
% 5.46/5.67 = zero_zero_int )
% 5.46/5.67 => ( ( A = zero_zero_int )
% 5.46/5.67 | ( B2 = zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % divisors_zero
% 5.46/5.67 thf(fact_2080_mult__not__zero,axiom,
% 5.46/5.67 ! [A: real,B2: real] :
% 5.46/5.67 ( ( ( times_times_real @ A @ B2 )
% 5.46/5.67 != zero_zero_real )
% 5.46/5.67 => ( ( A != zero_zero_real )
% 5.46/5.67 & ( B2 != zero_zero_real ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_not_zero
% 5.46/5.67 thf(fact_2081_mult__not__zero,axiom,
% 5.46/5.67 ! [A: rat,B2: rat] :
% 5.46/5.67 ( ( ( times_times_rat @ A @ B2 )
% 5.46/5.67 != zero_zero_rat )
% 5.46/5.67 => ( ( A != zero_zero_rat )
% 5.46/5.67 & ( B2 != zero_zero_rat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_not_zero
% 5.46/5.67 thf(fact_2082_mult__not__zero,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] :
% 5.46/5.67 ( ( ( times_times_nat @ A @ B2 )
% 5.46/5.67 != zero_zero_nat )
% 5.46/5.67 => ( ( A != zero_zero_nat )
% 5.46/5.67 & ( B2 != zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_not_zero
% 5.46/5.67 thf(fact_2083_mult__not__zero,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( ( times_times_int @ A @ B2 )
% 5.46/5.67 != zero_zero_int )
% 5.46/5.67 => ( ( A != zero_zero_int )
% 5.46/5.67 & ( B2 != zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % mult_not_zero
% 5.46/5.67 thf(fact_2084_zero__neq__one,axiom,
% 5.46/5.67 zero_zero_complex != one_one_complex ).
% 5.46/5.67
% 5.46/5.67 % zero_neq_one
% 5.46/5.67 thf(fact_2085_zero__neq__one,axiom,
% 5.46/5.67 zero_zero_real != one_one_real ).
% 5.46/5.67
% 5.46/5.67 % zero_neq_one
% 5.46/5.67 thf(fact_2086_zero__neq__one,axiom,
% 5.46/5.67 zero_zero_rat != one_one_rat ).
% 5.46/5.67
% 5.46/5.67 % zero_neq_one
% 5.46/5.67 thf(fact_2087_zero__neq__one,axiom,
% 5.46/5.67 zero_zero_nat != one_one_nat ).
% 5.46/5.67
% 5.46/5.67 % zero_neq_one
% 5.46/5.67 thf(fact_2088_zero__neq__one,axiom,
% 5.46/5.67 zero_zero_int != one_one_int ).
% 5.46/5.67
% 5.46/5.67 % zero_neq_one
% 5.46/5.67 thf(fact_2089_add_Ogroup__left__neutral,axiom,
% 5.46/5.67 ! [A: real] :
% 5.46/5.67 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.group_left_neutral
% 5.46/5.67 thf(fact_2090_add_Ogroup__left__neutral,axiom,
% 5.46/5.67 ! [A: rat] :
% 5.46/5.67 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.group_left_neutral
% 5.46/5.67 thf(fact_2091_add_Ogroup__left__neutral,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.group_left_neutral
% 5.46/5.67 thf(fact_2092_add_Ocomm__neutral,axiom,
% 5.46/5.67 ! [A: real] :
% 5.46/5.67 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.comm_neutral
% 5.46/5.67 thf(fact_2093_add_Ocomm__neutral,axiom,
% 5.46/5.67 ! [A: rat] :
% 5.46/5.67 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.comm_neutral
% 5.46/5.67 thf(fact_2094_add_Ocomm__neutral,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.comm_neutral
% 5.46/5.67 thf(fact_2095_add_Ocomm__neutral,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % add.comm_neutral
% 5.46/5.67 thf(fact_2096_comm__monoid__add__class_Oadd__0,axiom,
% 5.46/5.67 ! [A: real] :
% 5.46/5.67 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % comm_monoid_add_class.add_0
% 5.46/5.67 thf(fact_2097_comm__monoid__add__class_Oadd__0,axiom,
% 5.46/5.67 ! [A: rat] :
% 5.46/5.67 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % comm_monoid_add_class.add_0
% 5.46/5.67 thf(fact_2098_comm__monoid__add__class_Oadd__0,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % comm_monoid_add_class.add_0
% 5.46/5.67 thf(fact_2099_comm__monoid__add__class_Oadd__0,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % comm_monoid_add_class.add_0
% 5.46/5.67 thf(fact_2100_verit__sum__simplify,axiom,
% 5.46/5.67 ! [A: real] :
% 5.46/5.67 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % verit_sum_simplify
% 5.46/5.67 thf(fact_2101_verit__sum__simplify,axiom,
% 5.46/5.67 ! [A: rat] :
% 5.46/5.67 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % verit_sum_simplify
% 5.46/5.67 thf(fact_2102_verit__sum__simplify,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % verit_sum_simplify
% 5.46/5.67 thf(fact_2103_verit__sum__simplify,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.46/5.67 = A ) ).
% 5.46/5.67
% 5.46/5.67 % verit_sum_simplify
% 5.46/5.67 thf(fact_2104_eq__iff__diff__eq__0,axiom,
% 5.46/5.67 ( ( ^ [Y6: real,Z4: real] : ( Y6 = Z4 ) )
% 5.46/5.67 = ( ^ [A4: real,B3: real] :
% 5.46/5.67 ( ( minus_minus_real @ A4 @ B3 )
% 5.46/5.67 = zero_zero_real ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % eq_iff_diff_eq_0
% 5.46/5.67 thf(fact_2105_eq__iff__diff__eq__0,axiom,
% 5.46/5.67 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 5.46/5.67 = ( ^ [A4: rat,B3: rat] :
% 5.46/5.67 ( ( minus_minus_rat @ A4 @ B3 )
% 5.46/5.67 = zero_zero_rat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % eq_iff_diff_eq_0
% 5.46/5.67 thf(fact_2106_eq__iff__diff__eq__0,axiom,
% 5.46/5.67 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.67 = ( ^ [A4: int,B3: int] :
% 5.46/5.67 ( ( minus_minus_int @ A4 @ B3 )
% 5.46/5.67 = zero_zero_int ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % eq_iff_diff_eq_0
% 5.46/5.67 thf(fact_2107_power__not__zero,axiom,
% 5.46/5.67 ! [A: rat,N: nat] :
% 5.46/5.67 ( ( A != zero_zero_rat )
% 5.46/5.67 => ( ( power_power_rat @ A @ N )
% 5.46/5.67 != zero_zero_rat ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_not_zero
% 5.46/5.67 thf(fact_2108_power__not__zero,axiom,
% 5.46/5.67 ! [A: nat,N: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( power_power_nat @ A @ N )
% 5.46/5.67 != zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_not_zero
% 5.46/5.67 thf(fact_2109_power__not__zero,axiom,
% 5.46/5.67 ! [A: real,N: nat] :
% 5.46/5.67 ( ( A != zero_zero_real )
% 5.46/5.67 => ( ( power_power_real @ A @ N )
% 5.46/5.67 != zero_zero_real ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_not_zero
% 5.46/5.67 thf(fact_2110_power__not__zero,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( power_power_int @ A @ N )
% 5.46/5.67 != zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_not_zero
% 5.46/5.67 thf(fact_2111_power__not__zero,axiom,
% 5.46/5.67 ! [A: complex,N: nat] :
% 5.46/5.67 ( ( A != zero_zero_complex )
% 5.46/5.67 => ( ( power_power_complex @ A @ N )
% 5.46/5.67 != zero_zero_complex ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_not_zero
% 5.46/5.67 thf(fact_2112_not0__implies__Suc,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( N != zero_zero_nat )
% 5.46/5.67 => ? [M4: nat] :
% 5.46/5.67 ( N
% 5.46/5.67 = ( suc @ M4 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % not0_implies_Suc
% 5.46/5.67 thf(fact_2113_Zero__not__Suc,axiom,
% 5.46/5.67 ! [M: nat] :
% 5.46/5.67 ( zero_zero_nat
% 5.46/5.67 != ( suc @ M ) ) ).
% 5.46/5.67
% 5.46/5.67 % Zero_not_Suc
% 5.46/5.67 thf(fact_2114_Zero__neq__Suc,axiom,
% 5.46/5.67 ! [M: nat] :
% 5.46/5.67 ( zero_zero_nat
% 5.46/5.67 != ( suc @ M ) ) ).
% 5.46/5.67
% 5.46/5.67 % Zero_neq_Suc
% 5.46/5.67 thf(fact_2115_Suc__neq__Zero,axiom,
% 5.46/5.67 ! [M: nat] :
% 5.46/5.67 ( ( suc @ M )
% 5.46/5.67 != zero_zero_nat ) ).
% 5.46/5.67
% 5.46/5.67 % Suc_neq_Zero
% 5.46/5.67 thf(fact_2116_zero__induct,axiom,
% 5.46/5.67 ! [P: nat > $o,K: nat] :
% 5.46/5.67 ( ( P @ K )
% 5.46/5.67 => ( ! [N4: nat] :
% 5.46/5.67 ( ( P @ ( suc @ N4 ) )
% 5.46/5.67 => ( P @ N4 ) )
% 5.46/5.67 => ( P @ zero_zero_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_induct
% 5.46/5.67 thf(fact_2117_diff__induct,axiom,
% 5.46/5.67 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.46/5.67 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 5.46/5.67 => ( ! [Y4: nat] : ( P @ zero_zero_nat @ ( suc @ Y4 ) )
% 5.46/5.67 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.67 ( ( P @ X3 @ Y4 )
% 5.46/5.67 => ( P @ ( suc @ X3 ) @ ( suc @ Y4 ) ) )
% 5.46/5.67 => ( P @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % diff_induct
% 5.46/5.67 thf(fact_2118_nat__induct,axiom,
% 5.46/5.67 ! [P: nat > $o,N: nat] :
% 5.46/5.67 ( ( P @ zero_zero_nat )
% 5.46/5.67 => ( ! [N4: nat] :
% 5.46/5.67 ( ( P @ N4 )
% 5.46/5.67 => ( P @ ( suc @ N4 ) ) )
% 5.46/5.67 => ( P @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_induct
% 5.46/5.67 thf(fact_2119_old_Onat_Oexhaust,axiom,
% 5.46/5.67 ! [Y3: nat] :
% 5.46/5.67 ( ( Y3 != zero_zero_nat )
% 5.46/5.67 => ~ ! [Nat3: nat] :
% 5.46/5.67 ( Y3
% 5.46/5.67 != ( suc @ Nat3 ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % old.nat.exhaust
% 5.46/5.67 thf(fact_2120_nat_OdiscI,axiom,
% 5.46/5.67 ! [Nat: nat,X2: nat] :
% 5.46/5.67 ( ( Nat
% 5.46/5.67 = ( suc @ X2 ) )
% 5.46/5.67 => ( Nat != zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat.discI
% 5.46/5.67 thf(fact_2121_old_Onat_Odistinct_I1_J,axiom,
% 5.46/5.67 ! [Nat2: nat] :
% 5.46/5.67 ( zero_zero_nat
% 5.46/5.67 != ( suc @ Nat2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % old.nat.distinct(1)
% 5.46/5.67 thf(fact_2122_old_Onat_Odistinct_I2_J,axiom,
% 5.46/5.67 ! [Nat2: nat] :
% 5.46/5.67 ( ( suc @ Nat2 )
% 5.46/5.67 != zero_zero_nat ) ).
% 5.46/5.67
% 5.46/5.67 % old.nat.distinct(2)
% 5.46/5.67 thf(fact_2123_nat_Odistinct_I1_J,axiom,
% 5.46/5.67 ! [X2: nat] :
% 5.46/5.67 ( zero_zero_nat
% 5.46/5.67 != ( suc @ X2 ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat.distinct(1)
% 5.46/5.67 thf(fact_2124_infinite__descent0,axiom,
% 5.46/5.67 ! [P: nat > $o,N: nat] :
% 5.46/5.67 ( ( P @ zero_zero_nat )
% 5.46/5.67 => ( ! [N4: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.46/5.67 => ( ~ ( P @ N4 )
% 5.46/5.67 => ? [M5: nat] :
% 5.46/5.67 ( ( ord_less_nat @ M5 @ N4 )
% 5.46/5.67 & ~ ( P @ M5 ) ) ) )
% 5.46/5.67 => ( P @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % infinite_descent0
% 5.46/5.67 thf(fact_2125_gr__implies__not0,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ M @ N )
% 5.46/5.67 => ( N != zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % gr_implies_not0
% 5.46/5.67 thf(fact_2126_less__zeroE,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.46/5.67
% 5.46/5.67 % less_zeroE
% 5.46/5.67 thf(fact_2127_not__less0,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.46/5.67
% 5.46/5.67 % not_less0
% 5.46/5.67 thf(fact_2128_not__gr0,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.46/5.67 = ( N = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % not_gr0
% 5.46/5.67 thf(fact_2129_gr0I,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( N != zero_zero_nat )
% 5.46/5.67 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.67
% 5.46/5.67 % gr0I
% 5.46/5.67 thf(fact_2130_bot__nat__0_Oextremum__strict,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.46/5.67
% 5.46/5.67 % bot_nat_0.extremum_strict
% 5.46/5.67 thf(fact_2131_le__0__eq,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.46/5.67 = ( N = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % le_0_eq
% 5.46/5.67 thf(fact_2132_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.46/5.67 => ( A = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % bot_nat_0.extremum_uniqueI
% 5.46/5.67 thf(fact_2133_bot__nat__0_Oextremum__unique,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.46/5.67 = ( A = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % bot_nat_0.extremum_unique
% 5.46/5.67 thf(fact_2134_less__eq__nat_Osimps_I1_J,axiom,
% 5.46/5.67 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.46/5.67
% 5.46/5.67 % less_eq_nat.simps(1)
% 5.46/5.67 thf(fact_2135_add__eq__self__zero,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ( plus_plus_nat @ M @ N )
% 5.46/5.67 = M )
% 5.46/5.67 => ( N = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % add_eq_self_zero
% 5.46/5.67 thf(fact_2136_plus__nat_Oadd__0,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.46/5.67 = N ) ).
% 5.46/5.67
% 5.46/5.67 % plus_nat.add_0
% 5.46/5.67 thf(fact_2137_diffs0__imp__equal,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ( minus_minus_nat @ M @ N )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 => ( ( ( minus_minus_nat @ N @ M )
% 5.46/5.67 = zero_zero_nat )
% 5.46/5.67 => ( M = N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % diffs0_imp_equal
% 5.46/5.67 thf(fact_2138_minus__nat_Odiff__0,axiom,
% 5.46/5.67 ! [M: nat] :
% 5.46/5.67 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.46/5.67 = M ) ).
% 5.46/5.67
% 5.46/5.67 % minus_nat.diff_0
% 5.46/5.67 thf(fact_2139_nat__mult__eq__cancel__disj,axiom,
% 5.46/5.67 ! [K: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( ( times_times_nat @ K @ M )
% 5.46/5.67 = ( times_times_nat @ K @ N ) )
% 5.46/5.67 = ( ( K = zero_zero_nat )
% 5.46/5.67 | ( M = N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % nat_mult_eq_cancel_disj
% 5.46/5.67 thf(fact_2140_mult__0,axiom,
% 5.46/5.67 ! [N: nat] :
% 5.46/5.67 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.46/5.67 = zero_zero_nat ) ).
% 5.46/5.67
% 5.46/5.67 % mult_0
% 5.46/5.67 thf(fact_2141_even__zero,axiom,
% 5.46/5.67 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.46/5.67
% 5.46/5.67 % even_zero
% 5.46/5.67 thf(fact_2142_even__zero,axiom,
% 5.46/5.67 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.46/5.67
% 5.46/5.67 % even_zero
% 5.46/5.67 thf(fact_2143_even__zero,axiom,
% 5.46/5.67 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.46/5.67
% 5.46/5.67 % even_zero
% 5.46/5.67 thf(fact_2144_is__unitE,axiom,
% 5.46/5.67 ! [A: code_integer,C: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.67 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ! [B5: code_integer] :
% 5.46/5.67 ( ( B5 != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.46/5.67 = B5 )
% 5.46/5.67 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 5.46/5.67 = A )
% 5.46/5.67 => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 5.46/5.67 = one_one_Code_integer )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.46/5.67 != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unitE
% 5.46/5.67 thf(fact_2145_is__unitE,axiom,
% 5.46/5.67 ! [A: nat,C: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.67 => ~ ( ( A != zero_zero_nat )
% 5.46/5.67 => ! [B5: nat] :
% 5.46/5.67 ( ( B5 != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 5.46/5.67 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.46/5.67 = B5 )
% 5.46/5.67 => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 5.46/5.67 = A )
% 5.46/5.67 => ( ( ( times_times_nat @ A @ B5 )
% 5.46/5.67 = one_one_nat )
% 5.46/5.67 => ( ( divide_divide_nat @ C @ A )
% 5.46/5.67 != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unitE
% 5.46/5.67 thf(fact_2146_is__unitE,axiom,
% 5.46/5.67 ! [A: int,C: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.67 => ~ ( ( A != zero_zero_int )
% 5.46/5.67 => ! [B5: int] :
% 5.46/5.67 ( ( B5 != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 5.46/5.67 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.46/5.67 = B5 )
% 5.46/5.67 => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 5.46/5.67 = A )
% 5.46/5.67 => ( ( ( times_times_int @ A @ B5 )
% 5.46/5.67 = one_one_int )
% 5.46/5.67 => ( ( divide_divide_int @ C @ A )
% 5.46/5.67 != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unitE
% 5.46/5.67 thf(fact_2147_is__unit__div__mult__cancel__left,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B2 ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_left
% 5.46/5.67 thf(fact_2148_is__unit__div__mult__cancel__left,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B2 ) )
% 5.46/5.67 = ( divide_divide_nat @ one_one_nat @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_left
% 5.46/5.67 thf(fact_2149_is__unit__div__mult__cancel__left,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B2 ) )
% 5.46/5.67 = ( divide_divide_int @ one_one_int @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_left
% 5.46/5.67 thf(fact_2150_is__unit__div__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: code_integer,B2: code_integer] :
% 5.46/5.67 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B2 @ A ) )
% 5.46/5.67 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_right
% 5.46/5.67 thf(fact_2151_is__unit__div__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: nat,B2: nat] :
% 5.46/5.67 ( ( A != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B2 @ A ) )
% 5.46/5.67 = ( divide_divide_nat @ one_one_nat @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_right
% 5.46/5.67 thf(fact_2152_is__unit__div__mult__cancel__right,axiom,
% 5.46/5.67 ! [A: int,B2: int] :
% 5.46/5.67 ( ( A != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ A ) )
% 5.46/5.67 = ( divide_divide_int @ one_one_int @ B2 ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % is_unit_div_mult_cancel_right
% 5.46/5.67 thf(fact_2153_dvd__power__iff,axiom,
% 5.46/5.67 ! [X4: code_integer,M: nat,N: nat] :
% 5.46/5.67 ( ( X4 != zero_z3403309356797280102nteger )
% 5.46/5.67 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ M ) @ ( power_8256067586552552935nteger @ X4 @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_Code_integer @ X4 @ one_one_Code_integer )
% 5.46/5.67 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_iff
% 5.46/5.67 thf(fact_2154_dvd__power__iff,axiom,
% 5.46/5.67 ! [X4: nat,M: nat,N: nat] :
% 5.46/5.67 ( ( X4 != zero_zero_nat )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( power_power_nat @ X4 @ M ) @ ( power_power_nat @ X4 @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_nat @ X4 @ one_one_nat )
% 5.46/5.67 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_iff
% 5.46/5.67 thf(fact_2155_dvd__power__iff,axiom,
% 5.46/5.67 ! [X4: int,M: nat,N: nat] :
% 5.46/5.67 ( ( X4 != zero_zero_int )
% 5.46/5.67 => ( ( dvd_dvd_int @ ( power_power_int @ X4 @ M ) @ ( power_power_int @ X4 @ N ) )
% 5.46/5.67 = ( ( dvd_dvd_int @ X4 @ one_one_int )
% 5.46/5.67 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power_iff
% 5.46/5.67 thf(fact_2156_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X4: code_integer] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X4 = one_one_Code_integer ) )
% 5.46/5.67 => ( dvd_dvd_Code_integer @ X4 @ ( power_8256067586552552935nteger @ X4 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_2157_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X4: rat] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X4 = one_one_rat ) )
% 5.46/5.67 => ( dvd_dvd_rat @ X4 @ ( power_power_rat @ X4 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_2158_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X4: nat] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X4 = one_one_nat ) )
% 5.46/5.67 => ( dvd_dvd_nat @ X4 @ ( power_power_nat @ X4 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_2159_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X4: real] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X4 = one_one_real ) )
% 5.46/5.67 => ( dvd_dvd_real @ X4 @ ( power_power_real @ X4 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_2160_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X4: int] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X4 = one_one_int ) )
% 5.46/5.67 => ( dvd_dvd_int @ X4 @ ( power_power_int @ X4 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_2161_dvd__power,axiom,
% 5.46/5.67 ! [N: nat,X4: complex] :
% 5.46/5.67 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 | ( X4 = one_one_complex ) )
% 5.46/5.67 => ( dvd_dvd_complex @ X4 @ ( power_power_complex @ X4 @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_power
% 5.46/5.67 thf(fact_2162_enat__0__less__mult__iff,axiom,
% 5.46/5.67 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.67 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.46/5.67 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.46/5.67 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % enat_0_less_mult_iff
% 5.46/5.67 thf(fact_2163_not__iless0,axiom,
% 5.46/5.67 ! [N: extended_enat] :
% 5.46/5.67 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.46/5.67
% 5.46/5.67 % not_iless0
% 5.46/5.67 thf(fact_2164_iadd__is__0,axiom,
% 5.46/5.67 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.67 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.46/5.67 = zero_z5237406670263579293d_enat )
% 5.46/5.67 = ( ( M = zero_z5237406670263579293d_enat )
% 5.46/5.67 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % iadd_is_0
% 5.46/5.67 thf(fact_2165_ile0__eq,axiom,
% 5.46/5.67 ! [N: extended_enat] :
% 5.46/5.67 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.46/5.67 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.46/5.67
% 5.46/5.67 % ile0_eq
% 5.46/5.67 thf(fact_2166_i0__lb,axiom,
% 5.46/5.67 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.46/5.67
% 5.46/5.67 % i0_lb
% 5.46/5.67 thf(fact_2167_dvd__mult__cancel1,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.46/5.67 = ( N = one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel1
% 5.46/5.67 thf(fact_2168_dvd__mult__cancel2,axiom,
% 5.46/5.67 ! [M: nat,N: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.46/5.67 = ( N = one_one_nat ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % dvd_mult_cancel2
% 5.46/5.67 thf(fact_2169_power__eq__imp__eq__base,axiom,
% 5.46/5.67 ! [A: real,N: nat,B2: real] :
% 5.46/5.67 ( ( ( power_power_real @ A @ N )
% 5.46/5.67 = ( power_power_real @ B2 @ N ) )
% 5.46/5.67 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.67 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( A = B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_eq_imp_eq_base
% 5.46/5.67 thf(fact_2170_power__eq__imp__eq__base,axiom,
% 5.46/5.67 ! [A: rat,N: nat,B2: rat] :
% 5.46/5.67 ( ( ( power_power_rat @ A @ N )
% 5.46/5.67 = ( power_power_rat @ B2 @ N ) )
% 5.46/5.67 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.67 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( A = B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_eq_imp_eq_base
% 5.46/5.67 thf(fact_2171_power__eq__imp__eq__base,axiom,
% 5.46/5.67 ! [A: nat,N: nat,B2: nat] :
% 5.46/5.67 ( ( ( power_power_nat @ A @ N )
% 5.46/5.67 = ( power_power_nat @ B2 @ N ) )
% 5.46/5.67 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.67 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( A = B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_eq_imp_eq_base
% 5.46/5.67 thf(fact_2172_power__eq__imp__eq__base,axiom,
% 5.46/5.67 ! [A: int,N: nat,B2: int] :
% 5.46/5.67 ( ( ( power_power_int @ A @ N )
% 5.46/5.67 = ( power_power_int @ B2 @ N ) )
% 5.46/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( A = B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_eq_imp_eq_base
% 5.46/5.67 thf(fact_2173_power__eq__iff__eq__base,axiom,
% 5.46/5.67 ! [N: nat,A: real,B2: real] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.67 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.67 => ( ( ( power_power_real @ A @ N )
% 5.46/5.67 = ( power_power_real @ B2 @ N ) )
% 5.46/5.67 = ( A = B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_eq_iff_eq_base
% 5.46/5.67 thf(fact_2174_power__eq__iff__eq__base,axiom,
% 5.46/5.67 ! [N: nat,A: rat,B2: rat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.67 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.67 => ( ( ( power_power_rat @ A @ N )
% 5.46/5.67 = ( power_power_rat @ B2 @ N ) )
% 5.46/5.67 = ( A = B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_eq_iff_eq_base
% 5.46/5.67 thf(fact_2175_power__eq__iff__eq__base,axiom,
% 5.46/5.67 ! [N: nat,A: nat,B2: nat] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.67 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.67 => ( ( ( power_power_nat @ A @ N )
% 5.46/5.67 = ( power_power_nat @ B2 @ N ) )
% 5.46/5.67 = ( A = B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_eq_iff_eq_base
% 5.46/5.67 thf(fact_2176_power__eq__iff__eq__base,axiom,
% 5.46/5.67 ! [N: nat,A: int,B2: int] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.67 => ( ( ( power_power_int @ A @ N )
% 5.46/5.67 = ( power_power_int @ B2 @ N ) )
% 5.46/5.67 = ( A = B2 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_eq_iff_eq_base
% 5.46/5.67 thf(fact_2177_int__power__div__base,axiom,
% 5.46/5.67 ! [M: nat,K: int] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.67 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.67 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.46/5.67 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % int_power_div_base
% 5.46/5.67 thf(fact_2178_zero__less__power__eq,axiom,
% 5.46/5.67 ! [A: real,N: nat] :
% 5.46/5.67 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.46/5.67 = ( ( N = zero_zero_nat )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A != zero_zero_real ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_less_power_eq
% 5.46/5.67 thf(fact_2179_zero__less__power__eq,axiom,
% 5.46/5.67 ! [A: rat,N: nat] :
% 5.46/5.67 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.46/5.67 = ( ( N = zero_zero_nat )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A != zero_zero_rat ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_less_power_eq
% 5.46/5.67 thf(fact_2180_zero__less__power__eq,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.46/5.67 = ( ( N = zero_zero_nat )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A != zero_zero_int ) )
% 5.46/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % zero_less_power_eq
% 5.46/5.67 thf(fact_2181_even__signed__take__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.46/5.67 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_signed_take_bit_iff
% 5.46/5.67 thf(fact_2182_even__signed__take__bit__iff,axiom,
% 5.46/5.67 ! [M: nat,A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.46/5.67 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_signed_take_bit_iff
% 5.46/5.67 thf(fact_2183_realpow__pos__nth,axiom,
% 5.46/5.67 ! [N: nat,A: real] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.67 => ? [R3: real] :
% 5.46/5.67 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.46/5.67 & ( ( power_power_real @ R3 @ N )
% 5.46/5.67 = A ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % realpow_pos_nth
% 5.46/5.67 thf(fact_2184_realpow__pos__nth__unique,axiom,
% 5.46/5.67 ! [N: nat,A: real] :
% 5.46/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.67 => ? [X3: real] :
% 5.46/5.67 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.46/5.67 & ( ( power_power_real @ X3 @ N )
% 5.46/5.67 = A )
% 5.46/5.67 & ! [Y5: real] :
% 5.46/5.67 ( ( ( ord_less_real @ zero_zero_real @ Y5 )
% 5.46/5.67 & ( ( power_power_real @ Y5 @ N )
% 5.46/5.67 = A ) )
% 5.46/5.67 => ( Y5 = X3 ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % realpow_pos_nth_unique
% 5.46/5.67 thf(fact_2185_power__le__zero__eq,axiom,
% 5.46/5.67 ! [A: real,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq
% 5.46/5.67 thf(fact_2186_power__le__zero__eq,axiom,
% 5.46/5.67 ! [A: rat,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq
% 5.46/5.67 thf(fact_2187_power__le__zero__eq,axiom,
% 5.46/5.67 ! [A: int,N: nat] :
% 5.46/5.67 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.46/5.67 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.46/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.67 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.46/5.67
% 5.46/5.67 % power_le_zero_eq
% 5.46/5.67 thf(fact_2188_even__iff__mod__2__eq__zero,axiom,
% 5.46/5.67 ! [A: nat] :
% 5.46/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.67 = zero_zero_nat ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_iff_mod_2_eq_zero
% 5.46/5.67 thf(fact_2189_even__iff__mod__2__eq__zero,axiom,
% 5.46/5.67 ! [A: int] :
% 5.46/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.67 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.67 = zero_zero_int ) ) ).
% 5.46/5.67
% 5.46/5.67 % even_iff_mod_2_eq_zero
% 5.46/5.67 thf(fact_2190_even__iff__mod__2__eq__zero,axiom,
% 5.46/5.67 ! [A: code_integer] :
% 5.46/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % even_iff_mod_2_eq_zero
% 5.46/5.68 thf(fact_2191_odd__pos,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % odd_pos
% 5.46/5.68 thf(fact_2192_signed__take__bit__int__less__self__iff,axiom,
% 5.46/5.68 ! [N: nat,K: int] :
% 5.46/5.68 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.46/5.68 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_int_less_self_iff
% 5.46/5.68 thf(fact_2193_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.46/5.68 ! [K: int,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.46/5.68 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_int_greater_eq_self_iff
% 5.46/5.68 thf(fact_2194_signed__take__bit__int__less__exp,axiom,
% 5.46/5.68 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % signed_take_bit_int_less_exp
% 5.46/5.68 thf(fact_2195_is__unit__mult__iff,axiom,
% 5.46/5.68 ! [A: code_integer,B2: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B2 ) @ one_one_Code_integer )
% 5.46/5.68 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.68 & ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % is_unit_mult_iff
% 5.46/5.68 thf(fact_2196_is__unit__mult__iff,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ one_one_nat )
% 5.46/5.68 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.68 & ( dvd_dvd_nat @ B2 @ one_one_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % is_unit_mult_iff
% 5.46/5.68 thf(fact_2197_is__unit__mult__iff,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ one_one_int )
% 5.46/5.68 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.68 & ( dvd_dvd_int @ B2 @ one_one_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % is_unit_mult_iff
% 5.46/5.68 thf(fact_2198_dvd__mult__unit__iff,axiom,
% 5.46/5.68 ! [B2: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.68 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B2 ) )
% 5.46/5.68 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_mult_unit_iff
% 5.46/5.68 thf(fact_2199_dvd__mult__unit__iff,axiom,
% 5.46/5.68 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.68 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B2 ) )
% 5.46/5.68 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_mult_unit_iff
% 5.46/5.68 thf(fact_2200_dvd__mult__unit__iff,axiom,
% 5.46/5.68 ! [B2: int,A: int,C: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.68 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B2 ) )
% 5.46/5.68 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_mult_unit_iff
% 5.46/5.68 thf(fact_2201_mult__unit__dvd__iff,axiom,
% 5.46/5.68 ! [B2: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.68 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B2 ) @ C )
% 5.46/5.68 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_unit_dvd_iff
% 5.46/5.68 thf(fact_2202_mult__unit__dvd__iff,axiom,
% 5.46/5.68 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.68 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 5.46/5.68 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_unit_dvd_iff
% 5.46/5.68 thf(fact_2203_mult__unit__dvd__iff,axiom,
% 5.46/5.68 ! [B2: int,A: int,C: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.68 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ C )
% 5.46/5.68 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_unit_dvd_iff
% 5.46/5.68 thf(fact_2204_dvd__mult__unit__iff_H,axiom,
% 5.46/5.68 ! [B2: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.68 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 5.46/5.68 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_mult_unit_iff'
% 5.46/5.68 thf(fact_2205_dvd__mult__unit__iff_H,axiom,
% 5.46/5.68 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.68 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 5.46/5.68 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_mult_unit_iff'
% 5.46/5.68 thf(fact_2206_dvd__mult__unit__iff_H,axiom,
% 5.46/5.68 ! [B2: int,A: int,C: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.68 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B2 @ C ) )
% 5.46/5.68 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_mult_unit_iff'
% 5.46/5.68 thf(fact_2207_mult__unit__dvd__iff_H,axiom,
% 5.46/5.68 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.68 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B2 ) @ C )
% 5.46/5.68 = ( dvd_dvd_Code_integer @ B2 @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_unit_dvd_iff'
% 5.46/5.68 thf(fact_2208_mult__unit__dvd__iff_H,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.68 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B2 ) @ C )
% 5.46/5.68 = ( dvd_dvd_nat @ B2 @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_unit_dvd_iff'
% 5.46/5.68 thf(fact_2209_mult__unit__dvd__iff_H,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.68 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B2 ) @ C )
% 5.46/5.68 = ( dvd_dvd_int @ B2 @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_unit_dvd_iff'
% 5.46/5.68 thf(fact_2210_unit__mult__left__cancel,axiom,
% 5.46/5.68 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.68 => ( ( ( times_3573771949741848930nteger @ A @ B2 )
% 5.46/5.68 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.46/5.68 = ( B2 = C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % unit_mult_left_cancel
% 5.46/5.68 thf(fact_2211_unit__mult__left__cancel,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.68 => ( ( ( times_times_nat @ A @ B2 )
% 5.46/5.68 = ( times_times_nat @ A @ C ) )
% 5.46/5.68 = ( B2 = C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % unit_mult_left_cancel
% 5.46/5.68 thf(fact_2212_unit__mult__left__cancel,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.68 => ( ( ( times_times_int @ A @ B2 )
% 5.46/5.68 = ( times_times_int @ A @ C ) )
% 5.46/5.68 = ( B2 = C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % unit_mult_left_cancel
% 5.46/5.68 thf(fact_2213_unit__mult__right__cancel,axiom,
% 5.46/5.68 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.68 => ( ( ( times_3573771949741848930nteger @ B2 @ A )
% 5.46/5.68 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.46/5.68 = ( B2 = C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % unit_mult_right_cancel
% 5.46/5.68 thf(fact_2214_unit__mult__right__cancel,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.68 => ( ( ( times_times_nat @ B2 @ A )
% 5.46/5.68 = ( times_times_nat @ C @ A ) )
% 5.46/5.68 = ( B2 = C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % unit_mult_right_cancel
% 5.46/5.68 thf(fact_2215_unit__mult__right__cancel,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.68 => ( ( ( times_times_int @ B2 @ A )
% 5.46/5.68 = ( times_times_int @ C @ A ) )
% 5.46/5.68 = ( B2 = C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % unit_mult_right_cancel
% 5.46/5.68 thf(fact_2216_dvd__div__mult,axiom,
% 5.46/5.68 ! [C: code_integer,B2: code_integer,A: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.46/5.68 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B2 @ C ) @ A )
% 5.46/5.68 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B2 @ A ) @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_mult
% 5.46/5.68 thf(fact_2217_dvd__div__mult,axiom,
% 5.46/5.68 ! [C: nat,B2: nat,A: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ C @ B2 )
% 5.46/5.68 => ( ( times_times_nat @ ( divide_divide_nat @ B2 @ C ) @ A )
% 5.46/5.68 = ( divide_divide_nat @ ( times_times_nat @ B2 @ A ) @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_mult
% 5.46/5.68 thf(fact_2218_dvd__div__mult,axiom,
% 5.46/5.68 ! [C: int,B2: int,A: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ C @ B2 )
% 5.46/5.68 => ( ( times_times_int @ ( divide_divide_int @ B2 @ C ) @ A )
% 5.46/5.68 = ( divide_divide_int @ ( times_times_int @ B2 @ A ) @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_mult
% 5.46/5.68 thf(fact_2219_div__mult__swap,axiom,
% 5.46/5.68 ! [C: code_integer,B2: code_integer,A: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.46/5.68 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B2 @ C ) )
% 5.46/5.68 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_mult_swap
% 5.46/5.68 thf(fact_2220_div__mult__swap,axiom,
% 5.46/5.68 ! [C: nat,B2: nat,A: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ C @ B2 )
% 5.46/5.68 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B2 @ C ) )
% 5.46/5.68 = ( divide_divide_nat @ ( times_times_nat @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_mult_swap
% 5.46/5.68 thf(fact_2221_div__mult__swap,axiom,
% 5.46/5.68 ! [C: int,B2: int,A: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ C @ B2 )
% 5.46/5.68 => ( ( times_times_int @ A @ ( divide_divide_int @ B2 @ C ) )
% 5.46/5.68 = ( divide_divide_int @ ( times_times_int @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_mult_swap
% 5.46/5.68 thf(fact_2222_div__div__eq__right,axiom,
% 5.46/5.68 ! [C: code_integer,B2: code_integer,A: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.46/5.68 => ( ( dvd_dvd_Code_integer @ B2 @ A )
% 5.46/5.68 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B2 @ C ) )
% 5.46/5.68 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_div_eq_right
% 5.46/5.68 thf(fact_2223_div__div__eq__right,axiom,
% 5.46/5.68 ! [C: nat,B2: nat,A: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ C @ B2 )
% 5.46/5.68 => ( ( dvd_dvd_nat @ B2 @ A )
% 5.46/5.68 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B2 @ C ) )
% 5.46/5.68 = ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_div_eq_right
% 5.46/5.68 thf(fact_2224_div__div__eq__right,axiom,
% 5.46/5.68 ! [C: int,B2: int,A: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ C @ B2 )
% 5.46/5.68 => ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.68 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B2 @ C ) )
% 5.46/5.68 = ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_div_eq_right
% 5.46/5.68 thf(fact_2225_dvd__div__mult2__eq,axiom,
% 5.46/5.68 ! [B2: code_integer,C: code_integer,A: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B2 @ C ) @ A )
% 5.46/5.68 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 5.46/5.68 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_mult2_eq
% 5.46/5.68 thf(fact_2226_dvd__div__mult2__eq,axiom,
% 5.46/5.68 ! [B2: nat,C: nat,A: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( times_times_nat @ B2 @ C ) @ A )
% 5.46/5.68 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 5.46/5.68 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_mult2_eq
% 5.46/5.68 thf(fact_2227_dvd__div__mult2__eq,axiom,
% 5.46/5.68 ! [B2: int,C: int,A: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ ( times_times_int @ B2 @ C ) @ A )
% 5.46/5.68 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ C ) )
% 5.46/5.68 = ( divide_divide_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_mult2_eq
% 5.46/5.68 thf(fact_2228_dvd__mult__imp__div,axiom,
% 5.46/5.68 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B2 )
% 5.46/5.68 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B2 @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_mult_imp_div
% 5.46/5.68 thf(fact_2229_dvd__mult__imp__div,axiom,
% 5.46/5.68 ! [A: nat,C: nat,B2: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B2 )
% 5.46/5.68 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B2 @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_mult_imp_div
% 5.46/5.68 thf(fact_2230_dvd__mult__imp__div,axiom,
% 5.46/5.68 ! [A: int,C: int,B2: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B2 )
% 5.46/5.68 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B2 @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_mult_imp_div
% 5.46/5.68 thf(fact_2231_div__mult__div__if__dvd,axiom,
% 5.46/5.68 ! [B2: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ B2 @ A )
% 5.46/5.68 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.46/5.68 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.46/5.68 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B2 @ D ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_mult_div_if_dvd
% 5.46/5.68 thf(fact_2232_div__mult__div__if__dvd,axiom,
% 5.46/5.68 ! [B2: nat,A: nat,D: nat,C: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ B2 @ A )
% 5.46/5.68 => ( ( dvd_dvd_nat @ D @ C )
% 5.46/5.68 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ ( divide_divide_nat @ C @ D ) )
% 5.46/5.68 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_mult_div_if_dvd
% 5.46/5.68 thf(fact_2233_div__mult__div__if__dvd,axiom,
% 5.46/5.68 ! [B2: int,A: int,D: int,C: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.68 => ( ( dvd_dvd_int @ D @ C )
% 5.46/5.68 => ( ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ C @ D ) )
% 5.46/5.68 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_mult_div_if_dvd
% 5.46/5.68 thf(fact_2234_unit__div__cancel,axiom,
% 5.46/5.68 ! [A: code_integer,B2: code_integer,C: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.46/5.68 => ( ( ( divide6298287555418463151nteger @ B2 @ A )
% 5.46/5.68 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.46/5.68 = ( B2 = C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % unit_div_cancel
% 5.46/5.68 thf(fact_2235_unit__div__cancel,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.46/5.68 => ( ( ( divide_divide_nat @ B2 @ A )
% 5.46/5.68 = ( divide_divide_nat @ C @ A ) )
% 5.46/5.68 = ( B2 = C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % unit_div_cancel
% 5.46/5.68 thf(fact_2236_unit__div__cancel,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.46/5.68 => ( ( ( divide_divide_int @ B2 @ A )
% 5.46/5.68 = ( divide_divide_int @ C @ A ) )
% 5.46/5.68 = ( B2 = C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % unit_div_cancel
% 5.46/5.68 thf(fact_2237_div__unit__dvd__iff,axiom,
% 5.46/5.68 ! [B2: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.68 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B2 ) @ C )
% 5.46/5.68 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_unit_dvd_iff
% 5.46/5.68 thf(fact_2238_div__unit__dvd__iff,axiom,
% 5.46/5.68 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.68 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B2 ) @ C )
% 5.46/5.68 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_unit_dvd_iff
% 5.46/5.68 thf(fact_2239_div__unit__dvd__iff,axiom,
% 5.46/5.68 ! [B2: int,A: int,C: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.68 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B2 ) @ C )
% 5.46/5.68 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_unit_dvd_iff
% 5.46/5.68 thf(fact_2240_dvd__div__unit__iff,axiom,
% 5.46/5.68 ! [B2: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.68 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B2 ) )
% 5.46/5.68 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_unit_iff
% 5.46/5.68 thf(fact_2241_dvd__div__unit__iff,axiom,
% 5.46/5.68 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.68 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B2 ) )
% 5.46/5.68 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_unit_iff
% 5.46/5.68 thf(fact_2242_dvd__div__unit__iff,axiom,
% 5.46/5.68 ! [B2: int,A: int,C: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.68 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B2 ) )
% 5.46/5.68 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_div_unit_iff
% 5.46/5.68 thf(fact_2243_div__plus__div__distrib__dvd__right,axiom,
% 5.46/5.68 ! [C: code_integer,B2: code_integer,A: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ C @ B2 )
% 5.46/5.68 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) @ C )
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_plus_div_distrib_dvd_right
% 5.46/5.68 thf(fact_2244_div__plus__div__distrib__dvd__right,axiom,
% 5.46/5.68 ! [C: nat,B2: nat,A: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ C @ B2 )
% 5.46/5.68 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 5.46/5.68 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_plus_div_distrib_dvd_right
% 5.46/5.68 thf(fact_2245_div__plus__div__distrib__dvd__right,axiom,
% 5.46/5.68 ! [C: int,B2: int,A: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ C @ B2 )
% 5.46/5.68 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.46/5.68 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_plus_div_distrib_dvd_right
% 5.46/5.68 thf(fact_2246_div__plus__div__distrib__dvd__left,axiom,
% 5.46/5.68 ! [C: code_integer,A: code_integer,B2: code_integer] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.46/5.68 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) @ C )
% 5.46/5.68 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_plus_div_distrib_dvd_left
% 5.46/5.68 thf(fact_2247_div__plus__div__distrib__dvd__left,axiom,
% 5.46/5.68 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ C @ A )
% 5.46/5.68 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 5.46/5.68 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_plus_div_distrib_dvd_left
% 5.46/5.68 thf(fact_2248_div__plus__div__distrib__dvd__left,axiom,
% 5.46/5.68 ! [C: int,A: int,B2: int] :
% 5.46/5.68 ( ( dvd_dvd_int @ C @ A )
% 5.46/5.68 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 5.46/5.68 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_plus_div_distrib_dvd_left
% 5.46/5.68 thf(fact_2249_div__power,axiom,
% 5.46/5.68 ! [B2: code_integer,A: code_integer,N: nat] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ B2 @ A )
% 5.46/5.68 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ N )
% 5.46/5.68 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_power
% 5.46/5.68 thf(fact_2250_div__power,axiom,
% 5.46/5.68 ! [B2: nat,A: nat,N: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ B2 @ A )
% 5.46/5.68 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B2 ) @ N )
% 5.46/5.68 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B2 @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_power
% 5.46/5.68 thf(fact_2251_div__power,axiom,
% 5.46/5.68 ! [B2: int,A: int,N: nat] :
% 5.46/5.68 ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.68 => ( ( power_power_int @ ( divide_divide_int @ A @ B2 ) @ N )
% 5.46/5.68 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B2 @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % div_power
% 5.46/5.68 thf(fact_2252_power__strict__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,N: nat] :
% 5.46/5.68 ( ( ord_less_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.68 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B2 @ N ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_strict_mono
% 5.46/5.68 thf(fact_2253_power__strict__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,N: nat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.68 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_strict_mono
% 5.46/5.68 thf(fact_2254_power__strict__mono,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.68 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B2 @ N ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_strict_mono
% 5.46/5.68 thf(fact_2255_power__strict__mono,axiom,
% 5.46/5.68 ! [A: int,B2: int,N: nat] :
% 5.46/5.68 ( ( ord_less_int @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.68 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B2 @ N ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_strict_mono
% 5.46/5.68 thf(fact_2256_le__imp__power__dvd,axiom,
% 5.46/5.68 ! [M: nat,N: nat,A: code_integer] :
% 5.46/5.68 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_imp_power_dvd
% 5.46/5.68 thf(fact_2257_le__imp__power__dvd,axiom,
% 5.46/5.68 ! [M: nat,N: nat,A: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_imp_power_dvd
% 5.46/5.68 thf(fact_2258_le__imp__power__dvd,axiom,
% 5.46/5.68 ! [M: nat,N: nat,A: real] :
% 5.46/5.68 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_imp_power_dvd
% 5.46/5.68 thf(fact_2259_le__imp__power__dvd,axiom,
% 5.46/5.68 ! [M: nat,N: nat,A: int] :
% 5.46/5.68 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_imp_power_dvd
% 5.46/5.68 thf(fact_2260_le__imp__power__dvd,axiom,
% 5.46/5.68 ! [M: nat,N: nat,A: complex] :
% 5.46/5.68 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_imp_power_dvd
% 5.46/5.68 thf(fact_2261_power__le__dvd,axiom,
% 5.46/5.68 ! [A: code_integer,N: nat,B2: code_integer,M: nat] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_le_dvd
% 5.46/5.68 thf(fact_2262_power__le__dvd,axiom,
% 5.46/5.68 ! [A: nat,N: nat,B2: nat,M: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_le_dvd
% 5.46/5.68 thf(fact_2263_power__le__dvd,axiom,
% 5.46/5.68 ! [A: real,N: nat,B2: real,M: nat] :
% 5.46/5.68 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_le_dvd
% 5.46/5.68 thf(fact_2264_power__le__dvd,axiom,
% 5.46/5.68 ! [A: int,N: nat,B2: int,M: nat] :
% 5.46/5.68 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_le_dvd
% 5.46/5.68 thf(fact_2265_power__le__dvd,axiom,
% 5.46/5.68 ! [A: complex,N: nat,B2: complex,M: nat] :
% 5.46/5.68 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_le_dvd
% 5.46/5.68 thf(fact_2266_dvd__power__le,axiom,
% 5.46/5.68 ! [X4: code_integer,Y3: code_integer,N: nat,M: nat] :
% 5.46/5.68 ( ( dvd_dvd_Code_integer @ X4 @ Y3 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.68 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ N ) @ ( power_8256067586552552935nteger @ Y3 @ M ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_power_le
% 5.46/5.68 thf(fact_2267_dvd__power__le,axiom,
% 5.46/5.68 ! [X4: nat,Y3: nat,N: nat,M: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ X4 @ Y3 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.68 => ( dvd_dvd_nat @ ( power_power_nat @ X4 @ N ) @ ( power_power_nat @ Y3 @ M ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_power_le
% 5.46/5.68 thf(fact_2268_dvd__power__le,axiom,
% 5.46/5.68 ! [X4: real,Y3: real,N: nat,M: nat] :
% 5.46/5.68 ( ( dvd_dvd_real @ X4 @ Y3 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.68 => ( dvd_dvd_real @ ( power_power_real @ X4 @ N ) @ ( power_power_real @ Y3 @ M ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_power_le
% 5.46/5.68 thf(fact_2269_dvd__power__le,axiom,
% 5.46/5.68 ! [X4: int,Y3: int,N: nat,M: nat] :
% 5.46/5.68 ( ( dvd_dvd_int @ X4 @ Y3 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.68 => ( dvd_dvd_int @ ( power_power_int @ X4 @ N ) @ ( power_power_int @ Y3 @ M ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_power_le
% 5.46/5.68 thf(fact_2270_dvd__power__le,axiom,
% 5.46/5.68 ! [X4: complex,Y3: complex,N: nat,M: nat] :
% 5.46/5.68 ( ( dvd_dvd_complex @ X4 @ Y3 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.68 => ( dvd_dvd_complex @ ( power_power_complex @ X4 @ N ) @ ( power_power_complex @ Y3 @ M ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_power_le
% 5.46/5.68 thf(fact_2271_mod__eq__dvd__iff,axiom,
% 5.46/5.68 ! [A: int,C: int,B2: int] :
% 5.46/5.68 ( ( ( modulo_modulo_int @ A @ C )
% 5.46/5.68 = ( modulo_modulo_int @ B2 @ C ) )
% 5.46/5.68 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_eq_dvd_iff
% 5.46/5.68 thf(fact_2272_mod__eq__dvd__iff,axiom,
% 5.46/5.68 ! [A: code_integer,C: code_integer,B2: code_integer] :
% 5.46/5.68 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.46/5.68 = ( modulo364778990260209775nteger @ B2 @ C ) )
% 5.46/5.68 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_eq_dvd_iff
% 5.46/5.68 thf(fact_2273_dvd__minus__mod,axiom,
% 5.46/5.68 ! [B2: nat,A: nat] : ( dvd_dvd_nat @ B2 @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_minus_mod
% 5.46/5.68 thf(fact_2274_dvd__minus__mod,axiom,
% 5.46/5.68 ! [B2: int,A: int] : ( dvd_dvd_int @ B2 @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_minus_mod
% 5.46/5.68 thf(fact_2275_dvd__minus__mod,axiom,
% 5.46/5.68 ! [B2: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B2 @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_minus_mod
% 5.46/5.68 thf(fact_2276_dvd__minus__self,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.68 = ( ( ord_less_nat @ N @ M )
% 5.46/5.68 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_minus_self
% 5.46/5.68 thf(fact_2277_dvd__diffD,axiom,
% 5.46/5.68 ! [K: nat,M: nat,N: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.68 => ( ( dvd_dvd_nat @ K @ N )
% 5.46/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.68 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_diffD
% 5.46/5.68 thf(fact_2278_dvd__diffD1,axiom,
% 5.46/5.68 ! [K: nat,M: nat,N: nat] :
% 5.46/5.68 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.68 => ( ( dvd_dvd_nat @ K @ M )
% 5.46/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.68 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dvd_diffD1
% 5.46/5.68 thf(fact_2279_less__eq__dvd__minus,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.68 => ( ( dvd_dvd_nat @ M @ N )
% 5.46/5.68 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_eq_dvd_minus
% 5.46/5.68 thf(fact_2280_dbl__def,axiom,
% 5.46/5.68 ( neg_numeral_dbl_real
% 5.46/5.68 = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_def
% 5.46/5.68 thf(fact_2281_dbl__def,axiom,
% 5.46/5.68 ( neg_numeral_dbl_rat
% 5.46/5.68 = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_def
% 5.46/5.68 thf(fact_2282_dbl__def,axiom,
% 5.46/5.68 ( neg_numeral_dbl_int
% 5.46/5.68 = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % dbl_def
% 5.46/5.68 thf(fact_2283_zero__le__numeral,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_numeral
% 5.46/5.68 thf(fact_2284_zero__le__numeral,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_numeral
% 5.46/5.68 thf(fact_2285_zero__le__numeral,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_numeral
% 5.46/5.68 thf(fact_2286_zero__le__numeral,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_numeral
% 5.46/5.68 thf(fact_2287_not__numeral__le__zero,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_zero
% 5.46/5.68 thf(fact_2288_not__numeral__le__zero,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_zero
% 5.46/5.68 thf(fact_2289_not__numeral__le__zero,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_zero
% 5.46/5.68 thf(fact_2290_not__numeral__le__zero,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_le_zero
% 5.46/5.68 thf(fact_2291_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.46/5.68 thf(fact_2292_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.46/5.68 thf(fact_2293_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.46/5.68 thf(fact_2294_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.46/5.68 thf(fact_2295_zero__le__mult__iff,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 5.46/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.68 & ( ord_less_eq_real @ B2 @ zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_mult_iff
% 5.46/5.68 thf(fact_2296_zero__le__mult__iff,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) )
% 5.46/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_mult_iff
% 5.46/5.68 thf(fact_2297_zero__le__mult__iff,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 & ( ord_less_eq_int @ zero_zero_int @ B2 ) )
% 5.46/5.68 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.68 & ( ord_less_eq_int @ B2 @ zero_zero_int ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_mult_iff
% 5.46/5.68 thf(fact_2298_mult__nonneg__nonpos2,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ B2 @ A ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonpos2
% 5.46/5.68 thf(fact_2299_mult__nonneg__nonpos2,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ B2 @ A ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonpos2
% 5.46/5.68 thf(fact_2300_mult__nonneg__nonpos2,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 5.46/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ B2 @ A ) @ zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonpos2
% 5.46/5.68 thf(fact_2301_mult__nonneg__nonpos2,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ B2 @ A ) @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonpos2
% 5.46/5.68 thf(fact_2302_mult__nonpos__nonneg,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonpos_nonneg
% 5.46/5.68 thf(fact_2303_mult__nonpos__nonneg,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonpos_nonneg
% 5.46/5.68 thf(fact_2304_mult__nonpos__nonneg,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonpos_nonneg
% 5.46/5.68 thf(fact_2305_mult__nonpos__nonneg,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonpos_nonneg
% 5.46/5.68 thf(fact_2306_mult__nonneg__nonpos,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonpos
% 5.46/5.68 thf(fact_2307_mult__nonneg__nonpos,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonpos
% 5.46/5.68 thf(fact_2308_mult__nonneg__nonpos,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 5.46/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonpos
% 5.46/5.68 thf(fact_2309_mult__nonneg__nonpos,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonpos
% 5.46/5.68 thf(fact_2310_mult__nonneg__nonneg,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonneg
% 5.46/5.68 thf(fact_2311_mult__nonneg__nonneg,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonneg
% 5.46/5.68 thf(fact_2312_mult__nonneg__nonneg,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.68 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonneg
% 5.46/5.68 thf(fact_2313_mult__nonneg__nonneg,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonneg_nonneg
% 5.46/5.68 thf(fact_2314_split__mult__neg__le,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 5.46/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.68 & ( ord_less_eq_real @ zero_zero_real @ B2 ) ) )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_mult_neg_le
% 5.46/5.68 thf(fact_2315_split__mult__neg__le,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) )
% 5.46/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B2 ) @ zero_zero_rat ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_mult_neg_le
% 5.46/5.68 thf(fact_2316_split__mult__neg__le,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 & ( ord_less_eq_nat @ B2 @ zero_zero_nat ) )
% 5.46/5.68 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.46/5.68 & ( ord_less_eq_nat @ zero_zero_nat @ B2 ) ) )
% 5.46/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B2 ) @ zero_zero_nat ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_mult_neg_le
% 5.46/5.68 thf(fact_2317_split__mult__neg__le,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 & ( ord_less_eq_int @ B2 @ zero_zero_int ) )
% 5.46/5.68 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.68 & ( ord_less_eq_int @ zero_zero_int @ B2 ) ) )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_mult_neg_le
% 5.46/5.68 thf(fact_2318_mult__le__0__iff,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real )
% 5.46/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 5.46/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.68 & ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_le_0_iff
% 5.46/5.68 thf(fact_2319_mult__le__0__iff,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B2 ) @ zero_zero_rat )
% 5.46/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) )
% 5.46/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_le_0_iff
% 5.46/5.68 thf(fact_2320_mult__le__0__iff,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int )
% 5.46/5.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 & ( ord_less_eq_int @ B2 @ zero_zero_int ) )
% 5.46/5.68 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.68 & ( ord_less_eq_int @ zero_zero_int @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_le_0_iff
% 5.46/5.68 thf(fact_2321_mult__right__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_right_mono
% 5.46/5.68 thf(fact_2322_mult__right__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_right_mono
% 5.46/5.68 thf(fact_2323_mult__right__mono,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_right_mono
% 5.46/5.68 thf(fact_2324_mult__right__mono,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_right_mono
% 5.46/5.68 thf(fact_2325_mult__right__mono__neg,axiom,
% 5.46/5.68 ! [B2: real,A: real,C: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_right_mono_neg
% 5.46/5.68 thf(fact_2326_mult__right__mono__neg,axiom,
% 5.46/5.68 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_right_mono_neg
% 5.46/5.68 thf(fact_2327_mult__right__mono__neg,axiom,
% 5.46/5.68 ! [B2: int,A: int,C: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_right_mono_neg
% 5.46/5.68 thf(fact_2328_mult__left__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_left_mono
% 5.46/5.68 thf(fact_2329_mult__left__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_left_mono
% 5.46/5.68 thf(fact_2330_mult__left__mono,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_left_mono
% 5.46/5.68 thf(fact_2331_mult__left__mono,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_left_mono
% 5.46/5.68 thf(fact_2332_mult__nonpos__nonpos,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonpos_nonpos
% 5.46/5.68 thf(fact_2333_mult__nonpos__nonpos,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonpos_nonpos
% 5.46/5.68 thf(fact_2334_mult__nonpos__nonpos,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.46/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_nonpos_nonpos
% 5.46/5.68 thf(fact_2335_mult__left__mono__neg,axiom,
% 5.46/5.68 ! [B2: real,A: real,C: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_left_mono_neg
% 5.46/5.68 thf(fact_2336_mult__left__mono__neg,axiom,
% 5.46/5.68 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_left_mono_neg
% 5.46/5.68 thf(fact_2337_mult__left__mono__neg,axiom,
% 5.46/5.68 ! [B2: int,A: int,C: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_left_mono_neg
% 5.46/5.68 thf(fact_2338_split__mult__pos__le,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 5.46/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.68 & ( ord_less_eq_real @ B2 @ zero_zero_real ) ) )
% 5.46/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_mult_pos_le
% 5.46/5.68 thf(fact_2339_split__mult__pos__le,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) )
% 5.46/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) ) )
% 5.46/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_mult_pos_le
% 5.46/5.68 thf(fact_2340_split__mult__pos__le,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 & ( ord_less_eq_int @ zero_zero_int @ B2 ) )
% 5.46/5.68 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.68 & ( ord_less_eq_int @ B2 @ zero_zero_int ) ) )
% 5.46/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % split_mult_pos_le
% 5.46/5.68 thf(fact_2341_zero__le__square,axiom,
% 5.46/5.68 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_square
% 5.46/5.68 thf(fact_2342_zero__le__square,axiom,
% 5.46/5.68 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_square
% 5.46/5.68 thf(fact_2343_zero__le__square,axiom,
% 5.46/5.68 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_square
% 5.46/5.68 thf(fact_2344_mult__mono_H,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ C @ D )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_mono'
% 5.46/5.68 thf(fact_2345_mult__mono_H,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ C @ D )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_mono'
% 5.46/5.68 thf(fact_2346_mult__mono_H,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ C @ D )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_mono'
% 5.46/5.68 thf(fact_2347_mult__mono_H,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_int @ C @ D )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_mono'
% 5.46/5.68 thf(fact_2348_mult__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ C @ D )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_mono
% 5.46/5.68 thf(fact_2349_mult__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ C @ D )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_mono
% 5.46/5.68 thf(fact_2350_mult__mono,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ C @ D )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_mono
% 5.46/5.68 thf(fact_2351_mult__mono,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_int @ C @ D )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_mono
% 5.46/5.68 thf(fact_2352_not__numeral__less__zero,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_zero
% 5.46/5.68 thf(fact_2353_not__numeral__less__zero,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_zero
% 5.46/5.68 thf(fact_2354_not__numeral__less__zero,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_zero
% 5.46/5.68 thf(fact_2355_not__numeral__less__zero,axiom,
% 5.46/5.68 ! [N: num] :
% 5.46/5.68 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % not_numeral_less_zero
% 5.46/5.68 thf(fact_2356_zero__less__numeral,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_numeral
% 5.46/5.68 thf(fact_2357_zero__less__numeral,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_numeral
% 5.46/5.68 thf(fact_2358_zero__less__numeral,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_numeral
% 5.46/5.68 thf(fact_2359_zero__less__numeral,axiom,
% 5.46/5.68 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_numeral
% 5.46/5.68 thf(fact_2360_zero__less__one__class_Ozero__le__one,axiom,
% 5.46/5.68 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.46/5.68
% 5.46/5.68 % zero_less_one_class.zero_le_one
% 5.46/5.68 thf(fact_2361_zero__less__one__class_Ozero__le__one,axiom,
% 5.46/5.68 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.46/5.68
% 5.46/5.68 % zero_less_one_class.zero_le_one
% 5.46/5.68 thf(fact_2362_zero__less__one__class_Ozero__le__one,axiom,
% 5.46/5.68 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.46/5.68
% 5.46/5.68 % zero_less_one_class.zero_le_one
% 5.46/5.68 thf(fact_2363_zero__less__one__class_Ozero__le__one,axiom,
% 5.46/5.68 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.46/5.68
% 5.46/5.68 % zero_less_one_class.zero_le_one
% 5.46/5.68 thf(fact_2364_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.46/5.68 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.46/5.68
% 5.46/5.68 % linordered_nonzero_semiring_class.zero_le_one
% 5.46/5.68 thf(fact_2365_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.46/5.68 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.46/5.68
% 5.46/5.68 % linordered_nonzero_semiring_class.zero_le_one
% 5.46/5.68 thf(fact_2366_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.46/5.68 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.46/5.68
% 5.46/5.68 % linordered_nonzero_semiring_class.zero_le_one
% 5.46/5.68 thf(fact_2367_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.46/5.68 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.46/5.68
% 5.46/5.68 % linordered_nonzero_semiring_class.zero_le_one
% 5.46/5.68 thf(fact_2368_not__one__le__zero,axiom,
% 5.46/5.68 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_le_zero
% 5.46/5.68 thf(fact_2369_not__one__le__zero,axiom,
% 5.46/5.68 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_le_zero
% 5.46/5.68 thf(fact_2370_not__one__le__zero,axiom,
% 5.46/5.68 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_le_zero
% 5.46/5.68 thf(fact_2371_not__one__le__zero,axiom,
% 5.46/5.68 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_le_zero
% 5.46/5.68 thf(fact_2372_add__decreasing,axiom,
% 5.46/5.68 ! [A: real,C: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_eq_real @ C @ B2 )
% 5.46/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_decreasing
% 5.46/5.68 thf(fact_2373_add__decreasing,axiom,
% 5.46/5.68 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_eq_rat @ C @ B2 )
% 5.46/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_decreasing
% 5.46/5.68 thf(fact_2374_add__decreasing,axiom,
% 5.46/5.68 ! [A: nat,C: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.46/5.68 => ( ( ord_less_eq_nat @ C @ B2 )
% 5.46/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_decreasing
% 5.46/5.68 thf(fact_2375_add__decreasing,axiom,
% 5.46/5.68 ! [A: int,C: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_eq_int @ C @ B2 )
% 5.46/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_decreasing
% 5.46/5.68 thf(fact_2376_add__increasing,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_eq_real @ B2 @ C )
% 5.46/5.68 => ( ord_less_eq_real @ B2 @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_increasing
% 5.46/5.68 thf(fact_2377_add__increasing,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ B2 @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_increasing
% 5.46/5.68 thf(fact_2378_add__increasing,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_eq_nat @ B2 @ C )
% 5.46/5.68 => ( ord_less_eq_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_increasing
% 5.46/5.68 thf(fact_2379_add__increasing,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_eq_int @ B2 @ C )
% 5.46/5.68 => ( ord_less_eq_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_increasing
% 5.46/5.68 thf(fact_2380_add__decreasing2,axiom,
% 5.46/5.68 ! [C: real,A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_decreasing2
% 5.46/5.68 thf(fact_2381_add__decreasing2,axiom,
% 5.46/5.68 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_decreasing2
% 5.46/5.68 thf(fact_2382_add__decreasing2,axiom,
% 5.46/5.68 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.46/5.68 => ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_decreasing2
% 5.46/5.68 thf(fact_2383_add__decreasing2,axiom,
% 5.46/5.68 ! [C: int,A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_decreasing2
% 5.46/5.68 thf(fact_2384_add__increasing2,axiom,
% 5.46/5.68 ! [C: real,B2: real,A: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ord_less_eq_real @ B2 @ A )
% 5.46/5.68 => ( ord_less_eq_real @ B2 @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_increasing2
% 5.46/5.68 thf(fact_2385_add__increasing2,axiom,
% 5.46/5.68 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ord_less_eq_rat @ B2 @ A )
% 5.46/5.68 => ( ord_less_eq_rat @ B2 @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_increasing2
% 5.46/5.68 thf(fact_2386_add__increasing2,axiom,
% 5.46/5.68 ! [C: nat,B2: nat,A: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.68 => ( ( ord_less_eq_nat @ B2 @ A )
% 5.46/5.68 => ( ord_less_eq_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_increasing2
% 5.46/5.68 thf(fact_2387_add__increasing2,axiom,
% 5.46/5.68 ! [C: int,B2: int,A: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.68 => ( ( ord_less_eq_int @ B2 @ A )
% 5.46/5.68 => ( ord_less_eq_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_increasing2
% 5.46/5.68 thf(fact_2388_add__nonneg__nonneg,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonneg_nonneg
% 5.46/5.68 thf(fact_2389_add__nonneg__nonneg,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonneg_nonneg
% 5.46/5.68 thf(fact_2390_add__nonneg__nonneg,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.68 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonneg_nonneg
% 5.46/5.68 thf(fact_2391_add__nonneg__nonneg,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonneg_nonneg
% 5.46/5.68 thf(fact_2392_add__nonpos__nonpos,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonpos_nonpos
% 5.46/5.68 thf(fact_2393_add__nonpos__nonpos,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonpos_nonpos
% 5.46/5.68 thf(fact_2394_add__nonpos__nonpos,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.46/5.68 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 5.46/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonpos_nonpos
% 5.46/5.68 thf(fact_2395_add__nonpos__nonpos,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.46/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonpos_nonpos
% 5.46/5.68 thf(fact_2396_add__nonneg__eq__0__iff,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.68 => ( ( ( plus_plus_real @ X4 @ Y3 )
% 5.46/5.68 = zero_zero_real )
% 5.46/5.68 = ( ( X4 = zero_zero_real )
% 5.46/5.68 & ( Y3 = zero_zero_real ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonneg_eq_0_iff
% 5.46/5.68 thf(fact_2397_add__nonneg__eq__0__iff,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.46/5.68 => ( ( ( plus_plus_rat @ X4 @ Y3 )
% 5.46/5.68 = zero_zero_rat )
% 5.46/5.68 = ( ( X4 = zero_zero_rat )
% 5.46/5.68 & ( Y3 = zero_zero_rat ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonneg_eq_0_iff
% 5.46/5.68 thf(fact_2398_add__nonneg__eq__0__iff,axiom,
% 5.46/5.68 ! [X4: nat,Y3: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.46/5.68 => ( ( ( plus_plus_nat @ X4 @ Y3 )
% 5.46/5.68 = zero_zero_nat )
% 5.46/5.68 = ( ( X4 = zero_zero_nat )
% 5.46/5.68 & ( Y3 = zero_zero_nat ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonneg_eq_0_iff
% 5.46/5.68 thf(fact_2399_add__nonneg__eq__0__iff,axiom,
% 5.46/5.68 ! [X4: int,Y3: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.68 => ( ( ( plus_plus_int @ X4 @ Y3 )
% 5.46/5.68 = zero_zero_int )
% 5.46/5.68 = ( ( X4 = zero_zero_int )
% 5.46/5.68 & ( Y3 = zero_zero_int ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonneg_eq_0_iff
% 5.46/5.68 thf(fact_2400_add__nonpos__eq__0__iff,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.46/5.68 => ( ( ( plus_plus_real @ X4 @ Y3 )
% 5.46/5.68 = zero_zero_real )
% 5.46/5.68 = ( ( X4 = zero_zero_real )
% 5.46/5.68 & ( Y3 = zero_zero_real ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonpos_eq_0_iff
% 5.46/5.68 thf(fact_2401_add__nonpos__eq__0__iff,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 5.46/5.68 => ( ( ( plus_plus_rat @ X4 @ Y3 )
% 5.46/5.68 = zero_zero_rat )
% 5.46/5.68 = ( ( X4 = zero_zero_rat )
% 5.46/5.68 & ( Y3 = zero_zero_rat ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonpos_eq_0_iff
% 5.46/5.68 thf(fact_2402_add__nonpos__eq__0__iff,axiom,
% 5.46/5.68 ! [X4: nat,Y3: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ X4 @ zero_zero_nat )
% 5.46/5.68 => ( ( ord_less_eq_nat @ Y3 @ zero_zero_nat )
% 5.46/5.68 => ( ( ( plus_plus_nat @ X4 @ Y3 )
% 5.46/5.68 = zero_zero_nat )
% 5.46/5.68 = ( ( X4 = zero_zero_nat )
% 5.46/5.68 & ( Y3 = zero_zero_nat ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonpos_eq_0_iff
% 5.46/5.68 thf(fact_2403_add__nonpos__eq__0__iff,axiom,
% 5.46/5.68 ! [X4: int,Y3: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ X4 @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_eq_int @ Y3 @ zero_zero_int )
% 5.46/5.68 => ( ( ( plus_plus_int @ X4 @ Y3 )
% 5.46/5.68 = zero_zero_int )
% 5.46/5.68 = ( ( X4 = zero_zero_int )
% 5.46/5.68 & ( Y3 = zero_zero_int ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_nonpos_eq_0_iff
% 5.46/5.68 thf(fact_2404_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.46/5.68 thf(fact_2405_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.46/5.68 thf(fact_2406_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.68 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.46/5.68 thf(fact_2407_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( ord_less_int @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.68 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.46/5.68 thf(fact_2408_mult__less__cancel__right__disj,axiom,
% 5.46/5.68 ! [A: real,C: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 & ( ord_less_real @ A @ B2 ) )
% 5.46/5.68 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 & ( ord_less_real @ B2 @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_right_disj
% 5.46/5.68 thf(fact_2409_mult__less__cancel__right__disj,axiom,
% 5.46/5.68 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 & ( ord_less_rat @ A @ B2 ) )
% 5.46/5.68 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_right_disj
% 5.46/5.68 thf(fact_2410_mult__less__cancel__right__disj,axiom,
% 5.46/5.68 ! [A: int,C: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 5.46/5.68 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.68 & ( ord_less_int @ A @ B2 ) )
% 5.46/5.68 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.68 & ( ord_less_int @ B2 @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_right_disj
% 5.46/5.68 thf(fact_2411_mult__strict__right__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_right_mono
% 5.46/5.68 thf(fact_2412_mult__strict__right__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_right_mono
% 5.46/5.68 thf(fact_2413_mult__strict__right__mono,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.68 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_right_mono
% 5.46/5.68 thf(fact_2414_mult__strict__right__mono,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( ord_less_int @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.68 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_right_mono
% 5.46/5.68 thf(fact_2415_mult__strict__right__mono__neg,axiom,
% 5.46/5.68 ! [B2: real,A: real,C: real] :
% 5.46/5.68 ( ( ord_less_real @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_right_mono_neg
% 5.46/5.68 thf(fact_2416_mult__strict__right__mono__neg,axiom,
% 5.46/5.68 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_rat @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_right_mono_neg
% 5.46/5.68 thf(fact_2417_mult__strict__right__mono__neg,axiom,
% 5.46/5.68 ! [B2: int,A: int,C: int] :
% 5.46/5.68 ( ( ord_less_int @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.68 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_right_mono_neg
% 5.46/5.68 thf(fact_2418_mult__less__cancel__left__disj,axiom,
% 5.46/5.68 ! [C: real,A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 & ( ord_less_real @ A @ B2 ) )
% 5.46/5.68 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 & ( ord_less_real @ B2 @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_left_disj
% 5.46/5.68 thf(fact_2419_mult__less__cancel__left__disj,axiom,
% 5.46/5.68 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 & ( ord_less_rat @ A @ B2 ) )
% 5.46/5.68 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_left_disj
% 5.46/5.68 thf(fact_2420_mult__less__cancel__left__disj,axiom,
% 5.46/5.68 ! [C: int,A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.68 & ( ord_less_int @ A @ B2 ) )
% 5.46/5.68 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.68 & ( ord_less_int @ B2 @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_left_disj
% 5.46/5.68 thf(fact_2421_mult__strict__left__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_left_mono
% 5.46/5.68 thf(fact_2422_mult__strict__left__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_left_mono
% 5.46/5.68 thf(fact_2423_mult__strict__left__mono,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.68 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_left_mono
% 5.46/5.68 thf(fact_2424_mult__strict__left__mono,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( ord_less_int @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.68 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_left_mono
% 5.46/5.68 thf(fact_2425_mult__strict__left__mono__neg,axiom,
% 5.46/5.68 ! [B2: real,A: real,C: real] :
% 5.46/5.68 ( ( ord_less_real @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_left_mono_neg
% 5.46/5.68 thf(fact_2426_mult__strict__left__mono__neg,axiom,
% 5.46/5.68 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_rat @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_left_mono_neg
% 5.46/5.68 thf(fact_2427_mult__strict__left__mono__neg,axiom,
% 5.46/5.68 ! [B2: int,A: int,C: int] :
% 5.46/5.68 ( ( ord_less_int @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.68 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_strict_left_mono_neg
% 5.46/5.68 thf(fact_2428_mult__less__cancel__left__pos,axiom,
% 5.46/5.68 ! [C: real,A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.46/5.68 = ( ord_less_real @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_left_pos
% 5.46/5.68 thf(fact_2429_mult__less__cancel__left__pos,axiom,
% 5.46/5.68 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.68 = ( ord_less_rat @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_left_pos
% 5.46/5.68 thf(fact_2430_mult__less__cancel__left__pos,axiom,
% 5.46/5.68 ! [C: int,A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.68 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.46/5.68 = ( ord_less_int @ A @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_left_pos
% 5.46/5.68 thf(fact_2431_mult__less__cancel__left__neg,axiom,
% 5.46/5.68 ! [C: real,A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.46/5.68 = ( ord_less_real @ B2 @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_left_neg
% 5.46/5.68 thf(fact_2432_mult__less__cancel__left__neg,axiom,
% 5.46/5.68 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.68 = ( ord_less_rat @ B2 @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_left_neg
% 5.46/5.68 thf(fact_2433_mult__less__cancel__left__neg,axiom,
% 5.46/5.68 ! [C: int,A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.46/5.68 = ( ord_less_int @ B2 @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_cancel_left_neg
% 5.46/5.68 thf(fact_2434_zero__less__mult__pos2,axiom,
% 5.46/5.68 ! [B2: real,A: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B2 @ A ) )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ord_less_real @ zero_zero_real @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_pos2
% 5.46/5.68 thf(fact_2435_zero__less__mult__pos2,axiom,
% 5.46/5.68 ! [B2: rat,A: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B2 @ A ) )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_pos2
% 5.46/5.68 thf(fact_2436_zero__less__mult__pos2,axiom,
% 5.46/5.68 ! [B2: nat,A: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B2 @ A ) )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ord_less_nat @ zero_zero_nat @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_pos2
% 5.46/5.68 thf(fact_2437_zero__less__mult__pos2,axiom,
% 5.46/5.68 ! [B2: int,A: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B2 @ A ) )
% 5.46/5.68 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ord_less_int @ zero_zero_int @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_pos2
% 5.46/5.68 thf(fact_2438_zero__less__mult__pos,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ord_less_real @ zero_zero_real @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_pos
% 5.46/5.68 thf(fact_2439_zero__less__mult__pos,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_pos
% 5.46/5.68 thf(fact_2440_zero__less__mult__pos,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B2 ) )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ord_less_nat @ zero_zero_nat @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_pos
% 5.46/5.68 thf(fact_2441_zero__less__mult__pos,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) )
% 5.46/5.68 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ord_less_int @ zero_zero_int @ B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_pos
% 5.46/5.68 thf(fact_2442_zero__less__mult__iff,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 & ( ord_less_real @ zero_zero_real @ B2 ) )
% 5.46/5.68 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.68 & ( ord_less_real @ B2 @ zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_iff
% 5.46/5.68 thf(fact_2443_zero__less__mult__iff,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 & ( ord_less_rat @ zero_zero_rat @ B2 ) )
% 5.46/5.68 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_rat @ B2 @ zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_iff
% 5.46/5.68 thf(fact_2444_zero__less__mult__iff,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.68 & ( ord_less_int @ zero_zero_int @ B2 ) )
% 5.46/5.68 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.68 & ( ord_less_int @ B2 @ zero_zero_int ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_mult_iff
% 5.46/5.68 thf(fact_2445_mult__pos__neg2,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ B2 @ A ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_neg2
% 5.46/5.68 thf(fact_2446_mult__pos__neg2,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ B2 @ A ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_neg2
% 5.46/5.68 thf(fact_2447_mult__pos__neg2,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 5.46/5.68 => ( ord_less_nat @ ( times_times_nat @ B2 @ A ) @ zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_neg2
% 5.46/5.68 thf(fact_2448_mult__pos__neg2,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.46/5.68 => ( ord_less_int @ ( times_times_int @ B2 @ A ) @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_neg2
% 5.46/5.68 thf(fact_2449_mult__pos__pos,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.68 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_pos
% 5.46/5.68 thf(fact_2450_mult__pos__pos,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.46/5.68 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_pos
% 5.46/5.68 thf(fact_2451_mult__pos__pos,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.68 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_pos
% 5.46/5.68 thf(fact_2452_mult__pos__pos,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.68 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_pos
% 5.46/5.68 thf(fact_2453_mult__pos__neg,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_neg
% 5.46/5.68 thf(fact_2454_mult__pos__neg,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ A @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_neg
% 5.46/5.68 thf(fact_2455_mult__pos__neg,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 5.46/5.68 => ( ord_less_nat @ ( times_times_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_neg
% 5.46/5.68 thf(fact_2456_mult__pos__neg,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.46/5.68 => ( ord_less_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_pos_neg
% 5.46/5.68 thf(fact_2457_mult__neg__pos,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.68 => ( ord_less_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_pos
% 5.46/5.68 thf(fact_2458_mult__neg__pos,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.46/5.68 => ( ord_less_rat @ ( times_times_rat @ A @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_pos
% 5.46/5.68 thf(fact_2459_mult__neg__pos,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.68 => ( ord_less_nat @ ( times_times_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_pos
% 5.46/5.68 thf(fact_2460_mult__neg__pos,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.68 => ( ord_less_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_pos
% 5.46/5.68 thf(fact_2461_mult__less__0__iff,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 & ( ord_less_real @ B2 @ zero_zero_real ) )
% 5.46/5.68 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.68 & ( ord_less_real @ zero_zero_real @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_0_iff
% 5.46/5.68 thf(fact_2462_mult__less__0__iff,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( times_times_rat @ A @ B2 ) @ zero_zero_rat )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 & ( ord_less_rat @ B2 @ zero_zero_rat ) )
% 5.46/5.68 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_0_iff
% 5.46/5.68 thf(fact_2463_mult__less__0__iff,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ ( times_times_int @ A @ B2 ) @ zero_zero_int )
% 5.46/5.68 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.68 & ( ord_less_int @ B2 @ zero_zero_int ) )
% 5.46/5.68 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.68 & ( ord_less_int @ zero_zero_int @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_0_iff
% 5.46/5.68 thf(fact_2464_not__square__less__zero,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % not_square_less_zero
% 5.46/5.68 thf(fact_2465_not__square__less__zero,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % not_square_less_zero
% 5.46/5.68 thf(fact_2466_not__square__less__zero,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % not_square_less_zero
% 5.46/5.68 thf(fact_2467_mult__neg__neg,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_neg
% 5.46/5.68 thf(fact_2468_mult__neg__neg,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_neg
% 5.46/5.68 thf(fact_2469_mult__neg__neg,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.46/5.68 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_neg_neg
% 5.46/5.68 thf(fact_2470_le__iff__diff__le__0,axiom,
% 5.46/5.68 ( ord_less_eq_real
% 5.46/5.68 = ( ^ [A4: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_iff_diff_le_0
% 5.46/5.68 thf(fact_2471_le__iff__diff__le__0,axiom,
% 5.46/5.68 ( ord_less_eq_rat
% 5.46/5.68 = ( ^ [A4: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_iff_diff_le_0
% 5.46/5.68 thf(fact_2472_le__iff__diff__le__0,axiom,
% 5.46/5.68 ( ord_less_eq_int
% 5.46/5.68 = ( ^ [A4: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % le_iff_diff_le_0
% 5.46/5.68 thf(fact_2473_less__numeral__extra_I1_J,axiom,
% 5.46/5.68 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.46/5.68
% 5.46/5.68 % less_numeral_extra(1)
% 5.46/5.68 thf(fact_2474_less__numeral__extra_I1_J,axiom,
% 5.46/5.68 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.46/5.68
% 5.46/5.68 % less_numeral_extra(1)
% 5.46/5.68 thf(fact_2475_less__numeral__extra_I1_J,axiom,
% 5.46/5.68 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.46/5.68
% 5.46/5.68 % less_numeral_extra(1)
% 5.46/5.68 thf(fact_2476_less__numeral__extra_I1_J,axiom,
% 5.46/5.68 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.46/5.68
% 5.46/5.68 % less_numeral_extra(1)
% 5.46/5.68 thf(fact_2477_zero__less__one,axiom,
% 5.46/5.68 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.46/5.68
% 5.46/5.68 % zero_less_one
% 5.46/5.68 thf(fact_2478_zero__less__one,axiom,
% 5.46/5.68 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.46/5.68
% 5.46/5.68 % zero_less_one
% 5.46/5.68 thf(fact_2479_zero__less__one,axiom,
% 5.46/5.68 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.46/5.68
% 5.46/5.68 % zero_less_one
% 5.46/5.68 thf(fact_2480_zero__less__one,axiom,
% 5.46/5.68 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.46/5.68
% 5.46/5.68 % zero_less_one
% 5.46/5.68 thf(fact_2481_not__one__less__zero,axiom,
% 5.46/5.68 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_less_zero
% 5.46/5.68 thf(fact_2482_not__one__less__zero,axiom,
% 5.46/5.68 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_less_zero
% 5.46/5.68 thf(fact_2483_not__one__less__zero,axiom,
% 5.46/5.68 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_less_zero
% 5.46/5.68 thf(fact_2484_not__one__less__zero,axiom,
% 5.46/5.68 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % not_one_less_zero
% 5.46/5.68 thf(fact_2485_add__neg__neg,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( plus_plus_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_neg
% 5.46/5.68 thf(fact_2486_add__neg__neg,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( plus_plus_rat @ A @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_neg
% 5.46/5.68 thf(fact_2487_add__neg__neg,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.46/5.68 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 5.46/5.68 => ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_neg
% 5.46/5.68 thf(fact_2488_add__neg__neg,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.46/5.68 => ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_neg_neg
% 5.46/5.68 thf(fact_2489_add__pos__pos,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.68 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_pos_pos
% 5.46/5.68 thf(fact_2490_add__pos__pos,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.46/5.68 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_pos_pos
% 5.46/5.68 thf(fact_2491_add__pos__pos,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.68 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_pos_pos
% 5.46/5.68 thf(fact_2492_add__pos__pos,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.68 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_pos_pos
% 5.46/5.68 thf(fact_2493_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.68 => ~ ! [C3: nat] :
% 5.46/5.68 ( ( B2
% 5.46/5.68 = ( plus_plus_nat @ A @ C3 ) )
% 5.46/5.68 => ( C3 = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % canonically_ordered_monoid_add_class.lessE
% 5.46/5.68 thf(fact_2494_pos__add__strict,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.68 => ( ord_less_real @ B2 @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_add_strict
% 5.46/5.68 thf(fact_2495_pos__add__strict,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.68 => ( ord_less_rat @ B2 @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_add_strict
% 5.46/5.68 thf(fact_2496_pos__add__strict,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ( ord_less_nat @ B2 @ C )
% 5.46/5.68 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_add_strict
% 5.46/5.68 thf(fact_2497_pos__add__strict,axiom,
% 5.46/5.68 ! [A: int,B2: int,C: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( ord_less_int @ B2 @ C )
% 5.46/5.68 => ( ord_less_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_add_strict
% 5.46/5.68 thf(fact_2498_add__less__zeroD,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_real @ ( plus_plus_real @ X4 @ Y3 ) @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.46/5.68 | ( ord_less_real @ Y3 @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_less_zeroD
% 5.46/5.68 thf(fact_2499_add__less__zeroD,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( plus_plus_rat @ X4 @ Y3 ) @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_rat @ X4 @ zero_zero_rat )
% 5.46/5.68 | ( ord_less_rat @ Y3 @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_less_zeroD
% 5.46/5.68 thf(fact_2500_add__less__zeroD,axiom,
% 5.46/5.68 ! [X4: int,Y3: int] :
% 5.46/5.68 ( ( ord_less_int @ ( plus_plus_int @ X4 @ Y3 ) @ zero_zero_int )
% 5.46/5.68 => ( ( ord_less_int @ X4 @ zero_zero_int )
% 5.46/5.68 | ( ord_less_int @ Y3 @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_less_zeroD
% 5.46/5.68 thf(fact_2501_divide__le__0__iff,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B2 ) @ zero_zero_real )
% 5.46/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 & ( ord_less_eq_real @ B2 @ zero_zero_real ) )
% 5.46/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.68 & ( ord_less_eq_real @ zero_zero_real @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_le_0_iff
% 5.46/5.68 thf(fact_2502_divide__le__0__iff,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B2 ) @ zero_zero_rat )
% 5.46/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) )
% 5.46/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_le_0_iff
% 5.46/5.68 thf(fact_2503_divide__right__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_right_mono
% 5.46/5.68 thf(fact_2504_divide__right__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_right_mono
% 5.46/5.68 thf(fact_2505_zero__le__divide__iff,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 & ( ord_less_eq_real @ zero_zero_real @ B2 ) )
% 5.46/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.68 & ( ord_less_eq_real @ B2 @ zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_divide_iff
% 5.46/5.68 thf(fact_2506_zero__le__divide__iff,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B2 ) )
% 5.46/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_eq_rat @ B2 @ zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_divide_iff
% 5.46/5.68 thf(fact_2507_divide__nonneg__nonneg,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_nonneg_nonneg
% 5.46/5.68 thf(fact_2508_divide__nonneg__nonneg,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.46/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_nonneg_nonneg
% 5.46/5.68 thf(fact_2509_divide__nonneg__nonpos,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.68 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_nonneg_nonpos
% 5.46/5.68 thf(fact_2510_divide__nonneg__nonpos,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_nonneg_nonpos
% 5.46/5.68 thf(fact_2511_divide__nonpos__nonneg,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_nonpos_nonneg
% 5.46/5.68 thf(fact_2512_divide__nonpos__nonneg,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.46/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_nonpos_nonneg
% 5.46/5.68 thf(fact_2513_divide__nonpos__nonpos,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_nonpos_nonpos
% 5.46/5.68 thf(fact_2514_divide__nonpos__nonpos,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_eq_rat @ Y3 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_nonpos_nonpos
% 5.46/5.68 thf(fact_2515_divide__right__mono__neg,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_right_mono_neg
% 5.46/5.68 thf(fact_2516_divide__right__mono__neg,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_right_mono_neg
% 5.46/5.68 thf(fact_2517_less__iff__diff__less__0,axiom,
% 5.46/5.68 ( ord_less_real
% 5.46/5.68 = ( ^ [A4: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_iff_diff_less_0
% 5.46/5.68 thf(fact_2518_less__iff__diff__less__0,axiom,
% 5.46/5.68 ( ord_less_rat
% 5.46/5.68 = ( ^ [A4: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_iff_diff_less_0
% 5.46/5.68 thf(fact_2519_less__iff__diff__less__0,axiom,
% 5.46/5.68 ( ord_less_int
% 5.46/5.68 = ( ^ [A4: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_iff_diff_less_0
% 5.46/5.68 thf(fact_2520_divide__strict__right__mono__neg,axiom,
% 5.46/5.68 ! [B2: real,A: real,C: real] :
% 5.46/5.68 ( ( ord_less_real @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_strict_right_mono_neg
% 5.46/5.68 thf(fact_2521_divide__strict__right__mono__neg,axiom,
% 5.46/5.68 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_rat @ B2 @ A )
% 5.46/5.68 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_strict_right_mono_neg
% 5.46/5.68 thf(fact_2522_divide__strict__right__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( ord_less_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_strict_right_mono
% 5.46/5.68 thf(fact_2523_divide__strict__right__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_strict_right_mono
% 5.46/5.68 thf(fact_2524_zero__less__divide__iff,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 & ( ord_less_real @ zero_zero_real @ B2 ) )
% 5.46/5.68 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.68 & ( ord_less_real @ B2 @ zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_divide_iff
% 5.46/5.68 thf(fact_2525_zero__less__divide__iff,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B2 ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 & ( ord_less_rat @ zero_zero_rat @ B2 ) )
% 5.46/5.68 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_rat @ B2 @ zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_divide_iff
% 5.46/5.68 thf(fact_2526_divide__less__cancel,axiom,
% 5.46/5.68 ! [A: real,C: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.68 => ( ord_less_real @ A @ B2 ) )
% 5.46/5.68 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ B2 @ A ) )
% 5.46/5.68 & ( C != zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_less_cancel
% 5.46/5.68 thf(fact_2527_divide__less__cancel,axiom,
% 5.46/5.68 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.68 => ( ord_less_rat @ A @ B2 ) )
% 5.46/5.68 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ B2 @ A ) )
% 5.46/5.68 & ( C != zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_less_cancel
% 5.46/5.68 thf(fact_2528_divide__less__0__iff,axiom,
% 5.46/5.68 ! [A: real,B2: real] :
% 5.46/5.68 ( ( ord_less_real @ ( divide_divide_real @ A @ B2 ) @ zero_zero_real )
% 5.46/5.68 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 & ( ord_less_real @ B2 @ zero_zero_real ) )
% 5.46/5.68 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.68 & ( ord_less_real @ zero_zero_real @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_less_0_iff
% 5.46/5.68 thf(fact_2529_divide__less__0__iff,axiom,
% 5.46/5.68 ! [A: rat,B2: rat] :
% 5.46/5.68 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B2 ) @ zero_zero_rat )
% 5.46/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 & ( ord_less_rat @ B2 @ zero_zero_rat ) )
% 5.46/5.68 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.68 & ( ord_less_rat @ zero_zero_rat @ B2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_less_0_iff
% 5.46/5.68 thf(fact_2530_divide__pos__pos,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.68 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_pos_pos
% 5.46/5.68 thf(fact_2531_divide__pos__pos,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.46/5.68 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_pos_pos
% 5.46/5.68 thf(fact_2532_divide__pos__neg,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.68 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ ( divide_divide_real @ X4 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_pos_neg
% 5.46/5.68 thf(fact_2533_divide__pos__neg,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.46/5.68 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_pos_neg
% 5.46/5.68 thf(fact_2534_divide__neg__pos,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.68 => ( ord_less_real @ ( divide_divide_real @ X4 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_neg_pos
% 5.46/5.68 thf(fact_2535_divide__neg__pos,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_rat @ X4 @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.46/5.68 => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_neg_pos
% 5.46/5.68 thf(fact_2536_divide__neg__neg,axiom,
% 5.46/5.68 ! [X4: real,Y3: real] :
% 5.46/5.68 ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.46/5.68 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.46/5.68 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_neg_neg
% 5.46/5.68 thf(fact_2537_divide__neg__neg,axiom,
% 5.46/5.68 ! [X4: rat,Y3: rat] :
% 5.46/5.68 ( ( ord_less_rat @ X4 @ zero_zero_rat )
% 5.46/5.68 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.46/5.68 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_neg_neg
% 5.46/5.68 thf(fact_2538_zero__le__power,axiom,
% 5.46/5.68 ! [A: real,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_power
% 5.46/5.68 thf(fact_2539_zero__le__power,axiom,
% 5.46/5.68 ! [A: rat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_power
% 5.46/5.68 thf(fact_2540_zero__le__power,axiom,
% 5.46/5.68 ! [A: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_power
% 5.46/5.68 thf(fact_2541_zero__le__power,axiom,
% 5.46/5.68 ! [A: int,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_power
% 5.46/5.68 thf(fact_2542_power__mono,axiom,
% 5.46/5.68 ! [A: real,B2: real,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B2 @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_mono
% 5.46/5.68 thf(fact_2543_power__mono,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_mono
% 5.46/5.68 thf(fact_2544_power__mono,axiom,
% 5.46/5.68 ! [A: nat,B2: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B2 @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_mono
% 5.46/5.68 thf(fact_2545_power__mono,axiom,
% 5.46/5.68 ! [A: int,B2: int,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B2 @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % power_mono
% 5.46/5.68 thf(fact_2546_zero__less__power,axiom,
% 5.46/5.68 ! [A: real,N: nat] :
% 5.46/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.68 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_power
% 5.46/5.68 thf(fact_2547_zero__less__power,axiom,
% 5.46/5.68 ! [A: rat,N: nat] :
% 5.46/5.68 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.68 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_power
% 5.46/5.68 thf(fact_2548_zero__less__power,axiom,
% 5.46/5.68 ! [A: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_power
% 5.46/5.68 thf(fact_2549_zero__less__power,axiom,
% 5.46/5.68 ! [A: int,N: nat] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_less_power
% 5.46/5.68 thf(fact_2550_frac__eq__eq,axiom,
% 5.46/5.68 ! [Y3: complex,Z: complex,X4: complex,W: complex] :
% 5.46/5.68 ( ( Y3 != zero_zero_complex )
% 5.46/5.68 => ( ( Z != zero_zero_complex )
% 5.46/5.68 => ( ( ( divide1717551699836669952omplex @ X4 @ Y3 )
% 5.46/5.68 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.46/5.68 = ( ( times_times_complex @ X4 @ Z )
% 5.46/5.68 = ( times_times_complex @ W @ Y3 ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % frac_eq_eq
% 5.46/5.68 thf(fact_2551_frac__eq__eq,axiom,
% 5.46/5.68 ! [Y3: real,Z: real,X4: real,W: real] :
% 5.46/5.68 ( ( Y3 != zero_zero_real )
% 5.46/5.68 => ( ( Z != zero_zero_real )
% 5.46/5.68 => ( ( ( divide_divide_real @ X4 @ Y3 )
% 5.46/5.68 = ( divide_divide_real @ W @ Z ) )
% 5.46/5.68 = ( ( times_times_real @ X4 @ Z )
% 5.46/5.68 = ( times_times_real @ W @ Y3 ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % frac_eq_eq
% 5.46/5.68 thf(fact_2552_frac__eq__eq,axiom,
% 5.46/5.68 ! [Y3: rat,Z: rat,X4: rat,W: rat] :
% 5.46/5.68 ( ( Y3 != zero_zero_rat )
% 5.46/5.68 => ( ( Z != zero_zero_rat )
% 5.46/5.68 => ( ( ( divide_divide_rat @ X4 @ Y3 )
% 5.46/5.68 = ( divide_divide_rat @ W @ Z ) )
% 5.46/5.68 = ( ( times_times_rat @ X4 @ Z )
% 5.46/5.68 = ( times_times_rat @ W @ Y3 ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % frac_eq_eq
% 5.46/5.68 thf(fact_2553_divide__eq__eq,axiom,
% 5.46/5.68 ! [B2: complex,C: complex,A: complex] :
% 5.46/5.68 ( ( ( divide1717551699836669952omplex @ B2 @ C )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( ( C != zero_zero_complex )
% 5.46/5.68 => ( B2
% 5.46/5.68 = ( times_times_complex @ A @ C ) ) )
% 5.46/5.68 & ( ( C = zero_zero_complex )
% 5.46/5.68 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_eq
% 5.46/5.68 thf(fact_2554_divide__eq__eq,axiom,
% 5.46/5.68 ! [B2: real,C: real,A: real] :
% 5.46/5.68 ( ( ( divide_divide_real @ B2 @ C )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( ( C != zero_zero_real )
% 5.46/5.68 => ( B2
% 5.46/5.68 = ( times_times_real @ A @ C ) ) )
% 5.46/5.68 & ( ( C = zero_zero_real )
% 5.46/5.68 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_eq
% 5.46/5.68 thf(fact_2555_divide__eq__eq,axiom,
% 5.46/5.68 ! [B2: rat,C: rat,A: rat] :
% 5.46/5.68 ( ( ( divide_divide_rat @ B2 @ C )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( ( C != zero_zero_rat )
% 5.46/5.68 => ( B2
% 5.46/5.68 = ( times_times_rat @ A @ C ) ) )
% 5.46/5.68 & ( ( C = zero_zero_rat )
% 5.46/5.68 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_eq
% 5.46/5.68 thf(fact_2556_eq__divide__eq,axiom,
% 5.46/5.68 ! [A: complex,B2: complex,C: complex] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 5.46/5.68 = ( ( ( C != zero_zero_complex )
% 5.46/5.68 => ( ( times_times_complex @ A @ C )
% 5.46/5.68 = B2 ) )
% 5.46/5.68 & ( ( C = zero_zero_complex )
% 5.46/5.68 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_eq
% 5.46/5.68 thf(fact_2557_eq__divide__eq,axiom,
% 5.46/5.68 ! [A: real,B2: real,C: real] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( divide_divide_real @ B2 @ C ) )
% 5.46/5.68 = ( ( ( C != zero_zero_real )
% 5.46/5.68 => ( ( times_times_real @ A @ C )
% 5.46/5.68 = B2 ) )
% 5.46/5.68 & ( ( C = zero_zero_real )
% 5.46/5.68 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_eq
% 5.46/5.68 thf(fact_2558_eq__divide__eq,axiom,
% 5.46/5.68 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.68 ( ( A
% 5.46/5.68 = ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.68 = ( ( ( C != zero_zero_rat )
% 5.46/5.68 => ( ( times_times_rat @ A @ C )
% 5.46/5.68 = B2 ) )
% 5.46/5.68 & ( ( C = zero_zero_rat )
% 5.46/5.68 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_eq
% 5.46/5.68 thf(fact_2559_divide__eq__imp,axiom,
% 5.46/5.68 ! [C: complex,B2: complex,A: complex] :
% 5.46/5.68 ( ( C != zero_zero_complex )
% 5.46/5.68 => ( ( B2
% 5.46/5.68 = ( times_times_complex @ A @ C ) )
% 5.46/5.68 => ( ( divide1717551699836669952omplex @ B2 @ C )
% 5.46/5.68 = A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_imp
% 5.46/5.68 thf(fact_2560_divide__eq__imp,axiom,
% 5.46/5.68 ! [C: real,B2: real,A: real] :
% 5.46/5.68 ( ( C != zero_zero_real )
% 5.46/5.68 => ( ( B2
% 5.46/5.68 = ( times_times_real @ A @ C ) )
% 5.46/5.68 => ( ( divide_divide_real @ B2 @ C )
% 5.46/5.68 = A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_imp
% 5.46/5.68 thf(fact_2561_divide__eq__imp,axiom,
% 5.46/5.68 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.68 ( ( C != zero_zero_rat )
% 5.46/5.68 => ( ( B2
% 5.46/5.68 = ( times_times_rat @ A @ C ) )
% 5.46/5.68 => ( ( divide_divide_rat @ B2 @ C )
% 5.46/5.68 = A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % divide_eq_imp
% 5.46/5.68 thf(fact_2562_eq__divide__imp,axiom,
% 5.46/5.68 ! [C: complex,A: complex,B2: complex] :
% 5.46/5.68 ( ( C != zero_zero_complex )
% 5.46/5.68 => ( ( ( times_times_complex @ A @ C )
% 5.46/5.68 = B2 )
% 5.46/5.68 => ( A
% 5.46/5.68 = ( divide1717551699836669952omplex @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_imp
% 5.46/5.68 thf(fact_2563_eq__divide__imp,axiom,
% 5.46/5.68 ! [C: real,A: real,B2: real] :
% 5.46/5.68 ( ( C != zero_zero_real )
% 5.46/5.68 => ( ( ( times_times_real @ A @ C )
% 5.46/5.68 = B2 )
% 5.46/5.68 => ( A
% 5.46/5.68 = ( divide_divide_real @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_imp
% 5.46/5.68 thf(fact_2564_eq__divide__imp,axiom,
% 5.46/5.68 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.68 ( ( C != zero_zero_rat )
% 5.46/5.68 => ( ( ( times_times_rat @ A @ C )
% 5.46/5.68 = B2 )
% 5.46/5.68 => ( A
% 5.46/5.68 = ( divide_divide_rat @ B2 @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % eq_divide_imp
% 5.46/5.68 thf(fact_2565_nonzero__divide__eq__eq,axiom,
% 5.46/5.68 ! [C: complex,B2: complex,A: complex] :
% 5.46/5.68 ( ( C != zero_zero_complex )
% 5.46/5.68 => ( ( ( divide1717551699836669952omplex @ B2 @ C )
% 5.46/5.68 = A )
% 5.46/5.68 = ( B2
% 5.46/5.68 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_divide_eq_eq
% 5.46/5.68 thf(fact_2566_nonzero__divide__eq__eq,axiom,
% 5.46/5.68 ! [C: real,B2: real,A: real] :
% 5.46/5.68 ( ( C != zero_zero_real )
% 5.46/5.68 => ( ( ( divide_divide_real @ B2 @ C )
% 5.46/5.68 = A )
% 5.46/5.68 = ( B2
% 5.46/5.68 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_divide_eq_eq
% 5.46/5.68 thf(fact_2567_nonzero__divide__eq__eq,axiom,
% 5.46/5.68 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.68 ( ( C != zero_zero_rat )
% 5.46/5.68 => ( ( ( divide_divide_rat @ B2 @ C )
% 5.46/5.68 = A )
% 5.46/5.68 = ( B2
% 5.46/5.68 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_divide_eq_eq
% 5.46/5.68 thf(fact_2568_nonzero__eq__divide__eq,axiom,
% 5.46/5.68 ! [C: complex,A: complex,B2: complex] :
% 5.46/5.68 ( ( C != zero_zero_complex )
% 5.46/5.68 => ( ( A
% 5.46/5.68 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 5.46/5.68 = ( ( times_times_complex @ A @ C )
% 5.46/5.68 = B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_eq_divide_eq
% 5.46/5.68 thf(fact_2569_nonzero__eq__divide__eq,axiom,
% 5.46/5.68 ! [C: real,A: real,B2: real] :
% 5.46/5.68 ( ( C != zero_zero_real )
% 5.46/5.68 => ( ( A
% 5.46/5.68 = ( divide_divide_real @ B2 @ C ) )
% 5.46/5.68 = ( ( times_times_real @ A @ C )
% 5.46/5.68 = B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_eq_divide_eq
% 5.46/5.68 thf(fact_2570_nonzero__eq__divide__eq,axiom,
% 5.46/5.68 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.68 ( ( C != zero_zero_rat )
% 5.46/5.68 => ( ( A
% 5.46/5.68 = ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.68 = ( ( times_times_rat @ A @ C )
% 5.46/5.68 = B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nonzero_eq_divide_eq
% 5.46/5.68 thf(fact_2571_right__inverse__eq,axiom,
% 5.46/5.68 ! [B2: complex,A: complex] :
% 5.46/5.68 ( ( B2 != zero_zero_complex )
% 5.46/5.68 => ( ( ( divide1717551699836669952omplex @ A @ B2 )
% 5.46/5.68 = one_one_complex )
% 5.46/5.68 = ( A = B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % right_inverse_eq
% 5.46/5.68 thf(fact_2572_right__inverse__eq,axiom,
% 5.46/5.68 ! [B2: real,A: real] :
% 5.46/5.68 ( ( B2 != zero_zero_real )
% 5.46/5.68 => ( ( ( divide_divide_real @ A @ B2 )
% 5.46/5.68 = one_one_real )
% 5.46/5.68 = ( A = B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % right_inverse_eq
% 5.46/5.68 thf(fact_2573_right__inverse__eq,axiom,
% 5.46/5.68 ! [B2: rat,A: rat] :
% 5.46/5.68 ( ( B2 != zero_zero_rat )
% 5.46/5.68 => ( ( ( divide_divide_rat @ A @ B2 )
% 5.46/5.68 = one_one_rat )
% 5.46/5.68 = ( A = B2 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % right_inverse_eq
% 5.46/5.68 thf(fact_2574_not__exp__less__eq__0__int,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.46/5.68
% 5.46/5.68 % not_exp_less_eq_0_int
% 5.46/5.68 thf(fact_2575_pos__zdiv__mult__2,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.68 = ( divide_divide_int @ B2 @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % pos_zdiv_mult_2
% 5.46/5.68 thf(fact_2576_neg__zdiv__mult__2,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.68 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.68 = ( divide_divide_int @ ( plus_plus_int @ B2 @ one_one_int ) @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % neg_zdiv_mult_2
% 5.46/5.68 thf(fact_2577_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.46/5.68 ! [A: code_integer,B2: code_integer] :
% 5.46/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.68 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B2 ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.46/5.68 thf(fact_2578_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.68 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B2 ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.46/5.68 thf(fact_2579_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.68 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B2 ) @ A ) ) ).
% 5.46/5.68
% 5.46/5.68 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.46/5.68 thf(fact_2580_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.46/5.68 ! [B2: nat,A: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.68 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B2 ) @ B2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.46/5.68 thf(fact_2581_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.46/5.68 ! [B2: int,A: int] :
% 5.46/5.68 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.68 => ( ord_less_int @ ( modulo_modulo_int @ A @ B2 ) @ B2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.46/5.68 thf(fact_2582_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.46/5.68 ! [B2: code_integer,A: code_integer] :
% 5.46/5.68 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.46/5.68 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B2 ) @ B2 ) ) ).
% 5.46/5.68
% 5.46/5.68 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.46/5.68 thf(fact_2583_power__0,axiom,
% 5.46/5.68 ! [A: rat] :
% 5.46/5.68 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.46/5.68 = one_one_rat ) ).
% 5.46/5.68
% 5.46/5.68 % power_0
% 5.46/5.68 thf(fact_2584_power__0,axiom,
% 5.46/5.68 ! [A: nat] :
% 5.46/5.68 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.46/5.68 = one_one_nat ) ).
% 5.46/5.68
% 5.46/5.68 % power_0
% 5.46/5.68 thf(fact_2585_power__0,axiom,
% 5.46/5.68 ! [A: real] :
% 5.46/5.68 ( ( power_power_real @ A @ zero_zero_nat )
% 5.46/5.68 = one_one_real ) ).
% 5.46/5.68
% 5.46/5.68 % power_0
% 5.46/5.68 thf(fact_2586_power__0,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( power_power_int @ A @ zero_zero_nat )
% 5.46/5.68 = one_one_int ) ).
% 5.46/5.68
% 5.46/5.68 % power_0
% 5.46/5.68 thf(fact_2587_power__0,axiom,
% 5.46/5.68 ! [A: complex] :
% 5.46/5.68 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.46/5.68 = one_one_complex ) ).
% 5.46/5.68
% 5.46/5.68 % power_0
% 5.46/5.68 thf(fact_2588_mod__eq__self__iff__div__eq__0,axiom,
% 5.46/5.68 ! [A: nat,B2: nat] :
% 5.46/5.68 ( ( ( modulo_modulo_nat @ A @ B2 )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( divide_divide_nat @ A @ B2 )
% 5.46/5.68 = zero_zero_nat ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_eq_self_iff_div_eq_0
% 5.46/5.68 thf(fact_2589_mod__eq__self__iff__div__eq__0,axiom,
% 5.46/5.68 ! [A: int,B2: int] :
% 5.46/5.68 ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( divide_divide_int @ A @ B2 )
% 5.46/5.68 = zero_zero_int ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_eq_self_iff_div_eq_0
% 5.46/5.68 thf(fact_2590_mod__eq__self__iff__div__eq__0,axiom,
% 5.46/5.68 ! [A: code_integer,B2: code_integer] :
% 5.46/5.68 ( ( ( modulo364778990260209775nteger @ A @ B2 )
% 5.46/5.68 = A )
% 5.46/5.68 = ( ( divide6298287555418463151nteger @ A @ B2 )
% 5.46/5.68 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_eq_self_iff_div_eq_0
% 5.46/5.68 thf(fact_2591_less__Suc__eq__0__disj,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.46/5.68 = ( ( M = zero_zero_nat )
% 5.46/5.68 | ? [J3: nat] :
% 5.46/5.68 ( ( M
% 5.46/5.68 = ( suc @ J3 ) )
% 5.46/5.68 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_Suc_eq_0_disj
% 5.46/5.68 thf(fact_2592_gr0__implies__Suc,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.68 => ? [M4: nat] :
% 5.46/5.68 ( N
% 5.46/5.68 = ( suc @ M4 ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % gr0_implies_Suc
% 5.46/5.68 thf(fact_2593_All__less__Suc2,axiom,
% 5.46/5.68 ! [N: nat,P: nat > $o] :
% 5.46/5.68 ( ( ! [I2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.46/5.68 => ( P @ I2 ) ) )
% 5.46/5.68 = ( ( P @ zero_zero_nat )
% 5.46/5.68 & ! [I2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ I2 @ N )
% 5.46/5.68 => ( P @ ( suc @ I2 ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % All_less_Suc2
% 5.46/5.68 thf(fact_2594_gr0__conv__Suc,axiom,
% 5.46/5.68 ! [N: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.68 = ( ? [M6: nat] :
% 5.46/5.68 ( N
% 5.46/5.68 = ( suc @ M6 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % gr0_conv_Suc
% 5.46/5.68 thf(fact_2595_Ex__less__Suc2,axiom,
% 5.46/5.68 ! [N: nat,P: nat > $o] :
% 5.46/5.68 ( ( ? [I2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.46/5.68 & ( P @ I2 ) ) )
% 5.46/5.68 = ( ( P @ zero_zero_nat )
% 5.46/5.68 | ? [I2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ I2 @ N )
% 5.46/5.68 & ( P @ ( suc @ I2 ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Ex_less_Suc2
% 5.46/5.68 thf(fact_2596_add__is__1,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( ( plus_plus_nat @ M @ N )
% 5.46/5.68 = ( suc @ zero_zero_nat ) )
% 5.46/5.68 = ( ( ( M
% 5.46/5.68 = ( suc @ zero_zero_nat ) )
% 5.46/5.68 & ( N = zero_zero_nat ) )
% 5.46/5.68 | ( ( M = zero_zero_nat )
% 5.46/5.68 & ( N
% 5.46/5.68 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % add_is_1
% 5.46/5.68 thf(fact_2597_one__is__add,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( ( suc @ zero_zero_nat )
% 5.46/5.68 = ( plus_plus_nat @ M @ N ) )
% 5.46/5.68 = ( ( ( M
% 5.46/5.68 = ( suc @ zero_zero_nat ) )
% 5.46/5.68 & ( N = zero_zero_nat ) )
% 5.46/5.68 | ( ( M = zero_zero_nat )
% 5.46/5.68 & ( N
% 5.46/5.68 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % one_is_add
% 5.46/5.68 thf(fact_2598_ex__least__nat__le,axiom,
% 5.46/5.68 ! [P: nat > $o,N: nat] :
% 5.46/5.68 ( ( P @ N )
% 5.46/5.68 => ( ~ ( P @ zero_zero_nat )
% 5.46/5.68 => ? [K2: nat] :
% 5.46/5.68 ( ( ord_less_eq_nat @ K2 @ N )
% 5.46/5.68 & ! [I4: nat] :
% 5.46/5.68 ( ( ord_less_nat @ I4 @ K2 )
% 5.46/5.68 => ~ ( P @ I4 ) )
% 5.46/5.68 & ( P @ K2 ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % ex_least_nat_le
% 5.46/5.68 thf(fact_2599_less__imp__add__positive,axiom,
% 5.46/5.68 ! [I: nat,J: nat] :
% 5.46/5.68 ( ( ord_less_nat @ I @ J )
% 5.46/5.68 => ? [K2: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.46/5.68 & ( ( plus_plus_nat @ I @ K2 )
% 5.46/5.68 = J ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % less_imp_add_positive
% 5.46/5.68 thf(fact_2600_diff__less,axiom,
% 5.46/5.68 ! [N: nat,M: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.68 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % diff_less
% 5.46/5.68 thf(fact_2601_nat__mult__less__cancel1,axiom,
% 5.46/5.68 ! [K: nat,M: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.68 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.68 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nat_mult_less_cancel1
% 5.46/5.68 thf(fact_2602_nat__mult__eq__cancel1,axiom,
% 5.46/5.68 ! [K: nat,M: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.68 => ( ( ( times_times_nat @ K @ M )
% 5.46/5.68 = ( times_times_nat @ K @ N ) )
% 5.46/5.68 = ( M = N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nat_mult_eq_cancel1
% 5.46/5.68 thf(fact_2603_mult__less__mono2,axiom,
% 5.46/5.68 ! [I: nat,J: nat,K: nat] :
% 5.46/5.68 ( ( ord_less_nat @ I @ J )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.68 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_mono2
% 5.46/5.68 thf(fact_2604_mult__less__mono1,axiom,
% 5.46/5.68 ! [I: nat,J: nat,K: nat] :
% 5.46/5.68 ( ( ord_less_nat @ I @ J )
% 5.46/5.68 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.68 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_less_mono1
% 5.46/5.68 thf(fact_2605_One__nat__def,axiom,
% 5.46/5.68 ( one_one_nat
% 5.46/5.68 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.68
% 5.46/5.68 % One_nat_def
% 5.46/5.68 thf(fact_2606_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( ( divide_divide_nat @ M @ N )
% 5.46/5.68 = zero_zero_nat )
% 5.46/5.68 = ( ( ord_less_nat @ M @ N )
% 5.46/5.68 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % Euclidean_Division.div_eq_0_iff
% 5.46/5.68 thf(fact_2607_diff__add__0,axiom,
% 5.46/5.68 ! [N: nat,M: nat] :
% 5.46/5.68 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.68 = zero_zero_nat ) ).
% 5.46/5.68
% 5.46/5.68 % diff_add_0
% 5.46/5.68 thf(fact_2608_nat__power__less__imp__less,axiom,
% 5.46/5.68 ! [I: nat,M: nat,N: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.46/5.68 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.46/5.68 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % nat_power_less_imp_less
% 5.46/5.68 thf(fact_2609_mult__eq__self__implies__10,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( M
% 5.46/5.68 = ( times_times_nat @ M @ N ) )
% 5.46/5.68 => ( ( N = one_one_nat )
% 5.46/5.68 | ( M = zero_zero_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mult_eq_self_implies_10
% 5.46/5.68 thf(fact_2610_mod__Suc,axiom,
% 5.46/5.68 ! [M: nat,N: nat] :
% 5.46/5.68 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.68 = N )
% 5.46/5.68 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.46/5.68 = zero_zero_nat ) )
% 5.46/5.68 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.68 != N )
% 5.46/5.68 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.46/5.68 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_Suc
% 5.46/5.68 thf(fact_2611_mod__less__divisor,axiom,
% 5.46/5.68 ! [N: nat,M: nat] :
% 5.46/5.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.68 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod_less_divisor
% 5.46/5.68 thf(fact_2612_mod2__eq__if,axiom,
% 5.46/5.68 ! [A: nat] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = zero_zero_nat ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod2_eq_if
% 5.46/5.68 thf(fact_2613_mod2__eq__if,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.68 = zero_zero_int ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod2_eq_if
% 5.46/5.68 thf(fact_2614_mod2__eq__if,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 = zero_z3403309356797280102nteger ) )
% 5.46/5.68 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 = one_one_Code_integer ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % mod2_eq_if
% 5.46/5.68 thf(fact_2615_parity__cases,axiom,
% 5.46/5.68 ! [A: nat] :
% 5.46/5.68 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 != zero_zero_nat ) )
% 5.46/5.68 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.68 != one_one_nat ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % parity_cases
% 5.46/5.68 thf(fact_2616_parity__cases,axiom,
% 5.46/5.68 ! [A: int] :
% 5.46/5.68 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.68 != zero_zero_int ) )
% 5.46/5.68 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.68 != one_one_int ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % parity_cases
% 5.46/5.68 thf(fact_2617_parity__cases,axiom,
% 5.46/5.68 ! [A: code_integer] :
% 5.46/5.68 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 != zero_z3403309356797280102nteger ) )
% 5.46/5.68 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.68 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.68 != one_one_Code_integer ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % parity_cases
% 5.46/5.68 thf(fact_2618_pow_Osimps_I1_J,axiom,
% 5.46/5.68 ! [X4: num] :
% 5.46/5.68 ( ( pow @ X4 @ one )
% 5.46/5.68 = X4 ) ).
% 5.46/5.68
% 5.46/5.68 % pow.simps(1)
% 5.46/5.68 thf(fact_2619_zero__le__power__eq,axiom,
% 5.46/5.68 ! [A: real,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.46/5.68 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_power_eq
% 5.46/5.68 thf(fact_2620_zero__le__power__eq,axiom,
% 5.46/5.68 ! [A: rat,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.46/5.68 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_power_eq
% 5.46/5.68 thf(fact_2621_zero__le__power__eq,axiom,
% 5.46/5.68 ! [A: int,N: nat] :
% 5.46/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.46/5.68 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_power_eq
% 5.46/5.68 thf(fact_2622_zero__le__odd__power,axiom,
% 5.46/5.68 ! [N: nat,A: real] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.46/5.68 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_odd_power
% 5.46/5.68 thf(fact_2623_zero__le__odd__power,axiom,
% 5.46/5.68 ! [N: nat,A: rat] :
% 5.46/5.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.46/5.68 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.46/5.68
% 5.46/5.68 % zero_le_odd_power
% 5.46/5.68 thf(fact_2624_zero__le__odd__power,axiom,
% 5.46/5.69 ! [N: nat,A: int] :
% 5.46/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.46/5.69 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_odd_power
% 5.46/5.69 thf(fact_2625_zero__le__even__power,axiom,
% 5.46/5.69 ! [N: nat,A: real] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_even_power
% 5.46/5.69 thf(fact_2626_zero__le__even__power,axiom,
% 5.46/5.69 ! [N: nat,A: rat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_even_power
% 5.46/5.69 thf(fact_2627_zero__le__even__power,axiom,
% 5.46/5.69 ! [N: nat,A: int] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % zero_le_even_power
% 5.46/5.69 thf(fact_2628_mod__eq__0D,axiom,
% 5.46/5.69 ! [M: nat,D: nat] :
% 5.46/5.69 ( ( ( modulo_modulo_nat @ M @ D )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 => ? [Q3: nat] :
% 5.46/5.69 ( M
% 5.46/5.69 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mod_eq_0D
% 5.46/5.69 thf(fact_2629_div2__even__ext__nat,axiom,
% 5.46/5.69 ! [X4: nat,Y3: nat] :
% 5.46/5.69 ( ( ( divide_divide_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.69 = ( divide_divide_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.69 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 )
% 5.46/5.69 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y3 ) )
% 5.46/5.69 => ( X4 = Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div2_even_ext_nat
% 5.46/5.69 thf(fact_2630_even__numeral,axiom,
% 5.46/5.69 ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_numeral
% 5.46/5.69 thf(fact_2631_even__numeral,axiom,
% 5.46/5.69 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_numeral
% 5.46/5.69 thf(fact_2632_even__numeral,axiom,
% 5.46/5.69 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_numeral
% 5.46/5.69 thf(fact_2633_signed__take__bit__int__less__eq,axiom,
% 5.46/5.69 ! [N: nat,K: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.46/5.69 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % signed_take_bit_int_less_eq
% 5.46/5.69 thf(fact_2634_unit__eq__div1,axiom,
% 5.46/5.69 ! [B2: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.69 => ( ( ( divide6298287555418463151nteger @ A @ B2 )
% 5.46/5.69 = C )
% 5.46/5.69 = ( A
% 5.46/5.69 = ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_eq_div1
% 5.46/5.69 thf(fact_2635_unit__eq__div1,axiom,
% 5.46/5.69 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.69 => ( ( ( divide_divide_nat @ A @ B2 )
% 5.46/5.69 = C )
% 5.46/5.69 = ( A
% 5.46/5.69 = ( times_times_nat @ C @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_eq_div1
% 5.46/5.69 thf(fact_2636_unit__eq__div1,axiom,
% 5.46/5.69 ! [B2: int,A: int,C: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.69 => ( ( ( divide_divide_int @ A @ B2 )
% 5.46/5.69 = C )
% 5.46/5.69 = ( A
% 5.46/5.69 = ( times_times_int @ C @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_eq_div1
% 5.46/5.69 thf(fact_2637_unit__eq__div2,axiom,
% 5.46/5.69 ! [B2: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.69 => ( ( A
% 5.46/5.69 = ( divide6298287555418463151nteger @ C @ B2 ) )
% 5.46/5.69 = ( ( times_3573771949741848930nteger @ A @ B2 )
% 5.46/5.69 = C ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_eq_div2
% 5.46/5.69 thf(fact_2638_unit__eq__div2,axiom,
% 5.46/5.69 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.69 => ( ( A
% 5.46/5.69 = ( divide_divide_nat @ C @ B2 ) )
% 5.46/5.69 = ( ( times_times_nat @ A @ B2 )
% 5.46/5.69 = C ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_eq_div2
% 5.46/5.69 thf(fact_2639_unit__eq__div2,axiom,
% 5.46/5.69 ! [B2: int,A: int,C: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.69 => ( ( A
% 5.46/5.69 = ( divide_divide_int @ C @ B2 ) )
% 5.46/5.69 = ( ( times_times_int @ A @ B2 )
% 5.46/5.69 = C ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_eq_div2
% 5.46/5.69 thf(fact_2640_div__mult__unit2,axiom,
% 5.46/5.69 ! [C: code_integer,B2: code_integer,A: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.46/5.69 => ( ( dvd_dvd_Code_integer @ B2 @ A )
% 5.46/5.69 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 5.46/5.69 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_mult_unit2
% 5.46/5.69 thf(fact_2641_div__mult__unit2,axiom,
% 5.46/5.69 ! [C: nat,B2: nat,A: nat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.46/5.69 => ( ( dvd_dvd_nat @ B2 @ A )
% 5.46/5.69 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 5.46/5.69 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_mult_unit2
% 5.46/5.69 thf(fact_2642_div__mult__unit2,axiom,
% 5.46/5.69 ! [C: int,B2: int,A: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.46/5.69 => ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.69 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ C ) )
% 5.46/5.69 = ( divide_divide_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_mult_unit2
% 5.46/5.69 thf(fact_2643_unit__div__commute,axiom,
% 5.46/5.69 ! [B2: code_integer,A: code_integer,C: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.69 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ C )
% 5.46/5.69 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_div_commute
% 5.46/5.69 thf(fact_2644_unit__div__commute,axiom,
% 5.46/5.69 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.69 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B2 ) @ C )
% 5.46/5.69 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_div_commute
% 5.46/5.69 thf(fact_2645_unit__div__commute,axiom,
% 5.46/5.69 ! [B2: int,A: int,C: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.69 => ( ( times_times_int @ ( divide_divide_int @ A @ B2 ) @ C )
% 5.46/5.69 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_div_commute
% 5.46/5.69 thf(fact_2646_unit__div__mult__swap,axiom,
% 5.46/5.69 ! [C: code_integer,A: code_integer,B2: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.46/5.69 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B2 @ C ) )
% 5.46/5.69 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_div_mult_swap
% 5.46/5.69 thf(fact_2647_unit__div__mult__swap,axiom,
% 5.46/5.69 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.46/5.69 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B2 @ C ) )
% 5.46/5.69 = ( divide_divide_nat @ ( times_times_nat @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_div_mult_swap
% 5.46/5.69 thf(fact_2648_unit__div__mult__swap,axiom,
% 5.46/5.69 ! [C: int,A: int,B2: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.46/5.69 => ( ( times_times_int @ A @ ( divide_divide_int @ B2 @ C ) )
% 5.46/5.69 = ( divide_divide_int @ ( times_times_int @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unit_div_mult_swap
% 5.46/5.69 thf(fact_2649_is__unit__div__mult2__eq,axiom,
% 5.46/5.69 ! [B2: code_integer,C: code_integer,A: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.46/5.69 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.46/5.69 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 5.46/5.69 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % is_unit_div_mult2_eq
% 5.46/5.69 thf(fact_2650_is__unit__div__mult2__eq,axiom,
% 5.46/5.69 ! [B2: nat,C: nat,A: nat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.46/5.69 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.46/5.69 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 5.46/5.69 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % is_unit_div_mult2_eq
% 5.46/5.69 thf(fact_2651_is__unit__div__mult2__eq,axiom,
% 5.46/5.69 ! [B2: int,C: int,A: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.46/5.69 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.46/5.69 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ C ) )
% 5.46/5.69 = ( divide_divide_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % is_unit_div_mult2_eq
% 5.46/5.69 thf(fact_2652_mod__eq__dvd__iff__nat,axiom,
% 5.46/5.69 ! [N: nat,M: nat,Q2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.69 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.46/5.69 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.46/5.69 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mod_eq_dvd_iff_nat
% 5.46/5.69 thf(fact_2653_mult__less__le__imp__less,axiom,
% 5.46/5.69 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.69 ( ( ord_less_real @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ C @ D )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_le_imp_less
% 5.46/5.69 thf(fact_2654_mult__less__le__imp__less,axiom,
% 5.46/5.69 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.69 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ C @ D )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_le_imp_less
% 5.46/5.69 thf(fact_2655_mult__less__le__imp__less,axiom,
% 5.46/5.69 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.69 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_nat @ C @ D )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.69 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_le_imp_less
% 5.46/5.69 thf(fact_2656_mult__less__le__imp__less,axiom,
% 5.46/5.69 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.69 ( ( ord_less_int @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_int @ C @ D )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_le_imp_less
% 5.46/5.69 thf(fact_2657_mult__le__less__imp__less,axiom,
% 5.46/5.69 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_real @ C @ D )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_less_imp_less
% 5.46/5.69 thf(fact_2658_mult__le__less__imp__less,axiom,
% 5.46/5.69 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_rat @ C @ D )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_less_imp_less
% 5.46/5.69 thf(fact_2659_mult__le__less__imp__less,axiom,
% 5.46/5.69 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_nat @ C @ D )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.69 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_less_imp_less
% 5.46/5.69 thf(fact_2660_mult__le__less__imp__less,axiom,
% 5.46/5.69 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_int @ C @ D )
% 5.46/5.69 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_less_imp_less
% 5.46/5.69 thf(fact_2661_mult__right__le__imp__le,axiom,
% 5.46/5.69 ! [A: real,C: real,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_le_imp_le
% 5.46/5.69 thf(fact_2662_mult__right__le__imp__le,axiom,
% 5.46/5.69 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_le_imp_le
% 5.46/5.69 thf(fact_2663_mult__right__le__imp__le,axiom,
% 5.46/5.69 ! [A: nat,C: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.69 => ( ord_less_eq_nat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_le_imp_le
% 5.46/5.69 thf(fact_2664_mult__right__le__imp__le,axiom,
% 5.46/5.69 ! [A: int,C: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 5.46/5.69 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_le_imp_le
% 5.46/5.69 thf(fact_2665_mult__left__le__imp__le,axiom,
% 5.46/5.69 ! [C: real,A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le_imp_le
% 5.46/5.69 thf(fact_2666_mult__left__le__imp__le,axiom,
% 5.46/5.69 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le_imp_le
% 5.46/5.69 thf(fact_2667_mult__left__le__imp__le,axiom,
% 5.46/5.69 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.69 => ( ord_less_eq_nat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le_imp_le
% 5.46/5.69 thf(fact_2668_mult__left__le__imp__le,axiom,
% 5.46/5.69 ! [C: int,A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.46/5.69 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le_imp_le
% 5.46/5.69 thf(fact_2669_mult__le__cancel__left__pos,axiom,
% 5.46/5.69 ! [C: real,A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.46/5.69 = ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left_pos
% 5.46/5.69 thf(fact_2670_mult__le__cancel__left__pos,axiom,
% 5.46/5.69 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.69 = ( ord_less_eq_rat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left_pos
% 5.46/5.69 thf(fact_2671_mult__le__cancel__left__pos,axiom,
% 5.46/5.69 ! [C: int,A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.46/5.69 = ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left_pos
% 5.46/5.69 thf(fact_2672_mult__le__cancel__left__neg,axiom,
% 5.46/5.69 ! [C: real,A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.46/5.69 = ( ord_less_eq_real @ B2 @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left_neg
% 5.46/5.69 thf(fact_2673_mult__le__cancel__left__neg,axiom,
% 5.46/5.69 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.69 = ( ord_less_eq_rat @ B2 @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left_neg
% 5.46/5.69 thf(fact_2674_mult__le__cancel__left__neg,axiom,
% 5.46/5.69 ! [C: int,A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.46/5.69 = ( ord_less_eq_int @ B2 @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left_neg
% 5.46/5.69 thf(fact_2675_mult__less__cancel__right,axiom,
% 5.46/5.69 ! [A: real,C: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_right
% 5.46/5.69 thf(fact_2676_mult__less__cancel__right,axiom,
% 5.46/5.69 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_right
% 5.46/5.69 thf(fact_2677_mult__less__cancel__right,axiom,
% 5.46/5.69 ! [A: int,C: int,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_int @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_right
% 5.46/5.69 thf(fact_2678_mult__strict__mono_H,axiom,
% 5.46/5.69 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.69 ( ( ord_less_real @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_real @ C @ D )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_strict_mono'
% 5.46/5.69 thf(fact_2679_mult__strict__mono_H,axiom,
% 5.46/5.69 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.69 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_rat @ C @ D )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_strict_mono'
% 5.46/5.69 thf(fact_2680_mult__strict__mono_H,axiom,
% 5.46/5.69 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.69 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_nat @ C @ D )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.69 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_strict_mono'
% 5.46/5.69 thf(fact_2681_mult__strict__mono_H,axiom,
% 5.46/5.69 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.69 ( ( ord_less_int @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_int @ C @ D )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_strict_mono'
% 5.46/5.69 thf(fact_2682_mult__right__less__imp__less,axiom,
% 5.46/5.69 ! [A: real,C: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_less_imp_less
% 5.46/5.69 thf(fact_2683_mult__right__less__imp__less,axiom,
% 5.46/5.69 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_less_imp_less
% 5.46/5.69 thf(fact_2684_mult__right__less__imp__less,axiom,
% 5.46/5.69 ! [A: nat,C: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ C ) )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.69 => ( ord_less_nat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_less_imp_less
% 5.46/5.69 thf(fact_2685_mult__right__less__imp__less,axiom,
% 5.46/5.69 ! [A: int,C: int,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_less_imp_less
% 5.46/5.69 thf(fact_2686_mult__less__cancel__left,axiom,
% 5.46/5.69 ! [C: real,A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_left
% 5.46/5.69 thf(fact_2687_mult__less__cancel__left,axiom,
% 5.46/5.69 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_left
% 5.46/5.69 thf(fact_2688_mult__less__cancel__left,axiom,
% 5.46/5.69 ! [C: int,A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_int @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_left
% 5.46/5.69 thf(fact_2689_mult__strict__mono,axiom,
% 5.46/5.69 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.69 ( ( ord_less_real @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_real @ C @ D )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_strict_mono
% 5.46/5.69 thf(fact_2690_mult__strict__mono,axiom,
% 5.46/5.69 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.69 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_rat @ C @ D )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_strict_mono
% 5.46/5.69 thf(fact_2691_mult__strict__mono,axiom,
% 5.46/5.69 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.69 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_nat @ C @ D )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.69 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_strict_mono
% 5.46/5.69 thf(fact_2692_mult__strict__mono,axiom,
% 5.46/5.69 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.69 ( ( ord_less_int @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_int @ C @ D )
% 5.46/5.69 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_strict_mono
% 5.46/5.69 thf(fact_2693_mult__left__less__imp__less,axiom,
% 5.46/5.69 ! [C: real,A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_less_imp_less
% 5.46/5.69 thf(fact_2694_mult__left__less__imp__less,axiom,
% 5.46/5.69 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_less_imp_less
% 5.46/5.69 thf(fact_2695_mult__left__less__imp__less,axiom,
% 5.46/5.69 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B2 ) )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.69 => ( ord_less_nat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_less_imp_less
% 5.46/5.69 thf(fact_2696_mult__left__less__imp__less,axiom,
% 5.46/5.69 ! [C: int,A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_less_imp_less
% 5.46/5.69 thf(fact_2697_mult__le__cancel__right,axiom,
% 5.46/5.69 ! [A: real,C: real,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_right
% 5.46/5.69 thf(fact_2698_mult__le__cancel__right,axiom,
% 5.46/5.69 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_right
% 5.46/5.69 thf(fact_2699_mult__le__cancel__right,axiom,
% 5.46/5.69 ! [A: int,C: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_eq_int @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_eq_int @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_right
% 5.46/5.69 thf(fact_2700_mult__le__cancel__left,axiom,
% 5.46/5.69 ! [C: real,A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left
% 5.46/5.69 thf(fact_2701_mult__le__cancel__left,axiom,
% 5.46/5.69 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left
% 5.46/5.69 thf(fact_2702_mult__le__cancel__left,axiom,
% 5.46/5.69 ! [C: int,A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_eq_int @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_eq_int @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left
% 5.46/5.69 thf(fact_2703_add__strict__increasing2,axiom,
% 5.46/5.69 ! [A: real,B2: real,C: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.69 => ( ord_less_real @ B2 @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_strict_increasing2
% 5.46/5.69 thf(fact_2704_add__strict__increasing2,axiom,
% 5.46/5.69 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.69 => ( ord_less_rat @ B2 @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_strict_increasing2
% 5.46/5.69 thf(fact_2705_add__strict__increasing2,axiom,
% 5.46/5.69 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_nat @ B2 @ C )
% 5.46/5.69 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_strict_increasing2
% 5.46/5.69 thf(fact_2706_add__strict__increasing2,axiom,
% 5.46/5.69 ! [A: int,B2: int,C: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_int @ B2 @ C )
% 5.46/5.69 => ( ord_less_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_strict_increasing2
% 5.46/5.69 thf(fact_2707_add__strict__increasing,axiom,
% 5.46/5.69 ! [A: real,B2: real,C: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ B2 @ C )
% 5.46/5.69 => ( ord_less_real @ B2 @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_strict_increasing
% 5.46/5.69 thf(fact_2708_add__strict__increasing,axiom,
% 5.46/5.69 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.69 => ( ord_less_rat @ B2 @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_strict_increasing
% 5.46/5.69 thf(fact_2709_add__strict__increasing,axiom,
% 5.46/5.69 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_eq_nat @ B2 @ C )
% 5.46/5.69 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_strict_increasing
% 5.46/5.69 thf(fact_2710_add__strict__increasing,axiom,
% 5.46/5.69 ! [A: int,B2: int,C: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_eq_int @ B2 @ C )
% 5.46/5.69 => ( ord_less_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_strict_increasing
% 5.46/5.69 thf(fact_2711_add__pos__nonneg,axiom,
% 5.46/5.69 ! [A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_pos_nonneg
% 5.46/5.69 thf(fact_2712_add__pos__nonneg,axiom,
% 5.46/5.69 ! [A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_pos_nonneg
% 5.46/5.69 thf(fact_2713_add__pos__nonneg,axiom,
% 5.46/5.69 ! [A: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_pos_nonneg
% 5.46/5.69 thf(fact_2714_add__pos__nonneg,axiom,
% 5.46/5.69 ! [A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.69 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_pos_nonneg
% 5.46/5.69 thf(fact_2715_add__nonpos__neg,axiom,
% 5.46/5.69 ! [A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ ( plus_plus_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_nonpos_neg
% 5.46/5.69 thf(fact_2716_add__nonpos__neg,axiom,
% 5.46/5.69 ! [A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ ( plus_plus_rat @ A @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_nonpos_neg
% 5.46/5.69 thf(fact_2717_add__nonpos__neg,axiom,
% 5.46/5.69 ! [A: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.46/5.69 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 5.46/5.69 => ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_nonpos_neg
% 5.46/5.69 thf(fact_2718_add__nonpos__neg,axiom,
% 5.46/5.69 ! [A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.69 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.46/5.69 => ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_nonpos_neg
% 5.46/5.69 thf(fact_2719_add__nonneg__pos,axiom,
% 5.46/5.69 ! [A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_nonneg_pos
% 5.46/5.69 thf(fact_2720_add__nonneg__pos,axiom,
% 5.46/5.69 ! [A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_nonneg_pos
% 5.46/5.69 thf(fact_2721_add__nonneg__pos,axiom,
% 5.46/5.69 ! [A: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_nonneg_pos
% 5.46/5.69 thf(fact_2722_add__nonneg__pos,axiom,
% 5.46/5.69 ! [A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.69 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_nonneg_pos
% 5.46/5.69 thf(fact_2723_add__neg__nonpos,axiom,
% 5.46/5.69 ! [A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_eq_real @ B2 @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ ( plus_plus_real @ A @ B2 ) @ zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_neg_nonpos
% 5.46/5.69 thf(fact_2724_add__neg__nonpos,axiom,
% 5.46/5.69 ! [A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_eq_rat @ B2 @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ ( plus_plus_rat @ A @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_neg_nonpos
% 5.46/5.69 thf(fact_2725_add__neg__nonpos,axiom,
% 5.46/5.69 ! [A: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.46/5.69 => ( ( ord_less_eq_nat @ B2 @ zero_zero_nat )
% 5.46/5.69 => ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_neg_nonpos
% 5.46/5.69 thf(fact_2726_add__neg__nonpos,axiom,
% 5.46/5.69 ! [A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.69 => ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.46/5.69 => ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_neg_nonpos
% 5.46/5.69 thf(fact_2727_field__le__epsilon,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ( ! [E2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.46/5.69 => ( ord_less_eq_real @ X4 @ ( plus_plus_real @ Y3 @ E2 ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ X4 @ Y3 ) ) ).
% 5.46/5.69
% 5.46/5.69 % field_le_epsilon
% 5.46/5.69 thf(fact_2728_field__le__epsilon,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ( ! [E2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.46/5.69 => ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ Y3 @ E2 ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ X4 @ Y3 ) ) ).
% 5.46/5.69
% 5.46/5.69 % field_le_epsilon
% 5.46/5.69 thf(fact_2729_div__positive,axiom,
% 5.46/5.69 ! [B2: nat,A: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_nat @ B2 @ A )
% 5.46/5.69 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_positive
% 5.46/5.69 thf(fact_2730_div__positive,axiom,
% 5.46/5.69 ! [B2: int,A: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_int @ B2 @ A )
% 5.46/5.69 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_positive
% 5.46/5.69 thf(fact_2731_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.46/5.69 ! [A: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_nat @ A @ B2 )
% 5.46/5.69 => ( ( divide_divide_nat @ A @ B2 )
% 5.46/5.69 = zero_zero_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unique_euclidean_semiring_numeral_class.div_less
% 5.46/5.69 thf(fact_2732_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.46/5.69 ! [A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_int @ A @ B2 )
% 5.46/5.69 => ( ( divide_divide_int @ A @ B2 )
% 5.46/5.69 = zero_zero_int ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unique_euclidean_semiring_numeral_class.div_less
% 5.46/5.69 thf(fact_2733_divide__nonpos__pos,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.69 => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_nonpos_pos
% 5.46/5.69 thf(fact_2734_divide__nonpos__pos,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.46/5.69 => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_nonpos_pos
% 5.46/5.69 thf(fact_2735_divide__nonpos__neg,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_nonpos_neg
% 5.46/5.69 thf(fact_2736_divide__nonpos__neg,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_nonpos_neg
% 5.46/5.69 thf(fact_2737_divide__nonneg__pos,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_nonneg_pos
% 5.46/5.69 thf(fact_2738_divide__nonneg__pos,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_nonneg_pos
% 5.46/5.69 thf(fact_2739_divide__nonneg__neg,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.69 => ( ( ord_less_real @ Y3 @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y3 ) @ zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_nonneg_neg
% 5.46/5.69 thf(fact_2740_divide__nonneg__neg,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.69 => ( ( ord_less_rat @ Y3 @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ zero_zero_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_nonneg_neg
% 5.46/5.69 thf(fact_2741_divide__le__cancel,axiom,
% 5.46/5.69 ! [A: real,C: real,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_le_cancel
% 5.46/5.69 thf(fact_2742_divide__le__cancel,axiom,
% 5.46/5.69 ! [A: rat,C: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ A @ B2 ) )
% 5.46/5.69 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_le_cancel
% 5.46/5.69 thf(fact_2743_frac__less2,axiom,
% 5.46/5.69 ! [X4: real,Y3: real,W: real,Z: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.69 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.46/5.69 => ( ( ord_less_real @ W @ Z )
% 5.46/5.69 => ( ord_less_real @ ( divide_divide_real @ X4 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % frac_less2
% 5.46/5.69 thf(fact_2744_frac__less2,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat,W: rat,Z: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.46/5.69 => ( ( ord_less_rat @ W @ Z )
% 5.46/5.69 => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % frac_less2
% 5.46/5.69 thf(fact_2745_frac__less,axiom,
% 5.46/5.69 ! [X4: real,Y3: real,W: real,Z: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.69 => ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.46/5.69 => ( ( ord_less_eq_real @ W @ Z )
% 5.46/5.69 => ( ord_less_real @ ( divide_divide_real @ X4 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % frac_less
% 5.46/5.69 thf(fact_2746_frac__less,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat,W: rat,Z: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.69 => ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.46/5.69 => ( ( ord_less_eq_rat @ W @ Z )
% 5.46/5.69 => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % frac_less
% 5.46/5.69 thf(fact_2747_frac__le,axiom,
% 5.46/5.69 ! [Y3: real,X4: real,W: real,Z: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.46/5.69 => ( ( ord_less_eq_real @ W @ Z )
% 5.46/5.69 => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Z ) @ ( divide_divide_real @ Y3 @ W ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % frac_le
% 5.46/5.69 thf(fact_2748_frac__le,axiom,
% 5.46/5.69 ! [Y3: rat,X4: rat,W: rat,Z: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.46/5.69 => ( ( ord_less_eq_rat @ W @ Z )
% 5.46/5.69 => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Z ) @ ( divide_divide_rat @ Y3 @ W ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % frac_le
% 5.46/5.69 thf(fact_2749_mult__left__le__one__le,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( times_times_real @ Y3 @ X4 ) @ X4 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le_one_le
% 5.46/5.69 thf(fact_2750_mult__left__le__one__le,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ Y3 @ one_one_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ ( times_times_rat @ Y3 @ X4 ) @ X4 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le_one_le
% 5.46/5.69 thf(fact_2751_mult__left__le__one__le,axiom,
% 5.46/5.69 ! [X4: int,Y3: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_int @ Y3 @ one_one_int )
% 5.46/5.69 => ( ord_less_eq_int @ ( times_times_int @ Y3 @ X4 ) @ X4 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le_one_le
% 5.46/5.69 thf(fact_2752_mult__right__le__one__le,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( times_times_real @ X4 @ Y3 ) @ X4 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_le_one_le
% 5.46/5.69 thf(fact_2753_mult__right__le__one__le,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ Y3 @ one_one_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ ( times_times_rat @ X4 @ Y3 ) @ X4 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_le_one_le
% 5.46/5.69 thf(fact_2754_mult__right__le__one__le,axiom,
% 5.46/5.69 ! [X4: int,Y3: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_int @ Y3 @ one_one_int )
% 5.46/5.69 => ( ord_less_eq_int @ ( times_times_int @ X4 @ Y3 ) @ X4 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_right_le_one_le
% 5.46/5.69 thf(fact_2755_mult__le__one,axiom,
% 5.46/5.69 ! [A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ B2 @ one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ one_one_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_one
% 5.46/5.69 thf(fact_2756_mult__le__one,axiom,
% 5.46/5.69 ! [A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ B2 @ one_one_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B2 ) @ one_one_rat ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_one
% 5.46/5.69 thf(fact_2757_mult__le__one,axiom,
% 5.46/5.69 ! [A: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_nat @ B2 @ one_one_nat )
% 5.46/5.69 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B2 ) @ one_one_nat ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_one
% 5.46/5.69 thf(fact_2758_mult__le__one,axiom,
% 5.46/5.69 ! [A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_int @ B2 @ one_one_int )
% 5.46/5.69 => ( ord_less_eq_int @ ( times_times_int @ A @ B2 ) @ one_one_int ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_one
% 5.46/5.69 thf(fact_2759_mult__left__le,axiom,
% 5.46/5.69 ! [C: real,A: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le
% 5.46/5.69 thf(fact_2760_mult__left__le,axiom,
% 5.46/5.69 ! [C: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le
% 5.46/5.69 thf(fact_2761_mult__left__le,axiom,
% 5.46/5.69 ! [C: nat,A: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le
% 5.46/5.69 thf(fact_2762_mult__left__le,axiom,
% 5.46/5.69 ! [C: int,A: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_left_le
% 5.46/5.69 thf(fact_2763_sum__squares__le__zero__iff,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y3 @ Y3 ) ) @ zero_zero_real )
% 5.46/5.69 = ( ( X4 = zero_zero_real )
% 5.46/5.69 & ( Y3 = zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_squares_le_zero_iff
% 5.46/5.69 thf(fact_2764_sum__squares__le__zero__iff,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y3 @ Y3 ) ) @ zero_zero_rat )
% 5.46/5.69 = ( ( X4 = zero_zero_rat )
% 5.46/5.69 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_squares_le_zero_iff
% 5.46/5.69 thf(fact_2765_sum__squares__le__zero__iff,axiom,
% 5.46/5.69 ! [X4: int,Y3: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y3 @ Y3 ) ) @ zero_zero_int )
% 5.46/5.69 = ( ( X4 = zero_zero_int )
% 5.46/5.69 & ( Y3 = zero_zero_int ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_squares_le_zero_iff
% 5.46/5.69 thf(fact_2766_sum__squares__ge__zero,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y3 @ Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_squares_ge_zero
% 5.46/5.69 thf(fact_2767_sum__squares__ge__zero,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y3 @ Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_squares_ge_zero
% 5.46/5.69 thf(fact_2768_sum__squares__ge__zero,axiom,
% 5.46/5.69 ! [X4: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y3 @ Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_squares_ge_zero
% 5.46/5.69 thf(fact_2769_power__less__imp__less__base,axiom,
% 5.46/5.69 ! [A: real,N: nat,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B2 @ N ) )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.69 => ( ord_less_real @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_less_imp_less_base
% 5.46/5.69 thf(fact_2770_power__less__imp__less__base,axiom,
% 5.46/5.69 ! [A: rat,N: nat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B2 @ N ) )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.69 => ( ord_less_rat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_less_imp_less_base
% 5.46/5.69 thf(fact_2771_power__less__imp__less__base,axiom,
% 5.46/5.69 ! [A: nat,N: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B2 @ N ) )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.69 => ( ord_less_nat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_less_imp_less_base
% 5.46/5.69 thf(fact_2772_power__less__imp__less__base,axiom,
% 5.46/5.69 ! [A: int,N: nat,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B2 @ N ) )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.69 => ( ord_less_int @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_less_imp_less_base
% 5.46/5.69 thf(fact_2773_sum__squares__gt__zero__iff,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y3 @ Y3 ) ) )
% 5.46/5.69 = ( ( X4 != zero_zero_real )
% 5.46/5.69 | ( Y3 != zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_squares_gt_zero_iff
% 5.46/5.69 thf(fact_2774_sum__squares__gt__zero__iff,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y3 @ Y3 ) ) )
% 5.46/5.69 = ( ( X4 != zero_zero_rat )
% 5.46/5.69 | ( Y3 != zero_zero_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_squares_gt_zero_iff
% 5.46/5.69 thf(fact_2775_sum__squares__gt__zero__iff,axiom,
% 5.46/5.69 ! [X4: int,Y3: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y3 @ Y3 ) ) )
% 5.46/5.69 = ( ( X4 != zero_zero_int )
% 5.46/5.69 | ( Y3 != zero_zero_int ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % sum_squares_gt_zero_iff
% 5.46/5.69 thf(fact_2776_not__sum__squares__lt__zero,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y3 @ Y3 ) ) @ zero_zero_real ) ).
% 5.46/5.69
% 5.46/5.69 % not_sum_squares_lt_zero
% 5.46/5.69 thf(fact_2777_not__sum__squares__lt__zero,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y3 @ Y3 ) ) @ zero_zero_rat ) ).
% 5.46/5.69
% 5.46/5.69 % not_sum_squares_lt_zero
% 5.46/5.69 thf(fact_2778_not__sum__squares__lt__zero,axiom,
% 5.46/5.69 ! [X4: int,Y3: int] :
% 5.46/5.69 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y3 @ Y3 ) ) @ zero_zero_int ) ).
% 5.46/5.69
% 5.46/5.69 % not_sum_squares_lt_zero
% 5.46/5.69 thf(fact_2779_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.46/5.69 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.69 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 5.46/5.69 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.46/5.69 thf(fact_2780_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.46/5.69 ! [C: int,A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ( divide_divide_int @ A @ ( times_times_int @ B2 @ C ) )
% 5.46/5.69 = ( divide_divide_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.46/5.69 thf(fact_2781_zero__less__two,axiom,
% 5.46/5.69 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_two
% 5.46/5.69 thf(fact_2782_zero__less__two,axiom,
% 5.46/5.69 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_two
% 5.46/5.69 thf(fact_2783_zero__less__two,axiom,
% 5.46/5.69 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_two
% 5.46/5.69 thf(fact_2784_zero__less__two,axiom,
% 5.46/5.69 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.46/5.69
% 5.46/5.69 % zero_less_two
% 5.46/5.69 thf(fact_2785_divide__strict__left__mono__neg,axiom,
% 5.46/5.69 ! [A: real,B2: real,C: real] :
% 5.46/5.69 ( ( ord_less_real @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.69 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_strict_left_mono_neg
% 5.46/5.69 thf(fact_2786_divide__strict__left__mono__neg,axiom,
% 5.46/5.69 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.69 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_strict_left_mono_neg
% 5.46/5.69 thf(fact_2787_divide__strict__left__mono,axiom,
% 5.46/5.69 ! [B2: real,A: real,C: real] :
% 5.46/5.69 ( ( ord_less_real @ B2 @ A )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.69 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_strict_left_mono
% 5.46/5.69 thf(fact_2788_divide__strict__left__mono,axiom,
% 5.46/5.69 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_rat @ B2 @ A )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.69 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_strict_left_mono
% 5.46/5.69 thf(fact_2789_mult__imp__less__div__pos,axiom,
% 5.46/5.69 ! [Y3: real,Z: real,X4: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.69 => ( ( ord_less_real @ ( times_times_real @ Z @ Y3 ) @ X4 )
% 5.46/5.69 => ( ord_less_real @ Z @ ( divide_divide_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_imp_less_div_pos
% 5.46/5.69 thf(fact_2790_mult__imp__less__div__pos,axiom,
% 5.46/5.69 ! [Y3: rat,Z: rat,X4: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.46/5.69 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y3 ) @ X4 )
% 5.46/5.69 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_imp_less_div_pos
% 5.46/5.69 thf(fact_2791_mult__imp__div__pos__less,axiom,
% 5.46/5.69 ! [Y3: real,X4: real,Z: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.69 => ( ( ord_less_real @ X4 @ ( times_times_real @ Z @ Y3 ) )
% 5.46/5.69 => ( ord_less_real @ ( divide_divide_real @ X4 @ Y3 ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_imp_div_pos_less
% 5.46/5.69 thf(fact_2792_mult__imp__div__pos__less,axiom,
% 5.46/5.69 ! [Y3: rat,X4: rat,Z: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.46/5.69 => ( ( ord_less_rat @ X4 @ ( times_times_rat @ Z @ Y3 ) )
% 5.46/5.69 => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_imp_div_pos_less
% 5.46/5.69 thf(fact_2793_pos__less__divide__eq,axiom,
% 5.46/5.69 ! [C: real,A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ord_less_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.69 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % pos_less_divide_eq
% 5.46/5.69 thf(fact_2794_pos__less__divide__eq,axiom,
% 5.46/5.69 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.69 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % pos_less_divide_eq
% 5.46/5.69 thf(fact_2795_pos__divide__less__eq,axiom,
% 5.46/5.69 ! [C: real,B2: real,A: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 5.46/5.69 = ( ord_less_real @ B2 @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % pos_divide_less_eq
% 5.46/5.69 thf(fact_2796_pos__divide__less__eq,axiom,
% 5.46/5.69 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ C ) @ A )
% 5.46/5.69 = ( ord_less_rat @ B2 @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % pos_divide_less_eq
% 5.46/5.69 thf(fact_2797_neg__less__divide__eq,axiom,
% 5.46/5.69 ! [C: real,A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.69 = ( ord_less_real @ B2 @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_less_divide_eq
% 5.46/5.69 thf(fact_2798_neg__less__divide__eq,axiom,
% 5.46/5.69 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.69 = ( ord_less_rat @ B2 @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_less_divide_eq
% 5.46/5.69 thf(fact_2799_neg__divide__less__eq,axiom,
% 5.46/5.69 ! [C: real,B2: real,A: real] :
% 5.46/5.69 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 5.46/5.69 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_divide_less_eq
% 5.46/5.69 thf(fact_2800_neg__divide__less__eq,axiom,
% 5.46/5.69 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ C ) @ A )
% 5.46/5.69 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_divide_less_eq
% 5.46/5.69 thf(fact_2801_less__divide__eq,axiom,
% 5.46/5.69 ! [A: real,B2: real,C: real] :
% 5.46/5.69 ( ( ord_less_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ B2 @ ( times_times_real @ A @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % less_divide_eq
% 5.46/5.69 thf(fact_2802_less__divide__eq,axiom,
% 5.46/5.69 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ B2 @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % less_divide_eq
% 5.46/5.69 thf(fact_2803_divide__less__eq,axiom,
% 5.46/5.69 ! [B2: real,C: real,A: real] :
% 5.46/5.69 ( ( ord_less_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ B2 @ ( times_times_real @ A @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_less_eq
% 5.46/5.69 thf(fact_2804_divide__less__eq,axiom,
% 5.46/5.69 ! [B2: rat,C: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ C ) @ A )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ B2 @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_less_eq
% 5.46/5.69 thf(fact_2805_less__divide__eq__1,axiom,
% 5.46/5.69 ! [B2: real,A: real] :
% 5.46/5.69 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 & ( ord_less_real @ A @ B2 ) )
% 5.46/5.69 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.69 & ( ord_less_real @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % less_divide_eq_1
% 5.46/5.69 thf(fact_2806_less__divide__eq__1,axiom,
% 5.46/5.69 ! [B2: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 & ( ord_less_rat @ A @ B2 ) )
% 5.46/5.69 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.69 & ( ord_less_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % less_divide_eq_1
% 5.46/5.69 thf(fact_2807_divide__less__eq__1,axiom,
% 5.46/5.69 ! [B2: real,A: real] :
% 5.46/5.69 ( ( ord_less_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 & ( ord_less_real @ B2 @ A ) )
% 5.46/5.69 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.69 & ( ord_less_real @ A @ B2 ) )
% 5.46/5.69 | ( A = zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_less_eq_1
% 5.46/5.69 thf(fact_2808_divide__less__eq__1,axiom,
% 5.46/5.69 ! [B2: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ A ) @ one_one_rat )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 & ( ord_less_rat @ B2 @ A ) )
% 5.46/5.69 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.69 & ( ord_less_rat @ A @ B2 ) )
% 5.46/5.69 | ( A = zero_zero_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_less_eq_1
% 5.46/5.69 thf(fact_2809_power__le__one,axiom,
% 5.46/5.69 ! [A: real,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_le_one
% 5.46/5.69 thf(fact_2810_power__le__one,axiom,
% 5.46/5.69 ! [A: rat,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_le_one
% 5.46/5.69 thf(fact_2811_power__le__one,axiom,
% 5.46/5.69 ! [A: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.46/5.69 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_le_one
% 5.46/5.69 thf(fact_2812_power__le__one,axiom,
% 5.46/5.69 ! [A: int,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.46/5.69 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_le_one
% 5.46/5.69 thf(fact_2813_divide__eq__eq__numeral_I1_J,axiom,
% 5.46/5.69 ! [B2: complex,C: complex,W: num] :
% 5.46/5.69 ( ( ( divide1717551699836669952omplex @ B2 @ C )
% 5.46/5.69 = ( numera6690914467698888265omplex @ W ) )
% 5.46/5.69 = ( ( ( C != zero_zero_complex )
% 5.46/5.69 => ( B2
% 5.46/5.69 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.46/5.69 & ( ( C = zero_zero_complex )
% 5.46/5.69 => ( ( numera6690914467698888265omplex @ W )
% 5.46/5.69 = zero_zero_complex ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_eq_eq_numeral(1)
% 5.46/5.69 thf(fact_2814_divide__eq__eq__numeral_I1_J,axiom,
% 5.46/5.69 ! [B2: real,C: real,W: num] :
% 5.46/5.69 ( ( ( divide_divide_real @ B2 @ C )
% 5.46/5.69 = ( numeral_numeral_real @ W ) )
% 5.46/5.69 = ( ( ( C != zero_zero_real )
% 5.46/5.69 => ( B2
% 5.46/5.69 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.46/5.69 & ( ( C = zero_zero_real )
% 5.46/5.69 => ( ( numeral_numeral_real @ W )
% 5.46/5.69 = zero_zero_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_eq_eq_numeral(1)
% 5.46/5.69 thf(fact_2815_divide__eq__eq__numeral_I1_J,axiom,
% 5.46/5.69 ! [B2: rat,C: rat,W: num] :
% 5.46/5.69 ( ( ( divide_divide_rat @ B2 @ C )
% 5.46/5.69 = ( numeral_numeral_rat @ W ) )
% 5.46/5.69 = ( ( ( C != zero_zero_rat )
% 5.46/5.69 => ( B2
% 5.46/5.69 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.46/5.69 & ( ( C = zero_zero_rat )
% 5.46/5.69 => ( ( numeral_numeral_rat @ W )
% 5.46/5.69 = zero_zero_rat ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_eq_eq_numeral(1)
% 5.46/5.69 thf(fact_2816_eq__divide__eq__numeral_I1_J,axiom,
% 5.46/5.69 ! [W: num,B2: complex,C: complex] :
% 5.46/5.69 ( ( ( numera6690914467698888265omplex @ W )
% 5.46/5.69 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 5.46/5.69 = ( ( ( C != zero_zero_complex )
% 5.46/5.69 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.46/5.69 = B2 ) )
% 5.46/5.69 & ( ( C = zero_zero_complex )
% 5.46/5.69 => ( ( numera6690914467698888265omplex @ W )
% 5.46/5.69 = zero_zero_complex ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % eq_divide_eq_numeral(1)
% 5.46/5.69 thf(fact_2817_eq__divide__eq__numeral_I1_J,axiom,
% 5.46/5.69 ! [W: num,B2: real,C: real] :
% 5.46/5.69 ( ( ( numeral_numeral_real @ W )
% 5.46/5.69 = ( divide_divide_real @ B2 @ C ) )
% 5.46/5.69 = ( ( ( C != zero_zero_real )
% 5.46/5.69 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.46/5.69 = B2 ) )
% 5.46/5.69 & ( ( C = zero_zero_real )
% 5.46/5.69 => ( ( numeral_numeral_real @ W )
% 5.46/5.69 = zero_zero_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % eq_divide_eq_numeral(1)
% 5.46/5.69 thf(fact_2818_eq__divide__eq__numeral_I1_J,axiom,
% 5.46/5.69 ! [W: num,B2: rat,C: rat] :
% 5.46/5.69 ( ( ( numeral_numeral_rat @ W )
% 5.46/5.69 = ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.69 = ( ( ( C != zero_zero_rat )
% 5.46/5.69 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.46/5.69 = B2 ) )
% 5.46/5.69 & ( ( C = zero_zero_rat )
% 5.46/5.69 => ( ( numeral_numeral_rat @ W )
% 5.46/5.69 = zero_zero_rat ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % eq_divide_eq_numeral(1)
% 5.46/5.69 thf(fact_2819_add__divide__eq__if__simps_I2_J,axiom,
% 5.46/5.69 ! [Z: complex,A: complex,B2: complex] :
% 5.46/5.69 ( ( ( Z = zero_zero_complex )
% 5.46/5.69 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B2 )
% 5.46/5.69 = B2 ) )
% 5.46/5.69 & ( ( Z != zero_zero_complex )
% 5.46/5.69 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B2 )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_if_simps(2)
% 5.46/5.69 thf(fact_2820_add__divide__eq__if__simps_I2_J,axiom,
% 5.46/5.69 ! [Z: real,A: real,B2: real] :
% 5.46/5.69 ( ( ( Z = zero_zero_real )
% 5.46/5.69 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B2 )
% 5.46/5.69 = B2 ) )
% 5.46/5.69 & ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B2 )
% 5.46/5.69 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_if_simps(2)
% 5.46/5.69 thf(fact_2821_add__divide__eq__if__simps_I2_J,axiom,
% 5.46/5.69 ! [Z: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ( Z = zero_zero_rat )
% 5.46/5.69 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B2 )
% 5.46/5.69 = B2 ) )
% 5.46/5.69 & ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B2 )
% 5.46/5.69 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_if_simps(2)
% 5.46/5.69 thf(fact_2822_add__divide__eq__if__simps_I1_J,axiom,
% 5.46/5.69 ! [Z: complex,A: complex,B2: complex] :
% 5.46/5.69 ( ( ( Z = zero_zero_complex )
% 5.46/5.69 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B2 @ Z ) )
% 5.46/5.69 = A ) )
% 5.46/5.69 & ( ( Z != zero_zero_complex )
% 5.46/5.69 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B2 @ Z ) )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_if_simps(1)
% 5.46/5.69 thf(fact_2823_add__divide__eq__if__simps_I1_J,axiom,
% 5.46/5.69 ! [Z: real,A: real,B2: real] :
% 5.46/5.69 ( ( ( Z = zero_zero_real )
% 5.46/5.69 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B2 @ Z ) )
% 5.46/5.69 = A ) )
% 5.46/5.69 & ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B2 @ Z ) )
% 5.46/5.69 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_if_simps(1)
% 5.46/5.69 thf(fact_2824_add__divide__eq__if__simps_I1_J,axiom,
% 5.46/5.69 ! [Z: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ( Z = zero_zero_rat )
% 5.46/5.69 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B2 @ Z ) )
% 5.46/5.69 = A ) )
% 5.46/5.69 & ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B2 @ Z ) )
% 5.46/5.69 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_if_simps(1)
% 5.46/5.69 thf(fact_2825_add__frac__eq,axiom,
% 5.46/5.69 ! [Y3: complex,Z: complex,X4: complex,W: complex] :
% 5.46/5.69 ( ( Y3 != zero_zero_complex )
% 5.46/5.69 => ( ( Z != zero_zero_complex )
% 5.46/5.69 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Y3 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ W @ Y3 ) ) @ ( times_times_complex @ Y3 @ Z ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_frac_eq
% 5.46/5.69 thf(fact_2826_add__frac__eq,axiom,
% 5.46/5.69 ! [Y3: real,Z: real,X4: real,W: real] :
% 5.46/5.69 ( ( Y3 != zero_zero_real )
% 5.46/5.69 => ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 5.46/5.69 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_frac_eq
% 5.46/5.69 thf(fact_2827_add__frac__eq,axiom,
% 5.46/5.69 ! [Y3: rat,Z: rat,X4: rat,W: rat] :
% 5.46/5.69 ( ( Y3 != zero_zero_rat )
% 5.46/5.69 => ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.46/5.69 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_frac_eq
% 5.46/5.69 thf(fact_2828_add__frac__num,axiom,
% 5.46/5.69 ! [Y3: complex,X4: complex,Z: complex] :
% 5.46/5.69 ( ( Y3 != zero_zero_complex )
% 5.46/5.69 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Y3 ) @ Z )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_frac_num
% 5.46/5.69 thf(fact_2829_add__frac__num,axiom,
% 5.46/5.69 ! [Y3: real,X4: real,Z: real] :
% 5.46/5.69 ( ( Y3 != zero_zero_real )
% 5.46/5.69 => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Y3 ) @ Z )
% 5.46/5.69 = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_frac_num
% 5.46/5.69 thf(fact_2830_add__frac__num,axiom,
% 5.46/5.69 ! [Y3: rat,X4: rat,Z: rat] :
% 5.46/5.69 ( ( Y3 != zero_zero_rat )
% 5.46/5.69 => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ Z )
% 5.46/5.69 = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_frac_num
% 5.46/5.69 thf(fact_2831_add__num__frac,axiom,
% 5.46/5.69 ! [Y3: complex,Z: complex,X4: complex] :
% 5.46/5.69 ( ( Y3 != zero_zero_complex )
% 5.46/5.69 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X4 @ Y3 ) )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_num_frac
% 5.46/5.69 thf(fact_2832_add__num__frac,axiom,
% 5.46/5.69 ! [Y3: real,Z: real,X4: real] :
% 5.46/5.69 ( ( Y3 != zero_zero_real )
% 5.46/5.69 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X4 @ Y3 ) )
% 5.46/5.69 = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_num_frac
% 5.46/5.69 thf(fact_2833_add__num__frac,axiom,
% 5.46/5.69 ! [Y3: rat,Z: rat,X4: rat] :
% 5.46/5.69 ( ( Y3 != zero_zero_rat )
% 5.46/5.69 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X4 @ Y3 ) )
% 5.46/5.69 = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Z @ Y3 ) ) @ Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_num_frac
% 5.46/5.69 thf(fact_2834_add__divide__eq__iff,axiom,
% 5.46/5.69 ! [Z: complex,X4: complex,Y3: complex] :
% 5.46/5.69 ( ( Z != zero_zero_complex )
% 5.46/5.69 => ( ( plus_plus_complex @ X4 @ ( divide1717551699836669952omplex @ Y3 @ Z ) )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X4 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_iff
% 5.46/5.69 thf(fact_2835_add__divide__eq__iff,axiom,
% 5.46/5.69 ! [Z: real,X4: real,Y3: real] :
% 5.46/5.69 ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( plus_plus_real @ X4 @ ( divide_divide_real @ Y3 @ Z ) )
% 5.46/5.69 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X4 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_iff
% 5.46/5.69 thf(fact_2836_add__divide__eq__iff,axiom,
% 5.46/5.69 ! [Z: rat,X4: rat,Y3: rat] :
% 5.46/5.69 ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( plus_plus_rat @ X4 @ ( divide_divide_rat @ Y3 @ Z ) )
% 5.46/5.69 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_iff
% 5.46/5.69 thf(fact_2837_divide__add__eq__iff,axiom,
% 5.46/5.69 ! [Z: complex,X4: complex,Y3: complex] :
% 5.46/5.69 ( ( Z != zero_zero_complex )
% 5.46/5.69 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Z ) @ Y3 )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_add_eq_iff
% 5.46/5.69 thf(fact_2838_divide__add__eq__iff,axiom,
% 5.46/5.69 ! [Z: real,X4: real,Y3: real] :
% 5.46/5.69 ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Z ) @ Y3 )
% 5.46/5.69 = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_add_eq_iff
% 5.46/5.69 thf(fact_2839_divide__add__eq__iff,axiom,
% 5.46/5.69 ! [Z: rat,X4: rat,Y3: rat] :
% 5.46/5.69 ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Z ) @ Y3 )
% 5.46/5.69 = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_add_eq_iff
% 5.46/5.69 thf(fact_2840_power__le__imp__le__base,axiom,
% 5.46/5.69 ! [A: real,N: nat,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B2 @ ( suc @ N ) ) )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.69 => ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_le_imp_le_base
% 5.46/5.69 thf(fact_2841_power__le__imp__le__base,axiom,
% 5.46/5.69 ! [A: rat,N: nat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B2 @ ( suc @ N ) ) )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.69 => ( ord_less_eq_rat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_le_imp_le_base
% 5.46/5.69 thf(fact_2842_power__le__imp__le__base,axiom,
% 5.46/5.69 ! [A: nat,N: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B2 @ ( suc @ N ) ) )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.69 => ( ord_less_eq_nat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_le_imp_le_base
% 5.46/5.69 thf(fact_2843_power__le__imp__le__base,axiom,
% 5.46/5.69 ! [A: int,N: nat,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B2 @ ( suc @ N ) ) )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.69 => ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_le_imp_le_base
% 5.46/5.69 thf(fact_2844_power__inject__base,axiom,
% 5.46/5.69 ! [A: real,N: nat,B2: real] :
% 5.46/5.69 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.46/5.69 = ( power_power_real @ B2 @ ( suc @ N ) ) )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.69 => ( A = B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_inject_base
% 5.46/5.69 thf(fact_2845_power__inject__base,axiom,
% 5.46/5.69 ! [A: rat,N: nat,B2: rat] :
% 5.46/5.69 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.46/5.69 = ( power_power_rat @ B2 @ ( suc @ N ) ) )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.69 => ( A = B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_inject_base
% 5.46/5.69 thf(fact_2846_power__inject__base,axiom,
% 5.46/5.69 ! [A: nat,N: nat,B2: nat] :
% 5.46/5.69 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.46/5.69 = ( power_power_nat @ B2 @ ( suc @ N ) ) )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ B2 )
% 5.46/5.69 => ( A = B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_inject_base
% 5.46/5.69 thf(fact_2847_power__inject__base,axiom,
% 5.46/5.69 ! [A: int,N: nat,B2: int] :
% 5.46/5.69 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.46/5.69 = ( power_power_int @ B2 @ ( suc @ N ) ) )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.69 => ( A = B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_inject_base
% 5.46/5.69 thf(fact_2848_div__add__self1,axiom,
% 5.46/5.69 ! [B2: nat,A: nat] :
% 5.46/5.69 ( ( B2 != zero_zero_nat )
% 5.46/5.69 => ( ( divide_divide_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 5.46/5.69 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B2 ) @ one_one_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_add_self1
% 5.46/5.69 thf(fact_2849_div__add__self1,axiom,
% 5.46/5.69 ! [B2: int,A: int] :
% 5.46/5.69 ( ( B2 != zero_zero_int )
% 5.46/5.69 => ( ( divide_divide_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 5.46/5.69 = ( plus_plus_int @ ( divide_divide_int @ A @ B2 ) @ one_one_int ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_add_self1
% 5.46/5.69 thf(fact_2850_div__add__self2,axiom,
% 5.46/5.69 ! [B2: nat,A: nat] :
% 5.46/5.69 ( ( B2 != zero_zero_nat )
% 5.46/5.69 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 5.46/5.69 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B2 ) @ one_one_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_add_self2
% 5.46/5.69 thf(fact_2851_div__add__self2,axiom,
% 5.46/5.69 ! [B2: int,A: int] :
% 5.46/5.69 ( ( B2 != zero_zero_int )
% 5.46/5.69 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 5.46/5.69 = ( plus_plus_int @ ( divide_divide_int @ A @ B2 ) @ one_one_int ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_add_self2
% 5.46/5.69 thf(fact_2852_add__divide__eq__if__simps_I4_J,axiom,
% 5.46/5.69 ! [Z: complex,A: complex,B2: complex] :
% 5.46/5.69 ( ( ( Z = zero_zero_complex )
% 5.46/5.69 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B2 @ Z ) )
% 5.46/5.69 = A ) )
% 5.46/5.69 & ( ( Z != zero_zero_complex )
% 5.46/5.69 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B2 @ Z ) )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_if_simps(4)
% 5.46/5.69 thf(fact_2853_add__divide__eq__if__simps_I4_J,axiom,
% 5.46/5.69 ! [Z: real,A: real,B2: real] :
% 5.46/5.69 ( ( ( Z = zero_zero_real )
% 5.46/5.69 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B2 @ Z ) )
% 5.46/5.69 = A ) )
% 5.46/5.69 & ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B2 @ Z ) )
% 5.46/5.69 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_if_simps(4)
% 5.46/5.69 thf(fact_2854_add__divide__eq__if__simps_I4_J,axiom,
% 5.46/5.69 ! [Z: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ( Z = zero_zero_rat )
% 5.46/5.69 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B2 @ Z ) )
% 5.46/5.69 = A ) )
% 5.46/5.69 & ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B2 @ Z ) )
% 5.46/5.69 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B2 ) @ Z ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % add_divide_eq_if_simps(4)
% 5.46/5.69 thf(fact_2855_diff__frac__eq,axiom,
% 5.46/5.69 ! [Y3: complex,Z: complex,X4: complex,W: complex] :
% 5.46/5.69 ( ( Y3 != zero_zero_complex )
% 5.46/5.69 => ( ( Z != zero_zero_complex )
% 5.46/5.69 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X4 @ Y3 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ W @ Y3 ) ) @ ( times_times_complex @ Y3 @ Z ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_frac_eq
% 5.46/5.69 thf(fact_2856_diff__frac__eq,axiom,
% 5.46/5.69 ! [Y3: real,Z: real,X4: real,W: real] :
% 5.46/5.69 ( ( Y3 != zero_zero_real )
% 5.46/5.69 => ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( minus_minus_real @ ( divide_divide_real @ X4 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 5.46/5.69 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_frac_eq
% 5.46/5.69 thf(fact_2857_diff__frac__eq,axiom,
% 5.46/5.69 ! [Y3: rat,Z: rat,X4: rat,W: rat] :
% 5.46/5.69 ( ( Y3 != zero_zero_rat )
% 5.46/5.69 => ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( minus_minus_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.46/5.69 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_frac_eq
% 5.46/5.69 thf(fact_2858_diff__divide__eq__iff,axiom,
% 5.46/5.69 ! [Z: complex,X4: complex,Y3: complex] :
% 5.46/5.69 ( ( Z != zero_zero_complex )
% 5.46/5.69 => ( ( minus_minus_complex @ X4 @ ( divide1717551699836669952omplex @ Y3 @ Z ) )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X4 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_divide_eq_iff
% 5.46/5.69 thf(fact_2859_diff__divide__eq__iff,axiom,
% 5.46/5.69 ! [Z: real,X4: real,Y3: real] :
% 5.46/5.69 ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( minus_minus_real @ X4 @ ( divide_divide_real @ Y3 @ Z ) )
% 5.46/5.69 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_divide_eq_iff
% 5.46/5.69 thf(fact_2860_diff__divide__eq__iff,axiom,
% 5.46/5.69 ! [Z: rat,X4: rat,Y3: rat] :
% 5.46/5.69 ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( minus_minus_rat @ X4 @ ( divide_divide_rat @ Y3 @ Z ) )
% 5.46/5.69 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ Y3 ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_divide_eq_iff
% 5.46/5.69 thf(fact_2861_divide__diff__eq__iff,axiom,
% 5.46/5.69 ! [Z: complex,X4: complex,Y3: complex] :
% 5.46/5.69 ( ( Z != zero_zero_complex )
% 5.46/5.69 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X4 @ Z ) @ Y3 )
% 5.46/5.69 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X4 @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_diff_eq_iff
% 5.46/5.69 thf(fact_2862_divide__diff__eq__iff,axiom,
% 5.46/5.69 ! [Z: real,X4: real,Y3: real] :
% 5.46/5.69 ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( minus_minus_real @ ( divide_divide_real @ X4 @ Z ) @ Y3 )
% 5.46/5.69 = ( divide_divide_real @ ( minus_minus_real @ X4 @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_diff_eq_iff
% 5.46/5.69 thf(fact_2863_divide__diff__eq__iff,axiom,
% 5.46/5.69 ! [Z: rat,X4: rat,Y3: rat] :
% 5.46/5.69 ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( minus_minus_rat @ ( divide_divide_rat @ X4 @ Z ) @ Y3 )
% 5.46/5.69 = ( divide_divide_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_diff_eq_iff
% 5.46/5.69 thf(fact_2864_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.46/5.69 ! [B2: code_integer,A: code_integer] :
% 5.46/5.69 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.46/5.69 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.46/5.69 thf(fact_2865_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.46/5.69 ! [B2: nat,A: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.69 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.46/5.69 thf(fact_2866_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.46/5.69 ! [B2: int,A: int] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.46/5.69 thf(fact_2867_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.46/5.69 ! [A: code_integer,B2: code_integer] :
% 5.46/5.69 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.69 => ( ( ord_le6747313008572928689nteger @ A @ B2 )
% 5.46/5.69 => ( ( modulo364778990260209775nteger @ A @ B2 )
% 5.46/5.69 = A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unique_euclidean_semiring_numeral_class.mod_less
% 5.46/5.69 thf(fact_2868_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.46/5.69 ! [A: nat,B2: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_nat @ A @ B2 )
% 5.46/5.69 => ( ( modulo_modulo_nat @ A @ B2 )
% 5.46/5.69 = A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unique_euclidean_semiring_numeral_class.mod_less
% 5.46/5.69 thf(fact_2869_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.46/5.69 ! [A: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_int @ A @ B2 )
% 5.46/5.69 => ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.69 = A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % unique_euclidean_semiring_numeral_class.mod_less
% 5.46/5.69 thf(fact_2870_cong__exp__iff__simps_I2_J,axiom,
% 5.46/5.69 ! [N: num,Q2: num] :
% 5.46/5.69 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.46/5.69 = zero_zero_nat ) ) ).
% 5.46/5.69
% 5.46/5.69 % cong_exp_iff_simps(2)
% 5.46/5.69 thf(fact_2871_cong__exp__iff__simps_I2_J,axiom,
% 5.46/5.69 ! [N: num,Q2: num] :
% 5.46/5.69 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.69 = zero_zero_int )
% 5.46/5.69 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.46/5.69 = zero_zero_int ) ) ).
% 5.46/5.69
% 5.46/5.69 % cong_exp_iff_simps(2)
% 5.46/5.69 thf(fact_2872_cong__exp__iff__simps_I2_J,axiom,
% 5.46/5.69 ! [N: num,Q2: num] :
% 5.46/5.69 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.69 = zero_z3403309356797280102nteger )
% 5.46/5.69 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.46/5.69 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.69
% 5.46/5.69 % cong_exp_iff_simps(2)
% 5.46/5.69 thf(fact_2873_cong__exp__iff__simps_I1_J,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.46/5.69 = zero_zero_nat ) ).
% 5.46/5.69
% 5.46/5.69 % cong_exp_iff_simps(1)
% 5.46/5.69 thf(fact_2874_cong__exp__iff__simps_I1_J,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.46/5.69 = zero_zero_int ) ).
% 5.46/5.69
% 5.46/5.69 % cong_exp_iff_simps(1)
% 5.46/5.69 thf(fact_2875_cong__exp__iff__simps_I1_J,axiom,
% 5.46/5.69 ! [N: num] :
% 5.46/5.69 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.46/5.69 = zero_z3403309356797280102nteger ) ).
% 5.46/5.69
% 5.46/5.69 % cong_exp_iff_simps(1)
% 5.46/5.69 thf(fact_2876_numeral__1__eq__Suc__0,axiom,
% 5.46/5.69 ( ( numeral_numeral_nat @ one )
% 5.46/5.69 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.69
% 5.46/5.69 % numeral_1_eq_Suc_0
% 5.46/5.69 thf(fact_2877_ex__least__nat__less,axiom,
% 5.46/5.69 ! [P: nat > $o,N: nat] :
% 5.46/5.69 ( ( P @ N )
% 5.46/5.69 => ( ~ ( P @ zero_zero_nat )
% 5.46/5.69 => ? [K2: nat] :
% 5.46/5.69 ( ( ord_less_nat @ K2 @ N )
% 5.46/5.69 & ! [I4: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ I4 @ K2 )
% 5.46/5.69 => ~ ( P @ I4 ) )
% 5.46/5.69 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % ex_least_nat_less
% 5.46/5.69 thf(fact_2878_diff__Suc__less,axiom,
% 5.46/5.69 ! [N: nat,I: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.69 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % diff_Suc_less
% 5.46/5.69 thf(fact_2879_n__less__n__mult__m,axiom,
% 5.46/5.69 ! [N: nat,M: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.69 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.46/5.69 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % n_less_n_mult_m
% 5.46/5.69 thf(fact_2880_n__less__m__mult__n,axiom,
% 5.46/5.69 ! [N: nat,M: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.69 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.46/5.69 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % n_less_m_mult_n
% 5.46/5.69 thf(fact_2881_one__less__mult,axiom,
% 5.46/5.69 ! [N: nat,M: nat] :
% 5.46/5.69 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.69 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.46/5.69 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % one_less_mult
% 5.46/5.69 thf(fact_2882_realpow__pos__nth2,axiom,
% 5.46/5.69 ! [A: real,N: nat] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 => ? [R3: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.46/5.69 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.46/5.69 = A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % realpow_pos_nth2
% 5.46/5.69 thf(fact_2883_nat__induct__non__zero,axiom,
% 5.46/5.69 ! [N: nat,P: nat > $o] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.69 => ( ( P @ one_one_nat )
% 5.46/5.69 => ( ! [N4: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.46/5.69 => ( ( P @ N4 )
% 5.46/5.69 => ( P @ ( suc @ N4 ) ) ) )
% 5.46/5.69 => ( P @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nat_induct_non_zero
% 5.46/5.69 thf(fact_2884_nat__mult__le__cancel1,axiom,
% 5.46/5.69 ! [K: nat,M: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.69 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.69 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nat_mult_le_cancel1
% 5.46/5.69 thf(fact_2885_div__greater__zero__iff,axiom,
% 5.46/5.69 ! [M: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.69 = ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.69 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_greater_zero_iff
% 5.46/5.69 thf(fact_2886_div__le__mono2,axiom,
% 5.46/5.69 ! [M: nat,N: nat,K: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.69 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.69 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_le_mono2
% 5.46/5.69 thf(fact_2887_power__gt__expt,axiom,
% 5.46/5.69 ! [N: nat,K: nat] :
% 5.46/5.69 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.69 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_gt_expt
% 5.46/5.69 thf(fact_2888_nat__diff__split,axiom,
% 5.46/5.69 ! [P: nat > $o,A: nat,B2: nat] :
% 5.46/5.69 ( ( P @ ( minus_minus_nat @ A @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_nat @ A @ B2 )
% 5.46/5.69 => ( P @ zero_zero_nat ) )
% 5.46/5.69 & ! [D2: nat] :
% 5.46/5.69 ( ( A
% 5.46/5.69 = ( plus_plus_nat @ B2 @ D2 ) )
% 5.46/5.69 => ( P @ D2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nat_diff_split
% 5.46/5.69 thf(fact_2889_nat__diff__split__asm,axiom,
% 5.46/5.69 ! [P: nat > $o,A: nat,B2: nat] :
% 5.46/5.69 ( ( P @ ( minus_minus_nat @ A @ B2 ) )
% 5.46/5.69 = ( ~ ( ( ( ord_less_nat @ A @ B2 )
% 5.46/5.69 & ~ ( P @ zero_zero_nat ) )
% 5.46/5.69 | ? [D2: nat] :
% 5.46/5.69 ( ( A
% 5.46/5.69 = ( plus_plus_nat @ B2 @ D2 ) )
% 5.46/5.69 & ~ ( P @ D2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nat_diff_split_asm
% 5.46/5.69 thf(fact_2890_nat__one__le__power,axiom,
% 5.46/5.69 ! [I: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.46/5.69 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nat_one_le_power
% 5.46/5.69 thf(fact_2891_real__arch__pow__inv,axiom,
% 5.46/5.69 ! [Y3: real,X4: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.69 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.69 => ? [N4: nat] : ( ord_less_real @ ( power_power_real @ X4 @ N4 ) @ Y3 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % real_arch_pow_inv
% 5.46/5.69 thf(fact_2892_div__less__iff__less__mult,axiom,
% 5.46/5.69 ! [Q2: nat,M: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.46/5.69 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 5.46/5.69 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_less_iff_less_mult
% 5.46/5.69 thf(fact_2893_nat__mult__div__cancel1,axiom,
% 5.46/5.69 ! [K: nat,M: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.69 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.46/5.69 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % nat_mult_div_cancel1
% 5.46/5.69 thf(fact_2894_div__eq__dividend__iff,axiom,
% 5.46/5.69 ! [M: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.69 => ( ( ( divide_divide_nat @ M @ N )
% 5.46/5.69 = M )
% 5.46/5.69 = ( N = one_one_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_eq_dividend_iff
% 5.46/5.69 thf(fact_2895_div__less__dividend,axiom,
% 5.46/5.69 ! [N: nat,M: nat] :
% 5.46/5.69 ( ( ord_less_nat @ one_one_nat @ N )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.69 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_less_dividend
% 5.46/5.69 thf(fact_2896_mod__le__divisor,axiom,
% 5.46/5.69 ! [N: nat,M: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.69 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.46/5.69
% 5.46/5.69 % mod_le_divisor
% 5.46/5.69 thf(fact_2897_div__less__mono,axiom,
% 5.46/5.69 ! [A3: nat,B4: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_nat @ A3 @ B4 )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.69 => ( ( ( modulo_modulo_nat @ A3 @ N )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 => ( ( ( modulo_modulo_nat @ B4 @ N )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 => ( ord_less_nat @ ( divide_divide_nat @ A3 @ N ) @ ( divide_divide_nat @ B4 @ N ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % div_less_mono
% 5.46/5.69 thf(fact_2898_evenE,axiom,
% 5.46/5.69 ! [A: code_integer] :
% 5.46/5.69 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.69 => ~ ! [B5: code_integer] :
% 5.46/5.69 ( A
% 5.46/5.69 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % evenE
% 5.46/5.69 thf(fact_2899_evenE,axiom,
% 5.46/5.69 ! [A: nat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.69 => ~ ! [B5: nat] :
% 5.46/5.69 ( A
% 5.46/5.69 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % evenE
% 5.46/5.69 thf(fact_2900_evenE,axiom,
% 5.46/5.69 ! [A: int] :
% 5.46/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.69 => ~ ! [B5: int] :
% 5.46/5.69 ( A
% 5.46/5.69 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % evenE
% 5.46/5.69 thf(fact_2901_odd__one,axiom,
% 5.46/5.69 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.46/5.69
% 5.46/5.69 % odd_one
% 5.46/5.69 thf(fact_2902_odd__one,axiom,
% 5.46/5.69 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.46/5.69
% 5.46/5.69 % odd_one
% 5.46/5.69 thf(fact_2903_odd__one,axiom,
% 5.46/5.69 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.46/5.69
% 5.46/5.69 % odd_one
% 5.46/5.69 thf(fact_2904_odd__even__add,axiom,
% 5.46/5.69 ! [A: code_integer,B2: code_integer] :
% 5.46/5.69 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.69 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 )
% 5.46/5.69 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % odd_even_add
% 5.46/5.69 thf(fact_2905_odd__even__add,axiom,
% 5.46/5.69 ! [A: nat,B2: nat] :
% 5.46/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.69 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.46/5.69 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % odd_even_add
% 5.46/5.69 thf(fact_2906_odd__even__add,axiom,
% 5.46/5.69 ! [A: int,B2: int] :
% 5.46/5.69 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.69 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 )
% 5.46/5.69 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % odd_even_add
% 5.46/5.69 thf(fact_2907_bit__eq__rec,axiom,
% 5.46/5.69 ( ( ^ [Y6: code_integer,Z4: code_integer] : ( Y6 = Z4 ) )
% 5.46/5.69 = ( ^ [A4: code_integer,B3: code_integer] :
% 5.46/5.69 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 )
% 5.46/5.69 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) )
% 5.46/5.69 & ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.69 = ( divide6298287555418463151nteger @ B3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % bit_eq_rec
% 5.46/5.69 thf(fact_2908_bit__eq__rec,axiom,
% 5.46/5.69 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.46/5.69 = ( ^ [A4: nat,B3: nat] :
% 5.46/5.69 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 )
% 5.46/5.69 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) )
% 5.46/5.69 & ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.69 = ( divide_divide_nat @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % bit_eq_rec
% 5.46/5.69 thf(fact_2909_bit__eq__rec,axiom,
% 5.46/5.69 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.69 = ( ^ [A4: int,B3: int] :
% 5.46/5.69 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 )
% 5.46/5.69 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) )
% 5.46/5.69 & ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.69 = ( divide_divide_int @ B3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % bit_eq_rec
% 5.46/5.69 thf(fact_2910_even__mask__div__iff,axiom,
% 5.46/5.69 ! [M: nat,N: nat] :
% 5.46/5.69 ( ( 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 ) ) )
% 5.46/5.69 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 = zero_z3403309356797280102nteger )
% 5.46/5.69 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_mask_div_iff
% 5.46/5.69 thf(fact_2911_even__mask__div__iff,axiom,
% 5.46/5.69 ! [M: nat,N: nat] :
% 5.46/5.69 ( ( 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 ) ) )
% 5.46/5.69 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 = zero_zero_nat )
% 5.46/5.69 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_mask_div_iff
% 5.46/5.69 thf(fact_2912_even__mask__div__iff,axiom,
% 5.46/5.69 ! [M: nat,N: nat] :
% 5.46/5.69 ( ( 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 ) ) )
% 5.46/5.69 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.69 = zero_zero_int )
% 5.46/5.69 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % even_mask_div_iff
% 5.46/5.69 thf(fact_2913_dvd__minus__add,axiom,
% 5.46/5.69 ! [Q2: nat,N: nat,R2: nat,M: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ Q2 @ N )
% 5.46/5.69 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R2 @ M ) )
% 5.46/5.69 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 5.46/5.69 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % dvd_minus_add
% 5.46/5.69 thf(fact_2914_power__dvd__imp__le,axiom,
% 5.46/5.69 ! [I: nat,M: nat,N: nat] :
% 5.46/5.69 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.46/5.69 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.46/5.69 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_dvd_imp_le
% 5.46/5.69 thf(fact_2915_mod__nat__eqI,axiom,
% 5.46/5.69 ! [R2: nat,N: nat,M: nat] :
% 5.46/5.69 ( ( ord_less_nat @ R2 @ N )
% 5.46/5.69 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.46/5.69 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 5.46/5.69 => ( ( modulo_modulo_nat @ M @ N )
% 5.46/5.69 = R2 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mod_nat_eqI
% 5.46/5.69 thf(fact_2916_mult__less__cancel__right2,axiom,
% 5.46/5.69 ! [A: real,C: real] :
% 5.46/5.69 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.46/5.69 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ A @ one_one_real ) )
% 5.46/5.69 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_right2
% 5.46/5.69 thf(fact_2917_mult__less__cancel__right2,axiom,
% 5.46/5.69 ! [A: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.46/5.69 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.46/5.69 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_right2
% 5.46/5.69 thf(fact_2918_mult__less__cancel__right2,axiom,
% 5.46/5.69 ! [A: int,C: int] :
% 5.46/5.69 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.46/5.69 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ A @ one_one_int ) )
% 5.46/5.69 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_right2
% 5.46/5.69 thf(fact_2919_mult__less__cancel__right1,axiom,
% 5.46/5.69 ! [C: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ C @ ( times_times_real @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ one_one_real @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ B2 @ one_one_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_right1
% 5.46/5.69 thf(fact_2920_mult__less__cancel__right1,axiom,
% 5.46/5.69 ! [C: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ C @ ( times_times_rat @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ one_one_rat @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ B2 @ one_one_rat ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_right1
% 5.46/5.69 thf(fact_2921_mult__less__cancel__right1,axiom,
% 5.46/5.69 ! [C: int,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ C @ ( times_times_int @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ one_one_int @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_int @ B2 @ one_one_int ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_right1
% 5.46/5.69 thf(fact_2922_mult__less__cancel__left2,axiom,
% 5.46/5.69 ! [C: real,A: real] :
% 5.46/5.69 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.46/5.69 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ A @ one_one_real ) )
% 5.46/5.69 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_left2
% 5.46/5.69 thf(fact_2923_mult__less__cancel__left2,axiom,
% 5.46/5.69 ! [C: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.46/5.69 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.46/5.69 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_left2
% 5.46/5.69 thf(fact_2924_mult__less__cancel__left2,axiom,
% 5.46/5.69 ! [C: int,A: int] :
% 5.46/5.69 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.46/5.69 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ A @ one_one_int ) )
% 5.46/5.69 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_left2
% 5.46/5.69 thf(fact_2925_mult__less__cancel__left1,axiom,
% 5.46/5.69 ! [C: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ C @ ( times_times_real @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ one_one_real @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ B2 @ one_one_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_left1
% 5.46/5.69 thf(fact_2926_mult__less__cancel__left1,axiom,
% 5.46/5.69 ! [C: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ one_one_rat @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ B2 @ one_one_rat ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_left1
% 5.46/5.69 thf(fact_2927_mult__less__cancel__left1,axiom,
% 5.46/5.69 ! [C: int,B2: int] :
% 5.46/5.69 ( ( ord_less_int @ C @ ( times_times_int @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_int @ one_one_int @ B2 ) )
% 5.46/5.69 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_int @ B2 @ one_one_int ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_less_cancel_left1
% 5.46/5.69 thf(fact_2928_mult__le__cancel__right2,axiom,
% 5.46/5.69 ! [A: real,C: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.46/5.69 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_right2
% 5.46/5.69 thf(fact_2929_mult__le__cancel__right2,axiom,
% 5.46/5.69 ! [A: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.46/5.69 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_right2
% 5.46/5.69 thf(fact_2930_mult__le__cancel__right2,axiom,
% 5.46/5.69 ! [A: int,C: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.46/5.69 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.46/5.69 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_right2
% 5.46/5.69 thf(fact_2931_mult__le__cancel__right1,axiom,
% 5.46/5.69 ! [C: real,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ C @ ( times_times_real @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ one_one_real @ B2 ) )
% 5.46/5.69 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ B2 @ one_one_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_right1
% 5.46/5.69 thf(fact_2932_mult__le__cancel__right1,axiom,
% 5.46/5.69 ! [C: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ one_one_rat @ B2 ) )
% 5.46/5.69 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ B2 @ one_one_rat ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_right1
% 5.46/5.69 thf(fact_2933_mult__le__cancel__right1,axiom,
% 5.46/5.69 ! [C: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ C @ ( times_times_int @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_eq_int @ one_one_int @ B2 ) )
% 5.46/5.69 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_eq_int @ B2 @ one_one_int ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_right1
% 5.46/5.69 thf(fact_2934_mult__le__cancel__left2,axiom,
% 5.46/5.69 ! [C: real,A: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.46/5.69 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left2
% 5.46/5.69 thf(fact_2935_mult__le__cancel__left2,axiom,
% 5.46/5.69 ! [C: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.46/5.69 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left2
% 5.46/5.69 thf(fact_2936_mult__le__cancel__left2,axiom,
% 5.46/5.69 ! [C: int,A: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.46/5.69 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.46/5.69 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left2
% 5.46/5.69 thf(fact_2937_mult__le__cancel__left1,axiom,
% 5.46/5.69 ! [C: real,B2: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ one_one_real @ B2 ) )
% 5.46/5.69 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ B2 @ one_one_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left1
% 5.46/5.69 thf(fact_2938_mult__le__cancel__left1,axiom,
% 5.46/5.69 ! [C: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ one_one_rat @ B2 ) )
% 5.46/5.69 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ B2 @ one_one_rat ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left1
% 5.46/5.69 thf(fact_2939_mult__le__cancel__left1,axiom,
% 5.46/5.69 ! [C: int,B2: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B2 ) )
% 5.46/5.69 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.46/5.69 => ( ord_less_eq_int @ one_one_int @ B2 ) )
% 5.46/5.69 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.46/5.69 => ( ord_less_eq_int @ B2 @ one_one_int ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_le_cancel_left1
% 5.46/5.69 thf(fact_2940_field__le__mult__one__interval,axiom,
% 5.46/5.69 ! [X4: real,Y3: real] :
% 5.46/5.69 ( ! [Z2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.46/5.69 => ( ( ord_less_real @ Z2 @ one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( times_times_real @ Z2 @ X4 ) @ Y3 ) ) )
% 5.46/5.69 => ( ord_less_eq_real @ X4 @ Y3 ) ) ).
% 5.46/5.69
% 5.46/5.69 % field_le_mult_one_interval
% 5.46/5.69 thf(fact_2941_field__le__mult__one__interval,axiom,
% 5.46/5.69 ! [X4: rat,Y3: rat] :
% 5.46/5.69 ( ! [Z2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.46/5.69 => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X4 ) @ Y3 ) ) )
% 5.46/5.69 => ( ord_less_eq_rat @ X4 @ Y3 ) ) ).
% 5.46/5.69
% 5.46/5.69 % field_le_mult_one_interval
% 5.46/5.69 thf(fact_2942_divide__left__mono__neg,axiom,
% 5.46/5.69 ! [A: real,B2: real,C: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_left_mono_neg
% 5.46/5.69 thf(fact_2943_divide__left__mono__neg,axiom,
% 5.46/5.69 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_left_mono_neg
% 5.46/5.69 thf(fact_2944_mult__imp__le__div__pos,axiom,
% 5.46/5.69 ! [Y3: real,Z: real,X4: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y3 ) @ X4 )
% 5.46/5.69 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_imp_le_div_pos
% 5.46/5.69 thf(fact_2945_mult__imp__le__div__pos,axiom,
% 5.46/5.69 ! [Y3: rat,Z: rat,X4: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y3 ) @ X4 )
% 5.46/5.69 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_imp_le_div_pos
% 5.46/5.69 thf(fact_2946_mult__imp__div__pos__le,axiom,
% 5.46/5.69 ! [Y3: real,X4: real,Z: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_real @ X4 @ ( times_times_real @ Z @ Y3 ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y3 ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_imp_div_pos_le
% 5.46/5.69 thf(fact_2947_mult__imp__div__pos__le,axiom,
% 5.46/5.69 ! [Y3: rat,X4: rat,Z: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ X4 @ ( times_times_rat @ Z @ Y3 ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ Z ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % mult_imp_div_pos_le
% 5.46/5.69 thf(fact_2948_pos__le__divide__eq,axiom,
% 5.46/5.69 ! [C: real,A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.69 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % pos_le_divide_eq
% 5.46/5.69 thf(fact_2949_pos__le__divide__eq,axiom,
% 5.46/5.69 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.69 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % pos_le_divide_eq
% 5.46/5.69 thf(fact_2950_pos__divide__le__eq,axiom,
% 5.46/5.69 ! [C: real,B2: real,A: real] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 5.46/5.69 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % pos_divide_le_eq
% 5.46/5.69 thf(fact_2951_pos__divide__le__eq,axiom,
% 5.46/5.69 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C ) @ A )
% 5.46/5.69 = ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % pos_divide_le_eq
% 5.46/5.69 thf(fact_2952_neg__le__divide__eq,axiom,
% 5.46/5.69 ! [C: real,A: real,B2: real] :
% 5.46/5.69 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.69 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_le_divide_eq
% 5.46/5.69 thf(fact_2953_neg__le__divide__eq,axiom,
% 5.46/5.69 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.69 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.69 = ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_le_divide_eq
% 5.46/5.69 thf(fact_2954_neg__divide__le__eq,axiom,
% 5.46/5.69 ! [C: real,B2: real,A: real] :
% 5.46/5.69 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 5.46/5.69 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_divide_le_eq
% 5.46/5.69 thf(fact_2955_neg__divide__le__eq,axiom,
% 5.46/5.69 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C ) @ A )
% 5.46/5.69 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B2 ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % neg_divide_le_eq
% 5.46/5.69 thf(fact_2956_divide__left__mono,axiom,
% 5.46/5.69 ! [B2: real,A: real,C: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ B2 @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.69 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_left_mono
% 5.46/5.69 thf(fact_2957_divide__left__mono,axiom,
% 5.46/5.69 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ B2 @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.69 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B2 ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_left_mono
% 5.46/5.69 thf(fact_2958_le__divide__eq,axiom,
% 5.46/5.69 ! [A: real,B2: real,C: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % le_divide_eq
% 5.46/5.69 thf(fact_2959_le__divide__eq,axiom,
% 5.46/5.69 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % le_divide_eq
% 5.46/5.69 thf(fact_2960_divide__le__eq,axiom,
% 5.46/5.69 ! [B2: real,C: real,A: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ A )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_le_eq
% 5.46/5.69 thf(fact_2961_divide__le__eq,axiom,
% 5.46/5.69 ! [B2: rat,C: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C ) @ A )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_le_eq
% 5.46/5.69 thf(fact_2962_le__divide__eq__1,axiom,
% 5.46/5.69 ! [B2: real,A: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B2 @ A ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 & ( ord_less_eq_real @ A @ B2 ) )
% 5.46/5.69 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.69 & ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % le_divide_eq_1
% 5.46/5.69 thf(fact_2963_le__divide__eq__1,axiom,
% 5.46/5.69 ! [B2: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B2 @ A ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 & ( ord_less_eq_rat @ A @ B2 ) )
% 5.46/5.69 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.69 & ( ord_less_eq_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % le_divide_eq_1
% 5.46/5.69 thf(fact_2964_divide__le__eq__1,axiom,
% 5.46/5.69 ! [B2: real,A: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ A ) @ one_one_real )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 & ( ord_less_eq_real @ B2 @ A ) )
% 5.46/5.69 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.69 & ( ord_less_eq_real @ A @ B2 ) )
% 5.46/5.69 | ( A = zero_zero_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_le_eq_1
% 5.46/5.69 thf(fact_2965_divide__le__eq__1,axiom,
% 5.46/5.69 ! [B2: rat,A: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ A ) @ one_one_rat )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 & ( ord_less_eq_rat @ B2 @ A ) )
% 5.46/5.69 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.69 & ( ord_less_eq_rat @ A @ B2 ) )
% 5.46/5.69 | ( A = zero_zero_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_le_eq_1
% 5.46/5.69 thf(fact_2966_convex__bound__le,axiom,
% 5.46/5.69 ! [X4: real,A: real,Y3: real,U: real,V: real] :
% 5.46/5.69 ( ( ord_less_eq_real @ X4 @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ Y3 @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.46/5.69 => ( ( ( plus_plus_real @ U @ V )
% 5.46/5.69 = one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X4 ) @ ( times_times_real @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % convex_bound_le
% 5.46/5.69 thf(fact_2967_convex__bound__le,axiom,
% 5.46/5.69 ! [X4: rat,A: rat,Y3: rat,U: rat,V: rat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ X4 @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ Y3 @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.46/5.69 => ( ( ( plus_plus_rat @ U @ V )
% 5.46/5.69 = one_one_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X4 ) @ ( times_times_rat @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % convex_bound_le
% 5.46/5.69 thf(fact_2968_convex__bound__le,axiom,
% 5.46/5.69 ! [X4: int,A: int,Y3: int,U: int,V: int] :
% 5.46/5.69 ( ( ord_less_eq_int @ X4 @ A )
% 5.46/5.69 => ( ( ord_less_eq_int @ Y3 @ A )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.46/5.69 => ( ( ( plus_plus_int @ U @ V )
% 5.46/5.69 = one_one_int )
% 5.46/5.69 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X4 ) @ ( times_times_int @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % convex_bound_le
% 5.46/5.69 thf(fact_2969_divide__less__eq__numeral_I1_J,axiom,
% 5.46/5.69 ! [B2: real,C: real,W: num] :
% 5.46/5.69 ( ( ord_less_real @ ( divide_divide_real @ B2 @ C ) @ ( numeral_numeral_real @ W ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_less_eq_numeral(1)
% 5.46/5.69 thf(fact_2970_divide__less__eq__numeral_I1_J,axiom,
% 5.46/5.69 ! [B2: rat,C: rat,W: num] :
% 5.46/5.69 ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ B2 @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % divide_less_eq_numeral(1)
% 5.46/5.69 thf(fact_2971_less__divide__eq__numeral_I1_J,axiom,
% 5.46/5.69 ! [W: num,B2: real,C: real] :
% 5.46/5.69 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.69 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.69 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % less_divide_eq_numeral(1)
% 5.46/5.69 thf(fact_2972_less__divide__eq__numeral_I1_J,axiom,
% 5.46/5.69 ! [W: num,B2: rat,C: rat] :
% 5.46/5.69 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B2 ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.69 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ B2 @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.46/5.69 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.69 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % less_divide_eq_numeral(1)
% 5.46/5.69 thf(fact_2973_frac__le__eq,axiom,
% 5.46/5.69 ! [Y3: real,Z: real,X4: real,W: real] :
% 5.46/5.69 ( ( Y3 != zero_zero_real )
% 5.46/5.69 => ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 5.46/5.69 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % frac_le_eq
% 5.46/5.69 thf(fact_2974_frac__le__eq,axiom,
% 5.46/5.69 ! [Y3: rat,Z: rat,X4: rat,W: rat] :
% 5.46/5.69 ( ( Y3 != zero_zero_rat )
% 5.46/5.69 => ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.46/5.69 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % frac_le_eq
% 5.46/5.69 thf(fact_2975_frac__less__eq,axiom,
% 5.46/5.69 ! [Y3: real,Z: real,X4: real,W: real] :
% 5.46/5.69 ( ( Y3 != zero_zero_real )
% 5.46/5.69 => ( ( Z != zero_zero_real )
% 5.46/5.69 => ( ( ord_less_real @ ( divide_divide_real @ X4 @ Y3 ) @ ( divide_divide_real @ W @ Z ) )
% 5.46/5.69 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y3 ) ) @ ( times_times_real @ Y3 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % frac_less_eq
% 5.46/5.69 thf(fact_2976_frac__less__eq,axiom,
% 5.46/5.69 ! [Y3: rat,Z: rat,X4: rat,W: rat] :
% 5.46/5.69 ( ( Y3 != zero_zero_rat )
% 5.46/5.69 => ( ( Z != zero_zero_rat )
% 5.46/5.69 => ( ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y3 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.46/5.69 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y3 ) ) @ ( times_times_rat @ Y3 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % frac_less_eq
% 5.46/5.69 thf(fact_2977_power__Suc__less,axiom,
% 5.46/5.69 ! [A: real,N: nat] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_real @ A @ one_one_real )
% 5.46/5.69 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_less
% 5.46/5.69 thf(fact_2978_power__Suc__less,axiom,
% 5.46/5.69 ! [A: rat,N: nat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.46/5.69 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_less
% 5.46/5.69 thf(fact_2979_power__Suc__less,axiom,
% 5.46/5.69 ! [A: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.46/5.69 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_less
% 5.46/5.69 thf(fact_2980_power__Suc__less,axiom,
% 5.46/5.69 ! [A: int,N: nat] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_int @ A @ one_one_int )
% 5.46/5.69 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_less
% 5.46/5.69 thf(fact_2981_power__Suc__le__self,axiom,
% 5.46/5.69 ! [A: real,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_le_self
% 5.46/5.69 thf(fact_2982_power__Suc__le__self,axiom,
% 5.46/5.69 ! [A: rat,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_le_self
% 5.46/5.69 thf(fact_2983_power__Suc__le__self,axiom,
% 5.46/5.69 ! [A: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.46/5.69 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_le_self
% 5.46/5.69 thf(fact_2984_power__Suc__le__self,axiom,
% 5.46/5.69 ! [A: int,N: nat] :
% 5.46/5.69 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.46/5.69 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_le_self
% 5.46/5.69 thf(fact_2985_power__Suc__less__one,axiom,
% 5.46/5.69 ! [A: real,N: nat] :
% 5.46/5.69 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_real @ A @ one_one_real )
% 5.46/5.69 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_less_one
% 5.46/5.69 thf(fact_2986_power__Suc__less__one,axiom,
% 5.46/5.69 ! [A: rat,N: nat] :
% 5.46/5.69 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.46/5.69 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_less_one
% 5.46/5.69 thf(fact_2987_power__Suc__less__one,axiom,
% 5.46/5.69 ! [A: nat,N: nat] :
% 5.46/5.69 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.46/5.69 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_less_one
% 5.46/5.69 thf(fact_2988_power__Suc__less__one,axiom,
% 5.46/5.69 ! [A: int,N: nat] :
% 5.46/5.69 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_int @ A @ one_one_int )
% 5.46/5.69 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_Suc_less_one
% 5.46/5.69 thf(fact_2989_power__strict__decreasing,axiom,
% 5.46/5.69 ! [N: nat,N3: nat,A: real] :
% 5.46/5.69 ( ( ord_less_nat @ N @ N3 )
% 5.46/5.69 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_real @ A @ one_one_real )
% 5.46/5.69 => ( ord_less_real @ ( power_power_real @ A @ N3 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_strict_decreasing
% 5.46/5.69 thf(fact_2990_power__strict__decreasing,axiom,
% 5.46/5.69 ! [N: nat,N3: nat,A: rat] :
% 5.46/5.69 ( ( ord_less_nat @ N @ N3 )
% 5.46/5.69 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.46/5.69 => ( ord_less_rat @ ( power_power_rat @ A @ N3 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_strict_decreasing
% 5.46/5.69 thf(fact_2991_power__strict__decreasing,axiom,
% 5.46/5.69 ! [N: nat,N3: nat,A: nat] :
% 5.46/5.69 ( ( ord_less_nat @ N @ N3 )
% 5.46/5.69 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.46/5.69 => ( ord_less_nat @ ( power_power_nat @ A @ N3 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_strict_decreasing
% 5.46/5.69 thf(fact_2992_power__strict__decreasing,axiom,
% 5.46/5.69 ! [N: nat,N3: nat,A: int] :
% 5.46/5.69 ( ( ord_less_nat @ N @ N3 )
% 5.46/5.69 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_int @ A @ one_one_int )
% 5.46/5.69 => ( ord_less_int @ ( power_power_int @ A @ N3 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_strict_decreasing
% 5.46/5.69 thf(fact_2993_power__decreasing,axiom,
% 5.46/5.69 ! [N: nat,N3: nat,A: real] :
% 5.46/5.69 ( ( ord_less_eq_nat @ N @ N3 )
% 5.46/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.69 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.46/5.69 => ( ord_less_eq_real @ ( power_power_real @ A @ N3 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_decreasing
% 5.46/5.69 thf(fact_2994_power__decreasing,axiom,
% 5.46/5.69 ! [N: nat,N3: nat,A: rat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ N @ N3 )
% 5.46/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.69 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.46/5.69 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N3 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_decreasing
% 5.46/5.69 thf(fact_2995_power__decreasing,axiom,
% 5.46/5.69 ! [N: nat,N3: nat,A: nat] :
% 5.46/5.69 ( ( ord_less_eq_nat @ N @ N3 )
% 5.46/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.69 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.46/5.69 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N3 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_decreasing
% 5.46/5.69 thf(fact_2996_power__decreasing,axiom,
% 5.46/5.69 ! [N: nat,N3: nat,A: int] :
% 5.46/5.69 ( ( ord_less_eq_nat @ N @ N3 )
% 5.46/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.69 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.46/5.69 => ( ord_less_eq_int @ ( power_power_int @ A @ N3 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.46/5.69
% 5.46/5.69 % power_decreasing
% 5.46/5.69 thf(fact_2997_zero__power2,axiom,
% 5.46/5.69 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = zero_zero_rat ) ).
% 5.46/5.70
% 5.46/5.70 % zero_power2
% 5.46/5.70 thf(fact_2998_zero__power2,axiom,
% 5.46/5.70 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = zero_zero_nat ) ).
% 5.46/5.70
% 5.46/5.70 % zero_power2
% 5.46/5.70 thf(fact_2999_zero__power2,axiom,
% 5.46/5.70 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = zero_zero_real ) ).
% 5.46/5.70
% 5.46/5.70 % zero_power2
% 5.46/5.70 thf(fact_3000_zero__power2,axiom,
% 5.46/5.70 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % zero_power2
% 5.46/5.70 thf(fact_3001_zero__power2,axiom,
% 5.46/5.70 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = zero_zero_complex ) ).
% 5.46/5.70
% 5.46/5.70 % zero_power2
% 5.46/5.70 thf(fact_3002_self__le__power,axiom,
% 5.46/5.70 ! [A: real,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % self_le_power
% 5.46/5.70 thf(fact_3003_self__le__power,axiom,
% 5.46/5.70 ! [A: rat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % self_le_power
% 5.46/5.70 thf(fact_3004_self__le__power,axiom,
% 5.46/5.70 ! [A: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % self_le_power
% 5.46/5.70 thf(fact_3005_self__le__power,axiom,
% 5.46/5.70 ! [A: int,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % self_le_power
% 5.46/5.70 thf(fact_3006_one__less__power,axiom,
% 5.46/5.70 ! [A: real,N: nat] :
% 5.46/5.70 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_less_power
% 5.46/5.70 thf(fact_3007_one__less__power,axiom,
% 5.46/5.70 ! [A: rat,N: nat] :
% 5.46/5.70 ( ( ord_less_rat @ one_one_rat @ A )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_less_power
% 5.46/5.70 thf(fact_3008_one__less__power,axiom,
% 5.46/5.70 ! [A: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ one_one_nat @ A )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_less_power
% 5.46/5.70 thf(fact_3009_one__less__power,axiom,
% 5.46/5.70 ! [A: int,N: nat] :
% 5.46/5.70 ( ( ord_less_int @ one_one_int @ A )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % one_less_power
% 5.46/5.70 thf(fact_3010_numeral__2__eq__2,axiom,
% 5.46/5.70 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.46/5.70 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % numeral_2_eq_2
% 5.46/5.70 thf(fact_3011_pos2,axiom,
% 5.46/5.70 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.46/5.70
% 5.46/5.70 % pos2
% 5.46/5.70 thf(fact_3012_power__diff,axiom,
% 5.46/5.70 ! [A: complex,N: nat,M: nat] :
% 5.46/5.70 ( ( A != zero_zero_complex )
% 5.46/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.70 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_diff
% 5.46/5.70 thf(fact_3013_power__diff,axiom,
% 5.46/5.70 ! [A: real,N: nat,M: nat] :
% 5.46/5.70 ( ( A != zero_zero_real )
% 5.46/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_diff
% 5.46/5.70 thf(fact_3014_power__diff,axiom,
% 5.46/5.70 ! [A: rat,N: nat,M: nat] :
% 5.46/5.70 ( ( A != zero_zero_rat )
% 5.46/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_diff
% 5.46/5.70 thf(fact_3015_power__diff,axiom,
% 5.46/5.70 ! [A: nat,N: nat,M: nat] :
% 5.46/5.70 ( ( A != zero_zero_nat )
% 5.46/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_diff
% 5.46/5.70 thf(fact_3016_power__diff,axiom,
% 5.46/5.70 ! [A: int,N: nat,M: nat] :
% 5.46/5.70 ( ( A != zero_zero_int )
% 5.46/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.70 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_diff
% 5.46/5.70 thf(fact_3017_even__mult__exp__div__exp__iff,axiom,
% 5.46/5.70 ! [A: code_integer,M: nat,N: nat] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.70 = ( ( ord_less_nat @ N @ M )
% 5.46/5.70 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 = zero_z3403309356797280102nteger )
% 5.46/5.70 | ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_mult_exp_div_exp_iff
% 5.46/5.70 thf(fact_3018_even__mult__exp__div__exp__iff,axiom,
% 5.46/5.70 ! [A: nat,M: nat,N: nat] :
% 5.46/5.70 ( ( 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 ) ) )
% 5.46/5.70 = ( ( ord_less_nat @ N @ M )
% 5.46/5.70 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 = zero_zero_nat )
% 5.46/5.70 | ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 & ( 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 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_mult_exp_div_exp_iff
% 5.46/5.70 thf(fact_3019_even__mult__exp__div__exp__iff,axiom,
% 5.46/5.70 ! [A: int,M: nat,N: nat] :
% 5.46/5.70 ( ( 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 ) ) )
% 5.46/5.70 = ( ( ord_less_nat @ N @ M )
% 5.46/5.70 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 = zero_zero_int )
% 5.46/5.70 | ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.70 & ( 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 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_mult_exp_div_exp_iff
% 5.46/5.70 thf(fact_3020_div__if,axiom,
% 5.46/5.70 ( divide_divide_nat
% 5.46/5.70 = ( ^ [M6: nat,N2: nat] :
% 5.46/5.70 ( if_nat
% 5.46/5.70 @ ( ( ord_less_nat @ M6 @ N2 )
% 5.46/5.70 | ( N2 = zero_zero_nat ) )
% 5.46/5.70 @ zero_zero_nat
% 5.46/5.70 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % div_if
% 5.46/5.70 thf(fact_3021_div__geq,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ~ ( ord_less_nat @ M @ N )
% 5.46/5.70 => ( ( divide_divide_nat @ M @ N )
% 5.46/5.70 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % div_geq
% 5.46/5.70 thf(fact_3022_Suc__pred_H,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( N
% 5.46/5.70 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % Suc_pred'
% 5.46/5.70 thf(fact_3023_Suc__diff__eq__diff__pred,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.46/5.70 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % Suc_diff_eq_diff_pred
% 5.46/5.70 thf(fact_3024_less__eq__div__iff__mult__less__eq,axiom,
% 5.46/5.70 ! [Q2: nat,M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.46/5.70 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 5.46/5.70 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_eq_div_iff_mult_less_eq
% 5.46/5.70 thf(fact_3025_add__eq__if,axiom,
% 5.46/5.70 ( plus_plus_nat
% 5.46/5.70 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % add_eq_if
% 5.46/5.70 thf(fact_3026_dividend__less__times__div,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % dividend_less_times_div
% 5.46/5.70 thf(fact_3027_dividend__less__div__times,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % dividend_less_div_times
% 5.46/5.70 thf(fact_3028_split__div,axiom,
% 5.46/5.70 ! [P: nat > $o,M: nat,N: nat] :
% 5.46/5.70 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.70 = ( ( ( N = zero_zero_nat )
% 5.46/5.70 => ( P @ zero_zero_nat ) )
% 5.46/5.70 & ( ( N != zero_zero_nat )
% 5.46/5.70 => ! [I2: nat,J3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ J3 @ N )
% 5.46/5.70 => ( ( M
% 5.46/5.70 = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J3 ) )
% 5.46/5.70 => ( P @ I2 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % split_div
% 5.46/5.70 thf(fact_3029_mult__eq__if,axiom,
% 5.46/5.70 ( times_times_nat
% 5.46/5.70 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mult_eq_if
% 5.46/5.70 thf(fact_3030_split__mod,axiom,
% 5.46/5.70 ! [P: nat > $o,M: nat,N: nat] :
% 5.46/5.70 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.70 = ( ( ( N = zero_zero_nat )
% 5.46/5.70 => ( P @ M ) )
% 5.46/5.70 & ( ( N != zero_zero_nat )
% 5.46/5.70 => ! [I2: nat,J3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ J3 @ N )
% 5.46/5.70 => ( ( M
% 5.46/5.70 = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J3 ) )
% 5.46/5.70 => ( P @ J3 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % split_mod
% 5.46/5.70 thf(fact_3031_even__two__times__div__two,axiom,
% 5.46/5.70 ! [A: code_integer] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.46/5.70 = A ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_two_times_div_two
% 5.46/5.70 thf(fact_3032_even__two__times__div__two,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 = A ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_two_times_div_two
% 5.46/5.70 thf(fact_3033_even__two__times__div__two,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.46/5.70 = A ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_two_times_div_two
% 5.46/5.70 thf(fact_3034_odd__iff__mod__2__eq__one,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.70 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % odd_iff_mod_2_eq_one
% 5.46/5.70 thf(fact_3035_odd__iff__mod__2__eq__one,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.70 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.70 = one_one_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % odd_iff_mod_2_eq_one
% 5.46/5.70 thf(fact_3036_odd__iff__mod__2__eq__one,axiom,
% 5.46/5.70 ! [A: code_integer] :
% 5.46/5.70 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.70 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.70 = one_one_Code_integer ) ) ).
% 5.46/5.70
% 5.46/5.70 % odd_iff_mod_2_eq_one
% 5.46/5.70 thf(fact_3037_power__mono__odd,axiom,
% 5.46/5.70 ! [N: nat,A: real,B2: real] :
% 5.46/5.70 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 => ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.70 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B2 @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_mono_odd
% 5.46/5.70 thf(fact_3038_power__mono__odd,axiom,
% 5.46/5.70 ! [N: nat,A: rat,B2: rat] :
% 5.46/5.70 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 => ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.70 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_mono_odd
% 5.46/5.70 thf(fact_3039_power__mono__odd,axiom,
% 5.46/5.70 ! [N: nat,A: int,B2: int] :
% 5.46/5.70 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 => ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.70 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B2 @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_mono_odd
% 5.46/5.70 thf(fact_3040_dvd__power__iff__le,axiom,
% 5.46/5.70 ! [K: nat,M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.46/5.70 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.46/5.70 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % dvd_power_iff_le
% 5.46/5.70 thf(fact_3041_convex__bound__lt,axiom,
% 5.46/5.70 ! [X4: real,A: real,Y3: real,U: real,V: real] :
% 5.46/5.70 ( ( ord_less_real @ X4 @ A )
% 5.46/5.70 => ( ( ord_less_real @ Y3 @ A )
% 5.46/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.46/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.46/5.70 => ( ( ( plus_plus_real @ U @ V )
% 5.46/5.70 = one_one_real )
% 5.46/5.70 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X4 ) @ ( times_times_real @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_bound_lt
% 5.46/5.70 thf(fact_3042_convex__bound__lt,axiom,
% 5.46/5.70 ! [X4: rat,A: rat,Y3: rat,U: rat,V: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X4 @ A )
% 5.46/5.70 => ( ( ord_less_rat @ Y3 @ A )
% 5.46/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.46/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.46/5.70 => ( ( ( plus_plus_rat @ U @ V )
% 5.46/5.70 = one_one_rat )
% 5.46/5.70 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X4 ) @ ( times_times_rat @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_bound_lt
% 5.46/5.70 thf(fact_3043_convex__bound__lt,axiom,
% 5.46/5.70 ! [X4: int,A: int,Y3: int,U: int,V: int] :
% 5.46/5.70 ( ( ord_less_int @ X4 @ A )
% 5.46/5.70 => ( ( ord_less_int @ Y3 @ A )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.46/5.70 => ( ( ( plus_plus_int @ U @ V )
% 5.46/5.70 = one_one_int )
% 5.46/5.70 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X4 ) @ ( times_times_int @ V @ Y3 ) ) @ A ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % convex_bound_lt
% 5.46/5.70 thf(fact_3044_le__divide__eq__numeral_I1_J,axiom,
% 5.46/5.70 ! [W: num,B2: real,C: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.70 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.70 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B2 ) )
% 5.46/5.70 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.70 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.70 => ( ord_less_eq_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.46/5.70 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.70 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % le_divide_eq_numeral(1)
% 5.46/5.70 thf(fact_3045_le__divide__eq__numeral_I1_J,axiom,
% 5.46/5.70 ! [W: num,B2: rat,C: rat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.70 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B2 ) )
% 5.46/5.70 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.70 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.70 => ( ord_less_eq_rat @ B2 @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.46/5.70 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.70 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % le_divide_eq_numeral(1)
% 5.46/5.70 thf(fact_3046_divide__le__eq__numeral_I1_J,axiom,
% 5.46/5.70 ! [B2: real,C: real,W: num] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ ( numeral_numeral_real @ W ) )
% 5.46/5.70 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.70 => ( ord_less_eq_real @ B2 @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.46/5.70 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.70 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.70 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B2 ) )
% 5.46/5.70 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divide_le_eq_numeral(1)
% 5.46/5.70 thf(fact_3047_divide__le__eq__numeral_I1_J,axiom,
% 5.46/5.70 ! [B2: rat,C: rat,W: num] :
% 5.46/5.70 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.46/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.70 => ( ord_less_eq_rat @ B2 @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.46/5.70 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.70 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.70 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B2 ) )
% 5.46/5.70 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divide_le_eq_numeral(1)
% 5.46/5.70 thf(fact_3048_half__gt__zero,axiom,
% 5.46/5.70 ! [A: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.70 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % half_gt_zero
% 5.46/5.70 thf(fact_3049_half__gt__zero,axiom,
% 5.46/5.70 ! [A: rat] :
% 5.46/5.70 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.70 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % half_gt_zero
% 5.46/5.70 thf(fact_3050_half__gt__zero__iff,axiom,
% 5.46/5.70 ! [A: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.70 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % half_gt_zero_iff
% 5.46/5.70 thf(fact_3051_half__gt__zero__iff,axiom,
% 5.46/5.70 ! [A: rat] :
% 5.46/5.70 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % half_gt_zero_iff
% 5.46/5.70 thf(fact_3052_scaling__mono,axiom,
% 5.46/5.70 ! [U: real,V: real,R2: real,S: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ U @ V )
% 5.46/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.46/5.70 => ( ( ord_less_eq_real @ R2 @ S )
% 5.46/5.70 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % scaling_mono
% 5.46/5.70 thf(fact_3053_scaling__mono,axiom,
% 5.46/5.70 ! [U: rat,V: rat,R2: rat,S: rat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ U @ V )
% 5.46/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.46/5.70 => ( ( ord_less_eq_rat @ R2 @ S )
% 5.46/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % scaling_mono
% 5.46/5.70 thf(fact_3054_zero__le__power2,axiom,
% 5.46/5.70 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_le_power2
% 5.46/5.70 thf(fact_3055_zero__le__power2,axiom,
% 5.46/5.70 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_le_power2
% 5.46/5.70 thf(fact_3056_zero__le__power2,axiom,
% 5.46/5.70 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_le_power2
% 5.46/5.70 thf(fact_3057_power2__eq__imp__eq,axiom,
% 5.46/5.70 ! [X4: real,Y3: real] :
% 5.46/5.70 ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.70 => ( X4 = Y3 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_eq_imp_eq
% 5.46/5.70 thf(fact_3058_power2__eq__imp__eq,axiom,
% 5.46/5.70 ! [X4: rat,Y3: rat] :
% 5.46/5.70 ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.46/5.70 => ( X4 = Y3 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_eq_imp_eq
% 5.46/5.70 thf(fact_3059_power2__eq__imp__eq,axiom,
% 5.46/5.70 ! [X4: nat,Y3: nat] :
% 5.46/5.70 ( ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 5.46/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.46/5.70 => ( X4 = Y3 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_eq_imp_eq
% 5.46/5.70 thf(fact_3060_power2__eq__imp__eq,axiom,
% 5.46/5.70 ! [X4: int,Y3: int] :
% 5.46/5.70 ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.70 => ( X4 = Y3 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_eq_imp_eq
% 5.46/5.70 thf(fact_3061_power2__le__imp__le,axiom,
% 5.46/5.70 ! [X4: real,Y3: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.70 => ( ord_less_eq_real @ X4 @ Y3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_le_imp_le
% 5.46/5.70 thf(fact_3062_power2__le__imp__le,axiom,
% 5.46/5.70 ! [X4: rat,Y3: rat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.46/5.70 => ( ord_less_eq_rat @ X4 @ Y3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_le_imp_le
% 5.46/5.70 thf(fact_3063_power2__le__imp__le,axiom,
% 5.46/5.70 ! [X4: nat,Y3: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.46/5.70 => ( ord_less_eq_nat @ X4 @ Y3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_le_imp_le
% 5.46/5.70 thf(fact_3064_power2__le__imp__le,axiom,
% 5.46/5.70 ! [X4: int,Y3: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.70 => ( ord_less_eq_int @ X4 @ Y3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_le_imp_le
% 5.46/5.70 thf(fact_3065_power2__less__0,axiom,
% 5.46/5.70 ! [A: real] :
% 5.46/5.70 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.46/5.70
% 5.46/5.70 % power2_less_0
% 5.46/5.70 thf(fact_3066_power2__less__0,axiom,
% 5.46/5.70 ! [A: rat] :
% 5.46/5.70 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.46/5.70
% 5.46/5.70 % power2_less_0
% 5.46/5.70 thf(fact_3067_power2__less__0,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % power2_less_0
% 5.46/5.70 thf(fact_3068_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.46/5.70 ! [C: code_integer,A: code_integer,B2: code_integer] :
% 5.46/5.70 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.46/5.70 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B2 @ C ) )
% 5.46/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B2 @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B2 ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.46/5.70 thf(fact_3069_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.46/5.70 ! [C: nat,A: nat,B2: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.46/5.70 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 5.46/5.70 = ( plus_plus_nat @ ( times_times_nat @ B2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B2 ) @ C ) ) @ ( modulo_modulo_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.46/5.70 thf(fact_3070_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.46/5.70 ! [C: int,A: int,B2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.46/5.70 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B2 @ C ) )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ B2 @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B2 ) @ C ) ) @ ( modulo_modulo_int @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.46/5.70 thf(fact_3071_exp__add__not__zero__imp__left,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.70 != zero_zero_nat )
% 5.46/5.70 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.46/5.70 != zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_add_not_zero_imp_left
% 5.46/5.70 thf(fact_3072_exp__add__not__zero__imp__left,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.70 != zero_zero_int )
% 5.46/5.70 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.46/5.70 != zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_add_not_zero_imp_left
% 5.46/5.70 thf(fact_3073_exp__add__not__zero__imp__right,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.70 != zero_zero_nat )
% 5.46/5.70 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 != zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_add_not_zero_imp_right
% 5.46/5.70 thf(fact_3074_exp__add__not__zero__imp__right,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.70 != zero_zero_int )
% 5.46/5.70 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 != zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_add_not_zero_imp_right
% 5.46/5.70 thf(fact_3075_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 != zero_zero_nat )
% 5.46/5.70 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.70 != zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_not_zero_imp_exp_diff_not_zero
% 5.46/5.70 thf(fact_3076_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 != zero_zero_int )
% 5.46/5.70 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.70 != zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % exp_not_zero_imp_exp_diff_not_zero
% 5.46/5.70 thf(fact_3077_power__diff__power__eq,axiom,
% 5.46/5.70 ! [A: nat,N: nat,M: nat] :
% 5.46/5.70 ( ( A != zero_zero_nat )
% 5.46/5.70 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.46/5.70 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.46/5.70 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_diff_power_eq
% 5.46/5.70 thf(fact_3078_power__diff__power__eq,axiom,
% 5.46/5.70 ! [A: int,N: nat,M: nat] :
% 5.46/5.70 ( ( A != zero_zero_int )
% 5.46/5.70 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.46/5.70 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.46/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.46/5.70 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_diff_power_eq
% 5.46/5.70 thf(fact_3079_less__2__cases,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 => ( ( N = zero_zero_nat )
% 5.46/5.70 | ( N
% 5.46/5.70 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_2_cases
% 5.46/5.70 thf(fact_3080_less__2__cases__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = ( ( N = zero_zero_nat )
% 5.46/5.70 | ( N
% 5.46/5.70 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % less_2_cases_iff
% 5.46/5.70 thf(fact_3081_nat__induct2,axiom,
% 5.46/5.70 ! [P: nat > $o,N: nat] :
% 5.46/5.70 ( ( P @ zero_zero_nat )
% 5.46/5.70 => ( ( P @ one_one_nat )
% 5.46/5.70 => ( ! [N4: nat] :
% 5.46/5.70 ( ( P @ N4 )
% 5.46/5.70 => ( P @ ( plus_plus_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.70 => ( P @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % nat_induct2
% 5.46/5.70 thf(fact_3082_power__eq__if,axiom,
% 5.46/5.70 ( power_power_complex
% 5.46/5.70 = ( ^ [P3: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P3 @ ( power_power_complex @ P3 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_eq_if
% 5.46/5.70 thf(fact_3083_power__eq__if,axiom,
% 5.46/5.70 ( power_power_real
% 5.46/5.70 = ( ^ [P3: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P3 @ ( power_power_real @ P3 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_eq_if
% 5.46/5.70 thf(fact_3084_power__eq__if,axiom,
% 5.46/5.70 ( power_power_rat
% 5.46/5.70 = ( ^ [P3: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P3 @ ( power_power_rat @ P3 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_eq_if
% 5.46/5.70 thf(fact_3085_power__eq__if,axiom,
% 5.46/5.70 ( power_power_nat
% 5.46/5.70 = ( ^ [P3: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P3 @ ( power_power_nat @ P3 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_eq_if
% 5.46/5.70 thf(fact_3086_power__eq__if,axiom,
% 5.46/5.70 ( power_power_int
% 5.46/5.70 = ( ^ [P3: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P3 @ ( power_power_int @ P3 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_eq_if
% 5.46/5.70 thf(fact_3087_power__minus__mult,axiom,
% 5.46/5.70 ! [N: nat,A: complex] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.46/5.70 = ( power_power_complex @ A @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_minus_mult
% 5.46/5.70 thf(fact_3088_power__minus__mult,axiom,
% 5.46/5.70 ! [N: nat,A: real] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.46/5.70 = ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_minus_mult
% 5.46/5.70 thf(fact_3089_power__minus__mult,axiom,
% 5.46/5.70 ! [N: nat,A: rat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.46/5.70 = ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_minus_mult
% 5.46/5.70 thf(fact_3090_power__minus__mult,axiom,
% 5.46/5.70 ! [N: nat,A: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.46/5.70 = ( power_power_nat @ A @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_minus_mult
% 5.46/5.70 thf(fact_3091_power__minus__mult,axiom,
% 5.46/5.70 ! [N: nat,A: int] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.46/5.70 = ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power_minus_mult
% 5.46/5.70 thf(fact_3092_le__div__geq,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.70 => ( ( divide_divide_nat @ M @ N )
% 5.46/5.70 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % le_div_geq
% 5.46/5.70 thf(fact_3093_split__div_H,axiom,
% 5.46/5.70 ! [P: nat > $o,M: nat,N: nat] :
% 5.46/5.70 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.70 = ( ( ( N = zero_zero_nat )
% 5.46/5.70 & ( P @ zero_zero_nat ) )
% 5.46/5.70 | ? [Q4: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 5.46/5.70 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 5.46/5.70 & ( P @ Q4 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % split_div'
% 5.46/5.70 thf(fact_3094_Suc__times__mod__eq,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.46/5.70 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.46/5.70 = one_one_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % Suc_times_mod_eq
% 5.46/5.70 thf(fact_3095_oddE,axiom,
% 5.46/5.70 ! [A: code_integer] :
% 5.46/5.70 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ~ ! [B5: code_integer] :
% 5.46/5.70 ( A
% 5.46/5.70 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_integer ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % oddE
% 5.46/5.70 thf(fact_3096_oddE,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ~ ! [B5: nat] :
% 5.46/5.70 ( A
% 5.46/5.70 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) @ one_one_nat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % oddE
% 5.46/5.70 thf(fact_3097_oddE,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.70 => ~ ! [B5: int] :
% 5.46/5.70 ( A
% 5.46/5.70 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) @ one_one_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % oddE
% 5.46/5.70 thf(fact_3098_power2__less__imp__less,axiom,
% 5.46/5.70 ! [X4: real,Y3: real] :
% 5.46/5.70 ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.70 => ( ord_less_real @ X4 @ Y3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_less_imp_less
% 5.46/5.70 thf(fact_3099_power2__less__imp__less,axiom,
% 5.46/5.70 ! [X4: rat,Y3: rat] :
% 5.46/5.70 ( ( ord_less_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.46/5.70 => ( ord_less_rat @ X4 @ Y3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_less_imp_less
% 5.46/5.70 thf(fact_3100_power2__less__imp__less,axiom,
% 5.46/5.70 ! [X4: nat,Y3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y3 )
% 5.46/5.70 => ( ord_less_nat @ X4 @ Y3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_less_imp_less
% 5.46/5.70 thf(fact_3101_power2__less__imp__less,axiom,
% 5.46/5.70 ! [X4: int,Y3: int] :
% 5.46/5.70 ( ( ord_less_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.70 => ( ord_less_int @ X4 @ Y3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % power2_less_imp_less
% 5.46/5.70 thf(fact_3102_sum__power2__ge__zero,axiom,
% 5.46/5.70 ! [X4: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power2_ge_zero
% 5.46/5.70 thf(fact_3103_sum__power2__ge__zero,axiom,
% 5.46/5.70 ! [X4: rat,Y3: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power2_ge_zero
% 5.46/5.70 thf(fact_3104_sum__power2__ge__zero,axiom,
% 5.46/5.70 ! [X4: int,Y3: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power2_ge_zero
% 5.46/5.70 thf(fact_3105_sum__power2__le__zero__iff,axiom,
% 5.46/5.70 ! [X4: real,Y3: real] :
% 5.46/5.70 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.46/5.70 = ( ( X4 = zero_zero_real )
% 5.46/5.70 & ( Y3 = zero_zero_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power2_le_zero_iff
% 5.46/5.70 thf(fact_3106_sum__power2__le__zero__iff,axiom,
% 5.46/5.70 ! [X4: rat,Y3: rat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.46/5.70 = ( ( X4 = zero_zero_rat )
% 5.46/5.70 & ( Y3 = zero_zero_rat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power2_le_zero_iff
% 5.46/5.70 thf(fact_3107_sum__power2__le__zero__iff,axiom,
% 5.46/5.70 ! [X4: int,Y3: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.46/5.70 = ( ( X4 = zero_zero_int )
% 5.46/5.70 & ( Y3 = zero_zero_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power2_le_zero_iff
% 5.46/5.70 thf(fact_3108_not__sum__power2__lt__zero,axiom,
% 5.46/5.70 ! [X4: real,Y3: real] :
% 5.46/5.70 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.46/5.70
% 5.46/5.70 % not_sum_power2_lt_zero
% 5.46/5.70 thf(fact_3109_not__sum__power2__lt__zero,axiom,
% 5.46/5.70 ! [X4: rat,Y3: rat] :
% 5.46/5.70 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.46/5.70
% 5.46/5.70 % not_sum_power2_lt_zero
% 5.46/5.70 thf(fact_3110_not__sum__power2__lt__zero,axiom,
% 5.46/5.70 ! [X4: int,Y3: int] :
% 5.46/5.70 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % not_sum_power2_lt_zero
% 5.46/5.70 thf(fact_3111_sum__power2__gt__zero__iff,axiom,
% 5.46/5.70 ! [X4: real,Y3: real] :
% 5.46/5.70 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.70 = ( ( X4 != zero_zero_real )
% 5.46/5.70 | ( Y3 != zero_zero_real ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power2_gt_zero_iff
% 5.46/5.70 thf(fact_3112_sum__power2__gt__zero__iff,axiom,
% 5.46/5.70 ! [X4: rat,Y3: rat] :
% 5.46/5.70 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.70 = ( ( X4 != zero_zero_rat )
% 5.46/5.70 | ( Y3 != zero_zero_rat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power2_gt_zero_iff
% 5.46/5.70 thf(fact_3113_sum__power2__gt__zero__iff,axiom,
% 5.46/5.70 ! [X4: int,Y3: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.70 = ( ( X4 != zero_zero_int )
% 5.46/5.70 | ( Y3 != zero_zero_int ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % sum_power2_gt_zero_iff
% 5.46/5.70 thf(fact_3114_divmod__digit__0_I2_J,axiom,
% 5.46/5.70 ! [B2: nat,A: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.70 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.46/5.70 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 5.46/5.70 = ( modulo_modulo_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divmod_digit_0(2)
% 5.46/5.70 thf(fact_3115_divmod__digit__0_I2_J,axiom,
% 5.46/5.70 ! [B2: int,A: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.70 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.46/5.70 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 5.46/5.70 = ( modulo_modulo_int @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divmod_digit_0(2)
% 5.46/5.70 thf(fact_3116_divmod__digit__0_I2_J,axiom,
% 5.46/5.70 ! [B2: code_integer,A: code_integer] :
% 5.46/5.70 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.46/5.70 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.46/5.70 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 5.46/5.70 = ( modulo364778990260209775nteger @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divmod_digit_0(2)
% 5.46/5.70 thf(fact_3117_bits__stable__imp__add__self,axiom,
% 5.46/5.70 ! [A: nat] :
% 5.46/5.70 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.70 = A )
% 5.46/5.70 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.70 = zero_zero_nat ) ) ).
% 5.46/5.70
% 5.46/5.70 % bits_stable_imp_add_self
% 5.46/5.70 thf(fact_3118_bits__stable__imp__add__self,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.70 = A )
% 5.46/5.70 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.46/5.70 = zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % bits_stable_imp_add_self
% 5.46/5.70 thf(fact_3119_bits__stable__imp__add__self,axiom,
% 5.46/5.70 ! [A: code_integer] :
% 5.46/5.70 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.70 = A )
% 5.46/5.70 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.46/5.70 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.70
% 5.46/5.70 % bits_stable_imp_add_self
% 5.46/5.70 thf(fact_3120_zero__le__even__power_H,axiom,
% 5.46/5.70 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_le_even_power'
% 5.46/5.70 thf(fact_3121_zero__le__even__power_H,axiom,
% 5.46/5.70 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_le_even_power'
% 5.46/5.70 thf(fact_3122_zero__le__even__power_H,axiom,
% 5.46/5.70 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zero_le_even_power'
% 5.46/5.70 thf(fact_3123_nat__bit__induct,axiom,
% 5.46/5.70 ! [P: nat > $o,N: nat] :
% 5.46/5.70 ( ( P @ zero_zero_nat )
% 5.46/5.70 => ( ! [N4: nat] :
% 5.46/5.70 ( ( P @ N4 )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.46/5.70 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 5.46/5.70 => ( ! [N4: nat] :
% 5.46/5.70 ( ( P @ N4 )
% 5.46/5.70 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 5.46/5.70 => ( P @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % nat_bit_induct
% 5.46/5.70 thf(fact_3124_div__2__gt__zero,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.70 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % div_2_gt_zero
% 5.46/5.70 thf(fact_3125_Suc__n__div__2__gt__zero,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % Suc_n_div_2_gt_zero
% 5.46/5.70 thf(fact_3126_verit__le__mono__div,axiom,
% 5.46/5.70 ! [A3: nat,B4: nat,N: nat] :
% 5.46/5.70 ( ( ord_less_nat @ A3 @ B4 )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ord_less_eq_nat
% 5.46/5.70 @ ( plus_plus_nat @ ( divide_divide_nat @ A3 @ N )
% 5.46/5.70 @ ( if_nat
% 5.46/5.70 @ ( ( modulo_modulo_nat @ B4 @ N )
% 5.46/5.70 = zero_zero_nat )
% 5.46/5.70 @ one_one_nat
% 5.46/5.70 @ zero_zero_nat ) )
% 5.46/5.70 @ ( divide_divide_nat @ B4 @ N ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % verit_le_mono_div
% 5.46/5.70 thf(fact_3127_divmod__digit__0_I1_J,axiom,
% 5.46/5.70 ! [B2: nat,A: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.70 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.46/5.70 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.46/5.70 = ( divide_divide_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divmod_digit_0(1)
% 5.46/5.70 thf(fact_3128_divmod__digit__0_I1_J,axiom,
% 5.46/5.70 ! [B2: int,A: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.70 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.46/5.70 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.46/5.70 = ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divmod_digit_0(1)
% 5.46/5.70 thf(fact_3129_divmod__digit__0_I1_J,axiom,
% 5.46/5.70 ! [B2: code_integer,A: code_integer] :
% 5.46/5.70 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.46/5.70 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.46/5.70 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.46/5.70 = ( divide6298287555418463151nteger @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divmod_digit_0(1)
% 5.46/5.70 thf(fact_3130_odd__0__le__power__imp__0__le,axiom,
% 5.46/5.70 ! [A: real,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.46/5.70 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % odd_0_le_power_imp_0_le
% 5.46/5.70 thf(fact_3131_odd__0__le__power__imp__0__le,axiom,
% 5.46/5.70 ! [A: rat,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.46/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % odd_0_le_power_imp_0_le
% 5.46/5.70 thf(fact_3132_odd__0__le__power__imp__0__le,axiom,
% 5.46/5.70 ! [A: int,N: nat] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.46/5.70 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.46/5.70
% 5.46/5.70 % odd_0_le_power_imp_0_le
% 5.46/5.70 thf(fact_3133_odd__power__less__zero,axiom,
% 5.46/5.70 ! [A: real,N: nat] :
% 5.46/5.70 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.70 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % odd_power_less_zero
% 5.46/5.70 thf(fact_3134_odd__power__less__zero,axiom,
% 5.46/5.70 ! [A: rat,N: nat] :
% 5.46/5.70 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.70 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.46/5.70
% 5.46/5.70 % odd_power_less_zero
% 5.46/5.70 thf(fact_3135_odd__power__less__zero,axiom,
% 5.46/5.70 ! [A: int,N: nat] :
% 5.46/5.70 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.70 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % odd_power_less_zero
% 5.46/5.70 thf(fact_3136_even__mask__div__iff_H,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( 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 ) ) )
% 5.46/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_mask_div_iff'
% 5.46/5.70 thf(fact_3137_even__mask__div__iff_H,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( 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 ) ) )
% 5.46/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_mask_div_iff'
% 5.46/5.70 thf(fact_3138_even__mask__div__iff_H,axiom,
% 5.46/5.70 ! [M: nat,N: nat] :
% 5.46/5.70 ( ( 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 ) ) )
% 5.46/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_mask_div_iff'
% 5.46/5.70 thf(fact_3139_mod__double__modulus,axiom,
% 5.46/5.70 ! [M: code_integer,X4: code_integer] :
% 5.46/5.70 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.46/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 5.46/5.70 => ( ( ( modulo364778990260209775nteger @ X4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.70 = ( modulo364778990260209775nteger @ X4 @ M ) )
% 5.46/5.70 | ( ( modulo364778990260209775nteger @ X4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.70 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X4 @ M ) @ M ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_double_modulus
% 5.46/5.70 thf(fact_3140_mod__double__modulus,axiom,
% 5.46/5.70 ! [M: nat,X4: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 5.46/5.70 => ( ( ( modulo_modulo_nat @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.70 = ( modulo_modulo_nat @ X4 @ M ) )
% 5.46/5.70 | ( ( modulo_modulo_nat @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.70 = ( plus_plus_nat @ ( modulo_modulo_nat @ X4 @ M ) @ M ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_double_modulus
% 5.46/5.70 thf(fact_3141_mod__double__modulus,axiom,
% 5.46/5.70 ! [M: int,X4: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ M )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.70 => ( ( ( modulo_modulo_int @ X4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.70 = ( modulo_modulo_int @ X4 @ M ) )
% 5.46/5.70 | ( ( modulo_modulo_int @ X4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.70 = ( plus_plus_int @ ( modulo_modulo_int @ X4 @ M ) @ M ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_double_modulus
% 5.46/5.70 thf(fact_3142_divmod__digit__1_I2_J,axiom,
% 5.46/5.70 ! [A: code_integer,B2: code_integer] :
% 5.46/5.70 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.70 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.46/5.70 => ( ( ord_le3102999989581377725nteger @ B2 @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.46/5.70 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.46/5.70 = ( modulo364778990260209775nteger @ A @ B2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divmod_digit_1(2)
% 5.46/5.70 thf(fact_3143_divmod__digit__1_I2_J,axiom,
% 5.46/5.70 ! [A: nat,B2: nat] :
% 5.46/5.70 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 5.46/5.70 => ( ( ord_less_eq_nat @ B2 @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.46/5.70 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.46/5.70 = ( modulo_modulo_nat @ A @ B2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divmod_digit_1(2)
% 5.46/5.70 thf(fact_3144_divmod__digit__1_I2_J,axiom,
% 5.46/5.70 ! [A: int,B2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.70 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.70 => ( ( ord_less_eq_int @ B2 @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) )
% 5.46/5.70 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ B2 )
% 5.46/5.70 = ( modulo_modulo_int @ A @ B2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % divmod_digit_1(2)
% 5.46/5.70 thf(fact_3145_even__mod__4__div__2,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.70 = ( suc @ zero_zero_nat ) )
% 5.46/5.70 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_mod_4_div_2
% 5.46/5.70 thf(fact_3146_pow__divides__pow__iff,axiom,
% 5.46/5.70 ! [N: nat,A: nat,B2: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B2 @ N ) )
% 5.46/5.70 = ( dvd_dvd_nat @ A @ B2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pow_divides_pow_iff
% 5.46/5.70 thf(fact_3147_pow__divides__pow__iff,axiom,
% 5.46/5.70 ! [N: nat,A: int,B2: int] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B2 @ N ) )
% 5.46/5.70 = ( dvd_dvd_int @ A @ B2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pow_divides_pow_iff
% 5.46/5.70 thf(fact_3148_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.46/5.70 ! [X4: nat,N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.70 => ( ord_less_nat @ ( vEBT_VEBT_low @ X4 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % VEBT_internal.exp_split_high_low(2)
% 5.46/5.70 thf(fact_3149_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.46/5.70 ! [X4: nat,N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.70 => ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % VEBT_internal.exp_split_high_low(1)
% 5.46/5.70 thf(fact_3150_even__even__mod__4__iff,axiom,
% 5.46/5.70 ! [N: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.70 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_even_mod_4_iff
% 5.46/5.70 thf(fact_3151_double__eq__0__iff,axiom,
% 5.46/5.70 ! [A: real] :
% 5.46/5.70 ( ( ( plus_plus_real @ A @ A )
% 5.46/5.70 = zero_zero_real )
% 5.46/5.70 = ( A = zero_zero_real ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_eq_0_iff
% 5.46/5.70 thf(fact_3152_double__eq__0__iff,axiom,
% 5.46/5.70 ! [A: rat] :
% 5.46/5.70 ( ( ( plus_plus_rat @ A @ A )
% 5.46/5.70 = zero_zero_rat )
% 5.46/5.70 = ( A = zero_zero_rat ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_eq_0_iff
% 5.46/5.70 thf(fact_3153_double__eq__0__iff,axiom,
% 5.46/5.70 ! [A: int] :
% 5.46/5.70 ( ( ( plus_plus_int @ A @ A )
% 5.46/5.70 = zero_zero_int )
% 5.46/5.70 = ( A = zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % double_eq_0_iff
% 5.46/5.70 thf(fact_3154_inf__period_I3_J,axiom,
% 5.46/5.70 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.46/5.70 => ! [X5: code_integer,K4: code_integer] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) )
% 5.46/5.70 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(3)
% 5.46/5.70 thf(fact_3155_inf__period_I3_J,axiom,
% 5.46/5.70 ! [D: real,D4: real,T: real] :
% 5.46/5.70 ( ( dvd_dvd_real @ D @ D4 )
% 5.46/5.70 => ! [X5: real,K4: real] :
% 5.46/5.70 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) )
% 5.46/5.70 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(3)
% 5.46/5.70 thf(fact_3156_inf__period_I3_J,axiom,
% 5.46/5.70 ! [D: rat,D4: rat,T: rat] :
% 5.46/5.70 ( ( dvd_dvd_rat @ D @ D4 )
% 5.46/5.70 => ! [X5: rat,K4: rat] :
% 5.46/5.70 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) )
% 5.46/5.70 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(3)
% 5.46/5.70 thf(fact_3157_inf__period_I3_J,axiom,
% 5.46/5.70 ! [D: int,D4: int,T: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ D @ D4 )
% 5.46/5.70 => ! [X5: int,K4: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.46/5.70 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(3)
% 5.46/5.70 thf(fact_3158_inf__period_I4_J,axiom,
% 5.46/5.70 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.46/5.70 => ! [X5: code_integer,K4: code_integer] :
% 5.46/5.70 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) ) )
% 5.46/5.70 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(4)
% 5.46/5.70 thf(fact_3159_inf__period_I4_J,axiom,
% 5.46/5.70 ! [D: real,D4: real,T: real] :
% 5.46/5.70 ( ( dvd_dvd_real @ D @ D4 )
% 5.46/5.70 => ! [X5: real,K4: real] :
% 5.46/5.70 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) ) )
% 5.46/5.70 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(4)
% 5.46/5.70 thf(fact_3160_inf__period_I4_J,axiom,
% 5.46/5.70 ! [D: rat,D4: rat,T: rat] :
% 5.46/5.70 ( ( dvd_dvd_rat @ D @ D4 )
% 5.46/5.70 => ! [X5: rat,K4: rat] :
% 5.46/5.70 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) ) )
% 5.46/5.70 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(4)
% 5.46/5.70 thf(fact_3161_inf__period_I4_J,axiom,
% 5.46/5.70 ! [D: int,D4: int,T: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ D @ D4 )
% 5.46/5.70 => ! [X5: int,K4: int] :
% 5.46/5.70 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) ) )
% 5.46/5.70 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(4)
% 5.46/5.70 thf(fact_3162_unity__coeff__ex,axiom,
% 5.46/5.70 ! [P: code_integer > $o,L2: code_integer] :
% 5.46/5.70 ( ( ? [X: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X ) ) )
% 5.46/5.70 = ( ? [X: code_integer] :
% 5.46/5.70 ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X @ zero_z3403309356797280102nteger ) )
% 5.46/5.70 & ( P @ X ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unity_coeff_ex
% 5.46/5.70 thf(fact_3163_unity__coeff__ex,axiom,
% 5.46/5.70 ! [P: real > $o,L2: real] :
% 5.46/5.70 ( ( ? [X: real] : ( P @ ( times_times_real @ L2 @ X ) ) )
% 5.46/5.70 = ( ? [X: real] :
% 5.46/5.70 ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X @ zero_zero_real ) )
% 5.46/5.70 & ( P @ X ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unity_coeff_ex
% 5.46/5.70 thf(fact_3164_unity__coeff__ex,axiom,
% 5.46/5.70 ! [P: rat > $o,L2: rat] :
% 5.46/5.70 ( ( ? [X: rat] : ( P @ ( times_times_rat @ L2 @ X ) ) )
% 5.46/5.70 = ( ? [X: rat] :
% 5.46/5.70 ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X @ zero_zero_rat ) )
% 5.46/5.70 & ( P @ X ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unity_coeff_ex
% 5.46/5.70 thf(fact_3165_unity__coeff__ex,axiom,
% 5.46/5.70 ! [P: nat > $o,L2: nat] :
% 5.46/5.70 ( ( ? [X: nat] : ( P @ ( times_times_nat @ L2 @ X ) ) )
% 5.46/5.70 = ( ? [X: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X @ zero_zero_nat ) )
% 5.46/5.70 & ( P @ X ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unity_coeff_ex
% 5.46/5.70 thf(fact_3166_unity__coeff__ex,axiom,
% 5.46/5.70 ! [P: int > $o,L2: int] :
% 5.46/5.70 ( ( ? [X: int] : ( P @ ( times_times_int @ L2 @ X ) ) )
% 5.46/5.70 = ( ? [X: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X @ zero_zero_int ) )
% 5.46/5.70 & ( P @ X ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unity_coeff_ex
% 5.46/5.70 thf(fact_3167_unset__bit__nonnegative__int__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.46/5.70 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % unset_bit_nonnegative_int_iff
% 5.46/5.70 thf(fact_3168_flip__bit__nonnegative__int__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.46/5.70 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % flip_bit_nonnegative_int_iff
% 5.46/5.70 thf(fact_3169_set__bit__nonnegative__int__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.46/5.70 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % set_bit_nonnegative_int_iff
% 5.46/5.70 thf(fact_3170_set__bit__negative__int__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.70 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % set_bit_negative_int_iff
% 5.46/5.70 thf(fact_3171_flip__bit__negative__int__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.70 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % flip_bit_negative_int_iff
% 5.46/5.70 thf(fact_3172_unset__bit__negative__int__iff,axiom,
% 5.46/5.70 ! [N: nat,K: int] :
% 5.46/5.70 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.70 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % unset_bit_negative_int_iff
% 5.46/5.70 thf(fact_3173_zle__add1__eq__le,axiom,
% 5.46/5.70 ! [W: int,Z: int] :
% 5.46/5.70 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.46/5.70 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.46/5.70
% 5.46/5.70 % zle_add1_eq_le
% 5.46/5.70 thf(fact_3174_zle__diff1__eq,axiom,
% 5.46/5.70 ! [W: int,Z: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.46/5.70 = ( ord_less_int @ W @ Z ) ) ).
% 5.46/5.70
% 5.46/5.70 % zle_diff1_eq
% 5.46/5.70 thf(fact_3175_mod__pos__pos__trivial,axiom,
% 5.46/5.70 ! [K: int,L2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.70 => ( ( ord_less_int @ K @ L2 )
% 5.46/5.70 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.70 = K ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_pos_pos_trivial
% 5.46/5.70 thf(fact_3176_mod__neg__neg__trivial,axiom,
% 5.46/5.70 ! [K: int,L2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.46/5.70 => ( ( ord_less_int @ L2 @ K )
% 5.46/5.70 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.70 = K ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_neg_neg_trivial
% 5.46/5.70 thf(fact_3177_le__imp__0__less,axiom,
% 5.46/5.70 ! [Z: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.70 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % le_imp_0_less
% 5.46/5.70 thf(fact_3178_split__zmod,axiom,
% 5.46/5.70 ! [P: int > $o,N: int,K: int] :
% 5.46/5.70 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.46/5.70 = ( ( ( K = zero_zero_int )
% 5.46/5.70 => ( P @ N ) )
% 5.46/5.70 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.70 => ! [I2: int,J3: int] :
% 5.46/5.70 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.46/5.70 & ( ord_less_int @ J3 @ K )
% 5.46/5.70 & ( N
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.46/5.70 => ( P @ J3 ) ) )
% 5.46/5.70 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.70 => ! [I2: int,J3: int] :
% 5.46/5.70 ( ( ( ord_less_int @ K @ J3 )
% 5.46/5.70 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.46/5.70 & ( N
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.46/5.70 => ( P @ J3 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % split_zmod
% 5.46/5.70 thf(fact_3179_odd__less__0__iff,axiom,
% 5.46/5.70 ! [Z: int] :
% 5.46/5.70 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.46/5.70 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % odd_less_0_iff
% 5.46/5.70 thf(fact_3180_mod__pos__geq,axiom,
% 5.46/5.70 ! [L2: int,K: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.70 => ( ( ord_less_eq_int @ L2 @ K )
% 5.46/5.70 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.70 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_pos_geq
% 5.46/5.70 thf(fact_3181_q__pos__lemma,axiom,
% 5.46/5.70 ! [B: int,Q5: int,R4: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) )
% 5.46/5.70 => ( ( ord_less_int @ R4 @ B )
% 5.46/5.70 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.70 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % q_pos_lemma
% 5.46/5.70 thf(fact_3182_zmult__zless__mono2,axiom,
% 5.46/5.70 ! [I: int,J: int,K: int] :
% 5.46/5.70 ( ( ord_less_int @ I @ J )
% 5.46/5.70 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.70 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zmult_zless_mono2
% 5.46/5.70 thf(fact_3183_int__mod__neg__eq,axiom,
% 5.46/5.70 ! [A: int,B2: int,Q2: int,R2: int] :
% 5.46/5.70 ( ( A
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ B2 @ Q2 ) @ R2 ) )
% 5.46/5.70 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.46/5.70 => ( ( ord_less_int @ B2 @ R2 )
% 5.46/5.70 => ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.70 = R2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_mod_neg_eq
% 5.46/5.70 thf(fact_3184_int__mod__pos__eq,axiom,
% 5.46/5.70 ! [A: int,B2: int,Q2: int,R2: int] :
% 5.46/5.70 ( ( A
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ B2 @ Q2 ) @ R2 ) )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.46/5.70 => ( ( ord_less_int @ R2 @ B2 )
% 5.46/5.70 => ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.70 = R2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_mod_pos_eq
% 5.46/5.70 thf(fact_3185_pos__zmult__eq__1__iff,axiom,
% 5.46/5.70 ! [M: int,N: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ M )
% 5.46/5.70 => ( ( ( times_times_int @ M @ N )
% 5.46/5.70 = one_one_int )
% 5.46/5.70 = ( ( M = one_one_int )
% 5.46/5.70 & ( N = one_one_int ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pos_zmult_eq_1_iff
% 5.46/5.70 thf(fact_3186_plusinfinity,axiom,
% 5.46/5.70 ! [D: int,P4: int > $o,P: int > $o] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ D )
% 5.46/5.70 => ( ! [X3: int,K2: int] :
% 5.46/5.70 ( ( P4 @ X3 )
% 5.46/5.70 = ( P4 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.46/5.70 => ( ? [Z3: int] :
% 5.46/5.70 ! [X3: int] :
% 5.46/5.70 ( ( ord_less_int @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [X_12: int] : ( P4 @ X_12 )
% 5.46/5.70 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % plusinfinity
% 5.46/5.70 thf(fact_3187_zdiv__mono2__lemma,axiom,
% 5.46/5.70 ! [B2: int,Q2: int,R2: int,B: int,Q5: int,R4: int] :
% 5.46/5.70 ( ( ( plus_plus_int @ ( times_times_int @ B2 @ Q2 ) @ R2 )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) )
% 5.46/5.70 => ( ( ord_less_int @ R4 @ B )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.46/5.70 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.70 => ( ( ord_less_eq_int @ B @ B2 )
% 5.46/5.70 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdiv_mono2_lemma
% 5.46/5.70 thf(fact_3188_minusinfinity,axiom,
% 5.46/5.70 ! [D: int,P1: int > $o,P: int > $o] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ D )
% 5.46/5.70 => ( ! [X3: int,K2: int] :
% 5.46/5.70 ( ( P1 @ X3 )
% 5.46/5.70 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.46/5.70 => ( ? [Z3: int] :
% 5.46/5.70 ! [X3: int] :
% 5.46/5.70 ( ( ord_less_int @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P1 @ X3 ) ) )
% 5.46/5.70 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.46/5.70 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minusinfinity
% 5.46/5.70 thf(fact_3189_decr__mult__lemma,axiom,
% 5.46/5.70 ! [D: int,P: int > $o,K: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ D )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( P @ X3 )
% 5.46/5.70 => ( P @ ( minus_minus_int @ X3 @ D ) ) )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.70 => ! [X5: int] :
% 5.46/5.70 ( ( P @ X5 )
% 5.46/5.70 => ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % decr_mult_lemma
% 5.46/5.70 thf(fact_3190_incr__mult__lemma,axiom,
% 5.46/5.70 ! [D: int,P: int > $o,K: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ D )
% 5.46/5.70 => ( ! [X3: int] :
% 5.46/5.70 ( ( P @ X3 )
% 5.46/5.70 => ( P @ ( plus_plus_int @ X3 @ D ) ) )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.70 => ! [X5: int] :
% 5.46/5.70 ( ( P @ X5 )
% 5.46/5.70 => ( P @ ( plus_plus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % incr_mult_lemma
% 5.46/5.70 thf(fact_3191_zdiv__mono2__neg__lemma,axiom,
% 5.46/5.70 ! [B2: int,Q2: int,R2: int,B: int,Q5: int,R4: int] :
% 5.46/5.70 ( ( ( plus_plus_int @ ( times_times_int @ B2 @ Q2 ) @ R2 )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) )
% 5.46/5.70 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.46/5.70 => ( ( ord_less_int @ R2 @ B2 )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.46/5.70 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.46/5.70 => ( ( ord_less_eq_int @ B @ B2 )
% 5.46/5.70 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdiv_mono2_neg_lemma
% 5.46/5.70 thf(fact_3192_int__one__le__iff__zero__less,axiom,
% 5.46/5.70 ! [Z: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.46/5.70 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_one_le_iff_zero_less
% 5.46/5.70 thf(fact_3193_unique__quotient__lemma,axiom,
% 5.46/5.70 ! [B2: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B2 @ Q2 ) @ R2 ) )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.46/5.70 => ( ( ord_less_int @ R4 @ B2 )
% 5.46/5.70 => ( ( ord_less_int @ R2 @ B2 )
% 5.46/5.70 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unique_quotient_lemma
% 5.46/5.70 thf(fact_3194_unique__quotient__lemma__neg,axiom,
% 5.46/5.70 ! [B2: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B2 @ Q2 ) @ R2 ) )
% 5.46/5.70 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.46/5.70 => ( ( ord_less_int @ B2 @ R2 )
% 5.46/5.70 => ( ( ord_less_int @ B2 @ R4 )
% 5.46/5.70 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % unique_quotient_lemma_neg
% 5.46/5.70 thf(fact_3195_mod__pos__neg__trivial,axiom,
% 5.46/5.70 ! [K: int,L2: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.70 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.46/5.70 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.70 = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_pos_neg_trivial
% 5.46/5.70 thf(fact_3196_zdvd__reduce,axiom,
% 5.46/5.70 ! [K: int,N: int,M: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 5.46/5.70 = ( dvd_dvd_int @ K @ N ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdvd_reduce
% 5.46/5.70 thf(fact_3197_zdvd__period,axiom,
% 5.46/5.70 ! [A: int,D: int,X4: int,T: int,C: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ A @ D )
% 5.46/5.70 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X4 @ T ) )
% 5.46/5.70 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X4 @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdvd_period
% 5.46/5.70 thf(fact_3198_odd__nonzero,axiom,
% 5.46/5.70 ! [Z: int] :
% 5.46/5.70 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 5.46/5.70 != zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % odd_nonzero
% 5.46/5.70 thf(fact_3199_times__int__code_I2_J,axiom,
% 5.46/5.70 ! [L2: int] :
% 5.46/5.70 ( ( times_times_int @ zero_zero_int @ L2 )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % times_int_code(2)
% 5.46/5.70 thf(fact_3200_times__int__code_I1_J,axiom,
% 5.46/5.70 ! [K: int] :
% 5.46/5.70 ( ( times_times_int @ K @ zero_zero_int )
% 5.46/5.70 = zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % times_int_code(1)
% 5.46/5.70 thf(fact_3201_zmod__eq__0D,axiom,
% 5.46/5.70 ! [M: int,D: int] :
% 5.46/5.70 ( ( ( modulo_modulo_int @ M @ D )
% 5.46/5.70 = zero_zero_int )
% 5.46/5.70 => ? [Q3: int] :
% 5.46/5.70 ( M
% 5.46/5.70 = ( times_times_int @ D @ Q3 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zmod_eq_0D
% 5.46/5.70 thf(fact_3202_zdvd__mult__cancel,axiom,
% 5.46/5.70 ! [K: int,M: int,N: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 5.46/5.70 => ( ( K != zero_zero_int )
% 5.46/5.70 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdvd_mult_cancel
% 5.46/5.70 thf(fact_3203_zdvd__mono,axiom,
% 5.46/5.70 ! [K: int,M: int,T: int] :
% 5.46/5.70 ( ( K != zero_zero_int )
% 5.46/5.70 => ( ( dvd_dvd_int @ M @ T )
% 5.46/5.70 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdvd_mono
% 5.46/5.70 thf(fact_3204_zmod__eq__0__iff,axiom,
% 5.46/5.70 ! [M: int,D: int] :
% 5.46/5.70 ( ( ( modulo_modulo_int @ M @ D )
% 5.46/5.70 = zero_zero_int )
% 5.46/5.70 = ( ? [Q4: int] :
% 5.46/5.70 ( M
% 5.46/5.70 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zmod_eq_0_iff
% 5.46/5.70 thf(fact_3205_imult__is__0,axiom,
% 5.46/5.70 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.70 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.46/5.70 = zero_z5237406670263579293d_enat )
% 5.46/5.70 = ( ( M = zero_z5237406670263579293d_enat )
% 5.46/5.70 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % imult_is_0
% 5.46/5.70 thf(fact_3206_signed__take__bit__mult,axiom,
% 5.46/5.70 ! [N: nat,K: int,L2: int] :
% 5.46/5.70 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.46/5.70 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % signed_take_bit_mult
% 5.46/5.70 thf(fact_3207_Euclidean__Division_Opos__mod__bound,axiom,
% 5.46/5.70 ! [L2: int,K: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.70 => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 5.46/5.70
% 5.46/5.70 % Euclidean_Division.pos_mod_bound
% 5.46/5.70 thf(fact_3208_neg__mod__bound,axiom,
% 5.46/5.70 ! [L2: int,K: int] :
% 5.46/5.70 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.46/5.70 => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % neg_mod_bound
% 5.46/5.70 thf(fact_3209_Euclidean__Division_Opos__mod__sign,axiom,
% 5.46/5.70 ! [L2: int,K: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % Euclidean_Division.pos_mod_sign
% 5.46/5.70 thf(fact_3210_neg__mod__sign,axiom,
% 5.46/5.70 ! [L2: int,K: int] :
% 5.46/5.70 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.46/5.70 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 5.46/5.70
% 5.46/5.70 % neg_mod_sign
% 5.46/5.70 thf(fact_3211_zmod__le__nonneg__dividend,axiom,
% 5.46/5.70 ! [M: int,K: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.46/5.70 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.46/5.70
% 5.46/5.70 % zmod_le_nonneg_dividend
% 5.46/5.70 thf(fact_3212_zmod__trivial__iff,axiom,
% 5.46/5.70 ! [I: int,K: int] :
% 5.46/5.70 ( ( ( modulo_modulo_int @ I @ K )
% 5.46/5.70 = I )
% 5.46/5.70 = ( ( K = zero_zero_int )
% 5.46/5.70 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.46/5.70 & ( ord_less_int @ I @ K ) )
% 5.46/5.70 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.46/5.70 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zmod_trivial_iff
% 5.46/5.70 thf(fact_3213_mod__int__pos__iff,axiom,
% 5.46/5.70 ! [K: int,L2: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.46/5.70 = ( ( dvd_dvd_int @ L2 @ K )
% 5.46/5.70 | ( ( L2 = zero_zero_int )
% 5.46/5.70 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.46/5.70 | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % mod_int_pos_iff
% 5.46/5.70 thf(fact_3214_pos__mod__conj,axiom,
% 5.46/5.70 ! [B2: int,A: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B2 ) )
% 5.46/5.70 & ( ord_less_int @ ( modulo_modulo_int @ A @ B2 ) @ B2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pos_mod_conj
% 5.46/5.70 thf(fact_3215_neg__mod__conj,axiom,
% 5.46/5.70 ! [B2: int,A: int] :
% 5.46/5.70 ( ( ord_less_int @ B2 @ zero_zero_int )
% 5.46/5.70 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B2 ) @ zero_zero_int )
% 5.46/5.70 & ( ord_less_int @ B2 @ ( modulo_modulo_int @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % neg_mod_conj
% 5.46/5.70 thf(fact_3216_zdvd__not__zless,axiom,
% 5.46/5.70 ! [M: int,N: int] :
% 5.46/5.70 ( ( ord_less_int @ zero_zero_int @ M )
% 5.46/5.70 => ( ( ord_less_int @ M @ N )
% 5.46/5.70 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdvd_not_zless
% 5.46/5.70 thf(fact_3217_zdvd__imp__le,axiom,
% 5.46/5.70 ! [Z: int,N: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ Z @ N )
% 5.46/5.70 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.46/5.70 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdvd_imp_le
% 5.46/5.70 thf(fact_3218_less__int__code_I1_J,axiom,
% 5.46/5.70 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.46/5.70
% 5.46/5.70 % less_int_code(1)
% 5.46/5.70 thf(fact_3219_plus__int__code_I2_J,axiom,
% 5.46/5.70 ! [L2: int] :
% 5.46/5.70 ( ( plus_plus_int @ zero_zero_int @ L2 )
% 5.46/5.70 = L2 ) ).
% 5.46/5.70
% 5.46/5.70 % plus_int_code(2)
% 5.46/5.70 thf(fact_3220_plus__int__code_I1_J,axiom,
% 5.46/5.70 ! [K: int] :
% 5.46/5.70 ( ( plus_plus_int @ K @ zero_zero_int )
% 5.46/5.70 = K ) ).
% 5.46/5.70
% 5.46/5.70 % plus_int_code(1)
% 5.46/5.70 thf(fact_3221_minus__int__code_I1_J,axiom,
% 5.46/5.70 ! [K: int] :
% 5.46/5.70 ( ( minus_minus_int @ K @ zero_zero_int )
% 5.46/5.70 = K ) ).
% 5.46/5.70
% 5.46/5.70 % minus_int_code(1)
% 5.46/5.70 thf(fact_3222_zdvd__zdiffD,axiom,
% 5.46/5.70 ! [K: int,M: int,N: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 5.46/5.70 => ( ( dvd_dvd_int @ K @ N )
% 5.46/5.70 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zdvd_zdiffD
% 5.46/5.70 thf(fact_3223_signed__take__bit__add,axiom,
% 5.46/5.70 ! [N: nat,K: int,L2: int] :
% 5.46/5.70 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.46/5.70 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % signed_take_bit_add
% 5.46/5.70 thf(fact_3224_signed__take__bit__diff,axiom,
% 5.46/5.70 ! [N: nat,K: int,L2: int] :
% 5.46/5.70 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.46/5.70 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % signed_take_bit_diff
% 5.46/5.70 thf(fact_3225_zero__one__enat__neq_I1_J,axiom,
% 5.46/5.70 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.46/5.70
% 5.46/5.70 % zero_one_enat_neq(1)
% 5.46/5.70 thf(fact_3226_set__bit__greater__eq,axiom,
% 5.46/5.70 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 5.46/5.70
% 5.46/5.70 % set_bit_greater_eq
% 5.46/5.70 thf(fact_3227_unset__bit__less__eq,axiom,
% 5.46/5.70 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 5.46/5.70
% 5.46/5.70 % unset_bit_less_eq
% 5.46/5.70 thf(fact_3228_int__distrib_I4_J,axiom,
% 5.46/5.70 ! [W: int,Z1: int,Z22: int] :
% 5.46/5.70 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.46/5.70 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_distrib(4)
% 5.46/5.70 thf(fact_3229_int__distrib_I3_J,axiom,
% 5.46/5.70 ! [Z1: int,Z22: int,W: int] :
% 5.46/5.70 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.46/5.70 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_distrib(3)
% 5.46/5.70 thf(fact_3230_int__distrib_I2_J,axiom,
% 5.46/5.70 ! [W: int,Z1: int,Z22: int] :
% 5.46/5.70 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_distrib(2)
% 5.46/5.70 thf(fact_3231_int__distrib_I1_J,axiom,
% 5.46/5.70 ! [Z1: int,Z22: int,W: int] :
% 5.46/5.70 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.46/5.70 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_distrib(1)
% 5.46/5.70 thf(fact_3232_zless__imp__add1__zle,axiom,
% 5.46/5.70 ! [W: int,Z: int] :
% 5.46/5.70 ( ( ord_less_int @ W @ Z )
% 5.46/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.46/5.70
% 5.46/5.70 % zless_imp_add1_zle
% 5.46/5.70 thf(fact_3233_int__less__induct,axiom,
% 5.46/5.70 ! [I: int,K: int,P: int > $o] :
% 5.46/5.70 ( ( ord_less_int @ I @ K )
% 5.46/5.70 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.46/5.70 => ( ! [I3: int] :
% 5.46/5.70 ( ( ord_less_int @ I3 @ K )
% 5.46/5.70 => ( ( P @ I3 )
% 5.46/5.70 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.46/5.70 => ( P @ I ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_less_induct
% 5.46/5.70 thf(fact_3234_zless__add1__eq,axiom,
% 5.46/5.70 ! [W: int,Z: int] :
% 5.46/5.70 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.46/5.70 = ( ( ord_less_int @ W @ Z )
% 5.46/5.70 | ( W = Z ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % zless_add1_eq
% 5.46/5.70 thf(fact_3235_int__le__induct,axiom,
% 5.46/5.70 ! [I: int,K: int,P: int > $o] :
% 5.46/5.70 ( ( ord_less_eq_int @ I @ K )
% 5.46/5.70 => ( ( P @ K )
% 5.46/5.70 => ( ! [I3: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ I3 @ K )
% 5.46/5.70 => ( ( P @ I3 )
% 5.46/5.70 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.46/5.70 => ( P @ I ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_le_induct
% 5.46/5.70 thf(fact_3236_int__gr__induct,axiom,
% 5.46/5.70 ! [K: int,I: int,P: int > $o] :
% 5.46/5.70 ( ( ord_less_int @ K @ I )
% 5.46/5.70 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.46/5.70 => ( ! [I3: int] :
% 5.46/5.70 ( ( ord_less_int @ K @ I3 )
% 5.46/5.70 => ( ( P @ I3 )
% 5.46/5.70 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.46/5.70 => ( P @ I ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_gr_induct
% 5.46/5.70 thf(fact_3237_int__ge__induct,axiom,
% 5.46/5.70 ! [K: int,I: int,P: int > $o] :
% 5.46/5.70 ( ( ord_less_eq_int @ K @ I )
% 5.46/5.70 => ( ( P @ K )
% 5.46/5.70 => ( ! [I3: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ K @ I3 )
% 5.46/5.70 => ( ( P @ I3 )
% 5.46/5.70 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.46/5.70 => ( P @ I ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_ge_induct
% 5.46/5.70 thf(fact_3238_add1__zle__eq,axiom,
% 5.46/5.70 ! [W: int,Z: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.46/5.70 = ( ord_less_int @ W @ Z ) ) ).
% 5.46/5.70
% 5.46/5.70 % add1_zle_eq
% 5.46/5.70 thf(fact_3239_int__induct,axiom,
% 5.46/5.70 ! [P: int > $o,K: int,I: int] :
% 5.46/5.70 ( ( P @ K )
% 5.46/5.70 => ( ! [I3: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ K @ I3 )
% 5.46/5.70 => ( ( P @ I3 )
% 5.46/5.70 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.46/5.70 => ( ! [I3: int] :
% 5.46/5.70 ( ( ord_less_eq_int @ I3 @ K )
% 5.46/5.70 => ( ( P @ I3 )
% 5.46/5.70 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.46/5.70 => ( P @ I ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % int_induct
% 5.46/5.70 thf(fact_3240_even__diff__iff,axiom,
% 5.46/5.70 ! [K: int,L2: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 5.46/5.70 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % even_diff_iff
% 5.46/5.70 thf(fact_3241_minf_I7_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ X5 @ Z2 )
% 5.46/5.70 => ~ ( ord_less_real @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(7)
% 5.46/5.70 thf(fact_3242_minf_I7_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X5 @ Z2 )
% 5.46/5.70 => ~ ( ord_less_rat @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(7)
% 5.46/5.70 thf(fact_3243_minf_I7_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ X5 @ Z2 )
% 5.46/5.70 => ~ ( ord_less_num @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(7)
% 5.46/5.70 thf(fact_3244_minf_I7_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X5 @ Z2 )
% 5.46/5.70 => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(7)
% 5.46/5.70 thf(fact_3245_minf_I7_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ X5 @ Z2 )
% 5.46/5.70 => ~ ( ord_less_int @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(7)
% 5.46/5.70 thf(fact_3246_minf_I5_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ X5 @ Z2 )
% 5.46/5.70 => ( ord_less_real @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(5)
% 5.46/5.70 thf(fact_3247_minf_I5_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X5 @ Z2 )
% 5.46/5.70 => ( ord_less_rat @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(5)
% 5.46/5.70 thf(fact_3248_minf_I5_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ X5 @ Z2 )
% 5.46/5.70 => ( ord_less_num @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(5)
% 5.46/5.70 thf(fact_3249_minf_I5_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X5 @ Z2 )
% 5.46/5.70 => ( ord_less_nat @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(5)
% 5.46/5.70 thf(fact_3250_minf_I5_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ X5 @ Z2 )
% 5.46/5.70 => ( ord_less_int @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(5)
% 5.46/5.70 thf(fact_3251_minf_I4_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ X5 @ Z2 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(4)
% 5.46/5.70 thf(fact_3252_minf_I4_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X5 @ Z2 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(4)
% 5.46/5.70 thf(fact_3253_minf_I4_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ X5 @ Z2 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(4)
% 5.46/5.70 thf(fact_3254_minf_I4_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X5 @ Z2 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(4)
% 5.46/5.70 thf(fact_3255_minf_I4_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ X5 @ Z2 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(4)
% 5.46/5.70 thf(fact_3256_minf_I3_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ X5 @ Z2 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(3)
% 5.46/5.70 thf(fact_3257_minf_I3_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X5 @ Z2 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(3)
% 5.46/5.70 thf(fact_3258_minf_I3_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ X5 @ Z2 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(3)
% 5.46/5.70 thf(fact_3259_minf_I3_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X5 @ Z2 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(3)
% 5.46/5.70 thf(fact_3260_minf_I3_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ X5 @ Z2 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(3)
% 5.46/5.70 thf(fact_3261_minf_I2_J,axiom,
% 5.46/5.70 ! [P: real > $o,P4: real > $o,Q: real > $o,Q6: real > $o] :
% 5.46/5.70 ( ? [Z3: real] :
% 5.46/5.70 ! [X3: real] :
% 5.46/5.70 ( ( ord_less_real @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: real] :
% 5.46/5.70 ! [X3: real] :
% 5.46/5.70 ( ( ord_less_real @ X3 @ Z3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ X5 @ Z2 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(2)
% 5.46/5.70 thf(fact_3262_minf_I2_J,axiom,
% 5.46/5.70 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.46/5.70 ( ? [Z3: rat] :
% 5.46/5.70 ! [X3: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: rat] :
% 5.46/5.70 ! [X3: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X3 @ Z3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X5 @ Z2 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(2)
% 5.46/5.70 thf(fact_3263_minf_I2_J,axiom,
% 5.46/5.70 ! [P: num > $o,P4: num > $o,Q: num > $o,Q6: num > $o] :
% 5.46/5.70 ( ? [Z3: num] :
% 5.46/5.70 ! [X3: num] :
% 5.46/5.70 ( ( ord_less_num @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: num] :
% 5.46/5.70 ! [X3: num] :
% 5.46/5.70 ( ( ord_less_num @ X3 @ Z3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ X5 @ Z2 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(2)
% 5.46/5.70 thf(fact_3264_minf_I2_J,axiom,
% 5.46/5.70 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.46/5.70 ( ? [Z3: nat] :
% 5.46/5.70 ! [X3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: nat] :
% 5.46/5.70 ! [X3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X3 @ Z3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X5 @ Z2 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(2)
% 5.46/5.70 thf(fact_3265_minf_I2_J,axiom,
% 5.46/5.70 ! [P: int > $o,P4: int > $o,Q: int > $o,Q6: int > $o] :
% 5.46/5.70 ( ? [Z3: int] :
% 5.46/5.70 ! [X3: int] :
% 5.46/5.70 ( ( ord_less_int @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: int] :
% 5.46/5.70 ! [X3: int] :
% 5.46/5.70 ( ( ord_less_int @ X3 @ Z3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ X5 @ Z2 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(2)
% 5.46/5.70 thf(fact_3266_minf_I1_J,axiom,
% 5.46/5.70 ! [P: real > $o,P4: real > $o,Q: real > $o,Q6: real > $o] :
% 5.46/5.70 ( ? [Z3: real] :
% 5.46/5.70 ! [X3: real] :
% 5.46/5.70 ( ( ord_less_real @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: real] :
% 5.46/5.70 ! [X3: real] :
% 5.46/5.70 ( ( ord_less_real @ X3 @ Z3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ X5 @ Z2 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(1)
% 5.46/5.70 thf(fact_3267_minf_I1_J,axiom,
% 5.46/5.70 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.46/5.70 ( ? [Z3: rat] :
% 5.46/5.70 ! [X3: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: rat] :
% 5.46/5.70 ! [X3: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X3 @ Z3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X5 @ Z2 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(1)
% 5.46/5.70 thf(fact_3268_minf_I1_J,axiom,
% 5.46/5.70 ! [P: num > $o,P4: num > $o,Q: num > $o,Q6: num > $o] :
% 5.46/5.70 ( ? [Z3: num] :
% 5.46/5.70 ! [X3: num] :
% 5.46/5.70 ( ( ord_less_num @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: num] :
% 5.46/5.70 ! [X3: num] :
% 5.46/5.70 ( ( ord_less_num @ X3 @ Z3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ X5 @ Z2 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(1)
% 5.46/5.70 thf(fact_3269_minf_I1_J,axiom,
% 5.46/5.70 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.46/5.70 ( ? [Z3: nat] :
% 5.46/5.70 ! [X3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: nat] :
% 5.46/5.70 ! [X3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X3 @ Z3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X5 @ Z2 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(1)
% 5.46/5.70 thf(fact_3270_minf_I1_J,axiom,
% 5.46/5.70 ! [P: int > $o,P4: int > $o,Q: int > $o,Q6: int > $o] :
% 5.46/5.70 ( ? [Z3: int] :
% 5.46/5.70 ! [X3: int] :
% 5.46/5.70 ( ( ord_less_int @ X3 @ Z3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: int] :
% 5.46/5.70 ! [X3: int] :
% 5.46/5.70 ( ( ord_less_int @ X3 @ Z3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ X5 @ Z2 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(1)
% 5.46/5.70 thf(fact_3271_pinf_I7_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ Z2 @ X5 )
% 5.46/5.70 => ( ord_less_real @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(7)
% 5.46/5.70 thf(fact_3272_pinf_I7_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z2 @ X5 )
% 5.46/5.70 => ( ord_less_rat @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(7)
% 5.46/5.70 thf(fact_3273_pinf_I7_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ Z2 @ X5 )
% 5.46/5.70 => ( ord_less_num @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(7)
% 5.46/5.70 thf(fact_3274_pinf_I7_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z2 @ X5 )
% 5.46/5.70 => ( ord_less_nat @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(7)
% 5.46/5.70 thf(fact_3275_pinf_I7_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ Z2 @ X5 )
% 5.46/5.70 => ( ord_less_int @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(7)
% 5.46/5.70 thf(fact_3276_pinf_I5_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ Z2 @ X5 )
% 5.46/5.70 => ~ ( ord_less_real @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(5)
% 5.46/5.70 thf(fact_3277_pinf_I5_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z2 @ X5 )
% 5.46/5.70 => ~ ( ord_less_rat @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(5)
% 5.46/5.70 thf(fact_3278_pinf_I5_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ Z2 @ X5 )
% 5.46/5.70 => ~ ( ord_less_num @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(5)
% 5.46/5.70 thf(fact_3279_pinf_I5_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z2 @ X5 )
% 5.46/5.70 => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(5)
% 5.46/5.70 thf(fact_3280_pinf_I5_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ Z2 @ X5 )
% 5.46/5.70 => ~ ( ord_less_int @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(5)
% 5.46/5.70 thf(fact_3281_pinf_I4_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ Z2 @ X5 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(4)
% 5.46/5.70 thf(fact_3282_pinf_I4_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z2 @ X5 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(4)
% 5.46/5.70 thf(fact_3283_pinf_I4_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ Z2 @ X5 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(4)
% 5.46/5.70 thf(fact_3284_pinf_I4_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z2 @ X5 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(4)
% 5.46/5.70 thf(fact_3285_pinf_I4_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ Z2 @ X5 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(4)
% 5.46/5.70 thf(fact_3286_pinf_I3_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ Z2 @ X5 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(3)
% 5.46/5.70 thf(fact_3287_pinf_I3_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z2 @ X5 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(3)
% 5.46/5.70 thf(fact_3288_pinf_I3_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ Z2 @ X5 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(3)
% 5.46/5.70 thf(fact_3289_pinf_I3_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z2 @ X5 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(3)
% 5.46/5.70 thf(fact_3290_pinf_I3_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ Z2 @ X5 )
% 5.46/5.70 => ( X5 != T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(3)
% 5.46/5.70 thf(fact_3291_pinf_I2_J,axiom,
% 5.46/5.70 ! [P: real > $o,P4: real > $o,Q: real > $o,Q6: real > $o] :
% 5.46/5.70 ( ? [Z3: real] :
% 5.46/5.70 ! [X3: real] :
% 5.46/5.70 ( ( ord_less_real @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: real] :
% 5.46/5.70 ! [X3: real] :
% 5.46/5.70 ( ( ord_less_real @ Z3 @ X3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ Z2 @ X5 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(2)
% 5.46/5.70 thf(fact_3292_pinf_I2_J,axiom,
% 5.46/5.70 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.46/5.70 ( ? [Z3: rat] :
% 5.46/5.70 ! [X3: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: rat] :
% 5.46/5.70 ! [X3: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z3 @ X3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z2 @ X5 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(2)
% 5.46/5.70 thf(fact_3293_pinf_I2_J,axiom,
% 5.46/5.70 ! [P: num > $o,P4: num > $o,Q: num > $o,Q6: num > $o] :
% 5.46/5.70 ( ? [Z3: num] :
% 5.46/5.70 ! [X3: num] :
% 5.46/5.70 ( ( ord_less_num @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: num] :
% 5.46/5.70 ! [X3: num] :
% 5.46/5.70 ( ( ord_less_num @ Z3 @ X3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ Z2 @ X5 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(2)
% 5.46/5.70 thf(fact_3294_pinf_I2_J,axiom,
% 5.46/5.70 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.46/5.70 ( ? [Z3: nat] :
% 5.46/5.70 ! [X3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: nat] :
% 5.46/5.70 ! [X3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z3 @ X3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z2 @ X5 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(2)
% 5.46/5.70 thf(fact_3295_pinf_I2_J,axiom,
% 5.46/5.70 ! [P: int > $o,P4: int > $o,Q: int > $o,Q6: int > $o] :
% 5.46/5.70 ( ? [Z3: int] :
% 5.46/5.70 ! [X3: int] :
% 5.46/5.70 ( ( ord_less_int @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: int] :
% 5.46/5.70 ! [X3: int] :
% 5.46/5.70 ( ( ord_less_int @ Z3 @ X3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ Z2 @ X5 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(2)
% 5.46/5.70 thf(fact_3296_pinf_I1_J,axiom,
% 5.46/5.70 ! [P: real > $o,P4: real > $o,Q: real > $o,Q6: real > $o] :
% 5.46/5.70 ( ? [Z3: real] :
% 5.46/5.70 ! [X3: real] :
% 5.46/5.70 ( ( ord_less_real @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: real] :
% 5.46/5.70 ! [X3: real] :
% 5.46/5.70 ( ( ord_less_real @ Z3 @ X3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ Z2 @ X5 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(1)
% 5.46/5.70 thf(fact_3297_pinf_I1_J,axiom,
% 5.46/5.70 ! [P: rat > $o,P4: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.46/5.70 ( ? [Z3: rat] :
% 5.46/5.70 ! [X3: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: rat] :
% 5.46/5.70 ! [X3: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z3 @ X3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z2 @ X5 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(1)
% 5.46/5.70 thf(fact_3298_pinf_I1_J,axiom,
% 5.46/5.70 ! [P: num > $o,P4: num > $o,Q: num > $o,Q6: num > $o] :
% 5.46/5.70 ( ? [Z3: num] :
% 5.46/5.70 ! [X3: num] :
% 5.46/5.70 ( ( ord_less_num @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: num] :
% 5.46/5.70 ! [X3: num] :
% 5.46/5.70 ( ( ord_less_num @ Z3 @ X3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ Z2 @ X5 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(1)
% 5.46/5.70 thf(fact_3299_pinf_I1_J,axiom,
% 5.46/5.70 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.46/5.70 ( ? [Z3: nat] :
% 5.46/5.70 ! [X3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: nat] :
% 5.46/5.70 ! [X3: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z3 @ X3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z2 @ X5 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(1)
% 5.46/5.70 thf(fact_3300_pinf_I1_J,axiom,
% 5.46/5.70 ! [P: int > $o,P4: int > $o,Q: int > $o,Q6: int > $o] :
% 5.46/5.70 ( ? [Z3: int] :
% 5.46/5.70 ! [X3: int] :
% 5.46/5.70 ( ( ord_less_int @ Z3 @ X3 )
% 5.46/5.70 => ( ( P @ X3 )
% 5.46/5.70 = ( P4 @ X3 ) ) )
% 5.46/5.70 => ( ? [Z3: int] :
% 5.46/5.70 ! [X3: int] :
% 5.46/5.70 ( ( ord_less_int @ Z3 @ X3 )
% 5.46/5.70 => ( ( Q @ X3 )
% 5.46/5.70 = ( Q6 @ X3 ) ) )
% 5.46/5.70 => ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ Z2 @ X5 )
% 5.46/5.70 => ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P4 @ X5 )
% 5.46/5.70 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(1)
% 5.46/5.70 thf(fact_3301_vebt__buildup_Ocases,axiom,
% 5.46/5.70 ! [X4: nat] :
% 5.46/5.70 ( ( X4 != zero_zero_nat )
% 5.46/5.70 => ( ( X4
% 5.46/5.70 != ( suc @ zero_zero_nat ) )
% 5.46/5.70 => ~ ! [Va: nat] :
% 5.46/5.70 ( X4
% 5.46/5.70 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % vebt_buildup.cases
% 5.46/5.70 thf(fact_3302_Euclid__induct,axiom,
% 5.46/5.70 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 5.46/5.70 ( ! [A5: nat,B5: nat] :
% 5.46/5.70 ( ( P @ A5 @ B5 )
% 5.46/5.70 = ( P @ B5 @ A5 ) )
% 5.46/5.70 => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 5.46/5.70 => ( ! [A5: nat,B5: nat] :
% 5.46/5.70 ( ( P @ A5 @ B5 )
% 5.46/5.70 => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 5.46/5.70 => ( P @ A @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % Euclid_induct
% 5.46/5.70 thf(fact_3303_minf_I8_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ X5 @ Z2 )
% 5.46/5.70 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(8)
% 5.46/5.70 thf(fact_3304_minf_I8_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X5 @ Z2 )
% 5.46/5.70 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(8)
% 5.46/5.70 thf(fact_3305_minf_I8_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ X5 @ Z2 )
% 5.46/5.70 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(8)
% 5.46/5.70 thf(fact_3306_minf_I8_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X5 @ Z2 )
% 5.46/5.70 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(8)
% 5.46/5.70 thf(fact_3307_minf_I8_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ X5 @ Z2 )
% 5.46/5.70 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(8)
% 5.46/5.70 thf(fact_3308_minf_I6_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ X5 @ Z2 )
% 5.46/5.70 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(6)
% 5.46/5.70 thf(fact_3309_minf_I6_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ X5 @ Z2 )
% 5.46/5.70 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(6)
% 5.46/5.70 thf(fact_3310_minf_I6_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ X5 @ Z2 )
% 5.46/5.70 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(6)
% 5.46/5.70 thf(fact_3311_minf_I6_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ X5 @ Z2 )
% 5.46/5.70 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(6)
% 5.46/5.70 thf(fact_3312_minf_I6_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ X5 @ Z2 )
% 5.46/5.70 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % minf(6)
% 5.46/5.70 thf(fact_3313_pinf_I8_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ Z2 @ X5 )
% 5.46/5.70 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(8)
% 5.46/5.70 thf(fact_3314_pinf_I8_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z2 @ X5 )
% 5.46/5.70 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(8)
% 5.46/5.70 thf(fact_3315_pinf_I8_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ Z2 @ X5 )
% 5.46/5.70 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(8)
% 5.46/5.70 thf(fact_3316_pinf_I8_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z2 @ X5 )
% 5.46/5.70 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(8)
% 5.46/5.70 thf(fact_3317_pinf_I8_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ Z2 @ X5 )
% 5.46/5.70 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(8)
% 5.46/5.70 thf(fact_3318_pinf_I6_J,axiom,
% 5.46/5.70 ! [T: real] :
% 5.46/5.70 ? [Z2: real] :
% 5.46/5.70 ! [X5: real] :
% 5.46/5.70 ( ( ord_less_real @ Z2 @ X5 )
% 5.46/5.70 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(6)
% 5.46/5.70 thf(fact_3319_pinf_I6_J,axiom,
% 5.46/5.70 ! [T: rat] :
% 5.46/5.70 ? [Z2: rat] :
% 5.46/5.70 ! [X5: rat] :
% 5.46/5.70 ( ( ord_less_rat @ Z2 @ X5 )
% 5.46/5.70 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(6)
% 5.46/5.70 thf(fact_3320_pinf_I6_J,axiom,
% 5.46/5.70 ! [T: num] :
% 5.46/5.70 ? [Z2: num] :
% 5.46/5.70 ! [X5: num] :
% 5.46/5.70 ( ( ord_less_num @ Z2 @ X5 )
% 5.46/5.70 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(6)
% 5.46/5.70 thf(fact_3321_pinf_I6_J,axiom,
% 5.46/5.70 ! [T: nat] :
% 5.46/5.70 ? [Z2: nat] :
% 5.46/5.70 ! [X5: nat] :
% 5.46/5.70 ( ( ord_less_nat @ Z2 @ X5 )
% 5.46/5.70 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(6)
% 5.46/5.70 thf(fact_3322_pinf_I6_J,axiom,
% 5.46/5.70 ! [T: int] :
% 5.46/5.70 ? [Z2: int] :
% 5.46/5.70 ! [X5: int] :
% 5.46/5.70 ( ( ord_less_int @ Z2 @ X5 )
% 5.46/5.70 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.46/5.70
% 5.46/5.70 % pinf(6)
% 5.46/5.70 thf(fact_3323_inf__period_I2_J,axiom,
% 5.46/5.70 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.46/5.70 ( ! [X3: real,K2: real] :
% 5.46/5.70 ( ( P @ X3 )
% 5.46/5.70 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ( ! [X3: real,K2: real] :
% 5.46/5.70 ( ( Q @ X3 )
% 5.46/5.70 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ! [X5: real,K4: real] :
% 5.46/5.70 ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.46/5.70 | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(2)
% 5.46/5.70 thf(fact_3324_inf__period_I2_J,axiom,
% 5.46/5.70 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.46/5.70 ( ! [X3: rat,K2: rat] :
% 5.46/5.70 ( ( P @ X3 )
% 5.46/5.70 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ( ! [X3: rat,K2: rat] :
% 5.46/5.70 ( ( Q @ X3 )
% 5.46/5.70 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ! [X5: rat,K4: rat] :
% 5.46/5.70 ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.46/5.70 | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(2)
% 5.46/5.70 thf(fact_3325_inf__period_I2_J,axiom,
% 5.46/5.70 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.46/5.70 ( ! [X3: int,K2: int] :
% 5.46/5.70 ( ( P @ X3 )
% 5.46/5.70 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ( ! [X3: int,K2: int] :
% 5.46/5.70 ( ( Q @ X3 )
% 5.46/5.70 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ! [X5: int,K4: int] :
% 5.46/5.70 ( ( ( P @ X5 )
% 5.46/5.70 | ( Q @ X5 ) )
% 5.46/5.70 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.46/5.70 | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(2)
% 5.46/5.70 thf(fact_3326_inf__period_I1_J,axiom,
% 5.46/5.70 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.46/5.70 ( ! [X3: real,K2: real] :
% 5.46/5.70 ( ( P @ X3 )
% 5.46/5.70 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ( ! [X3: real,K2: real] :
% 5.46/5.70 ( ( Q @ X3 )
% 5.46/5.70 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ! [X5: real,K4: real] :
% 5.46/5.70 ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.46/5.70 & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(1)
% 5.46/5.70 thf(fact_3327_inf__period_I1_J,axiom,
% 5.46/5.70 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.46/5.70 ( ! [X3: rat,K2: rat] :
% 5.46/5.70 ( ( P @ X3 )
% 5.46/5.70 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ( ! [X3: rat,K2: rat] :
% 5.46/5.70 ( ( Q @ X3 )
% 5.46/5.70 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ! [X5: rat,K4: rat] :
% 5.46/5.70 ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.46/5.70 & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(1)
% 5.46/5.70 thf(fact_3328_inf__period_I1_J,axiom,
% 5.46/5.70 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.46/5.70 ( ! [X3: int,K2: int] :
% 5.46/5.70 ( ( P @ X3 )
% 5.46/5.70 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ( ! [X3: int,K2: int] :
% 5.46/5.70 ( ( Q @ X3 )
% 5.46/5.70 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.46/5.70 => ! [X5: int,K4: int] :
% 5.46/5.70 ( ( ( P @ X5 )
% 5.46/5.70 & ( Q @ X5 ) )
% 5.46/5.70 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.46/5.70 & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % inf_period(1)
% 5.46/5.70 thf(fact_3329_dvd__productE,axiom,
% 5.46/5.70 ! [P2: nat,A: nat,B2: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ P2 @ ( times_times_nat @ A @ B2 ) )
% 5.46/5.70 => ~ ! [X3: nat,Y4: nat] :
% 5.46/5.70 ( ( P2
% 5.46/5.70 = ( times_times_nat @ X3 @ Y4 ) )
% 5.46/5.70 => ( ( dvd_dvd_nat @ X3 @ A )
% 5.46/5.70 => ~ ( dvd_dvd_nat @ Y4 @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % dvd_productE
% 5.46/5.70 thf(fact_3330_dvd__productE,axiom,
% 5.46/5.70 ! [P2: int,A: int,B2: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ P2 @ ( times_times_int @ A @ B2 ) )
% 5.46/5.70 => ~ ! [X3: int,Y4: int] :
% 5.46/5.70 ( ( P2
% 5.46/5.70 = ( times_times_int @ X3 @ Y4 ) )
% 5.46/5.70 => ( ( dvd_dvd_int @ X3 @ A )
% 5.46/5.70 => ~ ( dvd_dvd_int @ Y4 @ B2 ) ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % dvd_productE
% 5.46/5.70 thf(fact_3331_division__decomp,axiom,
% 5.46/5.70 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.70 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B2 @ C ) )
% 5.46/5.70 => ? [B6: nat,C4: nat] :
% 5.46/5.70 ( ( A
% 5.46/5.70 = ( times_times_nat @ B6 @ C4 ) )
% 5.46/5.70 & ( dvd_dvd_nat @ B6 @ B2 )
% 5.46/5.70 & ( dvd_dvd_nat @ C4 @ C ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % division_decomp
% 5.46/5.70 thf(fact_3332_division__decomp,axiom,
% 5.46/5.70 ! [A: int,B2: int,C: int] :
% 5.46/5.70 ( ( dvd_dvd_int @ A @ ( times_times_int @ B2 @ C ) )
% 5.46/5.70 => ? [B6: int,C4: int] :
% 5.46/5.70 ( ( A
% 5.46/5.70 = ( times_times_int @ B6 @ C4 ) )
% 5.46/5.70 & ( dvd_dvd_int @ B6 @ B2 )
% 5.46/5.70 & ( dvd_dvd_int @ C4 @ C ) ) ) ).
% 5.46/5.70
% 5.46/5.70 % division_decomp
% 5.46/5.70 thf(fact_3333_dvd__pos__nat,axiom,
% 5.46/5.70 ! [N: nat,M: nat] :
% 5.46/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.70 => ( ( dvd_dvd_nat @ M @ N )
% 5.46/5.71 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dvd_pos_nat
% 5.46/5.71 thf(fact_3334_gcd__nat__induct,axiom,
% 5.46/5.71 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.46/5.71 ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 5.46/5.71 => ( ! [M4: nat,N4: nat] :
% 5.46/5.71 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.46/5.71 => ( ( P @ N4 @ ( modulo_modulo_nat @ M4 @ N4 ) )
% 5.46/5.71 => ( P @ M4 @ N4 ) ) )
% 5.46/5.71 => ( P @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % gcd_nat_induct
% 5.46/5.71 thf(fact_3335_pinf_I9_J,axiom,
% 5.46/5.71 ! [D: code_integer,S: code_integer] :
% 5.46/5.71 ? [Z2: code_integer] :
% 5.46/5.71 ! [X5: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ Z2 @ X5 )
% 5.46/5.71 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) )
% 5.46/5.71 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pinf(9)
% 5.46/5.71 thf(fact_3336_pinf_I9_J,axiom,
% 5.46/5.71 ! [D: real,S: real] :
% 5.46/5.71 ? [Z2: real] :
% 5.46/5.71 ! [X5: real] :
% 5.46/5.71 ( ( ord_less_real @ Z2 @ X5 )
% 5.46/5.71 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) )
% 5.46/5.71 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pinf(9)
% 5.46/5.71 thf(fact_3337_pinf_I9_J,axiom,
% 5.46/5.71 ! [D: rat,S: rat] :
% 5.46/5.71 ? [Z2: rat] :
% 5.46/5.71 ! [X5: rat] :
% 5.46/5.71 ( ( ord_less_rat @ Z2 @ X5 )
% 5.46/5.71 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) )
% 5.46/5.71 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pinf(9)
% 5.46/5.71 thf(fact_3338_pinf_I9_J,axiom,
% 5.46/5.71 ! [D: nat,S: nat] :
% 5.46/5.71 ? [Z2: nat] :
% 5.46/5.71 ! [X5: nat] :
% 5.46/5.71 ( ( ord_less_nat @ Z2 @ X5 )
% 5.46/5.71 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) )
% 5.46/5.71 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pinf(9)
% 5.46/5.71 thf(fact_3339_pinf_I9_J,axiom,
% 5.46/5.71 ! [D: int,S: int] :
% 5.46/5.71 ? [Z2: int] :
% 5.46/5.71 ! [X5: int] :
% 5.46/5.71 ( ( ord_less_int @ Z2 @ X5 )
% 5.46/5.71 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) )
% 5.46/5.71 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pinf(9)
% 5.46/5.71 thf(fact_3340_pinf_I10_J,axiom,
% 5.46/5.71 ! [D: code_integer,S: code_integer] :
% 5.46/5.71 ? [Z2: code_integer] :
% 5.46/5.71 ! [X5: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ Z2 @ X5 )
% 5.46/5.71 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) )
% 5.46/5.71 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pinf(10)
% 5.46/5.71 thf(fact_3341_pinf_I10_J,axiom,
% 5.46/5.71 ! [D: real,S: real] :
% 5.46/5.71 ? [Z2: real] :
% 5.46/5.71 ! [X5: real] :
% 5.46/5.71 ( ( ord_less_real @ Z2 @ X5 )
% 5.46/5.71 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) )
% 5.46/5.71 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pinf(10)
% 5.46/5.71 thf(fact_3342_pinf_I10_J,axiom,
% 5.46/5.71 ! [D: rat,S: rat] :
% 5.46/5.71 ? [Z2: rat] :
% 5.46/5.71 ! [X5: rat] :
% 5.46/5.71 ( ( ord_less_rat @ Z2 @ X5 )
% 5.46/5.71 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) )
% 5.46/5.71 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pinf(10)
% 5.46/5.71 thf(fact_3343_pinf_I10_J,axiom,
% 5.46/5.71 ! [D: nat,S: nat] :
% 5.46/5.71 ? [Z2: nat] :
% 5.46/5.71 ! [X5: nat] :
% 5.46/5.71 ( ( ord_less_nat @ Z2 @ X5 )
% 5.46/5.71 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) )
% 5.46/5.71 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pinf(10)
% 5.46/5.71 thf(fact_3344_pinf_I10_J,axiom,
% 5.46/5.71 ! [D: int,S: int] :
% 5.46/5.71 ? [Z2: int] :
% 5.46/5.71 ! [X5: int] :
% 5.46/5.71 ( ( ord_less_int @ Z2 @ X5 )
% 5.46/5.71 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) )
% 5.46/5.71 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % pinf(10)
% 5.46/5.71 thf(fact_3345_minf_I9_J,axiom,
% 5.46/5.71 ! [D: code_integer,S: code_integer] :
% 5.46/5.71 ? [Z2: code_integer] :
% 5.46/5.71 ! [X5: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ X5 @ Z2 )
% 5.46/5.71 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) )
% 5.46/5.71 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minf(9)
% 5.46/5.71 thf(fact_3346_minf_I9_J,axiom,
% 5.46/5.71 ! [D: real,S: real] :
% 5.46/5.71 ? [Z2: real] :
% 5.46/5.71 ! [X5: real] :
% 5.46/5.71 ( ( ord_less_real @ X5 @ Z2 )
% 5.46/5.71 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) )
% 5.46/5.71 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minf(9)
% 5.46/5.71 thf(fact_3347_minf_I9_J,axiom,
% 5.46/5.71 ! [D: rat,S: rat] :
% 5.46/5.71 ? [Z2: rat] :
% 5.46/5.71 ! [X5: rat] :
% 5.46/5.71 ( ( ord_less_rat @ X5 @ Z2 )
% 5.46/5.71 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) )
% 5.46/5.71 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minf(9)
% 5.46/5.71 thf(fact_3348_minf_I9_J,axiom,
% 5.46/5.71 ! [D: nat,S: nat] :
% 5.46/5.71 ? [Z2: nat] :
% 5.46/5.71 ! [X5: nat] :
% 5.46/5.71 ( ( ord_less_nat @ X5 @ Z2 )
% 5.46/5.71 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) )
% 5.46/5.71 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minf(9)
% 5.46/5.71 thf(fact_3349_minf_I9_J,axiom,
% 5.46/5.71 ! [D: int,S: int] :
% 5.46/5.71 ? [Z2: int] :
% 5.46/5.71 ! [X5: int] :
% 5.46/5.71 ( ( ord_less_int @ X5 @ Z2 )
% 5.46/5.71 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) )
% 5.46/5.71 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minf(9)
% 5.46/5.71 thf(fact_3350_minf_I10_J,axiom,
% 5.46/5.71 ! [D: code_integer,S: code_integer] :
% 5.46/5.71 ? [Z2: code_integer] :
% 5.46/5.71 ! [X5: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ X5 @ Z2 )
% 5.46/5.71 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) )
% 5.46/5.71 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minf(10)
% 5.46/5.71 thf(fact_3351_minf_I10_J,axiom,
% 5.46/5.71 ! [D: real,S: real] :
% 5.46/5.71 ? [Z2: real] :
% 5.46/5.71 ! [X5: real] :
% 5.46/5.71 ( ( ord_less_real @ X5 @ Z2 )
% 5.46/5.71 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) )
% 5.46/5.71 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minf(10)
% 5.46/5.71 thf(fact_3352_minf_I10_J,axiom,
% 5.46/5.71 ! [D: rat,S: rat] :
% 5.46/5.71 ? [Z2: rat] :
% 5.46/5.71 ! [X5: rat] :
% 5.46/5.71 ( ( ord_less_rat @ X5 @ Z2 )
% 5.46/5.71 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) )
% 5.46/5.71 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minf(10)
% 5.46/5.71 thf(fact_3353_minf_I10_J,axiom,
% 5.46/5.71 ! [D: nat,S: nat] :
% 5.46/5.71 ? [Z2: nat] :
% 5.46/5.71 ! [X5: nat] :
% 5.46/5.71 ( ( ord_less_nat @ X5 @ Z2 )
% 5.46/5.71 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) )
% 5.46/5.71 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minf(10)
% 5.46/5.71 thf(fact_3354_minf_I10_J,axiom,
% 5.46/5.71 ! [D: int,S: int] :
% 5.46/5.71 ? [Z2: int] :
% 5.46/5.71 ! [X5: int] :
% 5.46/5.71 ( ( ord_less_int @ X5 @ Z2 )
% 5.46/5.71 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) )
% 5.46/5.71 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minf(10)
% 5.46/5.71 thf(fact_3355_bezout__lemma__nat,axiom,
% 5.46/5.71 ! [D: nat,A: nat,B2: nat,X4: nat,Y3: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ D @ A )
% 5.46/5.71 => ( ( dvd_dvd_nat @ D @ B2 )
% 5.46/5.71 => ( ( ( ( times_times_nat @ A @ X4 )
% 5.46/5.71 = ( plus_plus_nat @ ( times_times_nat @ B2 @ Y3 ) @ D ) )
% 5.46/5.71 | ( ( times_times_nat @ B2 @ X4 )
% 5.46/5.71 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) )
% 5.46/5.71 => ? [X3: nat,Y4: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ D @ A )
% 5.46/5.71 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B2 ) )
% 5.46/5.71 & ( ( ( times_times_nat @ A @ X3 )
% 5.46/5.71 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ Y4 ) @ D ) )
% 5.46/5.71 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B2 ) @ X3 )
% 5.46/5.71 = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % bezout_lemma_nat
% 5.46/5.71 thf(fact_3356_bezout__add__nat,axiom,
% 5.46/5.71 ! [A: nat,B2: nat] :
% 5.46/5.71 ? [D3: nat,X3: nat,Y4: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ D3 @ A )
% 5.46/5.71 & ( dvd_dvd_nat @ D3 @ B2 )
% 5.46/5.71 & ( ( ( times_times_nat @ A @ X3 )
% 5.46/5.71 = ( plus_plus_nat @ ( times_times_nat @ B2 @ Y4 ) @ D3 ) )
% 5.46/5.71 | ( ( times_times_nat @ B2 @ X3 )
% 5.46/5.71 = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % bezout_add_nat
% 5.46/5.71 thf(fact_3357_bezout__add__strong__nat,axiom,
% 5.46/5.71 ! [A: nat,B2: nat] :
% 5.46/5.71 ( ( A != zero_zero_nat )
% 5.46/5.71 => ? [D3: nat,X3: nat,Y4: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ D3 @ A )
% 5.46/5.71 & ( dvd_dvd_nat @ D3 @ B2 )
% 5.46/5.71 & ( ( times_times_nat @ A @ X3 )
% 5.46/5.71 = ( plus_plus_nat @ ( times_times_nat @ B2 @ Y4 ) @ D3 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % bezout_add_strong_nat
% 5.46/5.71 thf(fact_3358_bezout1__nat,axiom,
% 5.46/5.71 ! [A: nat,B2: nat] :
% 5.46/5.71 ? [D3: nat,X3: nat,Y4: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ D3 @ A )
% 5.46/5.71 & ( dvd_dvd_nat @ D3 @ B2 )
% 5.46/5.71 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B2 @ Y4 ) )
% 5.46/5.71 = D3 )
% 5.46/5.71 | ( ( minus_minus_nat @ ( times_times_nat @ B2 @ X3 ) @ ( times_times_nat @ A @ Y4 ) )
% 5.46/5.71 = D3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % bezout1_nat
% 5.46/5.71 thf(fact_3359_Bolzano,axiom,
% 5.46/5.71 ! [A: real,B2: real,P: real > real > $o] :
% 5.46/5.71 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.71 => ( ! [A5: real,B5: real,C3: real] :
% 5.46/5.71 ( ( P @ A5 @ B5 )
% 5.46/5.71 => ( ( P @ B5 @ C3 )
% 5.46/5.71 => ( ( ord_less_eq_real @ A5 @ B5 )
% 5.46/5.71 => ( ( ord_less_eq_real @ B5 @ C3 )
% 5.46/5.71 => ( P @ A5 @ C3 ) ) ) ) )
% 5.46/5.71 => ( ! [X3: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.71 => ( ( ord_less_eq_real @ X3 @ B2 )
% 5.46/5.71 => ? [D5: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.46/5.71 & ! [A5: real,B5: real] :
% 5.46/5.71 ( ( ( ord_less_eq_real @ A5 @ X3 )
% 5.46/5.71 & ( ord_less_eq_real @ X3 @ B5 )
% 5.46/5.71 & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D5 ) )
% 5.46/5.71 => ( P @ A5 @ B5 ) ) ) ) )
% 5.46/5.71 => ( P @ A @ B2 ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Bolzano
% 5.46/5.71 thf(fact_3360_mult__le__cancel__iff1,axiom,
% 5.46/5.71 ! [Z: real,X4: real,Y3: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y3 @ Z ) )
% 5.46/5.71 = ( ord_less_eq_real @ X4 @ Y3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_le_cancel_iff1
% 5.46/5.71 thf(fact_3361_mult__le__cancel__iff1,axiom,
% 5.46/5.71 ! [Z: rat,X4: rat,Y3: rat] :
% 5.46/5.71 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.46/5.71 => ( ( ord_less_eq_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ Y3 @ Z ) )
% 5.46/5.71 = ( ord_less_eq_rat @ X4 @ Y3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_le_cancel_iff1
% 5.46/5.71 thf(fact_3362_mult__le__cancel__iff1,axiom,
% 5.46/5.71 ! [Z: int,X4: int,Y3: int] :
% 5.46/5.71 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.71 => ( ( ord_less_eq_int @ ( times_times_int @ X4 @ Z ) @ ( times_times_int @ Y3 @ Z ) )
% 5.46/5.71 = ( ord_less_eq_int @ X4 @ Y3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_le_cancel_iff1
% 5.46/5.71 thf(fact_3363_mult__le__cancel__iff2,axiom,
% 5.46/5.71 ! [Z: real,X4: real,Y3: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.46/5.71 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X4 ) @ ( times_times_real @ Z @ Y3 ) )
% 5.46/5.71 = ( ord_less_eq_real @ X4 @ Y3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_le_cancel_iff2
% 5.46/5.71 thf(fact_3364_mult__le__cancel__iff2,axiom,
% 5.46/5.71 ! [Z: rat,X4: rat,Y3: rat] :
% 5.46/5.71 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.46/5.71 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X4 ) @ ( times_times_rat @ Z @ Y3 ) )
% 5.46/5.71 = ( ord_less_eq_rat @ X4 @ Y3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_le_cancel_iff2
% 5.46/5.71 thf(fact_3365_mult__le__cancel__iff2,axiom,
% 5.46/5.71 ! [Z: int,X4: int,Y3: int] :
% 5.46/5.71 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.71 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X4 ) @ ( times_times_int @ Z @ Y3 ) )
% 5.46/5.71 = ( ord_less_eq_int @ X4 @ Y3 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_le_cancel_iff2
% 5.46/5.71 thf(fact_3366_triangle__def,axiom,
% 5.46/5.71 ( nat_triangle
% 5.46/5.71 = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % triangle_def
% 5.46/5.71 thf(fact_3367_signed__take__bit__rec,axiom,
% 5.46/5.71 ( bit_ri6519982836138164636nteger
% 5.46/5.71 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % signed_take_bit_rec
% 5.46/5.71 thf(fact_3368_signed__take__bit__rec,axiom,
% 5.46/5.71 ( bit_ri631733984087533419it_int
% 5.46/5.71 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % signed_take_bit_rec
% 5.46/5.71 thf(fact_3369_verit__minus__simplify_I4_J,axiom,
% 5.46/5.71 ! [B2: real] :
% 5.46/5.71 ( ( uminus_uminus_real @ ( uminus_uminus_real @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % verit_minus_simplify(4)
% 5.46/5.71 thf(fact_3370_verit__minus__simplify_I4_J,axiom,
% 5.46/5.71 ! [B2: int] :
% 5.46/5.71 ( ( uminus_uminus_int @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % verit_minus_simplify(4)
% 5.46/5.71 thf(fact_3371_verit__minus__simplify_I4_J,axiom,
% 5.46/5.71 ! [B2: complex] :
% 5.46/5.71 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % verit_minus_simplify(4)
% 5.46/5.71 thf(fact_3372_verit__minus__simplify_I4_J,axiom,
% 5.46/5.71 ! [B2: code_integer] :
% 5.46/5.71 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % verit_minus_simplify(4)
% 5.46/5.71 thf(fact_3373_verit__minus__simplify_I4_J,axiom,
% 5.46/5.71 ! [B2: rat] :
% 5.46/5.71 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % verit_minus_simplify(4)
% 5.46/5.71 thf(fact_3374_add_Oinverse__inverse,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.71 = A ) ).
% 5.46/5.71
% 5.46/5.71 % add.inverse_inverse
% 5.46/5.71 thf(fact_3375_add_Oinverse__inverse,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.71 = A ) ).
% 5.46/5.71
% 5.46/5.71 % add.inverse_inverse
% 5.46/5.71 thf(fact_3376_add_Oinverse__inverse,axiom,
% 5.46/5.71 ! [A: complex] :
% 5.46/5.71 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.71 = A ) ).
% 5.46/5.71
% 5.46/5.71 % add.inverse_inverse
% 5.46/5.71 thf(fact_3377_add_Oinverse__inverse,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.71 = A ) ).
% 5.46/5.71
% 5.46/5.71 % add.inverse_inverse
% 5.46/5.71 thf(fact_3378_add_Oinverse__inverse,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.71 = A ) ).
% 5.46/5.71
% 5.46/5.71 % add.inverse_inverse
% 5.46/5.71 thf(fact_3379_neg__equal__iff__equal,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( ( uminus_uminus_real @ A )
% 5.46/5.71 = ( uminus_uminus_real @ B2 ) )
% 5.46/5.71 = ( A = B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_iff_equal
% 5.46/5.71 thf(fact_3380_neg__equal__iff__equal,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( ( uminus_uminus_int @ A )
% 5.46/5.71 = ( uminus_uminus_int @ B2 ) )
% 5.46/5.71 = ( A = B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_iff_equal
% 5.46/5.71 thf(fact_3381_neg__equal__iff__equal,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.71 = ( A = B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_iff_equal
% 5.46/5.71 thf(fact_3382_neg__equal__iff__equal,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.71 = ( A = B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_iff_equal
% 5.46/5.71 thf(fact_3383_neg__equal__iff__equal,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( ( uminus_uminus_rat @ A )
% 5.46/5.71 = ( uminus_uminus_rat @ B2 ) )
% 5.46/5.71 = ( A = B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_iff_equal
% 5.46/5.71 thf(fact_3384_neg__le__iff__le,axiom,
% 5.46/5.71 ! [B2: real,A: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) )
% 5.46/5.71 = ( ord_less_eq_real @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_le_iff_le
% 5.46/5.71 thf(fact_3385_neg__le__iff__le,axiom,
% 5.46/5.71 ! [B2: code_integer,A: code_integer] :
% 5.46/5.71 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B2 ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.71 = ( ord_le3102999989581377725nteger @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_le_iff_le
% 5.46/5.71 thf(fact_3386_neg__le__iff__le,axiom,
% 5.46/5.71 ! [B2: rat,A: rat] :
% 5.46/5.71 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B2 ) @ ( uminus_uminus_rat @ A ) )
% 5.46/5.71 = ( ord_less_eq_rat @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_le_iff_le
% 5.46/5.71 thf(fact_3387_neg__le__iff__le,axiom,
% 5.46/5.71 ! [B2: int,A: int] :
% 5.46/5.71 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
% 5.46/5.71 = ( ord_less_eq_int @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_le_iff_le
% 5.46/5.71 thf(fact_3388_add_Oinverse__neutral,axiom,
% 5.46/5.71 ( ( uminus_uminus_real @ zero_zero_real )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % add.inverse_neutral
% 5.46/5.71 thf(fact_3389_add_Oinverse__neutral,axiom,
% 5.46/5.71 ( ( uminus_uminus_int @ zero_zero_int )
% 5.46/5.71 = zero_zero_int ) ).
% 5.46/5.71
% 5.46/5.71 % add.inverse_neutral
% 5.46/5.71 thf(fact_3390_add_Oinverse__neutral,axiom,
% 5.46/5.71 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.46/5.71 = zero_zero_complex ) ).
% 5.46/5.71
% 5.46/5.71 % add.inverse_neutral
% 5.46/5.71 thf(fact_3391_add_Oinverse__neutral,axiom,
% 5.46/5.71 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.46/5.71 = zero_z3403309356797280102nteger ) ).
% 5.46/5.71
% 5.46/5.71 % add.inverse_neutral
% 5.46/5.71 thf(fact_3392_add_Oinverse__neutral,axiom,
% 5.46/5.71 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.46/5.71 = zero_zero_rat ) ).
% 5.46/5.71
% 5.46/5.71 % add.inverse_neutral
% 5.46/5.71 thf(fact_3393_neg__0__equal__iff__equal,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( zero_zero_real
% 5.46/5.71 = ( uminus_uminus_real @ A ) )
% 5.46/5.71 = ( zero_zero_real = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_equal_iff_equal
% 5.46/5.71 thf(fact_3394_neg__0__equal__iff__equal,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( zero_zero_int
% 5.46/5.71 = ( uminus_uminus_int @ A ) )
% 5.46/5.71 = ( zero_zero_int = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_equal_iff_equal
% 5.46/5.71 thf(fact_3395_neg__0__equal__iff__equal,axiom,
% 5.46/5.71 ! [A: complex] :
% 5.46/5.71 ( ( zero_zero_complex
% 5.46/5.71 = ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.71 = ( zero_zero_complex = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_equal_iff_equal
% 5.46/5.71 thf(fact_3396_neg__0__equal__iff__equal,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( zero_z3403309356797280102nteger
% 5.46/5.71 = ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.71 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_equal_iff_equal
% 5.46/5.71 thf(fact_3397_neg__0__equal__iff__equal,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( zero_zero_rat
% 5.46/5.71 = ( uminus_uminus_rat @ A ) )
% 5.46/5.71 = ( zero_zero_rat = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_equal_iff_equal
% 5.46/5.71 thf(fact_3398_neg__equal__0__iff__equal,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( ( uminus_uminus_real @ A )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 = ( A = zero_zero_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_0_iff_equal
% 5.46/5.71 thf(fact_3399_neg__equal__0__iff__equal,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( ( uminus_uminus_int @ A )
% 5.46/5.71 = zero_zero_int )
% 5.46/5.71 = ( A = zero_zero_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_0_iff_equal
% 5.46/5.71 thf(fact_3400_neg__equal__0__iff__equal,axiom,
% 5.46/5.71 ! [A: complex] :
% 5.46/5.71 ( ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.71 = zero_zero_complex )
% 5.46/5.71 = ( A = zero_zero_complex ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_0_iff_equal
% 5.46/5.71 thf(fact_3401_neg__equal__0__iff__equal,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.71 = zero_z3403309356797280102nteger )
% 5.46/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_0_iff_equal
% 5.46/5.71 thf(fact_3402_neg__equal__0__iff__equal,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( ( uminus_uminus_rat @ A )
% 5.46/5.71 = zero_zero_rat )
% 5.46/5.71 = ( A = zero_zero_rat ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_0_iff_equal
% 5.46/5.71 thf(fact_3403_equal__neg__zero,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( uminus_uminus_real @ A ) )
% 5.46/5.71 = ( A = zero_zero_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % equal_neg_zero
% 5.46/5.71 thf(fact_3404_equal__neg__zero,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( uminus_uminus_int @ A ) )
% 5.46/5.71 = ( A = zero_zero_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % equal_neg_zero
% 5.46/5.71 thf(fact_3405_equal__neg__zero,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.71
% 5.46/5.71 % equal_neg_zero
% 5.46/5.71 thf(fact_3406_equal__neg__zero,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( uminus_uminus_rat @ A ) )
% 5.46/5.71 = ( A = zero_zero_rat ) ) ).
% 5.46/5.71
% 5.46/5.71 % equal_neg_zero
% 5.46/5.71 thf(fact_3407_neg__equal__zero,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( ( uminus_uminus_real @ A )
% 5.46/5.71 = A )
% 5.46/5.71 = ( A = zero_zero_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_zero
% 5.46/5.71 thf(fact_3408_neg__equal__zero,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( ( uminus_uminus_int @ A )
% 5.46/5.71 = A )
% 5.46/5.71 = ( A = zero_zero_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_zero
% 5.46/5.71 thf(fact_3409_neg__equal__zero,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.71 = A )
% 5.46/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_zero
% 5.46/5.71 thf(fact_3410_neg__equal__zero,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( ( uminus_uminus_rat @ A )
% 5.46/5.71 = A )
% 5.46/5.71 = ( A = zero_zero_rat ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_equal_zero
% 5.46/5.71 thf(fact_3411_neg__less__iff__less,axiom,
% 5.46/5.71 ! [B2: real,A: real] :
% 5.46/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) )
% 5.46/5.71 = ( ord_less_real @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_iff_less
% 5.46/5.71 thf(fact_3412_neg__less__iff__less,axiom,
% 5.46/5.71 ! [B2: int,A: int] :
% 5.46/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
% 5.46/5.71 = ( ord_less_int @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_iff_less
% 5.46/5.71 thf(fact_3413_neg__less__iff__less,axiom,
% 5.46/5.71 ! [B2: code_integer,A: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B2 ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.71 = ( ord_le6747313008572928689nteger @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_iff_less
% 5.46/5.71 thf(fact_3414_neg__less__iff__less,axiom,
% 5.46/5.71 ! [B2: rat,A: rat] :
% 5.46/5.71 ( ( ord_less_rat @ ( uminus_uminus_rat @ B2 ) @ ( uminus_uminus_rat @ A ) )
% 5.46/5.71 = ( ord_less_rat @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_iff_less
% 5.46/5.71 thf(fact_3415_neg__numeral__eq__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.71 = ( M = N ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_eq_iff
% 5.46/5.71 thf(fact_3416_neg__numeral__eq__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.46/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.71 = ( M = N ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_eq_iff
% 5.46/5.71 thf(fact_3417_neg__numeral__eq__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.71 = ( M = N ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_eq_iff
% 5.46/5.71 thf(fact_3418_neg__numeral__eq__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.71 = ( M = N ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_eq_iff
% 5.46/5.71 thf(fact_3419_neg__numeral__eq__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.46/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.71 = ( M = N ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_eq_iff
% 5.46/5.71 thf(fact_3420_mult__minus__right,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( times_times_real @ A @ ( uminus_uminus_real @ B2 ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( times_times_real @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus_right
% 5.46/5.71 thf(fact_3421_mult__minus__right,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( times_times_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.71 = ( uminus_uminus_int @ ( times_times_int @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus_right
% 5.46/5.71 thf(fact_3422_mult__minus__right,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus_right
% 5.46/5.71 thf(fact_3423_mult__minus__right,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus_right
% 5.46/5.71 thf(fact_3424_mult__minus__right,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B2 ) )
% 5.46/5.71 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus_right
% 5.46/5.71 thf(fact_3425_minus__mult__minus,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B2 ) )
% 5.46/5.71 = ( times_times_real @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_mult_minus
% 5.46/5.71 thf(fact_3426_minus__mult__minus,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.71 = ( times_times_int @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_mult_minus
% 5.46/5.71 thf(fact_3427_minus__mult__minus,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.71 = ( times_times_complex @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_mult_minus
% 5.46/5.71 thf(fact_3428_minus__mult__minus,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.71 = ( times_3573771949741848930nteger @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_mult_minus
% 5.46/5.71 thf(fact_3429_minus__mult__minus,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B2 ) )
% 5.46/5.71 = ( times_times_rat @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_mult_minus
% 5.46/5.71 thf(fact_3430_mult__minus__left,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B2 )
% 5.46/5.71 = ( uminus_uminus_real @ ( times_times_real @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus_left
% 5.46/5.71 thf(fact_3431_mult__minus__left,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.71 = ( uminus_uminus_int @ ( times_times_int @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus_left
% 5.46/5.71 thf(fact_3432_mult__minus__left,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B2 )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus_left
% 5.46/5.71 thf(fact_3433_mult__minus__left,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus_left
% 5.46/5.71 thf(fact_3434_mult__minus__left,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B2 )
% 5.46/5.71 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus_left
% 5.46/5.71 thf(fact_3435_minus__add__distrib,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B2 ) )
% 5.46/5.71 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_add_distrib
% 5.46/5.71 thf(fact_3436_minus__add__distrib,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B2 ) )
% 5.46/5.71 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_add_distrib
% 5.46/5.71 thf(fact_3437_minus__add__distrib,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B2 ) )
% 5.46/5.71 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_add_distrib
% 5.46/5.71 thf(fact_3438_minus__add__distrib,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) )
% 5.46/5.71 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_add_distrib
% 5.46/5.71 thf(fact_3439_minus__add__distrib,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B2 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_add_distrib
% 5.46/5.71 thf(fact_3440_minus__add__cancel,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % minus_add_cancel
% 5.46/5.71 thf(fact_3441_minus__add__cancel,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % minus_add_cancel
% 5.46/5.71 thf(fact_3442_minus__add__cancel,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % minus_add_cancel
% 5.46/5.71 thf(fact_3443_minus__add__cancel,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % minus_add_cancel
% 5.46/5.71 thf(fact_3444_minus__add__cancel,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % minus_add_cancel
% 5.46/5.71 thf(fact_3445_add__minus__cancel,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % add_minus_cancel
% 5.46/5.71 thf(fact_3446_add__minus__cancel,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % add_minus_cancel
% 5.46/5.71 thf(fact_3447_add__minus__cancel,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % add_minus_cancel
% 5.46/5.71 thf(fact_3448_add__minus__cancel,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % add_minus_cancel
% 5.46/5.71 thf(fact_3449_add__minus__cancel,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B2 ) )
% 5.46/5.71 = B2 ) ).
% 5.46/5.71
% 5.46/5.71 % add_minus_cancel
% 5.46/5.71 thf(fact_3450_minus__diff__eq,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B2 ) )
% 5.46/5.71 = ( minus_minus_real @ B2 @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_diff_eq
% 5.46/5.71 thf(fact_3451_minus__diff__eq,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B2 ) )
% 5.46/5.71 = ( minus_minus_int @ B2 @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_diff_eq
% 5.46/5.71 thf(fact_3452_minus__diff__eq,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B2 ) )
% 5.46/5.71 = ( minus_minus_complex @ B2 @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_diff_eq
% 5.46/5.71 thf(fact_3453_minus__diff__eq,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B2 ) )
% 5.46/5.71 = ( minus_8373710615458151222nteger @ B2 @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_diff_eq
% 5.46/5.71 thf(fact_3454_minus__diff__eq,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B2 ) )
% 5.46/5.71 = ( minus_minus_rat @ B2 @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_diff_eq
% 5.46/5.71 thf(fact_3455_div__minus__minus,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.71 = ( divide_divide_int @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % div_minus_minus
% 5.46/5.71 thf(fact_3456_div__minus__minus,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.71 = ( divide6298287555418463151nteger @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % div_minus_minus
% 5.46/5.71 thf(fact_3457_dvd__minus__iff,axiom,
% 5.46/5.71 ! [X4: real,Y3: real] :
% 5.46/5.71 ( ( dvd_dvd_real @ X4 @ ( uminus_uminus_real @ Y3 ) )
% 5.46/5.71 = ( dvd_dvd_real @ X4 @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % dvd_minus_iff
% 5.46/5.71 thf(fact_3458_dvd__minus__iff,axiom,
% 5.46/5.71 ! [X4: int,Y3: int] :
% 5.46/5.71 ( ( dvd_dvd_int @ X4 @ ( uminus_uminus_int @ Y3 ) )
% 5.46/5.71 = ( dvd_dvd_int @ X4 @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % dvd_minus_iff
% 5.46/5.71 thf(fact_3459_dvd__minus__iff,axiom,
% 5.46/5.71 ! [X4: complex,Y3: complex] :
% 5.46/5.71 ( ( dvd_dvd_complex @ X4 @ ( uminus1482373934393186551omplex @ Y3 ) )
% 5.46/5.71 = ( dvd_dvd_complex @ X4 @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % dvd_minus_iff
% 5.46/5.71 thf(fact_3460_dvd__minus__iff,axiom,
% 5.46/5.71 ! [X4: code_integer,Y3: code_integer] :
% 5.46/5.71 ( ( dvd_dvd_Code_integer @ X4 @ ( uminus1351360451143612070nteger @ Y3 ) )
% 5.46/5.71 = ( dvd_dvd_Code_integer @ X4 @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % dvd_minus_iff
% 5.46/5.71 thf(fact_3461_dvd__minus__iff,axiom,
% 5.46/5.71 ! [X4: rat,Y3: rat] :
% 5.46/5.71 ( ( dvd_dvd_rat @ X4 @ ( uminus_uminus_rat @ Y3 ) )
% 5.46/5.71 = ( dvd_dvd_rat @ X4 @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % dvd_minus_iff
% 5.46/5.71 thf(fact_3462_minus__dvd__iff,axiom,
% 5.46/5.71 ! [X4: real,Y3: real] :
% 5.46/5.71 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X4 ) @ Y3 )
% 5.46/5.71 = ( dvd_dvd_real @ X4 @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_dvd_iff
% 5.46/5.71 thf(fact_3463_minus__dvd__iff,axiom,
% 5.46/5.71 ! [X4: int,Y3: int] :
% 5.46/5.71 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X4 ) @ Y3 )
% 5.46/5.71 = ( dvd_dvd_int @ X4 @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_dvd_iff
% 5.46/5.71 thf(fact_3464_minus__dvd__iff,axiom,
% 5.46/5.71 ! [X4: complex,Y3: complex] :
% 5.46/5.71 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X4 ) @ Y3 )
% 5.46/5.71 = ( dvd_dvd_complex @ X4 @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_dvd_iff
% 5.46/5.71 thf(fact_3465_minus__dvd__iff,axiom,
% 5.46/5.71 ! [X4: code_integer,Y3: code_integer] :
% 5.46/5.71 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X4 ) @ Y3 )
% 5.46/5.71 = ( dvd_dvd_Code_integer @ X4 @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_dvd_iff
% 5.46/5.71 thf(fact_3466_minus__dvd__iff,axiom,
% 5.46/5.71 ! [X4: rat,Y3: rat] :
% 5.46/5.71 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X4 ) @ Y3 )
% 5.46/5.71 = ( dvd_dvd_rat @ X4 @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_dvd_iff
% 5.46/5.71 thf(fact_3467_mod__minus__minus,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.71 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mod_minus_minus
% 5.46/5.71 thf(fact_3468_mod__minus__minus,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mod_minus_minus
% 5.46/5.71 thf(fact_3469_real__add__minus__iff,axiom,
% 5.46/5.71 ! [X4: real,A: real] :
% 5.46/5.71 ( ( ( plus_plus_real @ X4 @ ( uminus_uminus_real @ A ) )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 = ( X4 = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % real_add_minus_iff
% 5.46/5.71 thf(fact_3470_neg__less__eq__nonneg,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.46/5.71 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_eq_nonneg
% 5.46/5.71 thf(fact_3471_neg__less__eq__nonneg,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.46/5.71 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_eq_nonneg
% 5.46/5.71 thf(fact_3472_neg__less__eq__nonneg,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.46/5.71 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_eq_nonneg
% 5.46/5.71 thf(fact_3473_neg__less__eq__nonneg,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.46/5.71 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_eq_nonneg
% 5.46/5.71 thf(fact_3474_less__eq__neg__nonpos,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.46/5.71 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_eq_neg_nonpos
% 5.46/5.71 thf(fact_3475_less__eq__neg__nonpos,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.71 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_eq_neg_nonpos
% 5.46/5.71 thf(fact_3476_less__eq__neg__nonpos,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.46/5.71 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_eq_neg_nonpos
% 5.46/5.71 thf(fact_3477_less__eq__neg__nonpos,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.46/5.71 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_eq_neg_nonpos
% 5.46/5.71 thf(fact_3478_neg__le__0__iff__le,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.46/5.71 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_le_0_iff_le
% 5.46/5.71 thf(fact_3479_neg__le__0__iff__le,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.46/5.71 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_le_0_iff_le
% 5.46/5.71 thf(fact_3480_neg__le__0__iff__le,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.46/5.71 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_le_0_iff_le
% 5.46/5.71 thf(fact_3481_neg__le__0__iff__le,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.46/5.71 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_le_0_iff_le
% 5.46/5.71 thf(fact_3482_neg__0__le__iff__le,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.71 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_le_iff_le
% 5.46/5.71 thf(fact_3483_neg__0__le__iff__le,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.71 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_le_iff_le
% 5.46/5.71 thf(fact_3484_neg__0__le__iff__le,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.71 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_le_iff_le
% 5.46/5.71 thf(fact_3485_neg__0__le__iff__le,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.71 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_le_iff_le
% 5.46/5.71 thf(fact_3486_neg__less__0__iff__less,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.46/5.71 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_0_iff_less
% 5.46/5.71 thf(fact_3487_neg__less__0__iff__less,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.46/5.71 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_0_iff_less
% 5.46/5.71 thf(fact_3488_neg__less__0__iff__less,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.46/5.71 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_0_iff_less
% 5.46/5.71 thf(fact_3489_neg__less__0__iff__less,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.46/5.71 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_0_iff_less
% 5.46/5.71 thf(fact_3490_neg__0__less__iff__less,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.71 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_less_iff_less
% 5.46/5.71 thf(fact_3491_neg__0__less__iff__less,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.71 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_less_iff_less
% 5.46/5.71 thf(fact_3492_neg__0__less__iff__less,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.71 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_less_iff_less
% 5.46/5.71 thf(fact_3493_neg__0__less__iff__less,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.71 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_0_less_iff_less
% 5.46/5.71 thf(fact_3494_neg__less__pos,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.46/5.71 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_pos
% 5.46/5.71 thf(fact_3495_neg__less__pos,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.46/5.71 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_pos
% 5.46/5.71 thf(fact_3496_neg__less__pos,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.46/5.71 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_pos
% 5.46/5.71 thf(fact_3497_neg__less__pos,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.46/5.71 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_less_pos
% 5.46/5.71 thf(fact_3498_less__neg__neg,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.46/5.71 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_neg_neg
% 5.46/5.71 thf(fact_3499_less__neg__neg,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.46/5.71 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_neg_neg
% 5.46/5.71 thf(fact_3500_less__neg__neg,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.71 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_neg_neg
% 5.46/5.71 thf(fact_3501_less__neg__neg,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.46/5.71 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_neg_neg
% 5.46/5.71 thf(fact_3502_ab__left__minus,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % ab_left_minus
% 5.46/5.71 thf(fact_3503_ab__left__minus,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.46/5.71 = zero_zero_int ) ).
% 5.46/5.71
% 5.46/5.71 % ab_left_minus
% 5.46/5.71 thf(fact_3504_ab__left__minus,axiom,
% 5.46/5.71 ! [A: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.46/5.71 = zero_zero_complex ) ).
% 5.46/5.71
% 5.46/5.71 % ab_left_minus
% 5.46/5.71 thf(fact_3505_ab__left__minus,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.46/5.71 = zero_z3403309356797280102nteger ) ).
% 5.46/5.71
% 5.46/5.71 % ab_left_minus
% 5.46/5.71 thf(fact_3506_ab__left__minus,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.46/5.71 = zero_zero_rat ) ).
% 5.46/5.71
% 5.46/5.71 % ab_left_minus
% 5.46/5.71 thf(fact_3507_add_Oright__inverse,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % add.right_inverse
% 5.46/5.71 thf(fact_3508_add_Oright__inverse,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.46/5.71 = zero_zero_int ) ).
% 5.46/5.71
% 5.46/5.71 % add.right_inverse
% 5.46/5.71 thf(fact_3509_add_Oright__inverse,axiom,
% 5.46/5.71 ! [A: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.71 = zero_zero_complex ) ).
% 5.46/5.71
% 5.46/5.71 % add.right_inverse
% 5.46/5.71 thf(fact_3510_add_Oright__inverse,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.71 = zero_z3403309356797280102nteger ) ).
% 5.46/5.71
% 5.46/5.71 % add.right_inverse
% 5.46/5.71 thf(fact_3511_add_Oright__inverse,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.46/5.71 = zero_zero_rat ) ).
% 5.46/5.71
% 5.46/5.71 % add.right_inverse
% 5.46/5.71 thf(fact_3512_diff__0,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.46/5.71 = ( uminus_uminus_real @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_0
% 5.46/5.71 thf(fact_3513_diff__0,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.46/5.71 = ( uminus_uminus_int @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_0
% 5.46/5.71 thf(fact_3514_diff__0,axiom,
% 5.46/5.71 ! [A: complex] :
% 5.46/5.71 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_0
% 5.46/5.71 thf(fact_3515_diff__0,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_0
% 5.46/5.71 thf(fact_3516_diff__0,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.46/5.71 = ( uminus_uminus_rat @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_0
% 5.46/5.71 thf(fact_3517_verit__minus__simplify_I3_J,axiom,
% 5.46/5.71 ! [B2: real] :
% 5.46/5.71 ( ( minus_minus_real @ zero_zero_real @ B2 )
% 5.46/5.71 = ( uminus_uminus_real @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_minus_simplify(3)
% 5.46/5.71 thf(fact_3518_verit__minus__simplify_I3_J,axiom,
% 5.46/5.71 ! [B2: int] :
% 5.46/5.71 ( ( minus_minus_int @ zero_zero_int @ B2 )
% 5.46/5.71 = ( uminus_uminus_int @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_minus_simplify(3)
% 5.46/5.71 thf(fact_3519_verit__minus__simplify_I3_J,axiom,
% 5.46/5.71 ! [B2: complex] :
% 5.46/5.71 ( ( minus_minus_complex @ zero_zero_complex @ B2 )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_minus_simplify(3)
% 5.46/5.71 thf(fact_3520_verit__minus__simplify_I3_J,axiom,
% 5.46/5.71 ! [B2: code_integer] :
% 5.46/5.71 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_minus_simplify(3)
% 5.46/5.71 thf(fact_3521_verit__minus__simplify_I3_J,axiom,
% 5.46/5.71 ! [B2: rat] :
% 5.46/5.71 ( ( minus_minus_rat @ zero_zero_rat @ B2 )
% 5.46/5.71 = ( uminus_uminus_rat @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_minus_simplify(3)
% 5.46/5.71 thf(fact_3522_add__neg__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_simps(3)
% 5.46/5.71 thf(fact_3523_add__neg__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.71 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_simps(3)
% 5.46/5.71 thf(fact_3524_add__neg__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_simps(3)
% 5.46/5.71 thf(fact_3525_add__neg__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_simps(3)
% 5.46/5.71 thf(fact_3526_add__neg__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.71 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_simps(3)
% 5.46/5.71 thf(fact_3527_mult__minus1,axiom,
% 5.46/5.71 ! [Z: real] :
% 5.46/5.71 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.46/5.71 = ( uminus_uminus_real @ Z ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus1
% 5.46/5.71 thf(fact_3528_mult__minus1,axiom,
% 5.46/5.71 ! [Z: int] :
% 5.46/5.71 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.46/5.71 = ( uminus_uminus_int @ Z ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus1
% 5.46/5.71 thf(fact_3529_mult__minus1,axiom,
% 5.46/5.71 ! [Z: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus1
% 5.46/5.71 thf(fact_3530_mult__minus1,axiom,
% 5.46/5.71 ! [Z: code_integer] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus1
% 5.46/5.71 thf(fact_3531_mult__minus1,axiom,
% 5.46/5.71 ! [Z: rat] :
% 5.46/5.71 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.46/5.71 = ( uminus_uminus_rat @ Z ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus1
% 5.46/5.71 thf(fact_3532_mult__minus1__right,axiom,
% 5.46/5.71 ! [Z: real] :
% 5.46/5.71 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.71 = ( uminus_uminus_real @ Z ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus1_right
% 5.46/5.71 thf(fact_3533_mult__minus1__right,axiom,
% 5.46/5.71 ! [Z: int] :
% 5.46/5.71 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = ( uminus_uminus_int @ Z ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus1_right
% 5.46/5.71 thf(fact_3534_mult__minus1__right,axiom,
% 5.46/5.71 ! [Z: complex] :
% 5.46/5.71 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus1_right
% 5.46/5.71 thf(fact_3535_mult__minus1__right,axiom,
% 5.46/5.71 ! [Z: code_integer] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus1_right
% 5.46/5.71 thf(fact_3536_mult__minus1__right,axiom,
% 5.46/5.71 ! [Z: rat] :
% 5.46/5.71 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.71 = ( uminus_uminus_rat @ Z ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_minus1_right
% 5.46/5.71 thf(fact_3537_uminus__add__conv__diff,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B2 )
% 5.46/5.71 = ( minus_minus_real @ B2 @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % uminus_add_conv_diff
% 5.46/5.71 thf(fact_3538_uminus__add__conv__diff,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.71 = ( minus_minus_int @ B2 @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % uminus_add_conv_diff
% 5.46/5.71 thf(fact_3539_uminus__add__conv__diff,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B2 )
% 5.46/5.71 = ( minus_minus_complex @ B2 @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % uminus_add_conv_diff
% 5.46/5.71 thf(fact_3540_uminus__add__conv__diff,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 )
% 5.46/5.71 = ( minus_8373710615458151222nteger @ B2 @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % uminus_add_conv_diff
% 5.46/5.71 thf(fact_3541_uminus__add__conv__diff,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B2 )
% 5.46/5.71 = ( minus_minus_rat @ B2 @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % uminus_add_conv_diff
% 5.46/5.71 thf(fact_3542_diff__minus__eq__add,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B2 ) )
% 5.46/5.71 = ( plus_plus_real @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_minus_eq_add
% 5.46/5.71 thf(fact_3543_diff__minus__eq__add,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.71 = ( plus_plus_int @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_minus_eq_add
% 5.46/5.71 thf(fact_3544_diff__minus__eq__add,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.71 = ( plus_plus_complex @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_minus_eq_add
% 5.46/5.71 thf(fact_3545_diff__minus__eq__add,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.71 = ( plus_p5714425477246183910nteger @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_minus_eq_add
% 5.46/5.71 thf(fact_3546_diff__minus__eq__add,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B2 ) )
% 5.46/5.71 = ( plus_plus_rat @ A @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_minus_eq_add
% 5.46/5.71 thf(fact_3547_div__minus1__right,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = ( uminus_uminus_int @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % div_minus1_right
% 5.46/5.71 thf(fact_3548_div__minus1__right,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % div_minus1_right
% 5.46/5.71 thf(fact_3549_divide__minus1,axiom,
% 5.46/5.71 ! [X4: real] :
% 5.46/5.71 ( ( divide_divide_real @ X4 @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.71 = ( uminus_uminus_real @ X4 ) ) ).
% 5.46/5.71
% 5.46/5.71 % divide_minus1
% 5.46/5.71 thf(fact_3550_divide__minus1,axiom,
% 5.46/5.71 ! [X4: complex] :
% 5.46/5.71 ( ( divide1717551699836669952omplex @ X4 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ X4 ) ) ).
% 5.46/5.71
% 5.46/5.71 % divide_minus1
% 5.46/5.71 thf(fact_3551_divide__minus1,axiom,
% 5.46/5.71 ! [X4: rat] :
% 5.46/5.71 ( ( divide_divide_rat @ X4 @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.71 = ( uminus_uminus_rat @ X4 ) ) ).
% 5.46/5.71
% 5.46/5.71 % divide_minus1
% 5.46/5.71 thf(fact_3552_minus__mod__self1,axiom,
% 5.46/5.71 ! [B2: int,A: int] :
% 5.46/5.71 ( ( modulo_modulo_int @ ( minus_minus_int @ B2 @ A ) @ B2 )
% 5.46/5.71 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_mod_self1
% 5.46/5.71 thf(fact_3553_minus__mod__self1,axiom,
% 5.46/5.71 ! [B2: code_integer,A: code_integer] :
% 5.46/5.71 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B2 @ A ) @ B2 )
% 5.46/5.71 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_mod_self1
% 5.46/5.71 thf(fact_3554_signed__take__bit__of__minus__1,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.71
% 5.46/5.71 % signed_take_bit_of_minus_1
% 5.46/5.71 thf(fact_3555_signed__take__bit__of__minus__1,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % signed_take_bit_of_minus_1
% 5.46/5.71 thf(fact_3556_dbl__simps_I1_J,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dbl_simps(1)
% 5.46/5.71 thf(fact_3557_dbl__simps_I1_J,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.71 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dbl_simps(1)
% 5.46/5.71 thf(fact_3558_dbl__simps_I1_J,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dbl_simps(1)
% 5.46/5.71 thf(fact_3559_dbl__simps_I1_J,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dbl_simps(1)
% 5.46/5.71 thf(fact_3560_dbl__simps_I1_J,axiom,
% 5.46/5.71 ! [K: num] :
% 5.46/5.71 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.46/5.71 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dbl_simps(1)
% 5.46/5.71 thf(fact_3561_triangle__Suc,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( nat_triangle @ ( suc @ N ) )
% 5.46/5.71 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % triangle_Suc
% 5.46/5.71 thf(fact_3562_add__neg__numeral__special_I8_J,axiom,
% 5.46/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(8)
% 5.46/5.71 thf(fact_3563_add__neg__numeral__special_I8_J,axiom,
% 5.46/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.46/5.71 = zero_zero_int ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(8)
% 5.46/5.71 thf(fact_3564_add__neg__numeral__special_I8_J,axiom,
% 5.46/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.46/5.71 = zero_zero_complex ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(8)
% 5.46/5.71 thf(fact_3565_add__neg__numeral__special_I8_J,axiom,
% 5.46/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.46/5.71 = zero_z3403309356797280102nteger ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(8)
% 5.46/5.71 thf(fact_3566_add__neg__numeral__special_I8_J,axiom,
% 5.46/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.46/5.71 = zero_zero_rat ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(8)
% 5.46/5.71 thf(fact_3567_add__neg__numeral__special_I7_J,axiom,
% 5.46/5.71 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(7)
% 5.46/5.71 thf(fact_3568_add__neg__numeral__special_I7_J,axiom,
% 5.46/5.71 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = zero_zero_int ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(7)
% 5.46/5.71 thf(fact_3569_add__neg__numeral__special_I7_J,axiom,
% 5.46/5.71 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.71 = zero_zero_complex ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(7)
% 5.46/5.71 thf(fact_3570_add__neg__numeral__special_I7_J,axiom,
% 5.46/5.71 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = zero_z3403309356797280102nteger ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(7)
% 5.46/5.71 thf(fact_3571_add__neg__numeral__special_I7_J,axiom,
% 5.46/5.71 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.71 = zero_zero_rat ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(7)
% 5.46/5.71 thf(fact_3572_diff__numeral__special_I12_J,axiom,
% 5.46/5.71 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.71 = zero_zero_real ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(12)
% 5.46/5.71 thf(fact_3573_diff__numeral__special_I12_J,axiom,
% 5.46/5.71 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = zero_zero_int ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(12)
% 5.46/5.71 thf(fact_3574_diff__numeral__special_I12_J,axiom,
% 5.46/5.71 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.71 = zero_zero_complex ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(12)
% 5.46/5.71 thf(fact_3575_diff__numeral__special_I12_J,axiom,
% 5.46/5.71 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = zero_z3403309356797280102nteger ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(12)
% 5.46/5.71 thf(fact_3576_diff__numeral__special_I12_J,axiom,
% 5.46/5.71 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.71 = zero_zero_rat ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(12)
% 5.46/5.71 thf(fact_3577_neg__one__eq__numeral__iff,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( ( uminus_uminus_real @ one_one_real )
% 5.46/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.71 = ( N = one ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_eq_numeral_iff
% 5.46/5.71 thf(fact_3578_neg__one__eq__numeral__iff,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( ( uminus_uminus_int @ one_one_int )
% 5.46/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.71 = ( N = one ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_eq_numeral_iff
% 5.46/5.71 thf(fact_3579_neg__one__eq__numeral__iff,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.71 = ( N = one ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_eq_numeral_iff
% 5.46/5.71 thf(fact_3580_neg__one__eq__numeral__iff,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.71 = ( N = one ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_eq_numeral_iff
% 5.46/5.71 thf(fact_3581_neg__one__eq__numeral__iff,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.46/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.71 = ( N = one ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_eq_numeral_iff
% 5.46/5.71 thf(fact_3582_numeral__eq__neg__one__iff,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.46/5.71 = ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.71 = ( N = one ) ) ).
% 5.46/5.71
% 5.46/5.71 % numeral_eq_neg_one_iff
% 5.46/5.71 thf(fact_3583_numeral__eq__neg__one__iff,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.46/5.71 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = ( N = one ) ) ).
% 5.46/5.71
% 5.46/5.71 % numeral_eq_neg_one_iff
% 5.46/5.71 thf(fact_3584_numeral__eq__neg__one__iff,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.71 = ( N = one ) ) ).
% 5.46/5.71
% 5.46/5.71 % numeral_eq_neg_one_iff
% 5.46/5.71 thf(fact_3585_numeral__eq__neg__one__iff,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = ( N = one ) ) ).
% 5.46/5.71
% 5.46/5.71 % numeral_eq_neg_one_iff
% 5.46/5.71 thf(fact_3586_numeral__eq__neg__one__iff,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.46/5.71 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.71 = ( N = one ) ) ).
% 5.46/5.71
% 5.46/5.71 % numeral_eq_neg_one_iff
% 5.46/5.71 thf(fact_3587_minus__one__mult__self,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % minus_one_mult_self
% 5.46/5.71 thf(fact_3588_minus__one__mult__self,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.46/5.71 = one_one_int ) ).
% 5.46/5.71
% 5.46/5.71 % minus_one_mult_self
% 5.46/5.71 thf(fact_3589_minus__one__mult__self,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.46/5.71 = one_one_complex ) ).
% 5.46/5.71
% 5.46/5.71 % minus_one_mult_self
% 5.46/5.71 thf(fact_3590_minus__one__mult__self,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.46/5.71 = one_one_Code_integer ) ).
% 5.46/5.71
% 5.46/5.71 % minus_one_mult_self
% 5.46/5.71 thf(fact_3591_minus__one__mult__self,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.46/5.71 = one_one_rat ) ).
% 5.46/5.71
% 5.46/5.71 % minus_one_mult_self
% 5.46/5.71 thf(fact_3592_left__minus__one__mult__self,axiom,
% 5.46/5.71 ! [N: nat,A: real] :
% 5.46/5.71 ( ( 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 ) )
% 5.46/5.71 = A ) ).
% 5.46/5.71
% 5.46/5.71 % left_minus_one_mult_self
% 5.46/5.71 thf(fact_3593_left__minus__one__mult__self,axiom,
% 5.46/5.71 ! [N: nat,A: int] :
% 5.46/5.71 ( ( 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 ) )
% 5.46/5.71 = A ) ).
% 5.46/5.71
% 5.46/5.71 % left_minus_one_mult_self
% 5.46/5.71 thf(fact_3594_left__minus__one__mult__self,axiom,
% 5.46/5.71 ! [N: nat,A: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.46/5.71 = A ) ).
% 5.46/5.71
% 5.46/5.71 % left_minus_one_mult_self
% 5.46/5.71 thf(fact_3595_left__minus__one__mult__self,axiom,
% 5.46/5.71 ! [N: nat,A: code_integer] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.46/5.71 = A ) ).
% 5.46/5.71
% 5.46/5.71 % left_minus_one_mult_self
% 5.46/5.71 thf(fact_3596_left__minus__one__mult__self,axiom,
% 5.46/5.71 ! [N: nat,A: rat] :
% 5.46/5.71 ( ( 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 ) )
% 5.46/5.71 = A ) ).
% 5.46/5.71
% 5.46/5.71 % left_minus_one_mult_self
% 5.46/5.71 thf(fact_3597_mod__minus1__right,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = zero_zero_int ) ).
% 5.46/5.71
% 5.46/5.71 % mod_minus1_right
% 5.46/5.71 thf(fact_3598_mod__minus1__right,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = zero_z3403309356797280102nteger ) ).
% 5.46/5.71
% 5.46/5.71 % mod_minus1_right
% 5.46/5.71 thf(fact_3599_semiring__norm_I168_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: real] :
% 5.46/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(168)
% 5.46/5.71 thf(fact_3600_semiring__norm_I168_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: int] :
% 5.46/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(168)
% 5.46/5.71 thf(fact_3601_semiring__norm_I168_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: complex] :
% 5.46/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(168)
% 5.46/5.71 thf(fact_3602_semiring__norm_I168_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: code_integer] :
% 5.46/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(168)
% 5.46/5.71 thf(fact_3603_semiring__norm_I168_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: rat] :
% 5.46/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(168)
% 5.46/5.71 thf(fact_3604_diff__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_simps(3)
% 5.46/5.71 thf(fact_3605_diff__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_simps(3)
% 5.46/5.71 thf(fact_3606_diff__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_simps(3)
% 5.46/5.71 thf(fact_3607_diff__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_simps(3)
% 5.46/5.71 thf(fact_3608_diff__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.46/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_simps(3)
% 5.46/5.71 thf(fact_3609_diff__numeral__simps_I2_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.71 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_simps(2)
% 5.46/5.71 thf(fact_3610_diff__numeral__simps_I2_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.71 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_simps(2)
% 5.46/5.71 thf(fact_3611_diff__numeral__simps_I2_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.71 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_simps(2)
% 5.46/5.71 thf(fact_3612_diff__numeral__simps_I2_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.71 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_simps(2)
% 5.46/5.71 thf(fact_3613_diff__numeral__simps_I2_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.71 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_simps(2)
% 5.46/5.71 thf(fact_3614_semiring__norm_I172_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: real] :
% 5.46/5.71 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(172)
% 5.46/5.71 thf(fact_3615_semiring__norm_I172_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: int] :
% 5.46/5.71 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(172)
% 5.46/5.71 thf(fact_3616_semiring__norm_I172_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(172)
% 5.46/5.71 thf(fact_3617_semiring__norm_I172_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: code_integer] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(172)
% 5.46/5.71 thf(fact_3618_semiring__norm_I172_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: rat] :
% 5.46/5.71 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(172)
% 5.46/5.71 thf(fact_3619_semiring__norm_I171_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: real] :
% 5.46/5.71 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(171)
% 5.46/5.71 thf(fact_3620_semiring__norm_I171_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: int] :
% 5.46/5.71 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(171)
% 5.46/5.71 thf(fact_3621_semiring__norm_I171_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(171)
% 5.46/5.71 thf(fact_3622_semiring__norm_I171_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: code_integer] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(171)
% 5.46/5.71 thf(fact_3623_semiring__norm_I171_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: rat] :
% 5.46/5.71 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y3 ) )
% 5.46/5.71 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(171)
% 5.46/5.71 thf(fact_3624_semiring__norm_I170_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: real] :
% 5.46/5.71 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y3 ) )
% 5.46/5.71 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(170)
% 5.46/5.71 thf(fact_3625_semiring__norm_I170_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: int] :
% 5.46/5.71 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y3 ) )
% 5.46/5.71 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(170)
% 5.46/5.71 thf(fact_3626_semiring__norm_I170_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: complex] :
% 5.46/5.71 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y3 ) )
% 5.46/5.71 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(170)
% 5.46/5.71 thf(fact_3627_semiring__norm_I170_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: code_integer] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y3 ) )
% 5.46/5.71 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(170)
% 5.46/5.71 thf(fact_3628_semiring__norm_I170_J,axiom,
% 5.46/5.71 ! [V: num,W: num,Y3: rat] :
% 5.46/5.71 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y3 ) )
% 5.46/5.71 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y3 ) ) ).
% 5.46/5.71
% 5.46/5.71 % semiring_norm(170)
% 5.46/5.71 thf(fact_3629_mult__neg__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(3)
% 5.46/5.71 thf(fact_3630_mult__neg__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(3)
% 5.46/5.71 thf(fact_3631_mult__neg__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(3)
% 5.46/5.71 thf(fact_3632_mult__neg__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(3)
% 5.46/5.71 thf(fact_3633_mult__neg__numeral__simps_I3_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(3)
% 5.46/5.71 thf(fact_3634_mult__neg__numeral__simps_I2_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(2)
% 5.46/5.71 thf(fact_3635_mult__neg__numeral__simps_I2_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(2)
% 5.46/5.71 thf(fact_3636_mult__neg__numeral__simps_I2_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(2)
% 5.46/5.71 thf(fact_3637_mult__neg__numeral__simps_I2_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(2)
% 5.46/5.71 thf(fact_3638_mult__neg__numeral__simps_I2_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.46/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(2)
% 5.46/5.71 thf(fact_3639_mult__neg__numeral__simps_I1_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.71 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(1)
% 5.46/5.71 thf(fact_3640_mult__neg__numeral__simps_I1_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.71 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(1)
% 5.46/5.71 thf(fact_3641_mult__neg__numeral__simps_I1_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.71 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(1)
% 5.46/5.71 thf(fact_3642_mult__neg__numeral__simps_I1_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.71 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(1)
% 5.46/5.71 thf(fact_3643_mult__neg__numeral__simps_I1_J,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.71 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % mult_neg_numeral_simps(1)
% 5.46/5.71 thf(fact_3644_neg__numeral__le__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.71 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_le_iff
% 5.46/5.71 thf(fact_3645_neg__numeral__le__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.71 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_le_iff
% 5.46/5.71 thf(fact_3646_neg__numeral__le__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.71 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_le_iff
% 5.46/5.71 thf(fact_3647_neg__numeral__le__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.71 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_le_iff
% 5.46/5.71 thf(fact_3648_neg__numeral__less__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.71 = ( ord_less_num @ N @ M ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_less_iff
% 5.46/5.71 thf(fact_3649_neg__numeral__less__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.71 = ( ord_less_num @ N @ M ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_less_iff
% 5.46/5.71 thf(fact_3650_neg__numeral__less__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.71 = ( ord_less_num @ N @ M ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_less_iff
% 5.46/5.71 thf(fact_3651_neg__numeral__less__iff,axiom,
% 5.46/5.71 ! [M: num,N: num] :
% 5.46/5.71 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.71 = ( ord_less_num @ N @ M ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_less_iff
% 5.46/5.71 thf(fact_3652_not__neg__one__le__neg__numeral__iff,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.46/5.71 = ( M != one ) ) ).
% 5.46/5.71
% 5.46/5.71 % not_neg_one_le_neg_numeral_iff
% 5.46/5.71 thf(fact_3653_not__neg__one__le__neg__numeral__iff,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.46/5.71 = ( M != one ) ) ).
% 5.46/5.71
% 5.46/5.71 % not_neg_one_le_neg_numeral_iff
% 5.46/5.71 thf(fact_3654_not__neg__one__le__neg__numeral__iff,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.46/5.71 = ( M != one ) ) ).
% 5.46/5.71
% 5.46/5.71 % not_neg_one_le_neg_numeral_iff
% 5.46/5.71 thf(fact_3655_not__neg__one__le__neg__numeral__iff,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.46/5.71 = ( M != one ) ) ).
% 5.46/5.71
% 5.46/5.71 % not_neg_one_le_neg_numeral_iff
% 5.46/5.71 thf(fact_3656_divide__le__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [B2: real,W: num,A: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.46/5.71 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % divide_le_eq_numeral1(2)
% 5.46/5.71 thf(fact_3657_divide__le__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [B2: rat,W: num,A: rat] :
% 5.46/5.71 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.46/5.71 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % divide_le_eq_numeral1(2)
% 5.46/5.71 thf(fact_3658_le__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [A: real,B2: real,W: num] :
% 5.46/5.71 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.46/5.71 = ( ord_less_eq_real @ B2 @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_divide_eq_numeral1(2)
% 5.46/5.71 thf(fact_3659_le__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [A: rat,B2: rat,W: num] :
% 5.46/5.71 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.46/5.71 = ( ord_less_eq_rat @ B2 @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_divide_eq_numeral1(2)
% 5.46/5.71 thf(fact_3660_divide__eq__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [B2: real,W: num,A: real] :
% 5.46/5.71 ( ( ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.71 = A )
% 5.46/5.71 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.71 != zero_zero_real )
% 5.46/5.71 => ( B2
% 5.46/5.71 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.46/5.71 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % divide_eq_eq_numeral1(2)
% 5.46/5.71 thf(fact_3661_divide__eq__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [B2: complex,W: num,A: complex] :
% 5.46/5.71 ( ( ( divide1717551699836669952omplex @ B2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.71 = A )
% 5.46/5.71 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.71 != zero_zero_complex )
% 5.46/5.71 => ( B2
% 5.46/5.71 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.46/5.71 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.71 = zero_zero_complex )
% 5.46/5.71 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % divide_eq_eq_numeral1(2)
% 5.46/5.71 thf(fact_3662_divide__eq__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [B2: rat,W: num,A: rat] :
% 5.46/5.71 ( ( ( divide_divide_rat @ B2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.71 = A )
% 5.46/5.71 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.71 != zero_zero_rat )
% 5.46/5.71 => ( B2
% 5.46/5.71 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.46/5.71 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.71 = zero_zero_rat )
% 5.46/5.71 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % divide_eq_eq_numeral1(2)
% 5.46/5.71 thf(fact_3663_eq__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [A: real,B2: real,W: num] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.46/5.71 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.71 != zero_zero_real )
% 5.46/5.71 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.71 = B2 ) )
% 5.46/5.71 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.71 = zero_zero_real )
% 5.46/5.71 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % eq_divide_eq_numeral1(2)
% 5.46/5.71 thf(fact_3664_eq__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [A: complex,B2: complex,W: num] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( divide1717551699836669952omplex @ B2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.46/5.71 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.71 != zero_zero_complex )
% 5.46/5.71 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.71 = B2 ) )
% 5.46/5.71 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.71 = zero_zero_complex )
% 5.46/5.71 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % eq_divide_eq_numeral1(2)
% 5.46/5.71 thf(fact_3665_eq__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [A: rat,B2: rat,W: num] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( divide_divide_rat @ B2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.46/5.71 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.71 != zero_zero_rat )
% 5.46/5.71 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.71 = B2 ) )
% 5.46/5.71 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.71 = zero_zero_rat )
% 5.46/5.71 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % eq_divide_eq_numeral1(2)
% 5.46/5.71 thf(fact_3666_neg__numeral__less__neg__one__iff,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.71 = ( M != one ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_less_neg_one_iff
% 5.46/5.71 thf(fact_3667_neg__numeral__less__neg__one__iff,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = ( M != one ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_less_neg_one_iff
% 5.46/5.71 thf(fact_3668_neg__numeral__less__neg__one__iff,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = ( M != one ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_less_neg_one_iff
% 5.46/5.71 thf(fact_3669_neg__numeral__less__neg__one__iff,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.71 = ( M != one ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_numeral_less_neg_one_iff
% 5.46/5.71 thf(fact_3670_divide__less__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [B2: real,W: num,A: real] :
% 5.46/5.71 ( ( ord_less_real @ ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.46/5.71 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % divide_less_eq_numeral1(2)
% 5.46/5.71 thf(fact_3671_divide__less__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [B2: rat,W: num,A: rat] :
% 5.46/5.71 ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.46/5.71 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B2 ) ) ).
% 5.46/5.71
% 5.46/5.71 % divide_less_eq_numeral1(2)
% 5.46/5.71 thf(fact_3672_less__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [A: real,B2: real,W: num] :
% 5.46/5.71 ( ( ord_less_real @ A @ ( divide_divide_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.46/5.71 = ( ord_less_real @ B2 @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_divide_eq_numeral1(2)
% 5.46/5.71 thf(fact_3673_less__divide__eq__numeral1_I2_J,axiom,
% 5.46/5.71 ! [A: rat,B2: rat,W: num] :
% 5.46/5.71 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.46/5.71 = ( ord_less_rat @ B2 @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_divide_eq_numeral1(2)
% 5.46/5.71 thf(fact_3674_power2__minus,axiom,
% 5.46/5.71 ! [A: real] :
% 5.46/5.71 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power2_minus
% 5.46/5.71 thf(fact_3675_power2__minus,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power2_minus
% 5.46/5.71 thf(fact_3676_power2__minus,axiom,
% 5.46/5.71 ! [A: complex] :
% 5.46/5.71 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power2_minus
% 5.46/5.71 thf(fact_3677_power2__minus,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power2_minus
% 5.46/5.71 thf(fact_3678_power2__minus,axiom,
% 5.46/5.71 ! [A: rat] :
% 5.46/5.71 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power2_minus
% 5.46/5.71 thf(fact_3679_add__neg__numeral__special_I9_J,axiom,
% 5.46/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(9)
% 5.46/5.71 thf(fact_3680_add__neg__numeral__special_I9_J,axiom,
% 5.46/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(9)
% 5.46/5.71 thf(fact_3681_add__neg__numeral__special_I9_J,axiom,
% 5.46/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(9)
% 5.46/5.71 thf(fact_3682_add__neg__numeral__special_I9_J,axiom,
% 5.46/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(9)
% 5.46/5.71 thf(fact_3683_add__neg__numeral__special_I9_J,axiom,
% 5.46/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % add_neg_numeral_special(9)
% 5.46/5.71 thf(fact_3684_diff__numeral__special_I11_J,axiom,
% 5.46/5.71 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.71 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(11)
% 5.46/5.71 thf(fact_3685_diff__numeral__special_I11_J,axiom,
% 5.46/5.71 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(11)
% 5.46/5.71 thf(fact_3686_diff__numeral__special_I11_J,axiom,
% 5.46/5.71 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.71 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(11)
% 5.46/5.71 thf(fact_3687_diff__numeral__special_I11_J,axiom,
% 5.46/5.71 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(11)
% 5.46/5.71 thf(fact_3688_diff__numeral__special_I11_J,axiom,
% 5.46/5.71 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.71 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(11)
% 5.46/5.71 thf(fact_3689_diff__numeral__special_I10_J,axiom,
% 5.46/5.71 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.46/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(10)
% 5.46/5.71 thf(fact_3690_diff__numeral__special_I10_J,axiom,
% 5.46/5.71 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.46/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(10)
% 5.46/5.71 thf(fact_3691_diff__numeral__special_I10_J,axiom,
% 5.46/5.71 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(10)
% 5.46/5.71 thf(fact_3692_diff__numeral__special_I10_J,axiom,
% 5.46/5.71 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(10)
% 5.46/5.71 thf(fact_3693_diff__numeral__special_I10_J,axiom,
% 5.46/5.71 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.46/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(10)
% 5.46/5.71 thf(fact_3694_minus__1__div__2__eq,axiom,
% 5.46/5.71 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_1_div_2_eq
% 5.46/5.71 thf(fact_3695_minus__1__div__2__eq,axiom,
% 5.46/5.71 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_1_div_2_eq
% 5.46/5.71 thf(fact_3696_minus__1__mod__2__eq,axiom,
% 5.46/5.71 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.71 = one_one_int ) ).
% 5.46/5.71
% 5.46/5.71 % minus_1_mod_2_eq
% 5.46/5.71 thf(fact_3697_minus__1__mod__2__eq,axiom,
% 5.46/5.71 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.71 = one_one_Code_integer ) ).
% 5.46/5.71
% 5.46/5.71 % minus_1_mod_2_eq
% 5.46/5.71 thf(fact_3698_bits__minus__1__mod__2__eq,axiom,
% 5.46/5.71 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.71 = one_one_int ) ).
% 5.46/5.71
% 5.46/5.71 % bits_minus_1_mod_2_eq
% 5.46/5.71 thf(fact_3699_bits__minus__1__mod__2__eq,axiom,
% 5.46/5.71 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.71 = one_one_Code_integer ) ).
% 5.46/5.71
% 5.46/5.71 % bits_minus_1_mod_2_eq
% 5.46/5.71 thf(fact_3700_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.71 ! [A: real,N: nat] :
% 5.46/5.71 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.71 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Power.ring_1_class.power_minus_even
% 5.46/5.71 thf(fact_3701_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.71 ! [A: int,N: nat] :
% 5.46/5.71 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.71 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Power.ring_1_class.power_minus_even
% 5.46/5.71 thf(fact_3702_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.71 ! [A: complex,N: nat] :
% 5.46/5.71 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.71 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Power.ring_1_class.power_minus_even
% 5.46/5.71 thf(fact_3703_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.71 ! [A: code_integer,N: nat] :
% 5.46/5.71 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.71 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Power.ring_1_class.power_minus_even
% 5.46/5.71 thf(fact_3704_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.71 ! [A: rat,N: nat] :
% 5.46/5.71 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.71 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Power.ring_1_class.power_minus_even
% 5.46/5.71 thf(fact_3705_power__minus__odd,axiom,
% 5.46/5.71 ! [N: nat,A: real] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.46/5.71 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_minus_odd
% 5.46/5.71 thf(fact_3706_power__minus__odd,axiom,
% 5.46/5.71 ! [N: nat,A: int] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.46/5.71 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_minus_odd
% 5.46/5.71 thf(fact_3707_power__minus__odd,axiom,
% 5.46/5.71 ! [N: nat,A: complex] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_minus_odd
% 5.46/5.71 thf(fact_3708_power__minus__odd,axiom,
% 5.46/5.71 ! [N: nat,A: code_integer] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_minus_odd
% 5.46/5.71 thf(fact_3709_power__minus__odd,axiom,
% 5.46/5.71 ! [N: nat,A: rat] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.46/5.71 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % power_minus_odd
% 5.46/5.71 thf(fact_3710_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.71 ! [N: nat,A: real] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.46/5.71 = ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Parity.ring_1_class.power_minus_even
% 5.46/5.71 thf(fact_3711_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.71 ! [N: nat,A: int] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.46/5.71 = ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Parity.ring_1_class.power_minus_even
% 5.46/5.71 thf(fact_3712_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.71 ! [N: nat,A: complex] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.46/5.71 = ( power_power_complex @ A @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Parity.ring_1_class.power_minus_even
% 5.46/5.71 thf(fact_3713_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.71 ! [N: nat,A: code_integer] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.46/5.71 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Parity.ring_1_class.power_minus_even
% 5.46/5.71 thf(fact_3714_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.46/5.71 ! [N: nat,A: rat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.46/5.71 = ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % Parity.ring_1_class.power_minus_even
% 5.46/5.71 thf(fact_3715_diff__numeral__special_I3_J,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.71 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(3)
% 5.46/5.71 thf(fact_3716_diff__numeral__special_I3_J,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.71 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(3)
% 5.46/5.71 thf(fact_3717_diff__numeral__special_I3_J,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.71 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(3)
% 5.46/5.71 thf(fact_3718_diff__numeral__special_I3_J,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.71 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(3)
% 5.46/5.71 thf(fact_3719_diff__numeral__special_I3_J,axiom,
% 5.46/5.71 ! [N: num] :
% 5.46/5.71 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.71 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(3)
% 5.46/5.71 thf(fact_3720_diff__numeral__special_I4_J,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.46/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(4)
% 5.46/5.71 thf(fact_3721_diff__numeral__special_I4_J,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.46/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(4)
% 5.46/5.71 thf(fact_3722_diff__numeral__special_I4_J,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(4)
% 5.46/5.71 thf(fact_3723_diff__numeral__special_I4_J,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(4)
% 5.46/5.71 thf(fact_3724_diff__numeral__special_I4_J,axiom,
% 5.46/5.71 ! [M: num] :
% 5.46/5.71 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.46/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % diff_numeral_special(4)
% 5.46/5.71 thf(fact_3725_signed__take__bit__Suc__minus__bit0,axiom,
% 5.46/5.71 ! [N: nat,K: num] :
% 5.46/5.71 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.71 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % signed_take_bit_Suc_minus_bit0
% 5.46/5.71 thf(fact_3726_dbl__simps_I4_J,axiom,
% 5.46/5.71 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dbl_simps(4)
% 5.46/5.71 thf(fact_3727_dbl__simps_I4_J,axiom,
% 5.46/5.71 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dbl_simps(4)
% 5.46/5.71 thf(fact_3728_dbl__simps_I4_J,axiom,
% 5.46/5.71 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dbl_simps(4)
% 5.46/5.71 thf(fact_3729_dbl__simps_I4_J,axiom,
% 5.46/5.71 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dbl_simps(4)
% 5.46/5.71 thf(fact_3730_dbl__simps_I4_J,axiom,
% 5.46/5.71 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % dbl_simps(4)
% 5.46/5.71 thf(fact_3731_power__minus1__even,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.71 = one_one_real ) ).
% 5.46/5.71
% 5.46/5.71 % power_minus1_even
% 5.46/5.71 thf(fact_3732_power__minus1__even,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.71 = one_one_int ) ).
% 5.46/5.71
% 5.46/5.71 % power_minus1_even
% 5.46/5.71 thf(fact_3733_power__minus1__even,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.71 = one_one_complex ) ).
% 5.46/5.71
% 5.46/5.71 % power_minus1_even
% 5.46/5.71 thf(fact_3734_power__minus1__even,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.71 = one_one_Code_integer ) ).
% 5.46/5.71
% 5.46/5.71 % power_minus1_even
% 5.46/5.71 thf(fact_3735_power__minus1__even,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.71 = one_one_rat ) ).
% 5.46/5.71
% 5.46/5.71 % power_minus1_even
% 5.46/5.71 thf(fact_3736_neg__one__odd__power,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.46/5.71 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_odd_power
% 5.46/5.71 thf(fact_3737_neg__one__odd__power,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.46/5.71 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_odd_power
% 5.46/5.71 thf(fact_3738_neg__one__odd__power,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.46/5.71 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_odd_power
% 5.46/5.71 thf(fact_3739_neg__one__odd__power,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_odd_power
% 5.46/5.71 thf(fact_3740_neg__one__odd__power,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.46/5.71 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_odd_power
% 5.46/5.71 thf(fact_3741_neg__one__even__power,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.46/5.71 = one_one_real ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_even_power
% 5.46/5.71 thf(fact_3742_neg__one__even__power,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.46/5.71 = one_one_int ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_even_power
% 5.46/5.71 thf(fact_3743_neg__one__even__power,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.46/5.71 = one_one_complex ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_even_power
% 5.46/5.71 thf(fact_3744_neg__one__even__power,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.46/5.71 = one_one_Code_integer ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_even_power
% 5.46/5.71 thf(fact_3745_neg__one__even__power,axiom,
% 5.46/5.71 ! [N: nat] :
% 5.46/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.71 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.46/5.71 = one_one_rat ) ) ).
% 5.46/5.71
% 5.46/5.71 % neg_one_even_power
% 5.46/5.71 thf(fact_3746_signed__take__bit__0,axiom,
% 5.46/5.71 ! [A: code_integer] :
% 5.46/5.71 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % signed_take_bit_0
% 5.46/5.71 thf(fact_3747_signed__take__bit__0,axiom,
% 5.46/5.71 ! [A: int] :
% 5.46/5.71 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.46/5.71 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % signed_take_bit_0
% 5.46/5.71 thf(fact_3748_verit__negate__coefficient_I3_J,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( A = B2 )
% 5.46/5.71 => ( ( uminus_uminus_real @ A )
% 5.46/5.71 = ( uminus_uminus_real @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_negate_coefficient(3)
% 5.46/5.71 thf(fact_3749_verit__negate__coefficient_I3_J,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( A = B2 )
% 5.46/5.71 => ( ( uminus_uminus_int @ A )
% 5.46/5.71 = ( uminus_uminus_int @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_negate_coefficient(3)
% 5.46/5.71 thf(fact_3750_verit__negate__coefficient_I3_J,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( A = B2 )
% 5.46/5.71 => ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.71 = ( uminus1351360451143612070nteger @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_negate_coefficient(3)
% 5.46/5.71 thf(fact_3751_verit__negate__coefficient_I3_J,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( A = B2 )
% 5.46/5.71 => ( ( uminus_uminus_rat @ A )
% 5.46/5.71 = ( uminus_uminus_rat @ B2 ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_negate_coefficient(3)
% 5.46/5.71 thf(fact_3752_equation__minus__iff,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( uminus_uminus_real @ B2 ) )
% 5.46/5.71 = ( B2
% 5.46/5.71 = ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % equation_minus_iff
% 5.46/5.71 thf(fact_3753_equation__minus__iff,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( uminus_uminus_int @ B2 ) )
% 5.46/5.71 = ( B2
% 5.46/5.71 = ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % equation_minus_iff
% 5.46/5.71 thf(fact_3754_equation__minus__iff,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.71 = ( B2
% 5.46/5.71 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % equation_minus_iff
% 5.46/5.71 thf(fact_3755_equation__minus__iff,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.71 = ( B2
% 5.46/5.71 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % equation_minus_iff
% 5.46/5.71 thf(fact_3756_equation__minus__iff,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( A
% 5.46/5.71 = ( uminus_uminus_rat @ B2 ) )
% 5.46/5.71 = ( B2
% 5.46/5.71 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % equation_minus_iff
% 5.46/5.71 thf(fact_3757_minus__equation__iff,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( ( uminus_uminus_real @ A )
% 5.46/5.71 = B2 )
% 5.46/5.71 = ( ( uminus_uminus_real @ B2 )
% 5.46/5.71 = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_equation_iff
% 5.46/5.71 thf(fact_3758_minus__equation__iff,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( ( uminus_uminus_int @ A )
% 5.46/5.71 = B2 )
% 5.46/5.71 = ( ( uminus_uminus_int @ B2 )
% 5.46/5.71 = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_equation_iff
% 5.46/5.71 thf(fact_3759_minus__equation__iff,axiom,
% 5.46/5.71 ! [A: complex,B2: complex] :
% 5.46/5.71 ( ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.71 = B2 )
% 5.46/5.71 = ( ( uminus1482373934393186551omplex @ B2 )
% 5.46/5.71 = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_equation_iff
% 5.46/5.71 thf(fact_3760_minus__equation__iff,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.71 = B2 )
% 5.46/5.71 = ( ( uminus1351360451143612070nteger @ B2 )
% 5.46/5.71 = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_equation_iff
% 5.46/5.71 thf(fact_3761_minus__equation__iff,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( ( uminus_uminus_rat @ A )
% 5.46/5.71 = B2 )
% 5.46/5.71 = ( ( uminus_uminus_rat @ B2 )
% 5.46/5.71 = A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_equation_iff
% 5.46/5.71 thf(fact_3762_le__imp__neg__le,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.71 => ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_imp_neg_le
% 5.46/5.71 thf(fact_3763_le__imp__neg__le,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( ord_le3102999989581377725nteger @ A @ B2 )
% 5.46/5.71 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B2 ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_imp_neg_le
% 5.46/5.71 thf(fact_3764_le__imp__neg__le,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.71 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B2 ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_imp_neg_le
% 5.46/5.71 thf(fact_3765_le__imp__neg__le,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.71 => ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_imp_neg_le
% 5.46/5.71 thf(fact_3766_minus__le__iff,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B2 )
% 5.46/5.71 = ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_le_iff
% 5.46/5.71 thf(fact_3767_minus__le__iff,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 )
% 5.46/5.71 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B2 ) @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_le_iff
% 5.46/5.71 thf(fact_3768_minus__le__iff,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B2 )
% 5.46/5.71 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B2 ) @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_le_iff
% 5.46/5.71 thf(fact_3769_minus__le__iff,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.71 = ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_le_iff
% 5.46/5.71 thf(fact_3770_le__minus__iff,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B2 ) )
% 5.46/5.71 = ( ord_less_eq_real @ B2 @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_minus_iff
% 5.46/5.71 thf(fact_3771_le__minus__iff,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.71 = ( ord_le3102999989581377725nteger @ B2 @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_minus_iff
% 5.46/5.71 thf(fact_3772_le__minus__iff,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B2 ) )
% 5.46/5.71 = ( ord_less_eq_rat @ B2 @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_minus_iff
% 5.46/5.71 thf(fact_3773_le__minus__iff,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.71 = ( ord_less_eq_int @ B2 @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % le_minus_iff
% 5.46/5.71 thf(fact_3774_minus__less__iff,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B2 )
% 5.46/5.71 = ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_less_iff
% 5.46/5.71 thf(fact_3775_minus__less__iff,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.71 = ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_less_iff
% 5.46/5.71 thf(fact_3776_minus__less__iff,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 )
% 5.46/5.71 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B2 ) @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_less_iff
% 5.46/5.71 thf(fact_3777_minus__less__iff,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B2 )
% 5.46/5.71 = ( ord_less_rat @ ( uminus_uminus_rat @ B2 ) @ A ) ) ).
% 5.46/5.71
% 5.46/5.71 % minus_less_iff
% 5.46/5.71 thf(fact_3778_less__minus__iff,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B2 ) )
% 5.46/5.71 = ( ord_less_real @ B2 @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_minus_iff
% 5.46/5.71 thf(fact_3779_less__minus__iff,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.71 = ( ord_less_int @ B2 @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_minus_iff
% 5.46/5.71 thf(fact_3780_less__minus__iff,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.71 = ( ord_le6747313008572928689nteger @ B2 @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_minus_iff
% 5.46/5.71 thf(fact_3781_less__minus__iff,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B2 ) )
% 5.46/5.71 = ( ord_less_rat @ B2 @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % less_minus_iff
% 5.46/5.71 thf(fact_3782_verit__negate__coefficient_I2_J,axiom,
% 5.46/5.71 ! [A: real,B2: real] :
% 5.46/5.71 ( ( ord_less_real @ A @ B2 )
% 5.46/5.71 => ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_negate_coefficient(2)
% 5.46/5.71 thf(fact_3783_verit__negate__coefficient_I2_J,axiom,
% 5.46/5.71 ! [A: int,B2: int] :
% 5.46/5.71 ( ( ord_less_int @ A @ B2 )
% 5.46/5.71 => ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_negate_coefficient(2)
% 5.46/5.71 thf(fact_3784_verit__negate__coefficient_I2_J,axiom,
% 5.46/5.71 ! [A: code_integer,B2: code_integer] :
% 5.46/5.71 ( ( ord_le6747313008572928689nteger @ A @ B2 )
% 5.46/5.71 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B2 ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_negate_coefficient(2)
% 5.46/5.71 thf(fact_3785_verit__negate__coefficient_I2_J,axiom,
% 5.46/5.71 ! [A: rat,B2: rat] :
% 5.46/5.71 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.71 => ( ord_less_rat @ ( uminus_uminus_rat @ B2 ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.71
% 5.46/5.71 % verit_negate_coefficient(2)
% 5.46/5.71 thf(fact_3786_neg__numeral__neq__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.46/5.72 != ( numeral_numeral_real @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_neq_numeral
% 5.46/5.72 thf(fact_3787_neg__numeral__neq__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.46/5.72 != ( numeral_numeral_int @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_neq_numeral
% 5.46/5.72 thf(fact_3788_neg__numeral__neq__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.46/5.72 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_neq_numeral
% 5.46/5.72 thf(fact_3789_neg__numeral__neq__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.46/5.72 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_neq_numeral
% 5.46/5.72 thf(fact_3790_neg__numeral__neq__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.46/5.72 != ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_neq_numeral
% 5.46/5.72 thf(fact_3791_numeral__neq__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( numeral_numeral_real @ M )
% 5.46/5.72 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_neq_neg_numeral
% 5.46/5.72 thf(fact_3792_numeral__neq__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( numeral_numeral_int @ M )
% 5.46/5.72 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_neq_neg_numeral
% 5.46/5.72 thf(fact_3793_numeral__neq__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( numera6690914467698888265omplex @ M )
% 5.46/5.72 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_neq_neg_numeral
% 5.46/5.72 thf(fact_3794_numeral__neq__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( numera6620942414471956472nteger @ M )
% 5.46/5.72 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_neq_neg_numeral
% 5.46/5.72 thf(fact_3795_numeral__neq__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( numeral_numeral_rat @ M )
% 5.46/5.72 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_neq_neg_numeral
% 5.46/5.72 thf(fact_3796_minus__mult__commute,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B2 )
% 5.46/5.72 = ( times_times_real @ A @ ( uminus_uminus_real @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_mult_commute
% 5.46/5.72 thf(fact_3797_minus__mult__commute,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.72 = ( times_times_int @ A @ ( uminus_uminus_int @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_mult_commute
% 5.46/5.72 thf(fact_3798_minus__mult__commute,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B2 )
% 5.46/5.72 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_mult_commute
% 5.46/5.72 thf(fact_3799_minus__mult__commute,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 )
% 5.46/5.72 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_mult_commute
% 5.46/5.72 thf(fact_3800_minus__mult__commute,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B2 )
% 5.46/5.72 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_mult_commute
% 5.46/5.72 thf(fact_3801_square__eq__iff,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( ( times_times_real @ A @ A )
% 5.46/5.72 = ( times_times_real @ B2 @ B2 ) )
% 5.46/5.72 = ( ( A = B2 )
% 5.46/5.72 | ( A
% 5.46/5.72 = ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_eq_iff
% 5.46/5.72 thf(fact_3802_square__eq__iff,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( ( times_times_int @ A @ A )
% 5.46/5.72 = ( times_times_int @ B2 @ B2 ) )
% 5.46/5.72 = ( ( A = B2 )
% 5.46/5.72 | ( A
% 5.46/5.72 = ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_eq_iff
% 5.46/5.72 thf(fact_3803_square__eq__iff,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( ( times_times_complex @ A @ A )
% 5.46/5.72 = ( times_times_complex @ B2 @ B2 ) )
% 5.46/5.72 = ( ( A = B2 )
% 5.46/5.72 | ( A
% 5.46/5.72 = ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_eq_iff
% 5.46/5.72 thf(fact_3804_square__eq__iff,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.46/5.72 = ( times_3573771949741848930nteger @ B2 @ B2 ) )
% 5.46/5.72 = ( ( A = B2 )
% 5.46/5.72 | ( A
% 5.46/5.72 = ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_eq_iff
% 5.46/5.72 thf(fact_3805_square__eq__iff,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( ( times_times_rat @ A @ A )
% 5.46/5.72 = ( times_times_rat @ B2 @ B2 ) )
% 5.46/5.72 = ( ( A = B2 )
% 5.46/5.72 | ( A
% 5.46/5.72 = ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_eq_iff
% 5.46/5.72 thf(fact_3806_one__neq__neg__one,axiom,
% 5.46/5.72 ( one_one_real
% 5.46/5.72 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_neq_neg_one
% 5.46/5.72 thf(fact_3807_one__neq__neg__one,axiom,
% 5.46/5.72 ( one_one_int
% 5.46/5.72 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_neq_neg_one
% 5.46/5.72 thf(fact_3808_one__neq__neg__one,axiom,
% 5.46/5.72 ( one_one_complex
% 5.46/5.72 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_neq_neg_one
% 5.46/5.72 thf(fact_3809_one__neq__neg__one,axiom,
% 5.46/5.72 ( one_one_Code_integer
% 5.46/5.72 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_neq_neg_one
% 5.46/5.72 thf(fact_3810_one__neq__neg__one,axiom,
% 5.46/5.72 ( one_one_rat
% 5.46/5.72 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_neq_neg_one
% 5.46/5.72 thf(fact_3811_add_Oinverse__distrib__swap,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B2 ) )
% 5.46/5.72 = ( plus_plus_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add.inverse_distrib_swap
% 5.46/5.72 thf(fact_3812_add_Oinverse__distrib__swap,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B2 ) )
% 5.46/5.72 = ( plus_plus_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add.inverse_distrib_swap
% 5.46/5.72 thf(fact_3813_add_Oinverse__distrib__swap,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B2 ) )
% 5.46/5.72 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B2 ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add.inverse_distrib_swap
% 5.46/5.72 thf(fact_3814_add_Oinverse__distrib__swap,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) )
% 5.46/5.72 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B2 ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add.inverse_distrib_swap
% 5.46/5.72 thf(fact_3815_add_Oinverse__distrib__swap,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B2 ) )
% 5.46/5.72 = ( plus_plus_rat @ ( uminus_uminus_rat @ B2 ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add.inverse_distrib_swap
% 5.46/5.72 thf(fact_3816_group__cancel_Oneg1,axiom,
% 5.46/5.72 ! [A3: real,K: real,A: real] :
% 5.46/5.72 ( ( A3
% 5.46/5.72 = ( plus_plus_real @ K @ A ) )
% 5.46/5.72 => ( ( uminus_uminus_real @ A3 )
% 5.46/5.72 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % group_cancel.neg1
% 5.46/5.72 thf(fact_3817_group__cancel_Oneg1,axiom,
% 5.46/5.72 ! [A3: int,K: int,A: int] :
% 5.46/5.72 ( ( A3
% 5.46/5.72 = ( plus_plus_int @ K @ A ) )
% 5.46/5.72 => ( ( uminus_uminus_int @ A3 )
% 5.46/5.72 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % group_cancel.neg1
% 5.46/5.72 thf(fact_3818_group__cancel_Oneg1,axiom,
% 5.46/5.72 ! [A3: complex,K: complex,A: complex] :
% 5.46/5.72 ( ( A3
% 5.46/5.72 = ( plus_plus_complex @ K @ A ) )
% 5.46/5.72 => ( ( uminus1482373934393186551omplex @ A3 )
% 5.46/5.72 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % group_cancel.neg1
% 5.46/5.72 thf(fact_3819_group__cancel_Oneg1,axiom,
% 5.46/5.72 ! [A3: code_integer,K: code_integer,A: code_integer] :
% 5.46/5.72 ( ( A3
% 5.46/5.72 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.46/5.72 => ( ( uminus1351360451143612070nteger @ A3 )
% 5.46/5.72 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % group_cancel.neg1
% 5.46/5.72 thf(fact_3820_group__cancel_Oneg1,axiom,
% 5.46/5.72 ! [A3: rat,K: rat,A: rat] :
% 5.46/5.72 ( ( A3
% 5.46/5.72 = ( plus_plus_rat @ K @ A ) )
% 5.46/5.72 => ( ( uminus_uminus_rat @ A3 )
% 5.46/5.72 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % group_cancel.neg1
% 5.46/5.72 thf(fact_3821_is__num__normalize_I8_J,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B2 ) )
% 5.46/5.72 = ( plus_plus_real @ ( uminus_uminus_real @ B2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % is_num_normalize(8)
% 5.46/5.72 thf(fact_3822_is__num__normalize_I8_J,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B2 ) )
% 5.46/5.72 = ( plus_plus_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % is_num_normalize(8)
% 5.46/5.72 thf(fact_3823_is__num__normalize_I8_J,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B2 ) )
% 5.46/5.72 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B2 ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % is_num_normalize(8)
% 5.46/5.72 thf(fact_3824_is__num__normalize_I8_J,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) )
% 5.46/5.72 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B2 ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % is_num_normalize(8)
% 5.46/5.72 thf(fact_3825_is__num__normalize_I8_J,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B2 ) )
% 5.46/5.72 = ( plus_plus_rat @ ( uminus_uminus_rat @ B2 ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % is_num_normalize(8)
% 5.46/5.72 thf(fact_3826_minus__diff__commute,axiom,
% 5.46/5.72 ! [B2: real,A: real] :
% 5.46/5.72 ( ( minus_minus_real @ ( uminus_uminus_real @ B2 ) @ A )
% 5.46/5.72 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_diff_commute
% 5.46/5.72 thf(fact_3827_minus__diff__commute,axiom,
% 5.46/5.72 ! [B2: int,A: int] :
% 5.46/5.72 ( ( minus_minus_int @ ( uminus_uminus_int @ B2 ) @ A )
% 5.46/5.72 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_diff_commute
% 5.46/5.72 thf(fact_3828_minus__diff__commute,axiom,
% 5.46/5.72 ! [B2: complex,A: complex] :
% 5.46/5.72 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B2 ) @ A )
% 5.46/5.72 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_diff_commute
% 5.46/5.72 thf(fact_3829_minus__diff__commute,axiom,
% 5.46/5.72 ! [B2: code_integer,A: code_integer] :
% 5.46/5.72 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B2 ) @ A )
% 5.46/5.72 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_diff_commute
% 5.46/5.72 thf(fact_3830_minus__diff__commute,axiom,
% 5.46/5.72 ! [B2: rat,A: rat] :
% 5.46/5.72 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B2 ) @ A )
% 5.46/5.72 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_diff_commute
% 5.46/5.72 thf(fact_3831_minus__diff__minus,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B2 ) )
% 5.46/5.72 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_diff_minus
% 5.46/5.72 thf(fact_3832_minus__diff__minus,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.72 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_diff_minus
% 5.46/5.72 thf(fact_3833_minus__diff__minus,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_diff_minus
% 5.46/5.72 thf(fact_3834_minus__diff__minus,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.72 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_diff_minus
% 5.46/5.72 thf(fact_3835_minus__diff__minus,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B2 ) )
% 5.46/5.72 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_diff_minus
% 5.46/5.72 thf(fact_3836_div__minus__right,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.72 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % div_minus_right
% 5.46/5.72 thf(fact_3837_div__minus__right,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.72 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % div_minus_right
% 5.46/5.72 thf(fact_3838_minus__divide__right,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.72 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_right
% 5.46/5.72 thf(fact_3839_minus__divide__right,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_right
% 5.46/5.72 thf(fact_3840_minus__divide__right,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B2 ) )
% 5.46/5.72 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_right
% 5.46/5.72 thf(fact_3841_minus__divide__divide,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B2 ) )
% 5.46/5.72 = ( divide_divide_real @ A @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_divide
% 5.46/5.72 thf(fact_3842_minus__divide__divide,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ A @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_divide
% 5.46/5.72 thf(fact_3843_minus__divide__divide,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B2 ) )
% 5.46/5.72 = ( divide_divide_rat @ A @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_divide
% 5.46/5.72 thf(fact_3844_minus__divide__left,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.72 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_left
% 5.46/5.72 thf(fact_3845_minus__divide__left,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_left
% 5.46/5.72 thf(fact_3846_minus__divide__left,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B2 ) )
% 5.46/5.72 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_left
% 5.46/5.72 thf(fact_3847_mod__minus__eq,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B2 ) ) @ B2 )
% 5.46/5.72 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mod_minus_eq
% 5.46/5.72 thf(fact_3848_mod__minus__eq,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B2 ) ) @ B2 )
% 5.46/5.72 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mod_minus_eq
% 5.46/5.72 thf(fact_3849_mod__minus__cong,axiom,
% 5.46/5.72 ! [A: int,B2: int,A2: int] :
% 5.46/5.72 ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.72 = ( modulo_modulo_int @ A2 @ B2 ) )
% 5.46/5.72 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.72 = ( modulo_modulo_int @ ( uminus_uminus_int @ A2 ) @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % mod_minus_cong
% 5.46/5.72 thf(fact_3850_mod__minus__cong,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer,A2: code_integer] :
% 5.46/5.72 ( ( ( modulo364778990260209775nteger @ A @ B2 )
% 5.46/5.72 = ( modulo364778990260209775nteger @ A2 @ B2 ) )
% 5.46/5.72 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 )
% 5.46/5.72 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % mod_minus_cong
% 5.46/5.72 thf(fact_3851_mod__minus__right,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.72 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % mod_minus_right
% 5.46/5.72 thf(fact_3852_mod__minus__right,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.72 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % mod_minus_right
% 5.46/5.72 thf(fact_3853_signed__take__bit__minus,axiom,
% 5.46/5.72 ! [N: nat,K: int] :
% 5.46/5.72 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 5.46/5.72 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_minus
% 5.46/5.72 thf(fact_3854_neg__numeral__le__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_numeral
% 5.46/5.72 thf(fact_3855_neg__numeral__le__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_numeral
% 5.46/5.72 thf(fact_3856_neg__numeral__le__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_numeral
% 5.46/5.72 thf(fact_3857_neg__numeral__le__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_numeral
% 5.46/5.72 thf(fact_3858_not__numeral__le__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_le_neg_numeral
% 5.46/5.72 thf(fact_3859_not__numeral__le__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_le_neg_numeral
% 5.46/5.72 thf(fact_3860_not__numeral__le__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_le_neg_numeral
% 5.46/5.72 thf(fact_3861_not__numeral__le__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_le_neg_numeral
% 5.46/5.72 thf(fact_3862_zero__neq__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( zero_zero_real
% 5.46/5.72 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_neq_neg_numeral
% 5.46/5.72 thf(fact_3863_zero__neq__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( zero_zero_int
% 5.46/5.72 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_neq_neg_numeral
% 5.46/5.72 thf(fact_3864_zero__neq__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( zero_zero_complex
% 5.46/5.72 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_neq_neg_numeral
% 5.46/5.72 thf(fact_3865_zero__neq__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( zero_z3403309356797280102nteger
% 5.46/5.72 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_neq_neg_numeral
% 5.46/5.72 thf(fact_3866_zero__neq__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( zero_zero_rat
% 5.46/5.72 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_neq_neg_numeral
% 5.46/5.72 thf(fact_3867_not__numeral__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_less_neg_numeral
% 5.46/5.72 thf(fact_3868_not__numeral__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_less_neg_numeral
% 5.46/5.72 thf(fact_3869_not__numeral__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_less_neg_numeral
% 5.46/5.72 thf(fact_3870_not__numeral__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_less_neg_numeral
% 5.46/5.72 thf(fact_3871_neg__numeral__less__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_numeral
% 5.46/5.72 thf(fact_3872_neg__numeral__less__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_numeral
% 5.46/5.72 thf(fact_3873_neg__numeral__less__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_numeral
% 5.46/5.72 thf(fact_3874_neg__numeral__less__numeral,axiom,
% 5.46/5.72 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_numeral
% 5.46/5.72 thf(fact_3875_le__minus__one__simps_I2_J,axiom,
% 5.46/5.72 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(2)
% 5.46/5.72 thf(fact_3876_le__minus__one__simps_I2_J,axiom,
% 5.46/5.72 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(2)
% 5.46/5.72 thf(fact_3877_le__minus__one__simps_I2_J,axiom,
% 5.46/5.72 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(2)
% 5.46/5.72 thf(fact_3878_le__minus__one__simps_I2_J,axiom,
% 5.46/5.72 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(2)
% 5.46/5.72 thf(fact_3879_le__minus__one__simps_I4_J,axiom,
% 5.46/5.72 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(4)
% 5.46/5.72 thf(fact_3880_le__minus__one__simps_I4_J,axiom,
% 5.46/5.72 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(4)
% 5.46/5.72 thf(fact_3881_le__minus__one__simps_I4_J,axiom,
% 5.46/5.72 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(4)
% 5.46/5.72 thf(fact_3882_le__minus__one__simps_I4_J,axiom,
% 5.46/5.72 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(4)
% 5.46/5.72 thf(fact_3883_zero__neq__neg__one,axiom,
% 5.46/5.72 ( zero_zero_real
% 5.46/5.72 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_neq_neg_one
% 5.46/5.72 thf(fact_3884_zero__neq__neg__one,axiom,
% 5.46/5.72 ( zero_zero_int
% 5.46/5.72 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_neq_neg_one
% 5.46/5.72 thf(fact_3885_zero__neq__neg__one,axiom,
% 5.46/5.72 ( zero_zero_complex
% 5.46/5.72 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_neq_neg_one
% 5.46/5.72 thf(fact_3886_zero__neq__neg__one,axiom,
% 5.46/5.72 ( zero_z3403309356797280102nteger
% 5.46/5.72 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_neq_neg_one
% 5.46/5.72 thf(fact_3887_zero__neq__neg__one,axiom,
% 5.46/5.72 ( zero_zero_rat
% 5.46/5.72 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % zero_neq_neg_one
% 5.46/5.72 thf(fact_3888_neg__eq__iff__add__eq__0,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( ( uminus_uminus_real @ A )
% 5.46/5.72 = B2 )
% 5.46/5.72 = ( ( plus_plus_real @ A @ B2 )
% 5.46/5.72 = zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_eq_iff_add_eq_0
% 5.46/5.72 thf(fact_3889_neg__eq__iff__add__eq__0,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( ( uminus_uminus_int @ A )
% 5.46/5.72 = B2 )
% 5.46/5.72 = ( ( plus_plus_int @ A @ B2 )
% 5.46/5.72 = zero_zero_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_eq_iff_add_eq_0
% 5.46/5.72 thf(fact_3890_neg__eq__iff__add__eq__0,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.72 = B2 )
% 5.46/5.72 = ( ( plus_plus_complex @ A @ B2 )
% 5.46/5.72 = zero_zero_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_eq_iff_add_eq_0
% 5.46/5.72 thf(fact_3891_neg__eq__iff__add__eq__0,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.72 = B2 )
% 5.46/5.72 = ( ( plus_p5714425477246183910nteger @ A @ B2 )
% 5.46/5.72 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_eq_iff_add_eq_0
% 5.46/5.72 thf(fact_3892_neg__eq__iff__add__eq__0,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( ( uminus_uminus_rat @ A )
% 5.46/5.72 = B2 )
% 5.46/5.72 = ( ( plus_plus_rat @ A @ B2 )
% 5.46/5.72 = zero_zero_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_eq_iff_add_eq_0
% 5.46/5.72 thf(fact_3893_eq__neg__iff__add__eq__0,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( A
% 5.46/5.72 = ( uminus_uminus_real @ B2 ) )
% 5.46/5.72 = ( ( plus_plus_real @ A @ B2 )
% 5.46/5.72 = zero_zero_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_neg_iff_add_eq_0
% 5.46/5.72 thf(fact_3894_eq__neg__iff__add__eq__0,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( A
% 5.46/5.72 = ( uminus_uminus_int @ B2 ) )
% 5.46/5.72 = ( ( plus_plus_int @ A @ B2 )
% 5.46/5.72 = zero_zero_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_neg_iff_add_eq_0
% 5.46/5.72 thf(fact_3895_eq__neg__iff__add__eq__0,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( A
% 5.46/5.72 = ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.72 = ( ( plus_plus_complex @ A @ B2 )
% 5.46/5.72 = zero_zero_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_neg_iff_add_eq_0
% 5.46/5.72 thf(fact_3896_eq__neg__iff__add__eq__0,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( A
% 5.46/5.72 = ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.72 = ( ( plus_p5714425477246183910nteger @ A @ B2 )
% 5.46/5.72 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_neg_iff_add_eq_0
% 5.46/5.72 thf(fact_3897_eq__neg__iff__add__eq__0,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( A
% 5.46/5.72 = ( uminus_uminus_rat @ B2 ) )
% 5.46/5.72 = ( ( plus_plus_rat @ A @ B2 )
% 5.46/5.72 = zero_zero_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_neg_iff_add_eq_0
% 5.46/5.72 thf(fact_3898_add_Oinverse__unique,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( ( plus_plus_real @ A @ B2 )
% 5.46/5.72 = zero_zero_real )
% 5.46/5.72 => ( ( uminus_uminus_real @ A )
% 5.46/5.72 = B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % add.inverse_unique
% 5.46/5.72 thf(fact_3899_add_Oinverse__unique,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( ( plus_plus_int @ A @ B2 )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 => ( ( uminus_uminus_int @ A )
% 5.46/5.72 = B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % add.inverse_unique
% 5.46/5.72 thf(fact_3900_add_Oinverse__unique,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( ( plus_plus_complex @ A @ B2 )
% 5.46/5.72 = zero_zero_complex )
% 5.46/5.72 => ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.72 = B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % add.inverse_unique
% 5.46/5.72 thf(fact_3901_add_Oinverse__unique,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( ( plus_p5714425477246183910nteger @ A @ B2 )
% 5.46/5.72 = zero_z3403309356797280102nteger )
% 5.46/5.72 => ( ( uminus1351360451143612070nteger @ A )
% 5.46/5.72 = B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % add.inverse_unique
% 5.46/5.72 thf(fact_3902_add_Oinverse__unique,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( ( plus_plus_rat @ A @ B2 )
% 5.46/5.72 = zero_zero_rat )
% 5.46/5.72 => ( ( uminus_uminus_rat @ A )
% 5.46/5.72 = B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % add.inverse_unique
% 5.46/5.72 thf(fact_3903_ab__group__add__class_Oab__left__minus,axiom,
% 5.46/5.72 ! [A: real] :
% 5.46/5.72 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.46/5.72 = zero_zero_real ) ).
% 5.46/5.72
% 5.46/5.72 % ab_group_add_class.ab_left_minus
% 5.46/5.72 thf(fact_3904_ab__group__add__class_Oab__left__minus,axiom,
% 5.46/5.72 ! [A: int] :
% 5.46/5.72 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.46/5.72 = zero_zero_int ) ).
% 5.46/5.72
% 5.46/5.72 % ab_group_add_class.ab_left_minus
% 5.46/5.72 thf(fact_3905_ab__group__add__class_Oab__left__minus,axiom,
% 5.46/5.72 ! [A: complex] :
% 5.46/5.72 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.46/5.72 = zero_zero_complex ) ).
% 5.46/5.72
% 5.46/5.72 % ab_group_add_class.ab_left_minus
% 5.46/5.72 thf(fact_3906_ab__group__add__class_Oab__left__minus,axiom,
% 5.46/5.72 ! [A: code_integer] :
% 5.46/5.72 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.46/5.72 = zero_z3403309356797280102nteger ) ).
% 5.46/5.72
% 5.46/5.72 % ab_group_add_class.ab_left_minus
% 5.46/5.72 thf(fact_3907_ab__group__add__class_Oab__left__minus,axiom,
% 5.46/5.72 ! [A: rat] :
% 5.46/5.72 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.46/5.72 = zero_zero_rat ) ).
% 5.46/5.72
% 5.46/5.72 % ab_group_add_class.ab_left_minus
% 5.46/5.72 thf(fact_3908_add__eq__0__iff,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( ( plus_plus_real @ A @ B2 )
% 5.46/5.72 = zero_zero_real )
% 5.46/5.72 = ( B2
% 5.46/5.72 = ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_eq_0_iff
% 5.46/5.72 thf(fact_3909_add__eq__0__iff,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( ( plus_plus_int @ A @ B2 )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 = ( B2
% 5.46/5.72 = ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_eq_0_iff
% 5.46/5.72 thf(fact_3910_add__eq__0__iff,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( ( plus_plus_complex @ A @ B2 )
% 5.46/5.72 = zero_zero_complex )
% 5.46/5.72 = ( B2
% 5.46/5.72 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_eq_0_iff
% 5.46/5.72 thf(fact_3911_add__eq__0__iff,axiom,
% 5.46/5.72 ! [A: code_integer,B2: code_integer] :
% 5.46/5.72 ( ( ( plus_p5714425477246183910nteger @ A @ B2 )
% 5.46/5.72 = zero_z3403309356797280102nteger )
% 5.46/5.72 = ( B2
% 5.46/5.72 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_eq_0_iff
% 5.46/5.72 thf(fact_3912_add__eq__0__iff,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( ( plus_plus_rat @ A @ B2 )
% 5.46/5.72 = zero_zero_rat )
% 5.46/5.72 = ( B2
% 5.46/5.72 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_eq_0_iff
% 5.46/5.72 thf(fact_3913_less__minus__one__simps_I2_J,axiom,
% 5.46/5.72 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(2)
% 5.46/5.72 thf(fact_3914_less__minus__one__simps_I2_J,axiom,
% 5.46/5.72 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(2)
% 5.46/5.72 thf(fact_3915_less__minus__one__simps_I2_J,axiom,
% 5.46/5.72 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(2)
% 5.46/5.72 thf(fact_3916_less__minus__one__simps_I2_J,axiom,
% 5.46/5.72 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(2)
% 5.46/5.72 thf(fact_3917_less__minus__one__simps_I4_J,axiom,
% 5.46/5.72 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(4)
% 5.46/5.72 thf(fact_3918_less__minus__one__simps_I4_J,axiom,
% 5.46/5.72 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(4)
% 5.46/5.72 thf(fact_3919_less__minus__one__simps_I4_J,axiom,
% 5.46/5.72 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(4)
% 5.46/5.72 thf(fact_3920_less__minus__one__simps_I4_J,axiom,
% 5.46/5.72 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(4)
% 5.46/5.72 thf(fact_3921_numeral__times__minus__swap,axiom,
% 5.46/5.72 ! [W: num,X4: real] :
% 5.46/5.72 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X4 ) )
% 5.46/5.72 = ( times_times_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_times_minus_swap
% 5.46/5.72 thf(fact_3922_numeral__times__minus__swap,axiom,
% 5.46/5.72 ! [W: num,X4: int] :
% 5.46/5.72 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X4 ) )
% 5.46/5.72 = ( times_times_int @ X4 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_times_minus_swap
% 5.46/5.72 thf(fact_3923_numeral__times__minus__swap,axiom,
% 5.46/5.72 ! [W: num,X4: complex] :
% 5.46/5.72 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X4 ) )
% 5.46/5.72 = ( times_times_complex @ X4 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_times_minus_swap
% 5.46/5.72 thf(fact_3924_numeral__times__minus__swap,axiom,
% 5.46/5.72 ! [W: num,X4: code_integer] :
% 5.46/5.72 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X4 ) )
% 5.46/5.72 = ( times_3573771949741848930nteger @ X4 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_times_minus_swap
% 5.46/5.72 thf(fact_3925_numeral__times__minus__swap,axiom,
% 5.46/5.72 ! [W: num,X4: rat] :
% 5.46/5.72 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X4 ) )
% 5.46/5.72 = ( times_times_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_times_minus_swap
% 5.46/5.72 thf(fact_3926_nonzero__minus__divide__right,axiom,
% 5.46/5.72 ! [B2: real,A: real] :
% 5.46/5.72 ( ( B2 != zero_zero_real )
% 5.46/5.72 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.72 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_minus_divide_right
% 5.46/5.72 thf(fact_3927_nonzero__minus__divide__right,axiom,
% 5.46/5.72 ! [B2: complex,A: complex] :
% 5.46/5.72 ( ( B2 != zero_zero_complex )
% 5.46/5.72 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_minus_divide_right
% 5.46/5.72 thf(fact_3928_nonzero__minus__divide__right,axiom,
% 5.46/5.72 ! [B2: rat,A: rat] :
% 5.46/5.72 ( ( B2 != zero_zero_rat )
% 5.46/5.72 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B2 ) )
% 5.46/5.72 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_minus_divide_right
% 5.46/5.72 thf(fact_3929_nonzero__minus__divide__divide,axiom,
% 5.46/5.72 ! [B2: real,A: real] :
% 5.46/5.72 ( ( B2 != zero_zero_real )
% 5.46/5.72 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B2 ) )
% 5.46/5.72 = ( divide_divide_real @ A @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_minus_divide_divide
% 5.46/5.72 thf(fact_3930_nonzero__minus__divide__divide,axiom,
% 5.46/5.72 ! [B2: complex,A: complex] :
% 5.46/5.72 ( ( B2 != zero_zero_complex )
% 5.46/5.72 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ A @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_minus_divide_divide
% 5.46/5.72 thf(fact_3931_nonzero__minus__divide__divide,axiom,
% 5.46/5.72 ! [B2: rat,A: rat] :
% 5.46/5.72 ( ( B2 != zero_zero_rat )
% 5.46/5.72 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B2 ) )
% 5.46/5.72 = ( divide_divide_rat @ A @ B2 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_minus_divide_divide
% 5.46/5.72 thf(fact_3932_one__neq__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( one_one_real
% 5.46/5.72 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_neq_neg_numeral
% 5.46/5.72 thf(fact_3933_one__neq__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( one_one_int
% 5.46/5.72 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_neq_neg_numeral
% 5.46/5.72 thf(fact_3934_one__neq__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( one_one_complex
% 5.46/5.72 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_neq_neg_numeral
% 5.46/5.72 thf(fact_3935_one__neq__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( one_one_Code_integer
% 5.46/5.72 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_neq_neg_numeral
% 5.46/5.72 thf(fact_3936_one__neq__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( one_one_rat
% 5.46/5.72 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % one_neq_neg_numeral
% 5.46/5.72 thf(fact_3937_numeral__neq__neg__one,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( ( numeral_numeral_real @ N )
% 5.46/5.72 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_neq_neg_one
% 5.46/5.72 thf(fact_3938_numeral__neq__neg__one,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( ( numeral_numeral_int @ N )
% 5.46/5.72 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_neq_neg_one
% 5.46/5.72 thf(fact_3939_numeral__neq__neg__one,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( ( numera6690914467698888265omplex @ N )
% 5.46/5.72 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_neq_neg_one
% 5.46/5.72 thf(fact_3940_numeral__neq__neg__one,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( ( numera6620942414471956472nteger @ N )
% 5.46/5.72 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_neq_neg_one
% 5.46/5.72 thf(fact_3941_numeral__neq__neg__one,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( ( numeral_numeral_rat @ N )
% 5.46/5.72 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % numeral_neq_neg_one
% 5.46/5.72 thf(fact_3942_square__eq__1__iff,axiom,
% 5.46/5.72 ! [X4: real] :
% 5.46/5.72 ( ( ( times_times_real @ X4 @ X4 )
% 5.46/5.72 = one_one_real )
% 5.46/5.72 = ( ( X4 = one_one_real )
% 5.46/5.72 | ( X4
% 5.46/5.72 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_eq_1_iff
% 5.46/5.72 thf(fact_3943_square__eq__1__iff,axiom,
% 5.46/5.72 ! [X4: int] :
% 5.46/5.72 ( ( ( times_times_int @ X4 @ X4 )
% 5.46/5.72 = one_one_int )
% 5.46/5.72 = ( ( X4 = one_one_int )
% 5.46/5.72 | ( X4
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_eq_1_iff
% 5.46/5.72 thf(fact_3944_square__eq__1__iff,axiom,
% 5.46/5.72 ! [X4: complex] :
% 5.46/5.72 ( ( ( times_times_complex @ X4 @ X4 )
% 5.46/5.72 = one_one_complex )
% 5.46/5.72 = ( ( X4 = one_one_complex )
% 5.46/5.72 | ( X4
% 5.46/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_eq_1_iff
% 5.46/5.72 thf(fact_3945_square__eq__1__iff,axiom,
% 5.46/5.72 ! [X4: code_integer] :
% 5.46/5.72 ( ( ( times_3573771949741848930nteger @ X4 @ X4 )
% 5.46/5.72 = one_one_Code_integer )
% 5.46/5.72 = ( ( X4 = one_one_Code_integer )
% 5.46/5.72 | ( X4
% 5.46/5.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_eq_1_iff
% 5.46/5.72 thf(fact_3946_square__eq__1__iff,axiom,
% 5.46/5.72 ! [X4: rat] :
% 5.46/5.72 ( ( ( times_times_rat @ X4 @ X4 )
% 5.46/5.72 = one_one_rat )
% 5.46/5.72 = ( ( X4 = one_one_rat )
% 5.46/5.72 | ( X4
% 5.46/5.72 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_eq_1_iff
% 5.46/5.72 thf(fact_3947_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.46/5.72 ( minus_minus_real
% 5.46/5.72 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.46/5.72 thf(fact_3948_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.46/5.72 ( minus_minus_int
% 5.46/5.72 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.46/5.72 thf(fact_3949_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.46/5.72 ( minus_minus_complex
% 5.46/5.72 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.46/5.72 thf(fact_3950_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.46/5.72 ( minus_8373710615458151222nteger
% 5.46/5.72 = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.46/5.72 thf(fact_3951_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.46/5.72 ( minus_minus_rat
% 5.46/5.72 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.46/5.72 thf(fact_3952_diff__conv__add__uminus,axiom,
% 5.46/5.72 ( minus_minus_real
% 5.46/5.72 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diff_conv_add_uminus
% 5.46/5.72 thf(fact_3953_diff__conv__add__uminus,axiom,
% 5.46/5.72 ( minus_minus_int
% 5.46/5.72 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diff_conv_add_uminus
% 5.46/5.72 thf(fact_3954_diff__conv__add__uminus,axiom,
% 5.46/5.72 ( minus_minus_complex
% 5.46/5.72 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diff_conv_add_uminus
% 5.46/5.72 thf(fact_3955_diff__conv__add__uminus,axiom,
% 5.46/5.72 ( minus_8373710615458151222nteger
% 5.46/5.72 = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diff_conv_add_uminus
% 5.46/5.72 thf(fact_3956_diff__conv__add__uminus,axiom,
% 5.46/5.72 ( minus_minus_rat
% 5.46/5.72 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % diff_conv_add_uminus
% 5.46/5.72 thf(fact_3957_group__cancel_Osub2,axiom,
% 5.46/5.72 ! [B4: real,K: real,B2: real,A: real] :
% 5.46/5.72 ( ( B4
% 5.46/5.72 = ( plus_plus_real @ K @ B2 ) )
% 5.46/5.72 => ( ( minus_minus_real @ A @ B4 )
% 5.46/5.72 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % group_cancel.sub2
% 5.46/5.72 thf(fact_3958_group__cancel_Osub2,axiom,
% 5.46/5.72 ! [B4: int,K: int,B2: int,A: int] :
% 5.46/5.72 ( ( B4
% 5.46/5.72 = ( plus_plus_int @ K @ B2 ) )
% 5.46/5.72 => ( ( minus_minus_int @ A @ B4 )
% 5.46/5.72 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % group_cancel.sub2
% 5.46/5.72 thf(fact_3959_group__cancel_Osub2,axiom,
% 5.46/5.72 ! [B4: complex,K: complex,B2: complex,A: complex] :
% 5.46/5.72 ( ( B4
% 5.46/5.72 = ( plus_plus_complex @ K @ B2 ) )
% 5.46/5.72 => ( ( minus_minus_complex @ A @ B4 )
% 5.46/5.72 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % group_cancel.sub2
% 5.46/5.72 thf(fact_3960_group__cancel_Osub2,axiom,
% 5.46/5.72 ! [B4: code_integer,K: code_integer,B2: code_integer,A: code_integer] :
% 5.46/5.72 ( ( B4
% 5.46/5.72 = ( plus_p5714425477246183910nteger @ K @ B2 ) )
% 5.46/5.72 => ( ( minus_8373710615458151222nteger @ A @ B4 )
% 5.46/5.72 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % group_cancel.sub2
% 5.46/5.72 thf(fact_3961_group__cancel_Osub2,axiom,
% 5.46/5.72 ! [B4: rat,K: rat,B2: rat,A: rat] :
% 5.46/5.72 ( ( B4
% 5.46/5.72 = ( plus_plus_rat @ K @ B2 ) )
% 5.46/5.72 => ( ( minus_minus_rat @ A @ B4 )
% 5.46/5.72 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % group_cancel.sub2
% 5.46/5.72 thf(fact_3962_dvd__div__neg,axiom,
% 5.46/5.72 ! [B2: real,A: real] :
% 5.46/5.72 ( ( dvd_dvd_real @ B2 @ A )
% 5.46/5.72 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B2 ) )
% 5.46/5.72 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % dvd_div_neg
% 5.46/5.72 thf(fact_3963_dvd__div__neg,axiom,
% 5.46/5.72 ! [B2: int,A: int] :
% 5.46/5.72 ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.72 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.72 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % dvd_div_neg
% 5.46/5.72 thf(fact_3964_dvd__div__neg,axiom,
% 5.46/5.72 ! [B2: complex,A: complex] :
% 5.46/5.72 ( ( dvd_dvd_complex @ B2 @ A )
% 5.46/5.72 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B2 ) )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % dvd_div_neg
% 5.46/5.72 thf(fact_3965_dvd__div__neg,axiom,
% 5.46/5.72 ! [B2: code_integer,A: code_integer] :
% 5.46/5.72 ( ( dvd_dvd_Code_integer @ B2 @ A )
% 5.46/5.72 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B2 ) )
% 5.46/5.72 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % dvd_div_neg
% 5.46/5.72 thf(fact_3966_dvd__div__neg,axiom,
% 5.46/5.72 ! [B2: rat,A: rat] :
% 5.46/5.72 ( ( dvd_dvd_rat @ B2 @ A )
% 5.46/5.72 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B2 ) )
% 5.46/5.72 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % dvd_div_neg
% 5.46/5.72 thf(fact_3967_dvd__neg__div,axiom,
% 5.46/5.72 ! [B2: real,A: real] :
% 5.46/5.72 ( ( dvd_dvd_real @ B2 @ A )
% 5.46/5.72 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % dvd_neg_div
% 5.46/5.72 thf(fact_3968_dvd__neg__div,axiom,
% 5.46/5.72 ! [B2: int,A: int] :
% 5.46/5.72 ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.72 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % dvd_neg_div
% 5.46/5.72 thf(fact_3969_dvd__neg__div,axiom,
% 5.46/5.72 ! [B2: complex,A: complex] :
% 5.46/5.72 ( ( dvd_dvd_complex @ B2 @ A )
% 5.46/5.72 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B2 )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % dvd_neg_div
% 5.46/5.72 thf(fact_3970_dvd__neg__div,axiom,
% 5.46/5.72 ! [B2: code_integer,A: code_integer] :
% 5.46/5.72 ( ( dvd_dvd_Code_integer @ B2 @ A )
% 5.46/5.72 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 )
% 5.46/5.72 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % dvd_neg_div
% 5.46/5.72 thf(fact_3971_dvd__neg__div,axiom,
% 5.46/5.72 ! [B2: rat,A: rat] :
% 5.46/5.72 ( ( dvd_dvd_rat @ B2 @ A )
% 5.46/5.72 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % dvd_neg_div
% 5.46/5.72 thf(fact_3972_real__minus__mult__self__le,axiom,
% 5.46/5.72 ! [U: real,X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X4 @ X4 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_minus_mult_self_le
% 5.46/5.72 thf(fact_3973_pos__zmult__eq__1__iff__lemma,axiom,
% 5.46/5.72 ! [M: int,N: int] :
% 5.46/5.72 ( ( ( times_times_int @ M @ N )
% 5.46/5.72 = one_one_int )
% 5.46/5.72 => ( ( M = one_one_int )
% 5.46/5.72 | ( M
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pos_zmult_eq_1_iff_lemma
% 5.46/5.72 thf(fact_3974_zmult__eq__1__iff,axiom,
% 5.46/5.72 ! [M: int,N: int] :
% 5.46/5.72 ( ( ( times_times_int @ M @ N )
% 5.46/5.72 = one_one_int )
% 5.46/5.72 = ( ( ( M = one_one_int )
% 5.46/5.72 & ( N = one_one_int ) )
% 5.46/5.72 | ( ( M
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.72 & ( N
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zmult_eq_1_iff
% 5.46/5.72 thf(fact_3975_minus__int__code_I2_J,axiom,
% 5.46/5.72 ! [L2: int] :
% 5.46/5.72 ( ( minus_minus_int @ zero_zero_int @ L2 )
% 5.46/5.72 = ( uminus_uminus_int @ L2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_int_code(2)
% 5.46/5.72 thf(fact_3976_zmod__zminus2__not__zero,axiom,
% 5.46/5.72 ! [K: int,L2: int] :
% 5.46/5.72 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L2 ) )
% 5.46/5.72 != zero_zero_int )
% 5.46/5.72 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.72 != zero_zero_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % zmod_zminus2_not_zero
% 5.46/5.72 thf(fact_3977_zmod__zminus1__not__zero,axiom,
% 5.46/5.72 ! [K: int,L2: int] :
% 5.46/5.72 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.46/5.72 != zero_zero_int )
% 5.46/5.72 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.72 != zero_zero_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % zmod_zminus1_not_zero
% 5.46/5.72 thf(fact_3978_minus__real__def,axiom,
% 5.46/5.72 ( minus_minus_real
% 5.46/5.72 = ( ^ [X: real,Y: real] : ( plus_plus_real @ X @ ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_real_def
% 5.46/5.72 thf(fact_3979_not__zero__le__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_zero_le_neg_numeral
% 5.46/5.72 thf(fact_3980_not__zero__le__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_zero_le_neg_numeral
% 5.46/5.72 thf(fact_3981_not__zero__le__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_zero_le_neg_numeral
% 5.46/5.72 thf(fact_3982_not__zero__le__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_zero_le_neg_numeral
% 5.46/5.72 thf(fact_3983_neg__numeral__le__zero,axiom,
% 5.46/5.72 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_zero
% 5.46/5.72 thf(fact_3984_neg__numeral__le__zero,axiom,
% 5.46/5.72 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_zero
% 5.46/5.72 thf(fact_3985_neg__numeral__le__zero,axiom,
% 5.46/5.72 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_zero
% 5.46/5.72 thf(fact_3986_neg__numeral__le__zero,axiom,
% 5.46/5.72 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_zero
% 5.46/5.72 thf(fact_3987_not__zero__less__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_zero_less_neg_numeral
% 5.46/5.72 thf(fact_3988_not__zero__less__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_zero_less_neg_numeral
% 5.46/5.72 thf(fact_3989_not__zero__less__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_zero_less_neg_numeral
% 5.46/5.72 thf(fact_3990_not__zero__less__neg__numeral,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_zero_less_neg_numeral
% 5.46/5.72 thf(fact_3991_neg__numeral__less__zero,axiom,
% 5.46/5.72 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_zero
% 5.46/5.72 thf(fact_3992_neg__numeral__less__zero,axiom,
% 5.46/5.72 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_zero
% 5.46/5.72 thf(fact_3993_neg__numeral__less__zero,axiom,
% 5.46/5.72 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_zero
% 5.46/5.72 thf(fact_3994_neg__numeral__less__zero,axiom,
% 5.46/5.72 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_zero
% 5.46/5.72 thf(fact_3995_le__minus__one__simps_I3_J,axiom,
% 5.46/5.72 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(3)
% 5.46/5.72 thf(fact_3996_le__minus__one__simps_I3_J,axiom,
% 5.46/5.72 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(3)
% 5.46/5.72 thf(fact_3997_le__minus__one__simps_I3_J,axiom,
% 5.46/5.72 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(3)
% 5.46/5.72 thf(fact_3998_le__minus__one__simps_I3_J,axiom,
% 5.46/5.72 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(3)
% 5.46/5.72 thf(fact_3999_le__minus__one__simps_I1_J,axiom,
% 5.46/5.72 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(1)
% 5.46/5.72 thf(fact_4000_le__minus__one__simps_I1_J,axiom,
% 5.46/5.72 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(1)
% 5.46/5.72 thf(fact_4001_le__minus__one__simps_I1_J,axiom,
% 5.46/5.72 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(1)
% 5.46/5.72 thf(fact_4002_le__minus__one__simps_I1_J,axiom,
% 5.46/5.72 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.46/5.72
% 5.46/5.72 % le_minus_one_simps(1)
% 5.46/5.72 thf(fact_4003_less__minus__one__simps_I3_J,axiom,
% 5.46/5.72 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(3)
% 5.46/5.72 thf(fact_4004_less__minus__one__simps_I3_J,axiom,
% 5.46/5.72 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(3)
% 5.46/5.72 thf(fact_4005_less__minus__one__simps_I3_J,axiom,
% 5.46/5.72 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(3)
% 5.46/5.72 thf(fact_4006_less__minus__one__simps_I3_J,axiom,
% 5.46/5.72 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(3)
% 5.46/5.72 thf(fact_4007_less__minus__one__simps_I1_J,axiom,
% 5.46/5.72 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(1)
% 5.46/5.72 thf(fact_4008_less__minus__one__simps_I1_J,axiom,
% 5.46/5.72 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(1)
% 5.46/5.72 thf(fact_4009_less__minus__one__simps_I1_J,axiom,
% 5.46/5.72 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(1)
% 5.46/5.72 thf(fact_4010_less__minus__one__simps_I1_J,axiom,
% 5.46/5.72 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.46/5.72
% 5.46/5.72 % less_minus_one_simps(1)
% 5.46/5.72 thf(fact_4011_not__one__le__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_one_le_neg_numeral
% 5.46/5.72 thf(fact_4012_not__one__le__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_one_le_neg_numeral
% 5.46/5.72 thf(fact_4013_not__one__le__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_one_le_neg_numeral
% 5.46/5.72 thf(fact_4014_not__one__le__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_one_le_neg_numeral
% 5.46/5.72 thf(fact_4015_not__numeral__le__neg__one,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_le_neg_one
% 5.46/5.72 thf(fact_4016_not__numeral__le__neg__one,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_le_neg_one
% 5.46/5.72 thf(fact_4017_not__numeral__le__neg__one,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_le_neg_one
% 5.46/5.72 thf(fact_4018_not__numeral__le__neg__one,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_le_neg_one
% 5.46/5.72 thf(fact_4019_neg__numeral__le__neg__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_neg_one
% 5.46/5.72 thf(fact_4020_neg__numeral__le__neg__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_neg_one
% 5.46/5.72 thf(fact_4021_neg__numeral__le__neg__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_neg_one
% 5.46/5.72 thf(fact_4022_neg__numeral__le__neg__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_neg_one
% 5.46/5.72 thf(fact_4023_neg__one__le__numeral,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_le_numeral
% 5.46/5.72 thf(fact_4024_neg__one__le__numeral,axiom,
% 5.46/5.72 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_le_numeral
% 5.46/5.72 thf(fact_4025_neg__one__le__numeral,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_le_numeral
% 5.46/5.72 thf(fact_4026_neg__one__le__numeral,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_le_numeral
% 5.46/5.72 thf(fact_4027_neg__numeral__le__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_one
% 5.46/5.72 thf(fact_4028_neg__numeral__le__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_one
% 5.46/5.72 thf(fact_4029_neg__numeral__le__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_one
% 5.46/5.72 thf(fact_4030_neg__numeral__le__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_le_one
% 5.46/5.72 thf(fact_4031_not__neg__one__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_neg_one_less_neg_numeral
% 5.46/5.72 thf(fact_4032_not__neg__one__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_neg_one_less_neg_numeral
% 5.46/5.72 thf(fact_4033_not__neg__one__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_neg_one_less_neg_numeral
% 5.46/5.72 thf(fact_4034_not__neg__one__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_neg_one_less_neg_numeral
% 5.46/5.72 thf(fact_4035_not__one__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_one_less_neg_numeral
% 5.46/5.72 thf(fact_4036_not__one__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_one_less_neg_numeral
% 5.46/5.72 thf(fact_4037_not__one__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_one_less_neg_numeral
% 5.46/5.72 thf(fact_4038_not__one__less__neg__numeral,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_one_less_neg_numeral
% 5.46/5.72 thf(fact_4039_not__numeral__less__neg__one,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_less_neg_one
% 5.46/5.72 thf(fact_4040_not__numeral__less__neg__one,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_less_neg_one
% 5.46/5.72 thf(fact_4041_not__numeral__less__neg__one,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_less_neg_one
% 5.46/5.72 thf(fact_4042_not__numeral__less__neg__one,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % not_numeral_less_neg_one
% 5.46/5.72 thf(fact_4043_neg__one__less__numeral,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_less_numeral
% 5.46/5.72 thf(fact_4044_neg__one__less__numeral,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_less_numeral
% 5.46/5.72 thf(fact_4045_neg__one__less__numeral,axiom,
% 5.46/5.72 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_less_numeral
% 5.46/5.72 thf(fact_4046_neg__one__less__numeral,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_less_numeral
% 5.46/5.72 thf(fact_4047_neg__numeral__less__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_one
% 5.46/5.72 thf(fact_4048_neg__numeral__less__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_one
% 5.46/5.72 thf(fact_4049_neg__numeral__less__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_one
% 5.46/5.72 thf(fact_4050_neg__numeral__less__one,axiom,
% 5.46/5.72 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.46/5.72
% 5.46/5.72 % neg_numeral_less_one
% 5.46/5.72 thf(fact_4051_eq__minus__divide__eq,axiom,
% 5.46/5.72 ! [A: real,B2: real,C: real] :
% 5.46/5.72 ( ( A
% 5.46/5.72 = ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 5.46/5.72 = ( ( ( C != zero_zero_real )
% 5.46/5.72 => ( ( times_times_real @ A @ C )
% 5.46/5.72 = ( uminus_uminus_real @ B2 ) ) )
% 5.46/5.72 & ( ( C = zero_zero_real )
% 5.46/5.72 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_minus_divide_eq
% 5.46/5.72 thf(fact_4052_eq__minus__divide__eq,axiom,
% 5.46/5.72 ! [A: complex,B2: complex,C: complex] :
% 5.46/5.72 ( ( A
% 5.46/5.72 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B2 @ C ) ) )
% 5.46/5.72 = ( ( ( C != zero_zero_complex )
% 5.46/5.72 => ( ( times_times_complex @ A @ C )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ B2 ) ) )
% 5.46/5.72 & ( ( C = zero_zero_complex )
% 5.46/5.72 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_minus_divide_eq
% 5.46/5.72 thf(fact_4053_eq__minus__divide__eq,axiom,
% 5.46/5.72 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.72 ( ( A
% 5.46/5.72 = ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) )
% 5.46/5.72 = ( ( ( C != zero_zero_rat )
% 5.46/5.72 => ( ( times_times_rat @ A @ C )
% 5.46/5.72 = ( uminus_uminus_rat @ B2 ) ) )
% 5.46/5.72 & ( ( C = zero_zero_rat )
% 5.46/5.72 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_minus_divide_eq
% 5.46/5.72 thf(fact_4054_minus__divide__eq__eq,axiom,
% 5.46/5.72 ! [B2: real,C: real,A: real] :
% 5.46/5.72 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.72 = A )
% 5.46/5.72 = ( ( ( C != zero_zero_real )
% 5.46/5.72 => ( ( uminus_uminus_real @ B2 )
% 5.46/5.72 = ( times_times_real @ A @ C ) ) )
% 5.46/5.72 & ( ( C = zero_zero_real )
% 5.46/5.72 => ( A = zero_zero_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_eq_eq
% 5.46/5.72 thf(fact_4055_minus__divide__eq__eq,axiom,
% 5.46/5.72 ! [B2: complex,C: complex,A: complex] :
% 5.46/5.72 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B2 @ C ) )
% 5.46/5.72 = A )
% 5.46/5.72 = ( ( ( C != zero_zero_complex )
% 5.46/5.72 => ( ( uminus1482373934393186551omplex @ B2 )
% 5.46/5.72 = ( times_times_complex @ A @ C ) ) )
% 5.46/5.72 & ( ( C = zero_zero_complex )
% 5.46/5.72 => ( A = zero_zero_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_eq_eq
% 5.46/5.72 thf(fact_4056_minus__divide__eq__eq,axiom,
% 5.46/5.72 ! [B2: rat,C: rat,A: rat] :
% 5.46/5.72 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.72 = A )
% 5.46/5.72 = ( ( ( C != zero_zero_rat )
% 5.46/5.72 => ( ( uminus_uminus_rat @ B2 )
% 5.46/5.72 = ( times_times_rat @ A @ C ) ) )
% 5.46/5.72 & ( ( C = zero_zero_rat )
% 5.46/5.72 => ( A = zero_zero_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_eq_eq
% 5.46/5.72 thf(fact_4057_nonzero__neg__divide__eq__eq,axiom,
% 5.46/5.72 ! [B2: real,A: real,C: real] :
% 5.46/5.72 ( ( B2 != zero_zero_real )
% 5.46/5.72 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.72 = C )
% 5.46/5.72 = ( ( uminus_uminus_real @ A )
% 5.46/5.72 = ( times_times_real @ C @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_neg_divide_eq_eq
% 5.46/5.72 thf(fact_4058_nonzero__neg__divide__eq__eq,axiom,
% 5.46/5.72 ! [B2: complex,A: complex,C: complex] :
% 5.46/5.72 ( ( B2 != zero_zero_complex )
% 5.46/5.72 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.72 = C )
% 5.46/5.72 = ( ( uminus1482373934393186551omplex @ A )
% 5.46/5.72 = ( times_times_complex @ C @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_neg_divide_eq_eq
% 5.46/5.72 thf(fact_4059_nonzero__neg__divide__eq__eq,axiom,
% 5.46/5.72 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.72 ( ( B2 != zero_zero_rat )
% 5.46/5.72 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B2 ) )
% 5.46/5.72 = C )
% 5.46/5.72 = ( ( uminus_uminus_rat @ A )
% 5.46/5.72 = ( times_times_rat @ C @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_neg_divide_eq_eq
% 5.46/5.72 thf(fact_4060_nonzero__neg__divide__eq__eq2,axiom,
% 5.46/5.72 ! [B2: real,C: real,A: real] :
% 5.46/5.72 ( ( B2 != zero_zero_real )
% 5.46/5.72 => ( ( C
% 5.46/5.72 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B2 ) ) )
% 5.46/5.72 = ( ( times_times_real @ C @ B2 )
% 5.46/5.72 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_neg_divide_eq_eq2
% 5.46/5.72 thf(fact_4061_nonzero__neg__divide__eq__eq2,axiom,
% 5.46/5.72 ! [B2: complex,C: complex,A: complex] :
% 5.46/5.72 ( ( B2 != zero_zero_complex )
% 5.46/5.72 => ( ( C
% 5.46/5.72 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B2 ) ) )
% 5.46/5.72 = ( ( times_times_complex @ C @ B2 )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_neg_divide_eq_eq2
% 5.46/5.72 thf(fact_4062_nonzero__neg__divide__eq__eq2,axiom,
% 5.46/5.72 ! [B2: rat,C: rat,A: rat] :
% 5.46/5.72 ( ( B2 != zero_zero_rat )
% 5.46/5.72 => ( ( C
% 5.46/5.72 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B2 ) ) )
% 5.46/5.72 = ( ( times_times_rat @ C @ B2 )
% 5.46/5.72 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % nonzero_neg_divide_eq_eq2
% 5.46/5.72 thf(fact_4063_mult__1s__ring__1_I2_J,axiom,
% 5.46/5.72 ! [B2: real] :
% 5.46/5.72 ( ( times_times_real @ B2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.46/5.72 = ( uminus_uminus_real @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_1s_ring_1(2)
% 5.46/5.72 thf(fact_4064_mult__1s__ring__1_I2_J,axiom,
% 5.46/5.72 ! [B2: int] :
% 5.46/5.72 ( ( times_times_int @ B2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.46/5.72 = ( uminus_uminus_int @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_1s_ring_1(2)
% 5.46/5.72 thf(fact_4065_mult__1s__ring__1_I2_J,axiom,
% 5.46/5.72 ! [B2: complex] :
% 5.46/5.72 ( ( times_times_complex @ B2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_1s_ring_1(2)
% 5.46/5.72 thf(fact_4066_mult__1s__ring__1_I2_J,axiom,
% 5.46/5.72 ! [B2: code_integer] :
% 5.46/5.72 ( ( times_3573771949741848930nteger @ B2 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.46/5.72 = ( uminus1351360451143612070nteger @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_1s_ring_1(2)
% 5.46/5.72 thf(fact_4067_mult__1s__ring__1_I2_J,axiom,
% 5.46/5.72 ! [B2: rat] :
% 5.46/5.72 ( ( times_times_rat @ B2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.46/5.72 = ( uminus_uminus_rat @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_1s_ring_1(2)
% 5.46/5.72 thf(fact_4068_mult__1s__ring__1_I1_J,axiom,
% 5.46/5.72 ! [B2: real] :
% 5.46/5.72 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_real @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_1s_ring_1(1)
% 5.46/5.72 thf(fact_4069_mult__1s__ring__1_I1_J,axiom,
% 5.46/5.72 ! [B2: int] :
% 5.46/5.72 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_int @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_1s_ring_1(1)
% 5.46/5.72 thf(fact_4070_mult__1s__ring__1_I1_J,axiom,
% 5.46/5.72 ! [B2: complex] :
% 5.46/5.72 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B2 )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_1s_ring_1(1)
% 5.46/5.72 thf(fact_4071_mult__1s__ring__1_I1_J,axiom,
% 5.46/5.72 ! [B2: code_integer] :
% 5.46/5.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B2 )
% 5.46/5.72 = ( uminus1351360451143612070nteger @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_1s_ring_1(1)
% 5.46/5.72 thf(fact_4072_mult__1s__ring__1_I1_J,axiom,
% 5.46/5.72 ! [B2: rat] :
% 5.46/5.72 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_rat @ B2 ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_1s_ring_1(1)
% 5.46/5.72 thf(fact_4073_divide__eq__minus__1__iff,axiom,
% 5.46/5.72 ! [A: real,B2: real] :
% 5.46/5.72 ( ( ( divide_divide_real @ A @ B2 )
% 5.46/5.72 = ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.72 = ( ( B2 != zero_zero_real )
% 5.46/5.72 & ( A
% 5.46/5.72 = ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_eq_minus_1_iff
% 5.46/5.72 thf(fact_4074_divide__eq__minus__1__iff,axiom,
% 5.46/5.72 ! [A: complex,B2: complex] :
% 5.46/5.72 ( ( ( divide1717551699836669952omplex @ A @ B2 )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.72 = ( ( B2 != zero_zero_complex )
% 5.46/5.72 & ( A
% 5.46/5.72 = ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_eq_minus_1_iff
% 5.46/5.72 thf(fact_4075_divide__eq__minus__1__iff,axiom,
% 5.46/5.72 ! [A: rat,B2: rat] :
% 5.46/5.72 ( ( ( divide_divide_rat @ A @ B2 )
% 5.46/5.72 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.72 = ( ( B2 != zero_zero_rat )
% 5.46/5.72 & ( A
% 5.46/5.72 = ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_eq_minus_1_iff
% 5.46/5.72 thf(fact_4076_uminus__numeral__One,axiom,
% 5.46/5.72 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.46/5.72 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % uminus_numeral_One
% 5.46/5.72 thf(fact_4077_uminus__numeral__One,axiom,
% 5.46/5.72 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % uminus_numeral_One
% 5.46/5.72 thf(fact_4078_uminus__numeral__One,axiom,
% 5.46/5.72 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % uminus_numeral_One
% 5.46/5.72 thf(fact_4079_uminus__numeral__One,axiom,
% 5.46/5.72 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.46/5.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % uminus_numeral_One
% 5.46/5.72 thf(fact_4080_uminus__numeral__One,axiom,
% 5.46/5.72 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.46/5.72 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % uminus_numeral_One
% 5.46/5.72 thf(fact_4081_power__minus,axiom,
% 5.46/5.72 ! [A: real,N: nat] :
% 5.46/5.72 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.46/5.72 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus
% 5.46/5.72 thf(fact_4082_power__minus,axiom,
% 5.46/5.72 ! [A: int,N: nat] :
% 5.46/5.72 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.46/5.72 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus
% 5.46/5.72 thf(fact_4083_power__minus,axiom,
% 5.46/5.72 ! [A: complex,N: nat] :
% 5.46/5.72 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.46/5.72 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus
% 5.46/5.72 thf(fact_4084_power__minus,axiom,
% 5.46/5.72 ! [A: code_integer,N: nat] :
% 5.46/5.72 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.46/5.72 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus
% 5.46/5.72 thf(fact_4085_power__minus,axiom,
% 5.46/5.72 ! [A: rat,N: nat] :
% 5.46/5.72 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.46/5.72 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus
% 5.46/5.72 thf(fact_4086_power__minus__Bit0,axiom,
% 5.46/5.72 ! [X4: real,K: num] :
% 5.46/5.72 ( ( power_power_real @ ( uminus_uminus_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.72 = ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus_Bit0
% 5.46/5.72 thf(fact_4087_power__minus__Bit0,axiom,
% 5.46/5.72 ! [X4: int,K: num] :
% 5.46/5.72 ( ( power_power_int @ ( uminus_uminus_int @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.72 = ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus_Bit0
% 5.46/5.72 thf(fact_4088_power__minus__Bit0,axiom,
% 5.46/5.72 ! [X4: complex,K: num] :
% 5.46/5.72 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.72 = ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus_Bit0
% 5.46/5.72 thf(fact_4089_power__minus__Bit0,axiom,
% 5.46/5.72 ! [X4: code_integer,K: num] :
% 5.46/5.72 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.72 = ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus_Bit0
% 5.46/5.72 thf(fact_4090_power__minus__Bit0,axiom,
% 5.46/5.72 ! [X4: rat,K: num] :
% 5.46/5.72 ( ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.72 = ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus_Bit0
% 5.46/5.72 thf(fact_4091_real__add__less__0__iff,axiom,
% 5.46/5.72 ! [X4: real,Y3: real] :
% 5.46/5.72 ( ( ord_less_real @ ( plus_plus_real @ X4 @ Y3 ) @ zero_zero_real )
% 5.46/5.72 = ( ord_less_real @ Y3 @ ( uminus_uminus_real @ X4 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_add_less_0_iff
% 5.46/5.72 thf(fact_4092_real__0__less__add__iff,axiom,
% 5.46/5.72 ! [X4: real,Y3: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.72 = ( ord_less_real @ ( uminus_uminus_real @ X4 ) @ Y3 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_0_less_add_iff
% 5.46/5.72 thf(fact_4093_real__0__le__add__iff,axiom,
% 5.46/5.72 ! [X4: real,Y3: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( uminus_uminus_real @ X4 ) @ Y3 ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_0_le_add_iff
% 5.46/5.72 thf(fact_4094_real__add__le__0__iff,axiom,
% 5.46/5.72 ! [X4: real,Y3: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( plus_plus_real @ X4 @ Y3 ) @ zero_zero_real )
% 5.46/5.72 = ( ord_less_eq_real @ Y3 @ ( uminus_uminus_real @ X4 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % real_add_le_0_iff
% 5.46/5.72 thf(fact_4095_zmod__zminus2__eq__if,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.72 = zero_zero_int ) )
% 5.46/5.72 & ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.72 != zero_zero_int )
% 5.46/5.72 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.72 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B2 ) @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zmod_zminus2_eq_if
% 5.46/5.72 thf(fact_4096_zmod__zminus1__eq__if,axiom,
% 5.46/5.72 ! [A: int,B2: int] :
% 5.46/5.72 ( ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.72 = zero_zero_int ) )
% 5.46/5.72 & ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.72 != zero_zero_int )
% 5.46/5.72 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.72 = ( minus_minus_int @ B2 @ ( modulo_modulo_int @ A @ B2 ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zmod_zminus1_eq_if
% 5.46/5.72 thf(fact_4097_pos__minus__divide__less__eq,axiom,
% 5.46/5.72 ! [C: real,B2: real,A: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pos_minus_divide_less_eq
% 5.46/5.72 thf(fact_4098_pos__minus__divide__less__eq,axiom,
% 5.46/5.72 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.72 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ord_less_rat @ ( uminus_uminus_rat @ B2 ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pos_minus_divide_less_eq
% 5.46/5.72 thf(fact_4099_pos__less__minus__divide__eq,axiom,
% 5.46/5.72 ! [C: real,A: real,B2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 5.46/5.72 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pos_less_minus_divide_eq
% 5.46/5.72 thf(fact_4100_pos__less__minus__divide__eq,axiom,
% 5.46/5.72 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.72 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) )
% 5.46/5.72 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pos_less_minus_divide_eq
% 5.46/5.72 thf(fact_4101_neg__minus__divide__less__eq,axiom,
% 5.46/5.72 ! [C: real,B2: real,A: real] :
% 5.46/5.72 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_minus_divide_less_eq
% 5.46/5.72 thf(fact_4102_neg__minus__divide__less__eq,axiom,
% 5.46/5.72 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.72 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_minus_divide_less_eq
% 5.46/5.72 thf(fact_4103_neg__less__minus__divide__eq,axiom,
% 5.46/5.72 ! [C: real,A: real,B2: real] :
% 5.46/5.72 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 5.46/5.72 = ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_less_minus_divide_eq
% 5.46/5.72 thf(fact_4104_neg__less__minus__divide__eq,axiom,
% 5.46/5.72 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.72 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) )
% 5.46/5.72 = ( ord_less_rat @ ( uminus_uminus_rat @ B2 ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_less_minus_divide_eq
% 5.46/5.72 thf(fact_4105_minus__divide__less__eq,axiom,
% 5.46/5.72 ! [B2: real,C: real,A: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_less_eq
% 5.46/5.72 thf(fact_4106_minus__divide__less__eq,axiom,
% 5.46/5.72 ! [B2: rat,C: rat,A: rat] :
% 5.46/5.72 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ord_less_rat @ ( uminus_uminus_rat @ B2 ) @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B2 ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_less_eq
% 5.46/5.72 thf(fact_4107_less__minus__divide__eq,axiom,
% 5.46/5.72 ! [A: real,B2: real,C: real] :
% 5.46/5.72 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 5.46/5.72 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_minus_divide_eq
% 5.46/5.72 thf(fact_4108_less__minus__divide__eq,axiom,
% 5.46/5.72 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.72 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) )
% 5.46/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B2 ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_rat @ ( uminus_uminus_rat @ B2 ) @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_minus_divide_eq
% 5.46/5.72 thf(fact_4109_divide__eq__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [B2: real,C: real,W: num] :
% 5.46/5.72 ( ( ( divide_divide_real @ B2 @ C )
% 5.46/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.72 = ( ( ( C != zero_zero_real )
% 5.46/5.72 => ( B2
% 5.46/5.72 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ( C = zero_zero_real )
% 5.46/5.72 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.72 = zero_zero_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_eq_eq_numeral(2)
% 5.46/5.72 thf(fact_4110_divide__eq__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [B2: complex,C: complex,W: num] :
% 5.46/5.72 ( ( ( divide1717551699836669952omplex @ B2 @ C )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.72 = ( ( ( C != zero_zero_complex )
% 5.46/5.72 => ( B2
% 5.46/5.72 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ( C = zero_zero_complex )
% 5.46/5.72 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.72 = zero_zero_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_eq_eq_numeral(2)
% 5.46/5.72 thf(fact_4111_divide__eq__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [B2: rat,C: rat,W: num] :
% 5.46/5.72 ( ( ( divide_divide_rat @ B2 @ C )
% 5.46/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.72 = ( ( ( C != zero_zero_rat )
% 5.46/5.72 => ( B2
% 5.46/5.72 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ( C = zero_zero_rat )
% 5.46/5.72 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.72 = zero_zero_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_eq_eq_numeral(2)
% 5.46/5.72 thf(fact_4112_eq__divide__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [W: num,B2: real,C: real] :
% 5.46/5.72 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.72 = ( divide_divide_real @ B2 @ C ) )
% 5.46/5.72 = ( ( ( C != zero_zero_real )
% 5.46/5.72 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.46/5.72 = B2 ) )
% 5.46/5.72 & ( ( C = zero_zero_real )
% 5.46/5.72 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.72 = zero_zero_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_divide_eq_numeral(2)
% 5.46/5.72 thf(fact_4113_eq__divide__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [W: num,B2: complex,C: complex] :
% 5.46/5.72 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.72 = ( divide1717551699836669952omplex @ B2 @ C ) )
% 5.46/5.72 = ( ( ( C != zero_zero_complex )
% 5.46/5.72 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.46/5.72 = B2 ) )
% 5.46/5.72 & ( ( C = zero_zero_complex )
% 5.46/5.72 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.72 = zero_zero_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_divide_eq_numeral(2)
% 5.46/5.72 thf(fact_4114_eq__divide__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [W: num,B2: rat,C: rat] :
% 5.46/5.72 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.72 = ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.72 = ( ( ( C != zero_zero_rat )
% 5.46/5.72 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.46/5.72 = B2 ) )
% 5.46/5.72 & ( ( C = zero_zero_rat )
% 5.46/5.72 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.72 = zero_zero_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % eq_divide_eq_numeral(2)
% 5.46/5.72 thf(fact_4115_add__divide__eq__if__simps_I3_J,axiom,
% 5.46/5.72 ! [Z: real,A: real,B2: real] :
% 5.46/5.72 ( ( ( Z = zero_zero_real )
% 5.46/5.72 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B2 )
% 5.46/5.72 = B2 ) )
% 5.46/5.72 & ( ( Z != zero_zero_real )
% 5.46/5.72 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B2 )
% 5.46/5.72 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_divide_eq_if_simps(3)
% 5.46/5.72 thf(fact_4116_add__divide__eq__if__simps_I3_J,axiom,
% 5.46/5.72 ! [Z: complex,A: complex,B2: complex] :
% 5.46/5.72 ( ( ( Z = zero_zero_complex )
% 5.46/5.72 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B2 )
% 5.46/5.72 = B2 ) )
% 5.46/5.72 & ( ( Z != zero_zero_complex )
% 5.46/5.72 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B2 )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_divide_eq_if_simps(3)
% 5.46/5.72 thf(fact_4117_add__divide__eq__if__simps_I3_J,axiom,
% 5.46/5.72 ! [Z: rat,A: rat,B2: rat] :
% 5.46/5.72 ( ( ( Z = zero_zero_rat )
% 5.46/5.72 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B2 )
% 5.46/5.72 = B2 ) )
% 5.46/5.72 & ( ( Z != zero_zero_rat )
% 5.46/5.72 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B2 )
% 5.46/5.72 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_divide_eq_if_simps(3)
% 5.46/5.72 thf(fact_4118_minus__divide__add__eq__iff,axiom,
% 5.46/5.72 ! [Z: real,X4: real,Y3: real] :
% 5.46/5.72 ( ( Z != zero_zero_real )
% 5.46/5.72 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X4 @ Z ) ) @ Y3 )
% 5.46/5.72 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_add_eq_iff
% 5.46/5.72 thf(fact_4119_minus__divide__add__eq__iff,axiom,
% 5.46/5.72 ! [Z: complex,X4: complex,Y3: complex] :
% 5.46/5.72 ( ( Z != zero_zero_complex )
% 5.46/5.72 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X4 @ Z ) ) @ Y3 )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_add_eq_iff
% 5.46/5.72 thf(fact_4120_minus__divide__add__eq__iff,axiom,
% 5.46/5.72 ! [Z: rat,X4: rat,Y3: rat] :
% 5.46/5.72 ( ( Z != zero_zero_rat )
% 5.46/5.72 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X4 @ Z ) ) @ Y3 )
% 5.46/5.72 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X4 ) @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_add_eq_iff
% 5.46/5.72 thf(fact_4121_add__divide__eq__if__simps_I6_J,axiom,
% 5.46/5.72 ! [Z: real,A: real,B2: real] :
% 5.46/5.72 ( ( ( Z = zero_zero_real )
% 5.46/5.72 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_real @ B2 ) ) )
% 5.46/5.72 & ( ( Z != zero_zero_real )
% 5.46/5.72 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B2 )
% 5.46/5.72 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_divide_eq_if_simps(6)
% 5.46/5.72 thf(fact_4122_add__divide__eq__if__simps_I6_J,axiom,
% 5.46/5.72 ! [Z: complex,A: complex,B2: complex] :
% 5.46/5.72 ( ( ( Z = zero_zero_complex )
% 5.46/5.72 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B2 )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ B2 ) ) )
% 5.46/5.72 & ( ( Z != zero_zero_complex )
% 5.46/5.72 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B2 )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_divide_eq_if_simps(6)
% 5.46/5.72 thf(fact_4123_add__divide__eq__if__simps_I6_J,axiom,
% 5.46/5.72 ! [Z: rat,A: rat,B2: rat] :
% 5.46/5.72 ( ( ( Z = zero_zero_rat )
% 5.46/5.72 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_rat @ B2 ) ) )
% 5.46/5.72 & ( ( Z != zero_zero_rat )
% 5.46/5.72 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B2 )
% 5.46/5.72 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_divide_eq_if_simps(6)
% 5.46/5.72 thf(fact_4124_add__divide__eq__if__simps_I5_J,axiom,
% 5.46/5.72 ! [Z: real,A: real,B2: real] :
% 5.46/5.72 ( ( ( Z = zero_zero_real )
% 5.46/5.72 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_real @ B2 ) ) )
% 5.46/5.72 & ( ( Z != zero_zero_real )
% 5.46/5.72 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B2 )
% 5.46/5.72 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_divide_eq_if_simps(5)
% 5.46/5.72 thf(fact_4125_add__divide__eq__if__simps_I5_J,axiom,
% 5.46/5.72 ! [Z: complex,A: complex,B2: complex] :
% 5.46/5.72 ( ( ( Z = zero_zero_complex )
% 5.46/5.72 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B2 )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ B2 ) ) )
% 5.46/5.72 & ( ( Z != zero_zero_complex )
% 5.46/5.72 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B2 )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_divide_eq_if_simps(5)
% 5.46/5.72 thf(fact_4126_add__divide__eq__if__simps_I5_J,axiom,
% 5.46/5.72 ! [Z: rat,A: rat,B2: rat] :
% 5.46/5.72 ( ( ( Z = zero_zero_rat )
% 5.46/5.72 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_rat @ B2 ) ) )
% 5.46/5.72 & ( ( Z != zero_zero_rat )
% 5.46/5.72 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B2 )
% 5.46/5.72 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B2 @ Z ) ) @ Z ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % add_divide_eq_if_simps(5)
% 5.46/5.72 thf(fact_4127_minus__divide__diff__eq__iff,axiom,
% 5.46/5.72 ! [Z: real,X4: real,Y3: real] :
% 5.46/5.72 ( ( Z != zero_zero_real )
% 5.46/5.72 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X4 @ Z ) ) @ Y3 )
% 5.46/5.72 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_diff_eq_iff
% 5.46/5.72 thf(fact_4128_minus__divide__diff__eq__iff,axiom,
% 5.46/5.72 ! [Z: complex,X4: complex,Y3: complex] :
% 5.46/5.72 ( ( Z != zero_zero_complex )
% 5.46/5.72 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X4 @ Z ) ) @ Y3 )
% 5.46/5.72 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( times_times_complex @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_diff_eq_iff
% 5.46/5.72 thf(fact_4129_minus__divide__diff__eq__iff,axiom,
% 5.46/5.72 ! [Z: rat,X4: rat,Y3: rat] :
% 5.46/5.72 ( ( Z != zero_zero_rat )
% 5.46/5.72 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X4 @ Z ) ) @ Y3 )
% 5.46/5.72 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X4 ) @ ( times_times_rat @ Y3 @ Z ) ) @ Z ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_diff_eq_iff
% 5.46/5.72 thf(fact_4130_even__minus,axiom,
% 5.46/5.72 ! [A: int] :
% 5.46/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.46/5.72 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.72
% 5.46/5.72 % even_minus
% 5.46/5.72 thf(fact_4131_even__minus,axiom,
% 5.46/5.72 ! [A: code_integer] :
% 5.46/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.72 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.46/5.72
% 5.46/5.72 % even_minus
% 5.46/5.72 thf(fact_4132_power2__eq__iff,axiom,
% 5.46/5.72 ! [X4: real,Y3: real] :
% 5.46/5.72 ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = ( ( X4 = Y3 )
% 5.46/5.72 | ( X4
% 5.46/5.72 = ( uminus_uminus_real @ Y3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_eq_iff
% 5.46/5.72 thf(fact_4133_power2__eq__iff,axiom,
% 5.46/5.72 ! [X4: int,Y3: int] :
% 5.46/5.72 ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = ( ( X4 = Y3 )
% 5.46/5.72 | ( X4
% 5.46/5.72 = ( uminus_uminus_int @ Y3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_eq_iff
% 5.46/5.72 thf(fact_4134_power2__eq__iff,axiom,
% 5.46/5.72 ! [X4: complex,Y3: complex] :
% 5.46/5.72 ( ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = ( power_power_complex @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = ( ( X4 = Y3 )
% 5.46/5.72 | ( X4
% 5.46/5.72 = ( uminus1482373934393186551omplex @ Y3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_eq_iff
% 5.46/5.72 thf(fact_4135_power2__eq__iff,axiom,
% 5.46/5.72 ! [X4: code_integer,Y3: code_integer] :
% 5.46/5.72 ( ( ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = ( ( X4 = Y3 )
% 5.46/5.72 | ( X4
% 5.46/5.72 = ( uminus1351360451143612070nteger @ Y3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_eq_iff
% 5.46/5.72 thf(fact_4136_power2__eq__iff,axiom,
% 5.46/5.72 ! [X4: rat,Y3: rat] :
% 5.46/5.72 ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.72 = ( ( X4 = Y3 )
% 5.46/5.72 | ( X4
% 5.46/5.72 = ( uminus_uminus_rat @ Y3 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_eq_iff
% 5.46/5.72 thf(fact_4137_verit__less__mono__div__int2,axiom,
% 5.46/5.72 ! [A3: int,B4: int,N: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ A3 @ B4 )
% 5.46/5.72 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.46/5.72 => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N ) @ ( divide_divide_int @ A3 @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % verit_less_mono_div_int2
% 5.46/5.72 thf(fact_4138_div__eq__minus1,axiom,
% 5.46/5.72 ! [B2: int] :
% 5.46/5.72 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.72 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % div_eq_minus1
% 5.46/5.72 thf(fact_4139_pos__minus__divide__le__eq,axiom,
% 5.46/5.72 ! [C: real,B2: real,A: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pos_minus_divide_le_eq
% 5.46/5.72 thf(fact_4140_pos__minus__divide__le__eq,axiom,
% 5.46/5.72 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.72 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B2 ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pos_minus_divide_le_eq
% 5.46/5.72 thf(fact_4141_pos__le__minus__divide__eq,axiom,
% 5.46/5.72 ! [C: real,A: real,B2: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pos_le_minus_divide_eq
% 5.46/5.72 thf(fact_4142_pos__le__minus__divide__eq,axiom,
% 5.46/5.72 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.72 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) )
% 5.46/5.72 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % pos_le_minus_divide_eq
% 5.46/5.72 thf(fact_4143_neg__minus__divide__le__eq,axiom,
% 5.46/5.72 ! [C: real,B2: real,A: real] :
% 5.46/5.72 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_minus_divide_le_eq
% 5.46/5.72 thf(fact_4144_neg__minus__divide__le__eq,axiom,
% 5.46/5.72 ! [C: rat,B2: rat,A: rat] :
% 5.46/5.72 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_minus_divide_le_eq
% 5.46/5.72 thf(fact_4145_neg__le__minus__divide__eq,axiom,
% 5.46/5.72 ! [C: real,A: real,B2: real] :
% 5.46/5.72 ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 5.46/5.72 = ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_le_minus_divide_eq
% 5.46/5.72 thf(fact_4146_neg__le__minus__divide__eq,axiom,
% 5.46/5.72 ! [C: rat,A: rat,B2: rat] :
% 5.46/5.72 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) )
% 5.46/5.72 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B2 ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_le_minus_divide_eq
% 5.46/5.72 thf(fact_4147_minus__divide__le__eq,axiom,
% 5.46/5.72 ! [B2: real,C: real,A: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_le_eq
% 5.46/5.72 thf(fact_4148_minus__divide__le__eq,axiom,
% 5.46/5.72 ! [B2: rat,C: rat,A: rat] :
% 5.46/5.72 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) @ A )
% 5.46/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B2 ) @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B2 ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_divide_le_eq
% 5.46/5.72 thf(fact_4149_le__minus__divide__eq,axiom,
% 5.46/5.72 ! [A: real,B2: real,C: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B2 @ C ) ) )
% 5.46/5.72 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B2 ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( uminus_uminus_real @ B2 ) @ ( times_times_real @ A @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_minus_divide_eq
% 5.46/5.72 thf(fact_4150_le__minus__divide__eq,axiom,
% 5.46/5.72 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.72 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B2 @ C ) ) )
% 5.46/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B2 ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B2 ) @ ( times_times_rat @ A @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_minus_divide_eq
% 5.46/5.72 thf(fact_4151_less__divide__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [W: num,B2: real,C: real] :
% 5.46/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.72 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B2 ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_real @ B2 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_divide_eq_numeral(2)
% 5.46/5.72 thf(fact_4152_less__divide__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [W: num,B2: rat,C: rat] :
% 5.46/5.72 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B2 ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_rat @ B2 @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % less_divide_eq_numeral(2)
% 5.46/5.72 thf(fact_4153_divide__less__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [B2: real,C: real,W: num] :
% 5.46/5.72 ( ( ord_less_real @ ( divide_divide_real @ B2 @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.72 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ord_less_real @ B2 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B2 ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_less_eq_numeral(2)
% 5.46/5.72 thf(fact_4154_divide__less__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [B2: rat,C: rat,W: num] :
% 5.46/5.72 ( ( ord_less_rat @ ( divide_divide_rat @ B2 @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ord_less_rat @ B2 @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B2 ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_less_eq_numeral(2)
% 5.46/5.72 thf(fact_4155_power2__eq__1__iff,axiom,
% 5.46/5.72 ! [A: real] :
% 5.46/5.72 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = one_one_real )
% 5.46/5.72 = ( ( A = one_one_real )
% 5.46/5.72 | ( A
% 5.46/5.72 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_eq_1_iff
% 5.46/5.72 thf(fact_4156_power2__eq__1__iff,axiom,
% 5.46/5.72 ! [A: int] :
% 5.46/5.72 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = one_one_int )
% 5.46/5.72 = ( ( A = one_one_int )
% 5.46/5.72 | ( A
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_eq_1_iff
% 5.46/5.72 thf(fact_4157_power2__eq__1__iff,axiom,
% 5.46/5.72 ! [A: complex] :
% 5.46/5.72 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = one_one_complex )
% 5.46/5.72 = ( ( A = one_one_complex )
% 5.46/5.72 | ( A
% 5.46/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_eq_1_iff
% 5.46/5.72 thf(fact_4158_power2__eq__1__iff,axiom,
% 5.46/5.72 ! [A: code_integer] :
% 5.46/5.72 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = one_one_Code_integer )
% 5.46/5.72 = ( ( A = one_one_Code_integer )
% 5.46/5.72 | ( A
% 5.46/5.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_eq_1_iff
% 5.46/5.72 thf(fact_4159_power2__eq__1__iff,axiom,
% 5.46/5.72 ! [A: rat] :
% 5.46/5.72 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.72 = one_one_rat )
% 5.46/5.72 = ( ( A = one_one_rat )
% 5.46/5.72 | ( A
% 5.46/5.72 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % power2_eq_1_iff
% 5.46/5.72 thf(fact_4160_uminus__power__if,axiom,
% 5.46/5.72 ! [N: nat,A: real] :
% 5.46/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.46/5.72 = ( power_power_real @ A @ N ) ) )
% 5.46/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.46/5.72 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % uminus_power_if
% 5.46/5.72 thf(fact_4161_uminus__power__if,axiom,
% 5.46/5.72 ! [N: nat,A: int] :
% 5.46/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.46/5.72 = ( power_power_int @ A @ N ) ) )
% 5.46/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.46/5.72 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % uminus_power_if
% 5.46/5.72 thf(fact_4162_uminus__power__if,axiom,
% 5.46/5.72 ! [N: nat,A: complex] :
% 5.46/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.46/5.72 = ( power_power_complex @ A @ N ) ) )
% 5.46/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % uminus_power_if
% 5.46/5.72 thf(fact_4163_uminus__power__if,axiom,
% 5.46/5.72 ! [N: nat,A: code_integer] :
% 5.46/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.46/5.72 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.46/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.46/5.72 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % uminus_power_if
% 5.46/5.72 thf(fact_4164_uminus__power__if,axiom,
% 5.46/5.72 ! [N: nat,A: rat] :
% 5.46/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.46/5.72 = ( power_power_rat @ A @ N ) ) )
% 5.46/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.46/5.72 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % uminus_power_if
% 5.46/5.72 thf(fact_4165_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.46/5.72 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_power_add_eq_neg_one_power_diff
% 5.46/5.72 thf(fact_4166_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.46/5.72 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_power_add_eq_neg_one_power_diff
% 5.46/5.72 thf(fact_4167_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.46/5.72 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_power_add_eq_neg_one_power_diff
% 5.46/5.72 thf(fact_4168_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.46/5.72 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_power_add_eq_neg_one_power_diff
% 5.46/5.72 thf(fact_4169_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.46/5.72 ! [K: nat,N: nat] :
% 5.46/5.72 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.46/5.72 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % neg_one_power_add_eq_neg_one_power_diff
% 5.46/5.72 thf(fact_4170_realpow__square__minus__le,axiom,
% 5.46/5.72 ! [U: real,X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % realpow_square_minus_le
% 5.46/5.72 thf(fact_4171_minus__mod__int__eq,axiom,
% 5.46/5.72 ! [L2: int,K: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.46/5.72 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.46/5.72 = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_mod_int_eq
% 5.46/5.72 thf(fact_4172_zmod__minus1,axiom,
% 5.46/5.72 ! [B2: int] :
% 5.46/5.72 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.72 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B2 )
% 5.46/5.72 = ( minus_minus_int @ B2 @ one_one_int ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zmod_minus1
% 5.46/5.72 thf(fact_4173_zdiv__zminus1__eq__if,axiom,
% 5.46/5.72 ! [B2: int,A: int] :
% 5.46/5.72 ( ( B2 != zero_zero_int )
% 5.46/5.72 => ( ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.72 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B2 ) ) ) )
% 5.46/5.72 & ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.72 != zero_zero_int )
% 5.46/5.72 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.72 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B2 ) ) @ one_one_int ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zdiv_zminus1_eq_if
% 5.46/5.72 thf(fact_4174_zdiv__zminus2__eq__if,axiom,
% 5.46/5.72 ! [B2: int,A: int] :
% 5.46/5.72 ( ( B2 != zero_zero_int )
% 5.46/5.72 => ( ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.72 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B2 ) ) ) )
% 5.46/5.72 & ( ( ( modulo_modulo_int @ A @ B2 )
% 5.46/5.72 != zero_zero_int )
% 5.46/5.72 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B2 ) )
% 5.46/5.72 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B2 ) ) @ one_one_int ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % zdiv_zminus2_eq_if
% 5.46/5.72 thf(fact_4175_le__divide__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [W: num,B2: real,C: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B2 @ C ) )
% 5.46/5.72 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B2 ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_eq_real @ B2 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_divide_eq_numeral(2)
% 5.46/5.72 thf(fact_4176_le__divide__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [W: num,B2: rat,C: rat] :
% 5.46/5.72 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B2 @ C ) )
% 5.46/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B2 ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_eq_rat @ B2 @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % le_divide_eq_numeral(2)
% 5.46/5.72 thf(fact_4177_divide__le__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [B2: real,C: real,W: num] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( divide_divide_real @ B2 @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.72 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ord_less_eq_real @ B2 @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.72 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B2 ) )
% 5.46/5.72 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.46/5.72 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_le_eq_numeral(2)
% 5.46/5.72 thf(fact_4178_divide__le__eq__numeral_I2_J,axiom,
% 5.46/5.72 ! [B2: rat,C: rat,W: num] :
% 5.46/5.72 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B2 @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ord_less_eq_rat @ B2 @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.46/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B2 ) )
% 5.46/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.46/5.72 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % divide_le_eq_numeral(2)
% 5.46/5.72 thf(fact_4179_square__le__1,axiom,
% 5.46/5.72 ! [X4: real] :
% 5.46/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.72 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.72 => ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_le_1
% 5.46/5.72 thf(fact_4180_square__le__1,axiom,
% 5.46/5.72 ! [X4: code_integer] :
% 5.46/5.72 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X4 )
% 5.46/5.72 => ( ( ord_le3102999989581377725nteger @ X4 @ one_one_Code_integer )
% 5.46/5.72 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_le_1
% 5.46/5.72 thf(fact_4181_square__le__1,axiom,
% 5.46/5.72 ! [X4: rat] :
% 5.46/5.72 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X4 )
% 5.46/5.72 => ( ( ord_less_eq_rat @ X4 @ one_one_rat )
% 5.46/5.72 => ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_le_1
% 5.46/5.72 thf(fact_4182_square__le__1,axiom,
% 5.46/5.72 ! [X4: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X4 )
% 5.46/5.72 => ( ( ord_less_eq_int @ X4 @ one_one_int )
% 5.46/5.72 => ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % square_le_1
% 5.46/5.72 thf(fact_4183_minus__power__mult__self,axiom,
% 5.46/5.72 ! [A: real,N: nat] :
% 5.46/5.72 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.46/5.72 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_power_mult_self
% 5.46/5.72 thf(fact_4184_minus__power__mult__self,axiom,
% 5.46/5.72 ! [A: int,N: nat] :
% 5.46/5.72 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.46/5.72 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_power_mult_self
% 5.46/5.72 thf(fact_4185_minus__power__mult__self,axiom,
% 5.46/5.72 ! [A: complex,N: nat] :
% 5.46/5.72 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.46/5.72 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_power_mult_self
% 5.46/5.72 thf(fact_4186_minus__power__mult__self,axiom,
% 5.46/5.72 ! [A: code_integer,N: nat] :
% 5.46/5.72 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.46/5.72 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_power_mult_self
% 5.46/5.72 thf(fact_4187_minus__power__mult__self,axiom,
% 5.46/5.72 ! [A: rat,N: nat] :
% 5.46/5.72 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.46/5.72 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_power_mult_self
% 5.46/5.72 thf(fact_4188_minus__one__power__iff,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.46/5.72 = one_one_real ) )
% 5.46/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.46/5.72 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_one_power_iff
% 5.46/5.72 thf(fact_4189_minus__one__power__iff,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.46/5.72 = one_one_int ) )
% 5.46/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_one_power_iff
% 5.46/5.72 thf(fact_4190_minus__one__power__iff,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.46/5.72 = one_one_complex ) )
% 5.46/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_one_power_iff
% 5.46/5.72 thf(fact_4191_minus__one__power__iff,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.46/5.72 = one_one_Code_integer ) )
% 5.46/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.46/5.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_one_power_iff
% 5.46/5.72 thf(fact_4192_minus__one__power__iff,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.46/5.72 = one_one_rat ) )
% 5.46/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.46/5.72 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_one_power_iff
% 5.46/5.72 thf(fact_4193_minus__1__div__exp__eq__int,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % minus_1_div_exp_eq_int
% 5.46/5.72 thf(fact_4194_div__pos__neg__trivial,axiom,
% 5.46/5.72 ! [K: int,L2: int] :
% 5.46/5.72 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.72 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.46/5.72 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % div_pos_neg_trivial
% 5.46/5.72 thf(fact_4195_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.46/5.72 ! [N: nat,K: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.46/5.72 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_int_less_eq_self_iff
% 5.46/5.72 thf(fact_4196_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.46/5.72 ! [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 ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_int_greater_eq_minus_exp
% 5.46/5.72 thf(fact_4197_signed__take__bit__int__greater__self__iff,axiom,
% 5.46/5.72 ! [K: int,N: nat] :
% 5.46/5.72 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.46/5.72 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_int_greater_self_iff
% 5.46/5.72 thf(fact_4198_power__minus1__odd,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.72 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus1_odd
% 5.46/5.72 thf(fact_4199_power__minus1__odd,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.72 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus1_odd
% 5.46/5.72 thf(fact_4200_power__minus1__odd,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus1_odd
% 5.46/5.72 thf(fact_4201_power__minus1__odd,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus1_odd
% 5.46/5.72 thf(fact_4202_power__minus1__odd,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.72 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.72
% 5.46/5.72 % power_minus1_odd
% 5.46/5.72 thf(fact_4203_int__bit__induct,axiom,
% 5.46/5.72 ! [P: int > $o,K: int] :
% 5.46/5.72 ( ( P @ zero_zero_int )
% 5.46/5.72 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.72 => ( ! [K2: int] :
% 5.46/5.72 ( ( P @ K2 )
% 5.46/5.72 => ( ( K2 != zero_zero_int )
% 5.46/5.72 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.72 => ( ! [K2: int] :
% 5.46/5.72 ( ( P @ K2 )
% 5.46/5.72 => ( ( K2
% 5.46/5.72 != ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.72 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.46/5.72 => ( P @ K ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % int_bit_induct
% 5.46/5.72 thf(fact_4204_signed__take__bit__int__eq__self,axiom,
% 5.46/5.72 ! [N: nat,K: int] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.46/5.72 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.72 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.46/5.72 = K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_int_eq_self
% 5.46/5.72 thf(fact_4205_signed__take__bit__int__eq__self__iff,axiom,
% 5.46/5.72 ! [N: nat,K: int] :
% 5.46/5.72 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.46/5.72 = K )
% 5.46/5.72 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.46/5.72 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_int_eq_self_iff
% 5.46/5.72 thf(fact_4206_signed__take__bit__int__greater__eq,axiom,
% 5.46/5.72 ! [K: int,N: nat] :
% 5.46/5.72 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.72 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_int_greater_eq
% 5.46/5.72 thf(fact_4207_mult__less__iff1,axiom,
% 5.46/5.72 ! [Z: real,X4: real,Y3: real] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.46/5.72 => ( ( ord_less_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y3 @ Z ) )
% 5.46/5.72 = ( ord_less_real @ X4 @ Y3 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_less_iff1
% 5.46/5.72 thf(fact_4208_mult__less__iff1,axiom,
% 5.46/5.72 ! [Z: rat,X4: rat,Y3: rat] :
% 5.46/5.72 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.46/5.72 => ( ( ord_less_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ Y3 @ Z ) )
% 5.46/5.72 = ( ord_less_rat @ X4 @ Y3 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_less_iff1
% 5.46/5.72 thf(fact_4209_mult__less__iff1,axiom,
% 5.46/5.72 ! [Z: int,X4: int,Y3: int] :
% 5.46/5.72 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.72 => ( ( ord_less_int @ ( times_times_int @ X4 @ Z ) @ ( times_times_int @ Y3 @ Z ) )
% 5.46/5.72 = ( ord_less_int @ X4 @ Y3 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % mult_less_iff1
% 5.46/5.72 thf(fact_4210_compl__le__compl__iff,axiom,
% 5.46/5.72 ! [X4: set_nat,Y3: set_nat] :
% 5.46/5.72 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X4 ) @ ( uminus5710092332889474511et_nat @ Y3 ) )
% 5.46/5.72 = ( ord_less_eq_set_nat @ Y3 @ X4 ) ) ).
% 5.46/5.72
% 5.46/5.72 % compl_le_compl_iff
% 5.46/5.72 thf(fact_4211_signed__take__bit__Suc__minus__bit1,axiom,
% 5.46/5.72 ! [N: nat,K: num] :
% 5.46/5.72 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.72 = ( 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 ) ) ).
% 5.46/5.72
% 5.46/5.72 % signed_take_bit_Suc_minus_bit1
% 5.46/5.72 thf(fact_4212_concat__bit__Suc,axiom,
% 5.46/5.72 ! [N: nat,K: int,L2: int] :
% 5.46/5.72 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 5.46/5.72 = ( 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 ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % concat_bit_Suc
% 5.46/5.72 thf(fact_4213_flip__bit__0,axiom,
% 5.46/5.72 ! [A: code_integer] :
% 5.46/5.72 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.46/5.72 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % flip_bit_0
% 5.46/5.72 thf(fact_4214_flip__bit__0,axiom,
% 5.46/5.72 ! [A: int] :
% 5.46/5.72 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.46/5.72 = ( 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 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % flip_bit_0
% 5.46/5.72 thf(fact_4215_flip__bit__0,axiom,
% 5.46/5.72 ! [A: nat] :
% 5.46/5.72 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.46/5.72 = ( 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 ) ) ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % flip_bit_0
% 5.46/5.72 thf(fact_4216_set__decode__0,axiom,
% 5.46/5.72 ! [X4: nat] :
% 5.46/5.72 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X4 ) )
% 5.46/5.72 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % set_decode_0
% 5.46/5.72 thf(fact_4217_semiring__norm_I90_J,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( ( bit1 @ M )
% 5.46/5.72 = ( bit1 @ N ) )
% 5.46/5.72 = ( M = N ) ) ).
% 5.46/5.72
% 5.46/5.72 % semiring_norm(90)
% 5.46/5.72 thf(fact_4218_verit__eq__simplify_I9_J,axiom,
% 5.46/5.72 ! [X32: num,Y32: num] :
% 5.46/5.72 ( ( ( bit1 @ X32 )
% 5.46/5.72 = ( bit1 @ Y32 ) )
% 5.46/5.72 = ( X32 = Y32 ) ) ).
% 5.46/5.72
% 5.46/5.72 % verit_eq_simplify(9)
% 5.46/5.72 thf(fact_4219_semiring__norm_I88_J,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( bit0 @ M )
% 5.46/5.72 != ( bit1 @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % semiring_norm(88)
% 5.46/5.72 thf(fact_4220_semiring__norm_I89_J,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( bit1 @ M )
% 5.46/5.72 != ( bit0 @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % semiring_norm(89)
% 5.46/5.72 thf(fact_4221_semiring__norm_I84_J,axiom,
% 5.46/5.72 ! [N: num] :
% 5.46/5.72 ( one
% 5.46/5.72 != ( bit1 @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % semiring_norm(84)
% 5.46/5.72 thf(fact_4222_semiring__norm_I86_J,axiom,
% 5.46/5.72 ! [M: num] :
% 5.46/5.72 ( ( bit1 @ M )
% 5.46/5.72 != one ) ).
% 5.46/5.72
% 5.46/5.72 % semiring_norm(86)
% 5.46/5.72 thf(fact_4223_of__bool__less__eq__iff,axiom,
% 5.46/5.72 ! [P: $o,Q: $o] :
% 5.46/5.72 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.46/5.72 = ( P
% 5.46/5.72 => Q ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_eq_iff
% 5.46/5.72 thf(fact_4224_of__bool__less__eq__iff,axiom,
% 5.46/5.72 ! [P: $o,Q: $o] :
% 5.46/5.72 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.46/5.72 = ( P
% 5.46/5.72 => Q ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_eq_iff
% 5.46/5.72 thf(fact_4225_of__bool__less__eq__iff,axiom,
% 5.46/5.72 ! [P: $o,Q: $o] :
% 5.46/5.72 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.46/5.72 = ( P
% 5.46/5.72 => Q ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_eq_iff
% 5.46/5.72 thf(fact_4226_of__bool__less__eq__iff,axiom,
% 5.46/5.72 ! [P: $o,Q: $o] :
% 5.46/5.72 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.46/5.72 = ( P
% 5.46/5.72 => Q ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_eq_iff
% 5.46/5.72 thf(fact_4227_of__bool__eq__0__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.46/5.72 = zero_zero_real )
% 5.46/5.72 = ~ P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_0_iff
% 5.46/5.72 thf(fact_4228_of__bool__eq__0__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.46/5.72 = zero_zero_rat )
% 5.46/5.72 = ~ P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_0_iff
% 5.46/5.72 thf(fact_4229_of__bool__eq__0__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.46/5.72 = zero_zero_nat )
% 5.46/5.72 = ~ P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_0_iff
% 5.46/5.72 thf(fact_4230_of__bool__eq__0__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.46/5.72 = zero_zero_int )
% 5.46/5.72 = ~ P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_0_iff
% 5.46/5.72 thf(fact_4231_of__bool__eq__0__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n356916108424825756nteger @ P )
% 5.46/5.72 = zero_z3403309356797280102nteger )
% 5.46/5.72 = ~ P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_0_iff
% 5.46/5.72 thf(fact_4232_of__bool__eq_I1_J,axiom,
% 5.46/5.72 ( ( zero_n3304061248610475627l_real @ $false )
% 5.46/5.72 = zero_zero_real ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(1)
% 5.46/5.72 thf(fact_4233_of__bool__eq_I1_J,axiom,
% 5.46/5.72 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.46/5.72 = zero_zero_rat ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(1)
% 5.46/5.72 thf(fact_4234_of__bool__eq_I1_J,axiom,
% 5.46/5.72 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.46/5.72 = zero_zero_nat ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(1)
% 5.46/5.72 thf(fact_4235_of__bool__eq_I1_J,axiom,
% 5.46/5.72 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.46/5.72 = zero_zero_int ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(1)
% 5.46/5.72 thf(fact_4236_of__bool__eq_I1_J,axiom,
% 5.46/5.72 ( ( zero_n356916108424825756nteger @ $false )
% 5.46/5.72 = zero_z3403309356797280102nteger ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(1)
% 5.46/5.72 thf(fact_4237_of__bool__less__iff,axiom,
% 5.46/5.72 ! [P: $o,Q: $o] :
% 5.46/5.72 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.46/5.72 = ( ~ P
% 5.46/5.72 & Q ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_iff
% 5.46/5.72 thf(fact_4238_of__bool__less__iff,axiom,
% 5.46/5.72 ! [P: $o,Q: $o] :
% 5.46/5.72 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.46/5.72 = ( ~ P
% 5.46/5.72 & Q ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_iff
% 5.46/5.72 thf(fact_4239_of__bool__less__iff,axiom,
% 5.46/5.72 ! [P: $o,Q: $o] :
% 5.46/5.72 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.46/5.72 = ( ~ P
% 5.46/5.72 & Q ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_iff
% 5.46/5.72 thf(fact_4240_of__bool__less__iff,axiom,
% 5.46/5.72 ! [P: $o,Q: $o] :
% 5.46/5.72 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.46/5.72 = ( ~ P
% 5.46/5.72 & Q ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_iff
% 5.46/5.72 thf(fact_4241_of__bool__less__iff,axiom,
% 5.46/5.72 ! [P: $o,Q: $o] :
% 5.46/5.72 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.46/5.72 = ( ~ P
% 5.46/5.72 & Q ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_iff
% 5.46/5.72 thf(fact_4242_of__bool__eq_I2_J,axiom,
% 5.46/5.72 ( ( zero_n1201886186963655149omplex @ $true )
% 5.46/5.72 = one_one_complex ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(2)
% 5.46/5.72 thf(fact_4243_of__bool__eq_I2_J,axiom,
% 5.46/5.72 ( ( zero_n3304061248610475627l_real @ $true )
% 5.46/5.72 = one_one_real ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(2)
% 5.46/5.72 thf(fact_4244_of__bool__eq_I2_J,axiom,
% 5.46/5.72 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.46/5.72 = one_one_rat ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(2)
% 5.46/5.72 thf(fact_4245_of__bool__eq_I2_J,axiom,
% 5.46/5.72 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.46/5.72 = one_one_nat ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(2)
% 5.46/5.72 thf(fact_4246_of__bool__eq_I2_J,axiom,
% 5.46/5.72 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.46/5.72 = one_one_int ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(2)
% 5.46/5.72 thf(fact_4247_of__bool__eq_I2_J,axiom,
% 5.46/5.72 ( ( zero_n356916108424825756nteger @ $true )
% 5.46/5.72 = one_one_Code_integer ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq(2)
% 5.46/5.72 thf(fact_4248_of__bool__eq__1__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.46/5.72 = one_one_complex )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_1_iff
% 5.46/5.72 thf(fact_4249_of__bool__eq__1__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.46/5.72 = one_one_real )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_1_iff
% 5.46/5.72 thf(fact_4250_of__bool__eq__1__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.46/5.72 = one_one_rat )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_1_iff
% 5.46/5.72 thf(fact_4251_of__bool__eq__1__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.46/5.72 = one_one_nat )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_1_iff
% 5.46/5.72 thf(fact_4252_of__bool__eq__1__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.46/5.72 = one_one_int )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_1_iff
% 5.46/5.72 thf(fact_4253_of__bool__eq__1__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ( zero_n356916108424825756nteger @ P )
% 5.46/5.72 = one_one_Code_integer )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_eq_1_iff
% 5.46/5.72 thf(fact_4254_concat__bit__0,axiom,
% 5.46/5.72 ! [K: int,L2: int] :
% 5.46/5.72 ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 5.46/5.72 = L2 ) ).
% 5.46/5.72
% 5.46/5.72 % concat_bit_0
% 5.46/5.72 thf(fact_4255_semiring__norm_I73_J,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.72 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % semiring_norm(73)
% 5.46/5.72 thf(fact_4256_semiring__norm_I80_J,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.72 = ( ord_less_num @ M @ N ) ) ).
% 5.46/5.72
% 5.46/5.72 % semiring_norm(80)
% 5.46/5.72 thf(fact_4257_zero__less__of__bool__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % zero_less_of_bool_iff
% 5.46/5.72 thf(fact_4258_zero__less__of__bool__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % zero_less_of_bool_iff
% 5.46/5.72 thf(fact_4259_zero__less__of__bool__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % zero_less_of_bool_iff
% 5.46/5.72 thf(fact_4260_zero__less__of__bool__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % zero_less_of_bool_iff
% 5.46/5.72 thf(fact_4261_zero__less__of__bool__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.46/5.72 = P ) ).
% 5.46/5.72
% 5.46/5.72 % zero_less_of_bool_iff
% 5.46/5.72 thf(fact_4262_of__bool__less__one__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.46/5.72 = ~ P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_one_iff
% 5.46/5.72 thf(fact_4263_of__bool__less__one__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.46/5.72 = ~ P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_one_iff
% 5.46/5.72 thf(fact_4264_of__bool__less__one__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.46/5.72 = ~ P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_one_iff
% 5.46/5.72 thf(fact_4265_of__bool__less__one__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.46/5.72 = ~ P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_one_iff
% 5.46/5.72 thf(fact_4266_of__bool__less__one__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.46/5.72 = ~ P ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_less_one_iff
% 5.46/5.72 thf(fact_4267_of__bool__not__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.46/5.72 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_not_iff
% 5.46/5.72 thf(fact_4268_of__bool__not__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.46/5.72 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_not_iff
% 5.46/5.72 thf(fact_4269_of__bool__not__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.46/5.72 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_not_iff
% 5.46/5.72 thf(fact_4270_of__bool__not__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.46/5.72 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_not_iff
% 5.46/5.72 thf(fact_4271_of__bool__not__iff,axiom,
% 5.46/5.72 ! [P: $o] :
% 5.46/5.72 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.46/5.72 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % of_bool_not_iff
% 5.46/5.72 thf(fact_4272_Suc__0__mod__eq,axiom,
% 5.46/5.72 ! [N: nat] :
% 5.46/5.72 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.72 = ( zero_n2687167440665602831ol_nat
% 5.46/5.72 @ ( N
% 5.46/5.72 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % Suc_0_mod_eq
% 5.46/5.72 thf(fact_4273_semiring__norm_I9_J,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.72 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % semiring_norm(9)
% 5.46/5.72 thf(fact_4274_semiring__norm_I7_J,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.72 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.46/5.72
% 5.46/5.72 % semiring_norm(7)
% 5.46/5.72 thf(fact_4275_semiring__norm_I15_J,axiom,
% 5.46/5.72 ! [M: num,N: num] :
% 5.46/5.72 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.73 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(15)
% 5.46/5.73 thf(fact_4276_semiring__norm_I14_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(14)
% 5.46/5.73 thf(fact_4277_semiring__norm_I72_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(72)
% 5.46/5.73 thf(fact_4278_semiring__norm_I81_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.73 = ( ord_less_num @ M @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(81)
% 5.46/5.73 thf(fact_4279_semiring__norm_I70_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(70)
% 5.46/5.73 thf(fact_4280_semiring__norm_I77_J,axiom,
% 5.46/5.73 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(77)
% 5.46/5.73 thf(fact_4281_concat__bit__nonnegative__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int,L2: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L2 ) )
% 5.46/5.73 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % concat_bit_nonnegative_iff
% 5.46/5.73 thf(fact_4282_concat__bit__negative__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int,L2: int] :
% 5.46/5.73 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L2 ) @ zero_zero_int )
% 5.46/5.73 = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % concat_bit_negative_iff
% 5.46/5.73 thf(fact_4283_zdiv__numeral__Bit1,axiom,
% 5.46/5.73 ! [V: num,W: num] :
% 5.46/5.73 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.46/5.73 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % zdiv_numeral_Bit1
% 5.46/5.73 thf(fact_4284_semiring__norm_I3_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 5.46/5.73 = ( bit1 @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(3)
% 5.46/5.73 thf(fact_4285_semiring__norm_I4_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 5.46/5.73 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(4)
% 5.46/5.73 thf(fact_4286_semiring__norm_I5_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.46/5.73 = ( bit1 @ M ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(5)
% 5.46/5.73 thf(fact_4287_semiring__norm_I8_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.46/5.73 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(8)
% 5.46/5.73 thf(fact_4288_semiring__norm_I10_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(10)
% 5.46/5.73 thf(fact_4289_semiring__norm_I16_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(16)
% 5.46/5.73 thf(fact_4290_semiring__norm_I74_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.73 = ( ord_less_num @ M @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(74)
% 5.46/5.73 thf(fact_4291_semiring__norm_I79_J,axiom,
% 5.46/5.73 ! [M: num,N: num] :
% 5.46/5.73 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.73 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_norm(79)
% 5.46/5.73 thf(fact_4292_odd__of__bool__self,axiom,
% 5.46/5.73 ! [P2: $o] :
% 5.46/5.73 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P2 ) ) )
% 5.46/5.73 = P2 ) ).
% 5.46/5.73
% 5.46/5.73 % odd_of_bool_self
% 5.46/5.73 thf(fact_4293_odd__of__bool__self,axiom,
% 5.46/5.73 ! [P2: $o] :
% 5.46/5.73 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P2 ) ) )
% 5.46/5.73 = P2 ) ).
% 5.46/5.73
% 5.46/5.73 % odd_of_bool_self
% 5.46/5.73 thf(fact_4294_odd__of__bool__self,axiom,
% 5.46/5.73 ! [P2: $o] :
% 5.46/5.73 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P2 ) ) )
% 5.46/5.73 = P2 ) ).
% 5.46/5.73
% 5.46/5.73 % odd_of_bool_self
% 5.46/5.73 thf(fact_4295_of__bool__half__eq__0,axiom,
% 5.46/5.73 ! [B2: $o] :
% 5.46/5.73 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_half_eq_0
% 5.46/5.73 thf(fact_4296_of__bool__half__eq__0,axiom,
% 5.46/5.73 ! [B2: $o] :
% 5.46/5.73 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_half_eq_0
% 5.46/5.73 thf(fact_4297_of__bool__half__eq__0,axiom,
% 5.46/5.73 ! [B2: $o] :
% 5.46/5.73 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.73 = zero_z3403309356797280102nteger ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_half_eq_0
% 5.46/5.73 thf(fact_4298_Suc__div__eq__add3__div__numeral,axiom,
% 5.46/5.73 ! [M: nat,V: num] :
% 5.46/5.73 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.46/5.73 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_div_eq_add3_div_numeral
% 5.46/5.73 thf(fact_4299_div__Suc__eq__div__add3,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.46/5.73 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % div_Suc_eq_div_add3
% 5.46/5.73 thf(fact_4300_mod__Suc__eq__mod__add3,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.46/5.73 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mod_Suc_eq_mod_add3
% 5.46/5.73 thf(fact_4301_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.46/5.73 ! [M: nat,V: num] :
% 5.46/5.73 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.46/5.73 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_mod_eq_add3_mod_numeral
% 5.46/5.73 thf(fact_4302_set__decode__Suc,axiom,
% 5.46/5.73 ! [N: nat,X4: nat] :
% 5.46/5.73 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X4 ) )
% 5.46/5.73 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % set_decode_Suc
% 5.46/5.73 thf(fact_4303_bits__1__div__exp,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bits_1_div_exp
% 5.46/5.73 thf(fact_4304_bits__1__div__exp,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bits_1_div_exp
% 5.46/5.73 thf(fact_4305_bits__1__div__exp,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bits_1_div_exp
% 5.46/5.73 thf(fact_4306_one__div__2__pow__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_div_2_pow_eq
% 5.46/5.73 thf(fact_4307_one__div__2__pow__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_div_2_pow_eq
% 5.46/5.73 thf(fact_4308_one__div__2__pow__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_div_2_pow_eq
% 5.46/5.73 thf(fact_4309_zmod__numeral__Bit1,axiom,
% 5.46/5.73 ! [V: num,W: num] :
% 5.46/5.73 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.46/5.73 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % zmod_numeral_Bit1
% 5.46/5.73 thf(fact_4310_one__mod__2__pow__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_mod_2_pow_eq
% 5.46/5.73 thf(fact_4311_one__mod__2__pow__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_mod_2_pow_eq
% 5.46/5.73 thf(fact_4312_one__mod__2__pow__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_mod_2_pow_eq
% 5.46/5.73 thf(fact_4313_signed__take__bit__Suc__bit1,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % signed_take_bit_Suc_bit1
% 5.46/5.73 thf(fact_4314_of__bool__eq__iff,axiom,
% 5.46/5.73 ! [P2: $o,Q2: $o] :
% 5.46/5.73 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 5.46/5.73 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 5.46/5.73 = ( P2 = Q2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_eq_iff
% 5.46/5.73 thf(fact_4315_of__bool__eq__iff,axiom,
% 5.46/5.73 ! [P2: $o,Q2: $o] :
% 5.46/5.73 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 5.46/5.73 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 5.46/5.73 = ( P2 = Q2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_eq_iff
% 5.46/5.73 thf(fact_4316_of__bool__eq__iff,axiom,
% 5.46/5.73 ! [P2: $o,Q2: $o] :
% 5.46/5.73 ( ( ( zero_n356916108424825756nteger @ P2 )
% 5.46/5.73 = ( zero_n356916108424825756nteger @ Q2 ) )
% 5.46/5.73 = ( P2 = Q2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_eq_iff
% 5.46/5.73 thf(fact_4317_of__bool__conj,axiom,
% 5.46/5.73 ! [P: $o,Q: $o] :
% 5.46/5.73 ( ( zero_n3304061248610475627l_real
% 5.46/5.73 @ ( P
% 5.46/5.73 & Q ) )
% 5.46/5.73 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_conj
% 5.46/5.73 thf(fact_4318_of__bool__conj,axiom,
% 5.46/5.73 ! [P: $o,Q: $o] :
% 5.46/5.73 ( ( zero_n2052037380579107095ol_rat
% 5.46/5.73 @ ( P
% 5.46/5.73 & Q ) )
% 5.46/5.73 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_conj
% 5.46/5.73 thf(fact_4319_of__bool__conj,axiom,
% 5.46/5.73 ! [P: $o,Q: $o] :
% 5.46/5.73 ( ( zero_n2687167440665602831ol_nat
% 5.46/5.73 @ ( P
% 5.46/5.73 & Q ) )
% 5.46/5.73 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_conj
% 5.46/5.73 thf(fact_4320_of__bool__conj,axiom,
% 5.46/5.73 ! [P: $o,Q: $o] :
% 5.46/5.73 ( ( zero_n2684676970156552555ol_int
% 5.46/5.73 @ ( P
% 5.46/5.73 & Q ) )
% 5.46/5.73 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_conj
% 5.46/5.73 thf(fact_4321_of__bool__conj,axiom,
% 5.46/5.73 ! [P: $o,Q: $o] :
% 5.46/5.73 ( ( zero_n356916108424825756nteger
% 5.46/5.73 @ ( P
% 5.46/5.73 & Q ) )
% 5.46/5.73 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_conj
% 5.46/5.73 thf(fact_4322_verit__eq__simplify_I14_J,axiom,
% 5.46/5.73 ! [X2: num,X32: num] :
% 5.46/5.73 ( ( bit0 @ X2 )
% 5.46/5.73 != ( bit1 @ X32 ) ) ).
% 5.46/5.73
% 5.46/5.73 % verit_eq_simplify(14)
% 5.46/5.73 thf(fact_4323_verit__eq__simplify_I12_J,axiom,
% 5.46/5.73 ! [X32: num] :
% 5.46/5.73 ( one
% 5.46/5.73 != ( bit1 @ X32 ) ) ).
% 5.46/5.73
% 5.46/5.73 % verit_eq_simplify(12)
% 5.46/5.73 thf(fact_4324_concat__bit__assoc,axiom,
% 5.46/5.73 ! [N: nat,K: int,M: nat,L2: int,R2: int] :
% 5.46/5.73 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R2 ) )
% 5.46/5.73 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % concat_bit_assoc
% 5.46/5.73 thf(fact_4325_subset__decode__imp__le,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.46/5.73 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % subset_decode_imp_le
% 5.46/5.73 thf(fact_4326_zero__less__eq__of__bool,axiom,
% 5.46/5.73 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.46/5.73
% 5.46/5.73 % zero_less_eq_of_bool
% 5.46/5.73 thf(fact_4327_zero__less__eq__of__bool,axiom,
% 5.46/5.73 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.46/5.73
% 5.46/5.73 % zero_less_eq_of_bool
% 5.46/5.73 thf(fact_4328_zero__less__eq__of__bool,axiom,
% 5.46/5.73 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.46/5.73
% 5.46/5.73 % zero_less_eq_of_bool
% 5.46/5.73 thf(fact_4329_zero__less__eq__of__bool,axiom,
% 5.46/5.73 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.46/5.73
% 5.46/5.73 % zero_less_eq_of_bool
% 5.46/5.73 thf(fact_4330_zero__less__eq__of__bool,axiom,
% 5.46/5.73 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.46/5.73
% 5.46/5.73 % zero_less_eq_of_bool
% 5.46/5.73 thf(fact_4331_of__bool__less__eq__one,axiom,
% 5.46/5.73 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_less_eq_one
% 5.46/5.73 thf(fact_4332_of__bool__less__eq__one,axiom,
% 5.46/5.73 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_less_eq_one
% 5.46/5.73 thf(fact_4333_of__bool__less__eq__one,axiom,
% 5.46/5.73 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_less_eq_one
% 5.46/5.73 thf(fact_4334_of__bool__less__eq__one,axiom,
% 5.46/5.73 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_less_eq_one
% 5.46/5.73 thf(fact_4335_of__bool__less__eq__one,axiom,
% 5.46/5.73 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_less_eq_one
% 5.46/5.73 thf(fact_4336_split__of__bool__asm,axiom,
% 5.46/5.73 ! [P: complex > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.46/5.73 = ( ~ ( ( P2
% 5.46/5.73 & ~ ( P @ one_one_complex ) )
% 5.46/5.73 | ( ~ P2
% 5.46/5.73 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool_asm
% 5.46/5.73 thf(fact_4337_split__of__bool__asm,axiom,
% 5.46/5.73 ! [P: real > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.46/5.73 = ( ~ ( ( P2
% 5.46/5.73 & ~ ( P @ one_one_real ) )
% 5.46/5.73 | ( ~ P2
% 5.46/5.73 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool_asm
% 5.46/5.73 thf(fact_4338_split__of__bool__asm,axiom,
% 5.46/5.73 ! [P: rat > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.46/5.73 = ( ~ ( ( P2
% 5.46/5.73 & ~ ( P @ one_one_rat ) )
% 5.46/5.73 | ( ~ P2
% 5.46/5.73 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool_asm
% 5.46/5.73 thf(fact_4339_split__of__bool__asm,axiom,
% 5.46/5.73 ! [P: nat > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.46/5.73 = ( ~ ( ( P2
% 5.46/5.73 & ~ ( P @ one_one_nat ) )
% 5.46/5.73 | ( ~ P2
% 5.46/5.73 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool_asm
% 5.46/5.73 thf(fact_4340_split__of__bool__asm,axiom,
% 5.46/5.73 ! [P: int > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.46/5.73 = ( ~ ( ( P2
% 5.46/5.73 & ~ ( P @ one_one_int ) )
% 5.46/5.73 | ( ~ P2
% 5.46/5.73 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool_asm
% 5.46/5.73 thf(fact_4341_split__of__bool__asm,axiom,
% 5.46/5.73 ! [P: code_integer > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.46/5.73 = ( ~ ( ( P2
% 5.46/5.73 & ~ ( P @ one_one_Code_integer ) )
% 5.46/5.73 | ( ~ P2
% 5.46/5.73 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool_asm
% 5.46/5.73 thf(fact_4342_split__of__bool,axiom,
% 5.46/5.73 ! [P: complex > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.46/5.73 = ( ( P2
% 5.46/5.73 => ( P @ one_one_complex ) )
% 5.46/5.73 & ( ~ P2
% 5.46/5.73 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool
% 5.46/5.73 thf(fact_4343_split__of__bool,axiom,
% 5.46/5.73 ! [P: real > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.46/5.73 = ( ( P2
% 5.46/5.73 => ( P @ one_one_real ) )
% 5.46/5.73 & ( ~ P2
% 5.46/5.73 => ( P @ zero_zero_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool
% 5.46/5.73 thf(fact_4344_split__of__bool,axiom,
% 5.46/5.73 ! [P: rat > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.46/5.73 = ( ( P2
% 5.46/5.73 => ( P @ one_one_rat ) )
% 5.46/5.73 & ( ~ P2
% 5.46/5.73 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool
% 5.46/5.73 thf(fact_4345_split__of__bool,axiom,
% 5.46/5.73 ! [P: nat > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.46/5.73 = ( ( P2
% 5.46/5.73 => ( P @ one_one_nat ) )
% 5.46/5.73 & ( ~ P2
% 5.46/5.73 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool
% 5.46/5.73 thf(fact_4346_split__of__bool,axiom,
% 5.46/5.73 ! [P: int > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.46/5.73 = ( ( P2
% 5.46/5.73 => ( P @ one_one_int ) )
% 5.46/5.73 & ( ~ P2
% 5.46/5.73 => ( P @ zero_zero_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool
% 5.46/5.73 thf(fact_4347_split__of__bool,axiom,
% 5.46/5.73 ! [P: code_integer > $o,P2: $o] :
% 5.46/5.73 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.46/5.73 = ( ( P2
% 5.46/5.73 => ( P @ one_one_Code_integer ) )
% 5.46/5.73 & ( ~ P2
% 5.46/5.73 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % split_of_bool
% 5.46/5.73 thf(fact_4348_of__bool__def,axiom,
% 5.46/5.73 ( zero_n1201886186963655149omplex
% 5.46/5.73 = ( ^ [P3: $o] : ( if_complex @ P3 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_def
% 5.46/5.73 thf(fact_4349_of__bool__def,axiom,
% 5.46/5.73 ( zero_n3304061248610475627l_real
% 5.46/5.73 = ( ^ [P3: $o] : ( if_real @ P3 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_def
% 5.46/5.73 thf(fact_4350_of__bool__def,axiom,
% 5.46/5.73 ( zero_n2052037380579107095ol_rat
% 5.46/5.73 = ( ^ [P3: $o] : ( if_rat @ P3 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_def
% 5.46/5.73 thf(fact_4351_of__bool__def,axiom,
% 5.46/5.73 ( zero_n2687167440665602831ol_nat
% 5.46/5.73 = ( ^ [P3: $o] : ( if_nat @ P3 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_def
% 5.46/5.73 thf(fact_4352_of__bool__def,axiom,
% 5.46/5.73 ( zero_n2684676970156552555ol_int
% 5.46/5.73 = ( ^ [P3: $o] : ( if_int @ P3 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_def
% 5.46/5.73 thf(fact_4353_of__bool__def,axiom,
% 5.46/5.73 ( zero_n356916108424825756nteger
% 5.46/5.73 = ( ^ [P3: $o] : ( if_Code_integer @ P3 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_def
% 5.46/5.73 thf(fact_4354_num_Oexhaust,axiom,
% 5.46/5.73 ! [Y3: num] :
% 5.46/5.73 ( ( Y3 != one )
% 5.46/5.73 => ( ! [X22: num] :
% 5.46/5.73 ( Y3
% 5.46/5.73 != ( bit0 @ X22 ) )
% 5.46/5.73 => ~ ! [X33: num] :
% 5.46/5.73 ( Y3
% 5.46/5.73 != ( bit1 @ X33 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % num.exhaust
% 5.46/5.73 thf(fact_4355_numeral__Bit1,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.46/5.73 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_Bit1
% 5.46/5.73 thf(fact_4356_numeral__Bit1,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.46/5.73 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_Bit1
% 5.46/5.73 thf(fact_4357_numeral__Bit1,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.46/5.73 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_Bit1
% 5.46/5.73 thf(fact_4358_numeral__Bit1,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.46/5.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_Bit1
% 5.46/5.73 thf(fact_4359_numeral__Bit1,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.46/5.73 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_Bit1
% 5.46/5.73 thf(fact_4360_eval__nat__numeral_I3_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.46/5.73 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % eval_nat_numeral(3)
% 5.46/5.73 thf(fact_4361_cong__exp__iff__simps_I10_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num,N: num] :
% 5.46/5.73 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(10)
% 5.46/5.73 thf(fact_4362_cong__exp__iff__simps_I10_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num,N: num] :
% 5.46/5.73 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(10)
% 5.46/5.73 thf(fact_4363_cong__exp__iff__simps_I10_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num,N: num] :
% 5.46/5.73 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(10)
% 5.46/5.73 thf(fact_4364_cong__exp__iff__simps_I12_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num,N: num] :
% 5.46/5.73 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(12)
% 5.46/5.73 thf(fact_4365_cong__exp__iff__simps_I12_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num,N: num] :
% 5.46/5.73 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(12)
% 5.46/5.73 thf(fact_4366_cong__exp__iff__simps_I12_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num,N: num] :
% 5.46/5.73 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(12)
% 5.46/5.73 thf(fact_4367_cong__exp__iff__simps_I13_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num,N: num] :
% 5.46/5.73 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.73 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.46/5.73 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(13)
% 5.46/5.73 thf(fact_4368_cong__exp__iff__simps_I13_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num,N: num] :
% 5.46/5.73 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.73 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.46/5.73 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(13)
% 5.46/5.73 thf(fact_4369_cong__exp__iff__simps_I13_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num,N: num] :
% 5.46/5.73 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.73 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.46/5.73 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(13)
% 5.46/5.73 thf(fact_4370_power__minus__Bit1,axiom,
% 5.46/5.73 ! [X4: real,K: num] :
% 5.46/5.73 ( ( power_power_real @ ( uminus_uminus_real @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % power_minus_Bit1
% 5.46/5.73 thf(fact_4371_power__minus__Bit1,axiom,
% 5.46/5.73 ! [X4: int,K: num] :
% 5.46/5.73 ( ( power_power_int @ ( uminus_uminus_int @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % power_minus_Bit1
% 5.46/5.73 thf(fact_4372_power__minus__Bit1,axiom,
% 5.46/5.73 ! [X4: complex,K: num] :
% 5.46/5.73 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % power_minus_Bit1
% 5.46/5.73 thf(fact_4373_power__minus__Bit1,axiom,
% 5.46/5.73 ! [X4: code_integer,K: num] :
% 5.46/5.73 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % power_minus_Bit1
% 5.46/5.73 thf(fact_4374_power__minus__Bit1,axiom,
% 5.46/5.73 ! [X4: rat,K: num] :
% 5.46/5.73 ( ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % power_minus_Bit1
% 5.46/5.73 thf(fact_4375_numeral__Bit1__div__2,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = ( numeral_numeral_nat @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_Bit1_div_2
% 5.46/5.73 thf(fact_4376_numeral__Bit1__div__2,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.73 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_Bit1_div_2
% 5.46/5.73 thf(fact_4377_odd__numeral,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % odd_numeral
% 5.46/5.73 thf(fact_4378_odd__numeral,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % odd_numeral
% 5.46/5.73 thf(fact_4379_odd__numeral,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % odd_numeral
% 5.46/5.73 thf(fact_4380_cong__exp__iff__simps_I3_J,axiom,
% 5.46/5.73 ! [N: num,Q2: num] :
% 5.46/5.73 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 != zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(3)
% 5.46/5.73 thf(fact_4381_cong__exp__iff__simps_I3_J,axiom,
% 5.46/5.73 ! [N: num,Q2: num] :
% 5.46/5.73 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 != zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(3)
% 5.46/5.73 thf(fact_4382_cong__exp__iff__simps_I3_J,axiom,
% 5.46/5.73 ! [N: num,Q2: num] :
% 5.46/5.73 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 != zero_z3403309356797280102nteger ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(3)
% 5.46/5.73 thf(fact_4383_power3__eq__cube,axiom,
% 5.46/5.73 ! [A: complex] :
% 5.46/5.73 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.46/5.73 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % power3_eq_cube
% 5.46/5.73 thf(fact_4384_power3__eq__cube,axiom,
% 5.46/5.73 ! [A: real] :
% 5.46/5.73 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.46/5.73 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % power3_eq_cube
% 5.46/5.73 thf(fact_4385_power3__eq__cube,axiom,
% 5.46/5.73 ! [A: rat] :
% 5.46/5.73 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.46/5.73 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % power3_eq_cube
% 5.46/5.73 thf(fact_4386_power3__eq__cube,axiom,
% 5.46/5.73 ! [A: nat] :
% 5.46/5.73 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.46/5.73 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % power3_eq_cube
% 5.46/5.73 thf(fact_4387_power3__eq__cube,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.46/5.73 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % power3_eq_cube
% 5.46/5.73 thf(fact_4388_numeral__3__eq__3,axiom,
% 5.46/5.73 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.46/5.73 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_3_eq_3
% 5.46/5.73 thf(fact_4389_Suc3__eq__add__3,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.46/5.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc3_eq_add_3
% 5.46/5.73 thf(fact_4390_of__bool__odd__eq__mod__2,axiom,
% 5.46/5.73 ! [A: nat] :
% 5.46/5.73 ( ( zero_n2687167440665602831ol_nat
% 5.46/5.73 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.73 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_odd_eq_mod_2
% 5.46/5.73 thf(fact_4391_of__bool__odd__eq__mod__2,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( zero_n2684676970156552555ol_int
% 5.46/5.73 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.73 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_odd_eq_mod_2
% 5.46/5.73 thf(fact_4392_of__bool__odd__eq__mod__2,axiom,
% 5.46/5.73 ! [A: code_integer] :
% 5.46/5.73 ( ( zero_n356916108424825756nteger
% 5.46/5.73 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.73 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_bool_odd_eq_mod_2
% 5.46/5.73 thf(fact_4393_cong__exp__iff__simps_I7_J,axiom,
% 5.46/5.73 ! [Q2: num,N: num] :
% 5.46/5.73 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.73 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.46/5.73 = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(7)
% 5.46/5.73 thf(fact_4394_cong__exp__iff__simps_I7_J,axiom,
% 5.46/5.73 ! [Q2: num,N: num] :
% 5.46/5.73 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.73 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.46/5.73 = zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(7)
% 5.46/5.73 thf(fact_4395_cong__exp__iff__simps_I7_J,axiom,
% 5.46/5.73 ! [Q2: num,N: num] :
% 5.46/5.73 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.73 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.46/5.73 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(7)
% 5.46/5.73 thf(fact_4396_cong__exp__iff__simps_I11_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num] :
% 5.46/5.73 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.73 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.46/5.73 = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(11)
% 5.46/5.73 thf(fact_4397_cong__exp__iff__simps_I11_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num] :
% 5.46/5.73 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.73 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.46/5.73 = zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(11)
% 5.46/5.73 thf(fact_4398_cong__exp__iff__simps_I11_J,axiom,
% 5.46/5.73 ! [M: num,Q2: num] :
% 5.46/5.73 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.46/5.73 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.46/5.73 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.46/5.73 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.73
% 5.46/5.73 % cong_exp_iff_simps(11)
% 5.46/5.73 thf(fact_4399_Suc__div__eq__add3__div,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.46/5.73 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_div_eq_add3_div
% 5.46/5.73 thf(fact_4400_Suc__mod__eq__add3__mod,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.46/5.73 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_mod_eq_add3_mod
% 5.46/5.73 thf(fact_4401_bits__induct,axiom,
% 5.46/5.73 ! [P: nat > $o,A: nat] :
% 5.46/5.73 ( ! [A5: nat] :
% 5.46/5.73 ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = A5 )
% 5.46/5.73 => ( P @ A5 ) )
% 5.46/5.73 => ( ! [A5: nat,B5: $o] :
% 5.46/5.73 ( ( P @ A5 )
% 5.46/5.73 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = A5 )
% 5.46/5.73 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.46/5.73 => ( P @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bits_induct
% 5.46/5.73 thf(fact_4402_bits__induct,axiom,
% 5.46/5.73 ! [P: int > $o,A: int] :
% 5.46/5.73 ( ! [A5: int] :
% 5.46/5.73 ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.73 = A5 )
% 5.46/5.73 => ( P @ A5 ) )
% 5.46/5.73 => ( ! [A5: int,B5: $o] :
% 5.46/5.73 ( ( P @ A5 )
% 5.46/5.73 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.73 = A5 )
% 5.46/5.73 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.46/5.73 => ( P @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bits_induct
% 5.46/5.73 thf(fact_4403_bits__induct,axiom,
% 5.46/5.73 ! [P: code_integer > $o,A: code_integer] :
% 5.46/5.73 ( ! [A5: code_integer] :
% 5.46/5.73 ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.73 = A5 )
% 5.46/5.73 => ( P @ A5 ) )
% 5.46/5.73 => ( ! [A5: code_integer,B5: $o] :
% 5.46/5.73 ( ( P @ A5 )
% 5.46/5.73 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.73 = A5 )
% 5.46/5.73 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.46/5.73 => ( P @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % bits_induct
% 5.46/5.73 thf(fact_4404_compl__le__swap2,axiom,
% 5.46/5.73 ! [Y3: set_nat,X4: set_nat] :
% 5.46/5.73 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y3 ) @ X4 )
% 5.46/5.73 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X4 ) @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % compl_le_swap2
% 5.46/5.73 thf(fact_4405_compl__le__swap1,axiom,
% 5.46/5.73 ! [Y3: set_nat,X4: set_nat] :
% 5.46/5.73 ( ( ord_less_eq_set_nat @ Y3 @ ( uminus5710092332889474511et_nat @ X4 ) )
% 5.46/5.73 => ( ord_less_eq_set_nat @ X4 @ ( uminus5710092332889474511et_nat @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % compl_le_swap1
% 5.46/5.73 thf(fact_4406_compl__mono,axiom,
% 5.46/5.73 ! [X4: set_nat,Y3: set_nat] :
% 5.46/5.73 ( ( ord_less_eq_set_nat @ X4 @ Y3 )
% 5.46/5.73 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y3 ) @ ( uminus5710092332889474511et_nat @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % compl_mono
% 5.46/5.73 thf(fact_4407_exp__mod__exp,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_mod_exp
% 5.46/5.73 thf(fact_4408_exp__mod__exp,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_mod_exp
% 5.46/5.73 thf(fact_4409_exp__mod__exp,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_mod_exp
% 5.46/5.73 thf(fact_4410_exp__div__exp__eq,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( times_times_nat
% 5.46/5.73 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.73 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.46/5.73 != zero_zero_nat )
% 5.46/5.73 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.46/5.73 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_div_exp_eq
% 5.46/5.73 thf(fact_4411_exp__div__exp__eq,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( times_times_int
% 5.46/5.73 @ ( zero_n2684676970156552555ol_int
% 5.46/5.73 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.46/5.73 != zero_zero_int )
% 5.46/5.73 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.46/5.73 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_div_exp_eq
% 5.46/5.73 thf(fact_4412_exp__div__exp__eq,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( times_3573771949741848930nteger
% 5.46/5.73 @ ( zero_n356916108424825756nteger
% 5.46/5.73 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.46/5.73 != zero_z3403309356797280102nteger )
% 5.46/5.73 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.46/5.73 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_div_exp_eq
% 5.46/5.73 thf(fact_4413_odd__mod__4__div__2,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.46/5.73 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % odd_mod_4_div_2
% 5.46/5.73 thf(fact_4414_mod__exhaust__less__4,axiom,
% 5.46/5.73 ! [M: nat] :
% 5.46/5.73 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = zero_zero_nat )
% 5.46/5.73 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = one_one_nat )
% 5.46/5.73 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mod_exhaust_less_4
% 5.46/5.73 thf(fact_4415_signed__take__bit__numeral__minus__bit1,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.73 = ( 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 ) ) ).
% 5.46/5.73
% 5.46/5.73 % signed_take_bit_numeral_minus_bit1
% 5.46/5.73 thf(fact_4416_dbl__dec__simps_I4_J,axiom,
% 5.46/5.73 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.73 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(4)
% 5.46/5.73 thf(fact_4417_dbl__dec__simps_I4_J,axiom,
% 5.46/5.73 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(4)
% 5.46/5.73 thf(fact_4418_dbl__dec__simps_I4_J,axiom,
% 5.46/5.73 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.73 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(4)
% 5.46/5.73 thf(fact_4419_dbl__dec__simps_I4_J,axiom,
% 5.46/5.73 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(4)
% 5.46/5.73 thf(fact_4420_dbl__dec__simps_I4_J,axiom,
% 5.46/5.73 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.73 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(4)
% 5.46/5.73 thf(fact_4421_signed__take__bit__numeral__bit1,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % signed_take_bit_numeral_bit1
% 5.46/5.73 thf(fact_4422_dbl__inc__simps_I3_J,axiom,
% 5.46/5.73 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.46/5.73 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(3)
% 5.46/5.73 thf(fact_4423_dbl__inc__simps_I3_J,axiom,
% 5.46/5.73 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.46/5.73 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(3)
% 5.46/5.73 thf(fact_4424_dbl__inc__simps_I3_J,axiom,
% 5.46/5.73 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.46/5.73 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(3)
% 5.46/5.73 thf(fact_4425_dbl__inc__simps_I3_J,axiom,
% 5.46/5.73 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.46/5.73 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(3)
% 5.46/5.73 thf(fact_4426_add__scale__eq__noteq,axiom,
% 5.46/5.73 ! [R2: real,A: real,B2: real,C: real,D: real] :
% 5.46/5.73 ( ( R2 != zero_zero_real )
% 5.46/5.73 => ( ( ( A = B2 )
% 5.46/5.73 & ( C != D ) )
% 5.46/5.73 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 5.46/5.73 != ( plus_plus_real @ B2 @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_scale_eq_noteq
% 5.46/5.73 thf(fact_4427_add__scale__eq__noteq,axiom,
% 5.46/5.73 ! [R2: rat,A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.73 ( ( R2 != zero_zero_rat )
% 5.46/5.73 => ( ( ( A = B2 )
% 5.46/5.73 & ( C != D ) )
% 5.46/5.73 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 5.46/5.73 != ( plus_plus_rat @ B2 @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_scale_eq_noteq
% 5.46/5.73 thf(fact_4428_add__scale__eq__noteq,axiom,
% 5.46/5.73 ! [R2: nat,A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.73 ( ( R2 != zero_zero_nat )
% 5.46/5.73 => ( ( ( A = B2 )
% 5.46/5.73 & ( C != D ) )
% 5.46/5.73 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 5.46/5.73 != ( plus_plus_nat @ B2 @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_scale_eq_noteq
% 5.46/5.73 thf(fact_4429_add__scale__eq__noteq,axiom,
% 5.46/5.73 ! [R2: int,A: int,B2: int,C: int,D: int] :
% 5.46/5.73 ( ( R2 != zero_zero_int )
% 5.46/5.73 => ( ( ( A = B2 )
% 5.46/5.73 & ( C != D ) )
% 5.46/5.73 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 5.46/5.73 != ( plus_plus_int @ B2 @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_scale_eq_noteq
% 5.46/5.73 thf(fact_4430_num_Osize__gen_I3_J,axiom,
% 5.46/5.73 ! [X32: num] :
% 5.46/5.73 ( ( size_num @ ( bit1 @ X32 ) )
% 5.46/5.73 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % num.size_gen(3)
% 5.46/5.73 thf(fact_4431_dbl__dec__simps_I3_J,axiom,
% 5.46/5.73 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.46/5.73 = one_one_complex ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(3)
% 5.46/5.73 thf(fact_4432_dbl__dec__simps_I3_J,axiom,
% 5.46/5.73 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.46/5.73 = one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(3)
% 5.46/5.73 thf(fact_4433_dbl__dec__simps_I3_J,axiom,
% 5.46/5.73 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.46/5.73 = one_one_rat ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(3)
% 5.46/5.73 thf(fact_4434_dbl__dec__simps_I3_J,axiom,
% 5.46/5.73 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(3)
% 5.46/5.73 thf(fact_4435_pred__numeral__simps_I1_J,axiom,
% 5.46/5.73 ( ( pred_numeral @ one )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % pred_numeral_simps(1)
% 5.46/5.73 thf(fact_4436_eq__numeral__Suc,axiom,
% 5.46/5.73 ! [K: num,N: nat] :
% 5.46/5.73 ( ( ( numeral_numeral_nat @ K )
% 5.46/5.73 = ( suc @ N ) )
% 5.46/5.73 = ( ( pred_numeral @ K )
% 5.46/5.73 = N ) ) ).
% 5.46/5.73
% 5.46/5.73 % eq_numeral_Suc
% 5.46/5.73 thf(fact_4437_Suc__eq__numeral,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( ( suc @ N )
% 5.46/5.73 = ( numeral_numeral_nat @ K ) )
% 5.46/5.73 = ( N
% 5.46/5.73 = ( pred_numeral @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_eq_numeral
% 5.46/5.73 thf(fact_4438_dbl__inc__simps_I2_J,axiom,
% 5.46/5.73 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.46/5.73 = one_one_complex ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(2)
% 5.46/5.73 thf(fact_4439_dbl__inc__simps_I2_J,axiom,
% 5.46/5.73 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.46/5.73 = one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(2)
% 5.46/5.73 thf(fact_4440_dbl__inc__simps_I2_J,axiom,
% 5.46/5.73 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.46/5.73 = one_one_rat ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(2)
% 5.46/5.73 thf(fact_4441_dbl__inc__simps_I2_J,axiom,
% 5.46/5.73 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(2)
% 5.46/5.73 thf(fact_4442_dbl__inc__simps_I4_J,axiom,
% 5.46/5.73 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.73 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(4)
% 5.46/5.73 thf(fact_4443_dbl__inc__simps_I4_J,axiom,
% 5.46/5.73 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(4)
% 5.46/5.73 thf(fact_4444_dbl__inc__simps_I4_J,axiom,
% 5.46/5.73 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.73 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(4)
% 5.46/5.73 thf(fact_4445_dbl__inc__simps_I4_J,axiom,
% 5.46/5.73 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(4)
% 5.46/5.73 thf(fact_4446_dbl__inc__simps_I4_J,axiom,
% 5.46/5.73 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.73 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(4)
% 5.46/5.73 thf(fact_4447_dbl__inc__simps_I5_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.46/5.73 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(5)
% 5.46/5.73 thf(fact_4448_dbl__inc__simps_I5_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.46/5.73 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(5)
% 5.46/5.73 thf(fact_4449_dbl__inc__simps_I5_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.46/5.73 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(5)
% 5.46/5.73 thf(fact_4450_dbl__inc__simps_I5_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.46/5.73 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(5)
% 5.46/5.73 thf(fact_4451_less__numeral__Suc,axiom,
% 5.46/5.73 ! [K: num,N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.46/5.73 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_numeral_Suc
% 5.46/5.73 thf(fact_4452_less__Suc__numeral,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.73 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_Suc_numeral
% 5.46/5.73 thf(fact_4453_pred__numeral__simps_I3_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.46/5.73 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % pred_numeral_simps(3)
% 5.46/5.73 thf(fact_4454_le__numeral__Suc,axiom,
% 5.46/5.73 ! [K: num,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.46/5.73 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % le_numeral_Suc
% 5.46/5.73 thf(fact_4455_le__Suc__numeral,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.73 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % le_Suc_numeral
% 5.46/5.73 thf(fact_4456_diff__Suc__numeral,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.73 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_Suc_numeral
% 5.46/5.73 thf(fact_4457_diff__numeral__Suc,axiom,
% 5.46/5.73 ! [K: num,N: nat] :
% 5.46/5.73 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.46/5.73 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_Suc
% 5.46/5.73 thf(fact_4458_dbl__dec__simps_I2_J,axiom,
% 5.46/5.73 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.46/5.73 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(2)
% 5.46/5.73 thf(fact_4459_dbl__dec__simps_I2_J,axiom,
% 5.46/5.73 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(2)
% 5.46/5.73 thf(fact_4460_dbl__dec__simps_I2_J,axiom,
% 5.46/5.73 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.46/5.73 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(2)
% 5.46/5.73 thf(fact_4461_dbl__dec__simps_I2_J,axiom,
% 5.46/5.73 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(2)
% 5.46/5.73 thf(fact_4462_dbl__dec__simps_I2_J,axiom,
% 5.46/5.73 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.46/5.73 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(2)
% 5.46/5.73 thf(fact_4463_dbl__dec__simps_I1_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(1)
% 5.46/5.73 thf(fact_4464_dbl__dec__simps_I1_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(1)
% 5.46/5.73 thf(fact_4465_dbl__dec__simps_I1_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.46/5.73 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(1)
% 5.46/5.73 thf(fact_4466_dbl__dec__simps_I1_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(1)
% 5.46/5.73 thf(fact_4467_dbl__dec__simps_I1_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_simps(1)
% 5.46/5.73 thf(fact_4468_dbl__inc__simps_I1_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(1)
% 5.46/5.73 thf(fact_4469_dbl__inc__simps_I1_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(1)
% 5.46/5.73 thf(fact_4470_dbl__inc__simps_I1_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.46/5.73 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(1)
% 5.46/5.73 thf(fact_4471_dbl__inc__simps_I1_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(1)
% 5.46/5.73 thf(fact_4472_dbl__inc__simps_I1_J,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_simps(1)
% 5.46/5.73 thf(fact_4473_signed__take__bit__numeral__bit0,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.46/5.73 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % signed_take_bit_numeral_bit0
% 5.46/5.73 thf(fact_4474_signed__take__bit__numeral__minus__bit0,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.73 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % signed_take_bit_numeral_minus_bit0
% 5.46/5.73 thf(fact_4475_numeral__eq__Suc,axiom,
% 5.46/5.73 ( numeral_numeral_nat
% 5.46/5.73 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_eq_Suc
% 5.46/5.73 thf(fact_4476_pred__numeral__def,axiom,
% 5.46/5.73 ( pred_numeral
% 5.46/5.73 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % pred_numeral_def
% 5.46/5.73 thf(fact_4477_dbl__inc__def,axiom,
% 5.46/5.73 ( neg_nu8557863876264182079omplex
% 5.46/5.73 = ( ^ [X: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_def
% 5.46/5.73 thf(fact_4478_dbl__inc__def,axiom,
% 5.46/5.73 ( neg_nu8295874005876285629c_real
% 5.46/5.73 = ( ^ [X: real] : ( plus_plus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_def
% 5.46/5.73 thf(fact_4479_dbl__inc__def,axiom,
% 5.46/5.73 ( neg_nu5219082963157363817nc_rat
% 5.46/5.73 = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_def
% 5.46/5.73 thf(fact_4480_dbl__inc__def,axiom,
% 5.46/5.73 ( neg_nu5851722552734809277nc_int
% 5.46/5.73 = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_inc_def
% 5.46/5.73 thf(fact_4481_num_Osize__gen_I1_J,axiom,
% 5.46/5.73 ( ( size_num @ one )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % num.size_gen(1)
% 5.46/5.73 thf(fact_4482_dbl__dec__def,axiom,
% 5.46/5.73 ( neg_nu6511756317524482435omplex
% 5.46/5.73 = ( ^ [X: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_def
% 5.46/5.73 thf(fact_4483_dbl__dec__def,axiom,
% 5.46/5.73 ( neg_nu6075765906172075777c_real
% 5.46/5.73 = ( ^ [X: real] : ( minus_minus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_def
% 5.46/5.73 thf(fact_4484_dbl__dec__def,axiom,
% 5.46/5.73 ( neg_nu3179335615603231917ec_rat
% 5.46/5.73 = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_def
% 5.46/5.73 thf(fact_4485_dbl__dec__def,axiom,
% 5.46/5.73 ( neg_nu3811975205180677377ec_int
% 5.46/5.73 = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % dbl_dec_def
% 5.46/5.73 thf(fact_4486_add__0__iff,axiom,
% 5.46/5.73 ! [B2: real,A: real] :
% 5.46/5.73 ( ( B2
% 5.46/5.73 = ( plus_plus_real @ B2 @ A ) )
% 5.46/5.73 = ( A = zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_0_iff
% 5.46/5.73 thf(fact_4487_add__0__iff,axiom,
% 5.46/5.73 ! [B2: rat,A: rat] :
% 5.46/5.73 ( ( B2
% 5.46/5.73 = ( plus_plus_rat @ B2 @ A ) )
% 5.46/5.73 = ( A = zero_zero_rat ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_0_iff
% 5.46/5.73 thf(fact_4488_add__0__iff,axiom,
% 5.46/5.73 ! [B2: nat,A: nat] :
% 5.46/5.73 ( ( B2
% 5.46/5.73 = ( plus_plus_nat @ B2 @ A ) )
% 5.46/5.73 = ( A = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_0_iff
% 5.46/5.73 thf(fact_4489_add__0__iff,axiom,
% 5.46/5.73 ! [B2: int,A: int] :
% 5.46/5.73 ( ( B2
% 5.46/5.73 = ( plus_plus_int @ B2 @ A ) )
% 5.46/5.73 = ( A = zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_0_iff
% 5.46/5.73 thf(fact_4490_crossproduct__noteq,axiom,
% 5.46/5.73 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.73 ( ( ( A != B2 )
% 5.46/5.73 & ( C != D ) )
% 5.46/5.73 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) )
% 5.46/5.73 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % crossproduct_noteq
% 5.46/5.73 thf(fact_4491_crossproduct__noteq,axiom,
% 5.46/5.73 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.73 ( ( ( A != B2 )
% 5.46/5.73 & ( C != D ) )
% 5.46/5.73 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B2 @ D ) )
% 5.46/5.73 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B2 @ C ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % crossproduct_noteq
% 5.46/5.73 thf(fact_4492_crossproduct__noteq,axiom,
% 5.46/5.73 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.73 ( ( ( A != B2 )
% 5.46/5.73 & ( C != D ) )
% 5.46/5.73 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B2 @ D ) )
% 5.46/5.73 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B2 @ C ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % crossproduct_noteq
% 5.46/5.73 thf(fact_4493_crossproduct__noteq,axiom,
% 5.46/5.73 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.73 ( ( ( A != B2 )
% 5.46/5.73 & ( C != D ) )
% 5.46/5.73 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) )
% 5.46/5.73 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B2 @ C ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % crossproduct_noteq
% 5.46/5.73 thf(fact_4494_crossproduct__eq,axiom,
% 5.46/5.73 ! [W: real,Y3: real,X4: real,Z: real] :
% 5.46/5.73 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y3 ) @ ( times_times_real @ X4 @ Z ) )
% 5.46/5.73 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X4 @ Y3 ) ) )
% 5.46/5.73 = ( ( W = X4 )
% 5.46/5.73 | ( Y3 = Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % crossproduct_eq
% 5.46/5.73 thf(fact_4495_crossproduct__eq,axiom,
% 5.46/5.73 ! [W: rat,Y3: rat,X4: rat,Z: rat] :
% 5.46/5.73 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y3 ) @ ( times_times_rat @ X4 @ Z ) )
% 5.46/5.73 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X4 @ Y3 ) ) )
% 5.46/5.73 = ( ( W = X4 )
% 5.46/5.73 | ( Y3 = Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % crossproduct_eq
% 5.46/5.73 thf(fact_4496_crossproduct__eq,axiom,
% 5.46/5.73 ! [W: nat,Y3: nat,X4: nat,Z: nat] :
% 5.46/5.73 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y3 ) @ ( times_times_nat @ X4 @ Z ) )
% 5.46/5.73 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X4 @ Y3 ) ) )
% 5.46/5.73 = ( ( W = X4 )
% 5.46/5.73 | ( Y3 = Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % crossproduct_eq
% 5.46/5.73 thf(fact_4497_crossproduct__eq,axiom,
% 5.46/5.73 ! [W: int,Y3: int,X4: int,Z: int] :
% 5.46/5.73 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y3 ) @ ( times_times_int @ X4 @ Z ) )
% 5.46/5.73 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X4 @ Y3 ) ) )
% 5.46/5.73 = ( ( W = X4 )
% 5.46/5.73 | ( Y3 = Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % crossproduct_eq
% 5.46/5.73 thf(fact_4498_eq__diff__eq_H,axiom,
% 5.46/5.73 ! [X4: real,Y3: real,Z: real] :
% 5.46/5.73 ( ( X4
% 5.46/5.73 = ( minus_minus_real @ Y3 @ Z ) )
% 5.46/5.73 = ( Y3
% 5.46/5.73 = ( plus_plus_real @ X4 @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % eq_diff_eq'
% 5.46/5.73 thf(fact_4499_num_Osize__gen_I2_J,axiom,
% 5.46/5.73 ! [X2: num] :
% 5.46/5.73 ( ( size_num @ ( bit0 @ X2 ) )
% 5.46/5.73 = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % num.size_gen(2)
% 5.46/5.73 thf(fact_4500_mask__numeral,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 5.46/5.73 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_numeral
% 5.46/5.73 thf(fact_4501_mask__numeral,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 5.46/5.73 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_numeral
% 5.46/5.73 thf(fact_4502_take__bit__rec,axiom,
% 5.46/5.73 ( bit_se1745604003318907178nteger
% 5.46/5.73 = ( ^ [N2: nat,A4: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_rec
% 5.46/5.73 thf(fact_4503_take__bit__rec,axiom,
% 5.46/5.73 ( bit_se2923211474154528505it_int
% 5.46/5.73 = ( ^ [N2: nat,A4: int] : ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_rec
% 5.46/5.73 thf(fact_4504_take__bit__rec,axiom,
% 5.46/5.73 ( bit_se2925701944663578781it_nat
% 5.46/5.73 = ( ^ [N2: nat,A4: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_rec
% 5.46/5.73 thf(fact_4505_and__int__unfold,axiom,
% 5.46/5.73 ( bit_se725231765392027082nd_int
% 5.46/5.73 = ( ^ [K3: int,L: int] :
% 5.46/5.73 ( if_int
% 5.46/5.73 @ ( ( K3 = zero_zero_int )
% 5.46/5.73 | ( L = zero_zero_int ) )
% 5.46/5.73 @ zero_zero_int
% 5.46/5.73 @ ( if_int
% 5.46/5.73 @ ( K3
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 @ L
% 5.46/5.73 @ ( if_int
% 5.46/5.73 @ ( L
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 @ K3
% 5.46/5.73 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_int_unfold
% 5.46/5.73 thf(fact_4506_exp__lower__Taylor__quadratic,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( divide_divide_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_lower_Taylor_quadratic
% 5.46/5.73 thf(fact_4507_sqrt__sum__squares__half__less,axiom,
% 5.46/5.73 ! [X4: real,U: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ X4 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.73 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sqrt_sum_squares_half_less
% 5.46/5.73 thf(fact_4508_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N ) )
% 5.46/5.73 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4509_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) )
% 5.46/5.73 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4510_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N ) )
% 5.46/5.73 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4511_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N ) )
% 5.46/5.73 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4512_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.46/5.73 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_less_of_int_cancel_iff
% 5.46/5.73 thf(fact_4513_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.46/5.73 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_less_of_int_cancel_iff
% 5.46/5.73 thf(fact_4514_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.46/5.73 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_less_of_int_cancel_iff
% 5.46/5.73 thf(fact_4515_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.46/5.73 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_less_of_int_cancel_iff
% 5.46/5.73 thf(fact_4516_and_Oright__idem,axiom,
% 5.46/5.73 ! [A: int,B2: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B2 ) @ B2 )
% 5.46/5.73 = ( bit_se725231765392027082nd_int @ A @ B2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % and.right_idem
% 5.46/5.73 thf(fact_4517_and_Oright__idem,axiom,
% 5.46/5.73 ! [A: nat,B2: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B2 ) @ B2 )
% 5.46/5.73 = ( bit_se727722235901077358nd_nat @ A @ B2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % and.right_idem
% 5.46/5.73 thf(fact_4518_and_Oleft__idem,axiom,
% 5.46/5.73 ! [A: int,B2: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B2 ) )
% 5.46/5.73 = ( bit_se725231765392027082nd_int @ A @ B2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % and.left_idem
% 5.46/5.73 thf(fact_4519_and_Oleft__idem,axiom,
% 5.46/5.73 ! [A: nat,B2: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B2 ) )
% 5.46/5.73 = ( bit_se727722235901077358nd_nat @ A @ B2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % and.left_idem
% 5.46/5.73 thf(fact_4520_and_Oidem,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.46/5.73 = A ) ).
% 5.46/5.73
% 5.46/5.73 % and.idem
% 5.46/5.73 thf(fact_4521_and_Oidem,axiom,
% 5.46/5.73 ! [A: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.46/5.73 = A ) ).
% 5.46/5.73
% 5.46/5.73 % and.idem
% 5.46/5.73 thf(fact_4522_real__sqrt__eq__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ( sqrt @ X4 )
% 5.46/5.73 = ( sqrt @ Y3 ) )
% 5.46/5.73 = ( X4 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_eq_iff
% 5.46/5.73 thf(fact_4523_mask__nat__positive__iff,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.46/5.73 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_nat_positive_iff
% 5.46/5.73 thf(fact_4524_take__bit__of__0,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_0
% 5.46/5.73 thf(fact_4525_take__bit__of__0,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_0
% 5.46/5.73 thf(fact_4526_bit_Oconj__zero__right,axiom,
% 5.46/5.73 ! [X4: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ X4 @ zero_zero_int )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % bit.conj_zero_right
% 5.46/5.73 thf(fact_4527_bit_Oconj__zero__left,axiom,
% 5.46/5.73 ! [X4: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X4 )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % bit.conj_zero_left
% 5.46/5.73 thf(fact_4528_zero__and__eq,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % zero_and_eq
% 5.46/5.73 thf(fact_4529_zero__and__eq,axiom,
% 5.46/5.73 ! [A: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % zero_and_eq
% 5.46/5.73 thf(fact_4530_and__zero__eq,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_zero_eq
% 5.46/5.73 thf(fact_4531_and__zero__eq,axiom,
% 5.46/5.73 ! [A: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % and_zero_eq
% 5.46/5.73 thf(fact_4532_real__sqrt__zero,axiom,
% 5.46/5.73 ( ( sqrt @ zero_zero_real )
% 5.46/5.73 = zero_zero_real ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_zero
% 5.46/5.73 thf(fact_4533_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ( sqrt @ X4 )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 = ( X4 = zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_eq_zero_cancel_iff
% 5.46/5.73 thf(fact_4534_real__sqrt__less__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ ( sqrt @ X4 ) @ ( sqrt @ Y3 ) )
% 5.46/5.73 = ( ord_less_real @ X4 @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_less_iff
% 5.46/5.73 thf(fact_4535_real__sqrt__le__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ ( sqrt @ Y3 ) )
% 5.46/5.73 = ( ord_less_eq_real @ X4 @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_le_iff
% 5.46/5.73 thf(fact_4536_real__sqrt__one,axiom,
% 5.46/5.73 ( ( sqrt @ one_one_real )
% 5.46/5.73 = one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_one
% 5.46/5.73 thf(fact_4537_real__sqrt__eq__1__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ( sqrt @ X4 )
% 5.46/5.73 = one_one_real )
% 5.46/5.73 = ( X4 = one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_eq_1_iff
% 5.46/5.73 thf(fact_4538_take__bit__and,axiom,
% 5.46/5.73 ! [N: nat,A: int,B2: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B2 ) )
% 5.46/5.73 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_and
% 5.46/5.73 thf(fact_4539_take__bit__and,axiom,
% 5.46/5.73 ! [N: nat,A: nat,B2: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B2 ) )
% 5.46/5.73 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_and
% 5.46/5.73 thf(fact_4540_concat__bit__of__zero__2,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % concat_bit_of_zero_2
% 5.46/5.73 thf(fact_4541_take__bit__0,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_0
% 5.46/5.73 thf(fact_4542_take__bit__0,axiom,
% 5.46/5.73 ! [A: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_0
% 5.46/5.73 thf(fact_4543_take__bit__Suc__1,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_1
% 5.46/5.73 thf(fact_4544_take__bit__Suc__1,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 5.46/5.73 = one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_1
% 5.46/5.73 thf(fact_4545_and_Oleft__neutral,axiom,
% 5.46/5.73 ! [A: code_integer] :
% 5.46/5.73 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.46/5.73 = A ) ).
% 5.46/5.73
% 5.46/5.73 % and.left_neutral
% 5.46/5.73 thf(fact_4546_and_Oleft__neutral,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.46/5.73 = A ) ).
% 5.46/5.73
% 5.46/5.73 % and.left_neutral
% 5.46/5.73 thf(fact_4547_and_Oright__neutral,axiom,
% 5.46/5.73 ! [A: code_integer] :
% 5.46/5.73 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 = A ) ).
% 5.46/5.73
% 5.46/5.73 % and.right_neutral
% 5.46/5.73 thf(fact_4548_and_Oright__neutral,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = A ) ).
% 5.46/5.73
% 5.46/5.73 % and.right_neutral
% 5.46/5.73 thf(fact_4549_bit_Oconj__one__right,axiom,
% 5.46/5.73 ! [X4: code_integer] :
% 5.46/5.73 ( ( bit_se3949692690581998587nteger @ X4 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 = X4 ) ).
% 5.46/5.73
% 5.46/5.73 % bit.conj_one_right
% 5.46/5.73 thf(fact_4550_bit_Oconj__one__right,axiom,
% 5.46/5.73 ! [X4: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ X4 @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = X4 ) ).
% 5.46/5.73
% 5.46/5.73 % bit.conj_one_right
% 5.46/5.73 thf(fact_4551_of__int__eq__numeral__iff,axiom,
% 5.46/5.73 ! [Z: int,N: num] :
% 5.46/5.73 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.46/5.73 = ( numera6690914467698888265omplex @ N ) )
% 5.46/5.73 = ( Z
% 5.46/5.73 = ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_numeral_iff
% 5.46/5.73 thf(fact_4552_of__int__eq__numeral__iff,axiom,
% 5.46/5.73 ! [Z: int,N: num] :
% 5.46/5.73 ( ( ( ring_1_of_int_real @ Z )
% 5.46/5.73 = ( numeral_numeral_real @ N ) )
% 5.46/5.73 = ( Z
% 5.46/5.73 = ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_numeral_iff
% 5.46/5.73 thf(fact_4553_of__int__eq__numeral__iff,axiom,
% 5.46/5.73 ! [Z: int,N: num] :
% 5.46/5.73 ( ( ( ring_1_of_int_rat @ Z )
% 5.46/5.73 = ( numeral_numeral_rat @ N ) )
% 5.46/5.73 = ( Z
% 5.46/5.73 = ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_numeral_iff
% 5.46/5.73 thf(fact_4554_of__int__eq__numeral__iff,axiom,
% 5.46/5.73 ! [Z: int,N: num] :
% 5.46/5.73 ( ( ( ring_1_of_int_int @ Z )
% 5.46/5.73 = ( numeral_numeral_int @ N ) )
% 5.46/5.73 = ( Z
% 5.46/5.73 = ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_numeral_iff
% 5.46/5.73 thf(fact_4555_of__int__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.46/5.73 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_numeral
% 5.46/5.73 thf(fact_4556_of__int__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.46/5.73 = ( numeral_numeral_real @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_numeral
% 5.46/5.73 thf(fact_4557_of__int__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.46/5.73 = ( numeral_numeral_rat @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_numeral
% 5.46/5.73 thf(fact_4558_of__int__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.46/5.73 = ( numeral_numeral_int @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_numeral
% 5.46/5.73 thf(fact_4559_of__int__le__iff,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_iff
% 5.46/5.73 thf(fact_4560_of__int__le__iff,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_iff
% 5.46/5.73 thf(fact_4561_of__int__le__iff,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_iff
% 5.46/5.73 thf(fact_4562_take__bit__numeral__1,axiom,
% 5.46/5.73 ! [L2: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ one_one_int )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_1
% 5.46/5.73 thf(fact_4563_take__bit__numeral__1,axiom,
% 5.46/5.73 ! [L2: num] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ one_one_nat )
% 5.46/5.73 = one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_1
% 5.46/5.73 thf(fact_4564_of__int__less__iff,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.73 = ( ord_less_int @ W @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_iff
% 5.46/5.73 thf(fact_4565_of__int__less__iff,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.73 = ( ord_less_int @ W @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_iff
% 5.46/5.73 thf(fact_4566_of__int__less__iff,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.73 = ( ord_less_int @ W @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_iff
% 5.46/5.73 thf(fact_4567_of__int__1,axiom,
% 5.46/5.73 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.46/5.73 = one_one_complex ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_1
% 5.46/5.73 thf(fact_4568_of__int__1,axiom,
% 5.46/5.73 ( ( ring_1_of_int_int @ one_one_int )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_1
% 5.46/5.73 thf(fact_4569_of__int__1,axiom,
% 5.46/5.73 ( ( ring_1_of_int_real @ one_one_int )
% 5.46/5.73 = one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_1
% 5.46/5.73 thf(fact_4570_of__int__1,axiom,
% 5.46/5.73 ( ( ring_1_of_int_rat @ one_one_int )
% 5.46/5.73 = one_one_rat ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_1
% 5.46/5.73 thf(fact_4571_of__int__eq__1__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.46/5.73 = one_one_complex )
% 5.46/5.73 = ( Z = one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_1_iff
% 5.46/5.73 thf(fact_4572_of__int__eq__1__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ( ring_1_of_int_int @ Z )
% 5.46/5.73 = one_one_int )
% 5.46/5.73 = ( Z = one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_1_iff
% 5.46/5.73 thf(fact_4573_of__int__eq__1__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ( ring_1_of_int_real @ Z )
% 5.46/5.73 = one_one_real )
% 5.46/5.73 = ( Z = one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_1_iff
% 5.46/5.73 thf(fact_4574_of__int__eq__1__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ( ring_1_of_int_rat @ Z )
% 5.46/5.73 = one_one_rat )
% 5.46/5.73 = ( Z = one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_1_iff
% 5.46/5.73 thf(fact_4575_of__int__mult,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.46/5.73 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_mult
% 5.46/5.73 thf(fact_4576_of__int__mult,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.46/5.73 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_mult
% 5.46/5.73 thf(fact_4577_of__int__mult,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.46/5.73 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_mult
% 5.46/5.73 thf(fact_4578_of__int__add,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.46/5.73 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_add
% 5.46/5.73 thf(fact_4579_of__int__add,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.46/5.73 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_add
% 5.46/5.73 thf(fact_4580_of__int__add,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.46/5.73 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_add
% 5.46/5.73 thf(fact_4581_real__sqrt__lt__0__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ ( sqrt @ X4 ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_lt_0_iff
% 5.46/5.73 thf(fact_4582_real__sqrt__gt__0__iff,axiom,
% 5.46/5.73 ! [Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y3 ) )
% 5.46/5.73 = ( ord_less_real @ zero_zero_real @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_gt_0_iff
% 5.46/5.73 thf(fact_4583_real__sqrt__ge__0__iff,axiom,
% 5.46/5.73 ! [Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y3 ) )
% 5.46/5.73 = ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_ge_0_iff
% 5.46/5.73 thf(fact_4584_real__sqrt__le__0__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_le_0_iff
% 5.46/5.73 thf(fact_4585_mask__eq__0__iff,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ( bit_se2002935070580805687sk_nat @ N )
% 5.46/5.73 = zero_zero_nat )
% 5.46/5.73 = ( N = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_eq_0_iff
% 5.46/5.73 thf(fact_4586_mask__eq__0__iff,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ( bit_se2000444600071755411sk_int @ N )
% 5.46/5.73 = zero_zero_int )
% 5.46/5.73 = ( N = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_eq_0_iff
% 5.46/5.73 thf(fact_4587_mask__0,axiom,
% 5.46/5.73 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % mask_0
% 5.46/5.73 thf(fact_4588_mask__0,axiom,
% 5.46/5.73 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % mask_0
% 5.46/5.73 thf(fact_4589_of__int__diff,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 5.46/5.73 = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_diff
% 5.46/5.73 thf(fact_4590_of__int__diff,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 5.46/5.73 = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_diff
% 5.46/5.73 thf(fact_4591_of__int__diff,axiom,
% 5.46/5.73 ! [W: int,Z: int] :
% 5.46/5.73 ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 5.46/5.73 = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_diff
% 5.46/5.73 thf(fact_4592_real__sqrt__lt__1__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ ( sqrt @ X4 ) @ one_one_real )
% 5.46/5.73 = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_lt_1_iff
% 5.46/5.73 thf(fact_4593_real__sqrt__gt__1__iff,axiom,
% 5.46/5.73 ! [Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y3 ) )
% 5.46/5.73 = ( ord_less_real @ one_one_real @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_gt_1_iff
% 5.46/5.73 thf(fact_4594_real__sqrt__le__1__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ one_one_real )
% 5.46/5.73 = ( ord_less_eq_real @ X4 @ one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_le_1_iff
% 5.46/5.73 thf(fact_4595_real__sqrt__ge__1__iff,axiom,
% 5.46/5.73 ! [Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y3 ) )
% 5.46/5.73 = ( ord_less_eq_real @ one_one_real @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_ge_1_iff
% 5.46/5.73 thf(fact_4596_of__int__power,axiom,
% 5.46/5.73 ! [Z: int,N: nat] :
% 5.46/5.73 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 5.46/5.73 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power
% 5.46/5.73 thf(fact_4597_of__int__power,axiom,
% 5.46/5.73 ! [Z: int,N: nat] :
% 5.46/5.73 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 5.46/5.73 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power
% 5.46/5.73 thf(fact_4598_of__int__power,axiom,
% 5.46/5.73 ! [Z: int,N: nat] :
% 5.46/5.73 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 5.46/5.73 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power
% 5.46/5.73 thf(fact_4599_of__int__power,axiom,
% 5.46/5.73 ! [Z: int,N: nat] :
% 5.46/5.73 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 5.46/5.73 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power
% 5.46/5.73 thf(fact_4600_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.46/5.73 ! [B2: int,W: nat,X4: int] :
% 5.46/5.73 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W )
% 5.46/5.73 = ( ring_1_of_int_rat @ X4 ) )
% 5.46/5.73 = ( ( power_power_int @ B2 @ W )
% 5.46/5.73 = X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_of_int_power_cancel_iff
% 5.46/5.73 thf(fact_4601_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.46/5.73 ! [B2: int,W: nat,X4: int] :
% 5.46/5.73 ( ( ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W )
% 5.46/5.73 = ( ring_1_of_int_real @ X4 ) )
% 5.46/5.73 = ( ( power_power_int @ B2 @ W )
% 5.46/5.73 = X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_of_int_power_cancel_iff
% 5.46/5.73 thf(fact_4602_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.46/5.73 ! [B2: int,W: nat,X4: int] :
% 5.46/5.73 ( ( ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W )
% 5.46/5.73 = ( ring_1_of_int_int @ X4 ) )
% 5.46/5.73 = ( ( power_power_int @ B2 @ W )
% 5.46/5.73 = X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_of_int_power_cancel_iff
% 5.46/5.73 thf(fact_4603_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.46/5.73 ! [B2: int,W: nat,X4: int] :
% 5.46/5.73 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B2 ) @ W )
% 5.46/5.73 = ( ring_17405671764205052669omplex @ X4 ) )
% 5.46/5.73 = ( ( power_power_int @ B2 @ W )
% 5.46/5.73 = X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_of_int_power_cancel_iff
% 5.46/5.73 thf(fact_4604_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: int,B2: int,W: nat] :
% 5.46/5.73 ( ( ( ring_1_of_int_rat @ X4 )
% 5.46/5.73 = ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W ) )
% 5.46/5.73 = ( X4
% 5.46/5.73 = ( power_power_int @ B2 @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4605_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: int,B2: int,W: nat] :
% 5.46/5.73 ( ( ( ring_1_of_int_real @ X4 )
% 5.46/5.73 = ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W ) )
% 5.46/5.73 = ( X4
% 5.46/5.73 = ( power_power_int @ B2 @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4606_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: int,B2: int,W: nat] :
% 5.46/5.73 ( ( ( ring_1_of_int_int @ X4 )
% 5.46/5.73 = ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W ) )
% 5.46/5.73 = ( X4
% 5.46/5.73 = ( power_power_int @ B2 @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4607_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: int,B2: int,W: nat] :
% 5.46/5.73 ( ( ( ring_17405671764205052669omplex @ X4 )
% 5.46/5.73 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B2 ) @ W ) )
% 5.46/5.73 = ( X4
% 5.46/5.73 = ( power_power_int @ B2 @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4608_and__nonnegative__int__iff,axiom,
% 5.46/5.73 ! [K: int,L2: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.46/5.73 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.73 | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_nonnegative_int_iff
% 5.46/5.73 thf(fact_4609_and__negative__int__iff,axiom,
% 5.46/5.73 ! [K: int,L2: int] :
% 5.46/5.73 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 5.46/5.73 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.73 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_negative_int_iff
% 5.46/5.73 thf(fact_4610_take__bit__of__1__eq__0__iff,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.46/5.73 = zero_zero_int )
% 5.46/5.73 = ( N = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_1_eq_0_iff
% 5.46/5.73 thf(fact_4611_take__bit__of__1__eq__0__iff,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.46/5.73 = zero_zero_nat )
% 5.46/5.73 = ( N = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_1_eq_0_iff
% 5.46/5.73 thf(fact_4612_and__numerals_I2_J,axiom,
% 5.46/5.73 ! [Y3: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(2)
% 5.46/5.73 thf(fact_4613_and__numerals_I2_J,axiom,
% 5.46/5.73 ! [Y3: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.46/5.73 = one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(2)
% 5.46/5.73 thf(fact_4614_and__numerals_I8_J,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ one_one_int )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(8)
% 5.46/5.73 thf(fact_4615_and__numerals_I8_J,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ one_one_nat )
% 5.46/5.73 = one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(8)
% 5.46/5.73 thf(fact_4616_real__sqrt__four,axiom,
% 5.46/5.73 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.73 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_four
% 5.46/5.73 thf(fact_4617_mask__Suc__0,axiom,
% 5.46/5.73 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % mask_Suc_0
% 5.46/5.73 thf(fact_4618_mask__Suc__0,axiom,
% 5.46/5.73 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % mask_Suc_0
% 5.46/5.73 thf(fact_4619_take__bit__minus__one__eq__mask,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_minus_one_eq_mask
% 5.46/5.73 thf(fact_4620_take__bit__minus__one__eq__mask,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_minus_one_eq_mask
% 5.46/5.73 thf(fact_4621_take__bit__of__Suc__0,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_Suc_0
% 5.46/5.73 thf(fact_4622_and__numerals_I1_J,axiom,
% 5.46/5.73 ! [Y3: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(1)
% 5.46/5.73 thf(fact_4623_and__numerals_I1_J,axiom,
% 5.46/5.73 ! [Y3: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(1)
% 5.46/5.73 thf(fact_4624_and__numerals_I5_J,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ one_one_int )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(5)
% 5.46/5.73 thf(fact_4625_and__numerals_I5_J,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ one_one_nat )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(5)
% 5.46/5.73 thf(fact_4626_and__numerals_I3_J,axiom,
% 5.46/5.73 ! [X4: num,Y3: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 5.46/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(3)
% 5.46/5.73 thf(fact_4627_and__numerals_I3_J,axiom,
% 5.46/5.73 ! [X4: num,Y3: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.46/5.73 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(3)
% 5.46/5.73 thf(fact_4628_of__int__le__0__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_0_iff
% 5.46/5.73 thf(fact_4629_of__int__le__0__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.46/5.73 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_0_iff
% 5.46/5.73 thf(fact_4630_of__int__le__0__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.46/5.73 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_0_iff
% 5.46/5.73 thf(fact_4631_of__int__0__le__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_0_le_iff
% 5.46/5.73 thf(fact_4632_of__int__0__le__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_0_le_iff
% 5.46/5.73 thf(fact_4633_of__int__0__le__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_0_le_iff
% 5.46/5.73 thf(fact_4634_of__int__0__less__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.73 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_0_less_iff
% 5.46/5.73 thf(fact_4635_of__int__0__less__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.73 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_0_less_iff
% 5.46/5.73 thf(fact_4636_of__int__0__less__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.73 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_0_less_iff
% 5.46/5.73 thf(fact_4637_of__int__less__0__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_0_iff
% 5.46/5.73 thf(fact_4638_of__int__less__0__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.46/5.73 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_0_iff
% 5.46/5.73 thf(fact_4639_of__int__less__0__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.46/5.73 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_0_iff
% 5.46/5.73 thf(fact_4640_of__int__le__numeral__iff,axiom,
% 5.46/5.73 ! [Z: int,N: num] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.73 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_numeral_iff
% 5.46/5.73 thf(fact_4641_of__int__le__numeral__iff,axiom,
% 5.46/5.73 ! [Z: int,N: num] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.46/5.73 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_numeral_iff
% 5.46/5.73 thf(fact_4642_of__int__le__numeral__iff,axiom,
% 5.46/5.73 ! [Z: int,N: num] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_numeral_iff
% 5.46/5.73 thf(fact_4643_of__int__numeral__le__iff,axiom,
% 5.46/5.73 ! [N: num,Z: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_numeral_le_iff
% 5.46/5.73 thf(fact_4644_of__int__numeral__le__iff,axiom,
% 5.46/5.73 ! [N: num,Z: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_numeral_le_iff
% 5.46/5.73 thf(fact_4645_of__int__numeral__le__iff,axiom,
% 5.46/5.73 ! [N: num,Z: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_numeral_le_iff
% 5.46/5.73 thf(fact_4646_of__int__less__numeral__iff,axiom,
% 5.46/5.73 ! [Z: int,N: num] :
% 5.46/5.73 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.73 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_numeral_iff
% 5.46/5.73 thf(fact_4647_of__int__less__numeral__iff,axiom,
% 5.46/5.73 ! [Z: int,N: num] :
% 5.46/5.73 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.46/5.73 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_numeral_iff
% 5.46/5.73 thf(fact_4648_of__int__less__numeral__iff,axiom,
% 5.46/5.73 ! [Z: int,N: num] :
% 5.46/5.73 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_numeral_iff
% 5.46/5.73 thf(fact_4649_of__int__numeral__less__iff,axiom,
% 5.46/5.73 ! [N: num,Z: int] :
% 5.46/5.73 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.73 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_numeral_less_iff
% 5.46/5.73 thf(fact_4650_of__int__numeral__less__iff,axiom,
% 5.46/5.73 ! [N: num,Z: int] :
% 5.46/5.73 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.73 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_numeral_less_iff
% 5.46/5.73 thf(fact_4651_of__int__numeral__less__iff,axiom,
% 5.46/5.73 ! [N: num,Z: int] :
% 5.46/5.73 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.73 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_numeral_less_iff
% 5.46/5.73 thf(fact_4652_of__int__le__1__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.46/5.73 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_1_iff
% 5.46/5.73 thf(fact_4653_of__int__le__1__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.46/5.73 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_1_iff
% 5.46/5.73 thf(fact_4654_of__int__le__1__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.46/5.73 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_1_iff
% 5.46/5.73 thf(fact_4655_of__int__1__le__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_1_le_iff
% 5.46/5.73 thf(fact_4656_of__int__1__le__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_1_le_iff
% 5.46/5.73 thf(fact_4657_of__int__1__le__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.73 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_1_le_iff
% 5.46/5.73 thf(fact_4658_of__int__less__1__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.46/5.73 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_1_iff
% 5.46/5.73 thf(fact_4659_of__int__less__1__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.46/5.73 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_1_iff
% 5.46/5.73 thf(fact_4660_of__int__less__1__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.46/5.73 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_1_iff
% 5.46/5.73 thf(fact_4661_of__int__1__less__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.73 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_1_less_iff
% 5.46/5.73 thf(fact_4662_of__int__1__less__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.73 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_1_less_iff
% 5.46/5.73 thf(fact_4663_of__int__1__less__iff,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.46/5.73 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_1_less_iff
% 5.46/5.73 thf(fact_4664_take__bit__of__1,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 5.46/5.73 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_1
% 5.46/5.73 thf(fact_4665_take__bit__of__1,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.46/5.73 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_1
% 5.46/5.73 thf(fact_4666_take__bit__of__1,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.46/5.73 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_1
% 5.46/5.73 thf(fact_4667_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,Y3: int] :
% 5.46/5.73 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N )
% 5.46/5.73 = ( ring_17405671764205052669omplex @ Y3 ) )
% 5.46/5.73 = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N )
% 5.46/5.73 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4668_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,Y3: int] :
% 5.46/5.73 ( ( ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N )
% 5.46/5.73 = ( ring_1_of_int_real @ Y3 ) )
% 5.46/5.73 = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N )
% 5.46/5.73 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4669_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,Y3: int] :
% 5.46/5.73 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N )
% 5.46/5.73 = ( ring_1_of_int_rat @ Y3 ) )
% 5.46/5.73 = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N )
% 5.46/5.73 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4670_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,Y3: int] :
% 5.46/5.73 ( ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N )
% 5.46/5.73 = ( ring_1_of_int_int @ Y3 ) )
% 5.46/5.73 = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N )
% 5.46/5.73 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4671_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [Y3: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ( ring_17405671764205052669omplex @ Y3 )
% 5.46/5.73 = ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N ) )
% 5.46/5.73 = ( Y3
% 5.46/5.73 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4672_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [Y3: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ( ring_1_of_int_real @ Y3 )
% 5.46/5.73 = ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N ) )
% 5.46/5.73 = ( Y3
% 5.46/5.73 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4673_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [Y3: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ( ring_1_of_int_rat @ Y3 )
% 5.46/5.73 = ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N ) )
% 5.46/5.73 = ( Y3
% 5.46/5.73 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4674_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [Y3: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ( ring_1_of_int_int @ Y3 )
% 5.46/5.73 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) )
% 5.46/5.73 = ( Y3
% 5.46/5.73 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4675_of__int__le__of__int__power__cancel__iff,axiom,
% 5.46/5.73 ! [B2: int,W: nat,X4: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W ) @ ( ring_1_of_int_real @ X4 ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_of_int_power_cancel_iff
% 5.46/5.73 thf(fact_4676_of__int__le__of__int__power__cancel__iff,axiom,
% 5.46/5.73 ! [B2: int,W: nat,X4: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W ) @ ( ring_1_of_int_rat @ X4 ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_of_int_power_cancel_iff
% 5.46/5.73 thf(fact_4677_of__int__le__of__int__power__cancel__iff,axiom,
% 5.46/5.73 ! [B2: int,W: nat,X4: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W ) @ ( ring_1_of_int_int @ X4 ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_of_int_power_cancel_iff
% 5.46/5.73 thf(fact_4678_of__int__power__le__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: int,B2: int,W: nat] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W ) )
% 5.46/5.73 = ( ord_less_eq_int @ X4 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power_le_of_int_cancel_iff
% 5.46/5.73 thf(fact_4679_of__int__power__le__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: int,B2: int,W: nat] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W ) )
% 5.46/5.73 = ( ord_less_eq_int @ X4 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power_le_of_int_cancel_iff
% 5.46/5.73 thf(fact_4680_of__int__power__le__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: int,B2: int,W: nat] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X4 ) @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W ) )
% 5.46/5.73 = ( ord_less_eq_int @ X4 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power_le_of_int_cancel_iff
% 5.46/5.73 thf(fact_4681_of__int__less__of__int__power__cancel__iff,axiom,
% 5.46/5.73 ! [B2: int,W: nat,X4: int] :
% 5.46/5.73 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W ) @ ( ring_1_of_int_real @ X4 ) )
% 5.46/5.73 = ( ord_less_int @ ( power_power_int @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_of_int_power_cancel_iff
% 5.46/5.73 thf(fact_4682_of__int__less__of__int__power__cancel__iff,axiom,
% 5.46/5.73 ! [B2: int,W: nat,X4: int] :
% 5.46/5.73 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W ) @ ( ring_1_of_int_rat @ X4 ) )
% 5.46/5.73 = ( ord_less_int @ ( power_power_int @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_of_int_power_cancel_iff
% 5.46/5.73 thf(fact_4683_of__int__less__of__int__power__cancel__iff,axiom,
% 5.46/5.73 ! [B2: int,W: nat,X4: int] :
% 5.46/5.73 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W ) @ ( ring_1_of_int_int @ X4 ) )
% 5.46/5.73 = ( ord_less_int @ ( power_power_int @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_of_int_power_cancel_iff
% 5.46/5.73 thf(fact_4684_of__int__power__less__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: int,B2: int,W: nat] :
% 5.46/5.73 ( ( ord_less_real @ ( ring_1_of_int_real @ X4 ) @ ( power_power_real @ ( ring_1_of_int_real @ B2 ) @ W ) )
% 5.46/5.73 = ( ord_less_int @ X4 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power_less_of_int_cancel_iff
% 5.46/5.73 thf(fact_4685_of__int__power__less__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: int,B2: int,W: nat] :
% 5.46/5.73 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X4 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B2 ) @ W ) )
% 5.46/5.73 = ( ord_less_int @ X4 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power_less_of_int_cancel_iff
% 5.46/5.73 thf(fact_4686_of__int__power__less__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: int,B2: int,W: nat] :
% 5.46/5.73 ( ( ord_less_int @ ( ring_1_of_int_int @ X4 ) @ ( power_power_int @ ( ring_1_of_int_int @ B2 ) @ W ) )
% 5.46/5.73 = ( ord_less_int @ X4 @ ( power_power_int @ B2 @ W ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_power_less_of_int_cancel_iff
% 5.46/5.73 thf(fact_4687_and__minus__numerals_I6_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_minus_numerals(6)
% 5.46/5.73 thf(fact_4688_and__minus__numerals_I2_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.73 = one_one_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_minus_numerals(2)
% 5.46/5.73 thf(fact_4689_and__numerals_I4_J,axiom,
% 5.46/5.73 ! [X4: num,Y3: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 5.46/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(4)
% 5.46/5.73 thf(fact_4690_and__numerals_I4_J,axiom,
% 5.46/5.73 ! [X4: num,Y3: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.46/5.73 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(4)
% 5.46/5.73 thf(fact_4691_and__numerals_I6_J,axiom,
% 5.46/5.73 ! [X4: num,Y3: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 5.46/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(6)
% 5.46/5.73 thf(fact_4692_and__numerals_I6_J,axiom,
% 5.46/5.73 ! [X4: num,Y3: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.46/5.73 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(6)
% 5.46/5.73 thf(fact_4693_even__take__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,A: code_integer] :
% 5.46/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 5.46/5.73 = ( ( N = zero_zero_nat )
% 5.46/5.73 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_take_bit_eq
% 5.46/5.73 thf(fact_4694_even__take__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,A: int] :
% 5.46/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.46/5.73 = ( ( N = zero_zero_nat )
% 5.46/5.73 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_take_bit_eq
% 5.46/5.73 thf(fact_4695_even__take__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,A: nat] :
% 5.46/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.46/5.73 = ( ( N = zero_zero_nat )
% 5.46/5.73 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_take_bit_eq
% 5.46/5.73 thf(fact_4696_and__minus__numerals_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_minus_numerals(5)
% 5.46/5.73 thf(fact_4697_and__minus__numerals_I1_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.73 = zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % and_minus_numerals(1)
% 5.46/5.73 thf(fact_4698_take__bit__Suc__0,axiom,
% 5.46/5.73 ! [A: code_integer] :
% 5.46/5.73 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 5.46/5.73 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_0
% 5.46/5.73 thf(fact_4699_take__bit__Suc__0,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.46/5.73 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_0
% 5.46/5.73 thf(fact_4700_take__bit__Suc__0,axiom,
% 5.46/5.73 ! [A: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.46/5.73 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_0
% 5.46/5.73 thf(fact_4701_real__sqrt__pow2__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ( power_power_real @ ( sqrt @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = X4 )
% 5.46/5.73 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_pow2_iff
% 5.46/5.73 thf(fact_4702_real__sqrt__pow2,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( power_power_real @ ( sqrt @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_pow2
% 5.46/5.73 thf(fact_4703_numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_power_le_of_int_cancel_iff
% 5.46/5.73 thf(fact_4704_numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_power_le_of_int_cancel_iff
% 5.46/5.73 thf(fact_4705_numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_power_le_of_int_cancel_iff
% 5.46/5.73 thf(fact_4706_of__int__le__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N ) )
% 5.46/5.73 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4707_of__int__le__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N ) )
% 5.46/5.73 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4708_of__int__le__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) )
% 5.46/5.73 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4709_numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.46/5.73 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_power_less_of_int_cancel_iff
% 5.46/5.73 thf(fact_4710_numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.46/5.73 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_power_less_of_int_cancel_iff
% 5.46/5.73 thf(fact_4711_numeral__power__less__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.46/5.73 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_power_less_of_int_cancel_iff
% 5.46/5.73 thf(fact_4712_of__int__less__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N ) )
% 5.46/5.73 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4713_of__int__less__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N ) )
% 5.46/5.73 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4714_of__int__less__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) )
% 5.46/5.73 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_less_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4715_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.46/5.73 ! [X4: real,Y3: real,Xa: real,Ya: real] :
% 5.46/5.73 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_sum_squares_mult_squared_eq
% 5.46/5.73 thf(fact_4716_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [Y3: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ( ring_1_of_int_real @ Y3 )
% 5.46/5.73 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N ) )
% 5.46/5.73 = ( Y3
% 5.46/5.73 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4717_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [Y3: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ( ring_1_of_int_int @ Y3 )
% 5.46/5.73 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) )
% 5.46/5.73 = ( Y3
% 5.46/5.73 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4718_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [Y3: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ( ring_17405671764205052669omplex @ Y3 )
% 5.46/5.73 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X4 ) ) @ N ) )
% 5.46/5.73 = ( Y3
% 5.46/5.73 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4719_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [Y3: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ( ring_18347121197199848620nteger @ Y3 )
% 5.46/5.73 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N ) )
% 5.46/5.73 = ( Y3
% 5.46/5.73 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4720_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [Y3: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ( ring_1_of_int_rat @ Y3 )
% 5.46/5.73 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N ) )
% 5.46/5.73 = ( Y3
% 5.46/5.73 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_eq_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4721_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,Y3: int] :
% 5.46/5.73 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N )
% 5.46/5.73 = ( ring_1_of_int_real @ Y3 ) )
% 5.46/5.73 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N )
% 5.46/5.73 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4722_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,Y3: int] :
% 5.46/5.73 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N )
% 5.46/5.73 = ( ring_1_of_int_int @ Y3 ) )
% 5.46/5.73 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N )
% 5.46/5.73 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4723_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,Y3: int] :
% 5.46/5.73 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X4 ) ) @ N )
% 5.46/5.73 = ( ring_17405671764205052669omplex @ Y3 ) )
% 5.46/5.73 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N )
% 5.46/5.73 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4724_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,Y3: int] :
% 5.46/5.73 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N )
% 5.46/5.73 = ( ring_18347121197199848620nteger @ Y3 ) )
% 5.46/5.73 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N )
% 5.46/5.73 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4725_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,Y3: int] :
% 5.46/5.73 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N )
% 5.46/5.73 = ( ring_1_of_int_rat @ Y3 ) )
% 5.46/5.73 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N )
% 5.46/5.73 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_eq_of_int_cancel_iff
% 5.46/5.73 thf(fact_4726_and__numerals_I7_J,axiom,
% 5.46/5.73 ! [X4: num,Y3: num] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 5.46/5.73 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(7)
% 5.46/5.73 thf(fact_4727_and__numerals_I7_J,axiom,
% 5.46/5.73 ! [X4: num,Y3: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.46/5.73 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_numerals(7)
% 5.46/5.73 thf(fact_4728_take__bit__of__exp,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_exp
% 5.46/5.73 thf(fact_4729_take__bit__of__exp,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_exp
% 5.46/5.73 thf(fact_4730_take__bit__of__exp,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_exp
% 5.46/5.73 thf(fact_4731_take__bit__of__2,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.73 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_2
% 5.46/5.73 thf(fact_4732_take__bit__of__2,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.73 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_2
% 5.46/5.73 thf(fact_4733_take__bit__of__2,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_2
% 5.46/5.73 thf(fact_4734_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_le_of_int_cancel_iff
% 5.46/5.73 thf(fact_4735_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_le_of_int_cancel_iff
% 5.46/5.73 thf(fact_4736_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_le_of_int_cancel_iff
% 5.46/5.73 thf(fact_4737_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.46/5.73 ! [X4: num,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % neg_numeral_power_le_of_int_cancel_iff
% 5.46/5.73 thf(fact_4738_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N ) )
% 5.46/5.73 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4739_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N ) )
% 5.46/5.73 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4740_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N ) )
% 5.46/5.73 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4741_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.46/5.73 ! [A: int,X4: num,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) )
% 5.46/5.73 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_le_neg_numeral_power_cancel_iff
% 5.46/5.73 thf(fact_4742_take__bit__eq__mask,axiom,
% 5.46/5.73 ( bit_se2923211474154528505it_int
% 5.46/5.73 = ( ^ [N2: nat,A4: int] : ( bit_se725231765392027082nd_int @ A4 @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_eq_mask
% 5.46/5.73 thf(fact_4743_take__bit__eq__mask,axiom,
% 5.46/5.73 ( bit_se2925701944663578781it_nat
% 5.46/5.73 = ( ^ [N2: nat,A4: nat] : ( bit_se727722235901077358nd_nat @ A4 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_eq_mask
% 5.46/5.73 thf(fact_4744_and_Oleft__commute,axiom,
% 5.46/5.73 ! [B2: int,A: int,C: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ B2 @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.46/5.73 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B2 @ C ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and.left_commute
% 5.46/5.73 thf(fact_4745_and_Oleft__commute,axiom,
% 5.46/5.73 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ B2 @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.46/5.73 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B2 @ C ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and.left_commute
% 5.46/5.73 thf(fact_4746_and_Ocommute,axiom,
% 5.46/5.73 ( bit_se725231765392027082nd_int
% 5.46/5.73 = ( ^ [A4: int,B3: int] : ( bit_se725231765392027082nd_int @ B3 @ A4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and.commute
% 5.46/5.73 thf(fact_4747_and_Ocommute,axiom,
% 5.46/5.73 ( bit_se727722235901077358nd_nat
% 5.46/5.73 = ( ^ [A4: nat,B3: nat] : ( bit_se727722235901077358nd_nat @ B3 @ A4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and.commute
% 5.46/5.73 thf(fact_4748_take__bit__of__int,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 5.46/5.73 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_of_int
% 5.46/5.73 thf(fact_4749_of__int__mask__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.73 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_mask_eq
% 5.46/5.73 thf(fact_4750_and_Oassoc,axiom,
% 5.46/5.73 ! [A: int,B2: int,C: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B2 ) @ C )
% 5.46/5.73 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B2 @ C ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and.assoc
% 5.46/5.73 thf(fact_4751_and_Oassoc,axiom,
% 5.46/5.73 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B2 ) @ C )
% 5.46/5.73 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B2 @ C ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and.assoc
% 5.46/5.73 thf(fact_4752_of__int__and__eq,axiom,
% 5.46/5.73 ! [K: int,L2: int] :
% 5.46/5.73 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.46/5.73 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_and_eq
% 5.46/5.73 thf(fact_4753_take__bit__add,axiom,
% 5.46/5.73 ! [N: nat,A: int,B2: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B2 ) ) )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_add
% 5.46/5.73 thf(fact_4754_take__bit__add,axiom,
% 5.46/5.73 ! [N: nat,A: nat,B2: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B2 ) ) )
% 5.46/5.73 = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_add
% 5.46/5.73 thf(fact_4755_take__bit__tightened,axiom,
% 5.46/5.73 ! [N: nat,A: int,B2: int,M: nat] :
% 5.46/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ N @ B2 ) )
% 5.46/5.73 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ M @ B2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_tightened
% 5.46/5.73 thf(fact_4756_take__bit__tightened,axiom,
% 5.46/5.73 ! [N: nat,A: nat,B2: nat,M: nat] :
% 5.46/5.73 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.46/5.73 = ( bit_se2925701944663578781it_nat @ N @ B2 ) )
% 5.46/5.73 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.73 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.46/5.73 = ( bit_se2925701944663578781it_nat @ M @ B2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_tightened
% 5.46/5.73 thf(fact_4757_take__bit__nat__less__eq__self,axiom,
% 5.46/5.73 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_nat_less_eq_self
% 5.46/5.73 thf(fact_4758_take__bit__tightened__less__eq__nat,axiom,
% 5.46/5.73 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.73 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_tightened_less_eq_nat
% 5.46/5.73 thf(fact_4759_real__sqrt__less__mono,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.73 => ( ord_less_real @ ( sqrt @ X4 ) @ ( sqrt @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_less_mono
% 5.46/5.73 thf(fact_4760_real__sqrt__le__mono,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.73 => ( ord_less_eq_real @ ( sqrt @ X4 ) @ ( sqrt @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_le_mono
% 5.46/5.73 thf(fact_4761_mult__of__int__commute,axiom,
% 5.46/5.73 ! [X4: int,Y3: real] :
% 5.46/5.73 ( ( times_times_real @ ( ring_1_of_int_real @ X4 ) @ Y3 )
% 5.46/5.73 = ( times_times_real @ Y3 @ ( ring_1_of_int_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mult_of_int_commute
% 5.46/5.73 thf(fact_4762_mult__of__int__commute,axiom,
% 5.46/5.73 ! [X4: int,Y3: rat] :
% 5.46/5.73 ( ( times_times_rat @ ( ring_1_of_int_rat @ X4 ) @ Y3 )
% 5.46/5.73 = ( times_times_rat @ Y3 @ ( ring_1_of_int_rat @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mult_of_int_commute
% 5.46/5.73 thf(fact_4763_mult__of__int__commute,axiom,
% 5.46/5.73 ! [X4: int,Y3: int] :
% 5.46/5.73 ( ( times_times_int @ ( ring_1_of_int_int @ X4 ) @ Y3 )
% 5.46/5.73 = ( times_times_int @ Y3 @ ( ring_1_of_int_int @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mult_of_int_commute
% 5.46/5.73 thf(fact_4764_real__sqrt__divide,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( sqrt @ ( divide_divide_real @ X4 @ Y3 ) )
% 5.46/5.73 = ( divide_divide_real @ ( sqrt @ X4 ) @ ( sqrt @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_divide
% 5.46/5.73 thf(fact_4765_real__sqrt__mult,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( sqrt @ ( times_times_real @ X4 @ Y3 ) )
% 5.46/5.73 = ( times_times_real @ ( sqrt @ X4 ) @ ( sqrt @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_mult
% 5.46/5.73 thf(fact_4766_real__sqrt__power,axiom,
% 5.46/5.73 ! [X4: real,K: nat] :
% 5.46/5.73 ( ( sqrt @ ( power_power_real @ X4 @ K ) )
% 5.46/5.73 = ( power_power_real @ ( sqrt @ X4 ) @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_power
% 5.46/5.73 thf(fact_4767_real__sqrt__minus,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( sqrt @ ( uminus_uminus_real @ X4 ) )
% 5.46/5.73 = ( uminus_uminus_real @ ( sqrt @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_minus
% 5.46/5.73 thf(fact_4768_take__bit__minus,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_minus
% 5.46/5.73 thf(fact_4769_take__bit__mult,axiom,
% 5.46/5.73 ! [N: nat,K: int,L2: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_mult
% 5.46/5.73 thf(fact_4770_take__bit__diff,axiom,
% 5.46/5.73 ! [N: nat,K: int,L2: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_diff
% 5.46/5.73 thf(fact_4771_concat__bit__take__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,B2: int] :
% 5.46/5.73 ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B2 ) )
% 5.46/5.73 = ( bit_concat_bit @ N @ B2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % concat_bit_take_bit_eq
% 5.46/5.73 thf(fact_4772_concat__bit__eq__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int,L2: int,R2: int,S: int] :
% 5.46/5.73 ( ( ( bit_concat_bit @ N @ K @ L2 )
% 5.46/5.73 = ( bit_concat_bit @ N @ R2 @ S ) )
% 5.46/5.73 = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ N @ R2 ) )
% 5.46/5.73 & ( L2 = S ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % concat_bit_eq_iff
% 5.46/5.73 thf(fact_4773_less__eq__mask,axiom,
% 5.46/5.73 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_eq_mask
% 5.46/5.73 thf(fact_4774_take__bit__eq__mask__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.73 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.73 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.46/5.73 = zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_eq_mask_iff
% 5.46/5.73 thf(fact_4775_and__eq__minus__1__iff,axiom,
% 5.46/5.73 ! [A: code_integer,B2: code_integer] :
% 5.46/5.73 ( ( ( bit_se3949692690581998587nteger @ A @ B2 )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 = ( ( A
% 5.46/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 & ( B2
% 5.46/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_eq_minus_1_iff
% 5.46/5.73 thf(fact_4776_and__eq__minus__1__iff,axiom,
% 5.46/5.73 ! [A: int,B2: int] :
% 5.46/5.73 ( ( ( bit_se725231765392027082nd_int @ A @ B2 )
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = ( ( A
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 & ( B2
% 5.46/5.73 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_eq_minus_1_iff
% 5.46/5.73 thf(fact_4777_real__sqrt__gt__zero,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_gt_zero
% 5.46/5.73 thf(fact_4778_real__sqrt__ge__zero,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_ge_zero
% 5.46/5.73 thf(fact_4779_real__sqrt__eq__zero__cancel,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ( sqrt @ X4 )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 => ( X4 = zero_zero_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_eq_zero_cancel
% 5.46/5.73 thf(fact_4780_real__sqrt__ge__one,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.46/5.73 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_ge_one
% 5.46/5.73 thf(fact_4781_take__bit__tightened__less__eq__int,axiom,
% 5.46/5.73 ! [M: nat,N: nat,K: int] :
% 5.46/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.73 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_tightened_less_eq_int
% 5.46/5.73 thf(fact_4782_AND__upper2_H,axiom,
% 5.46/5.73 ! [Y3: int,Z: int,X4: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.73 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.46/5.73 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y3 ) @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % AND_upper2'
% 5.46/5.73 thf(fact_4783_AND__upper1_H,axiom,
% 5.46/5.73 ! [Y3: int,Z: int,Ya: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.73 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.46/5.73 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y3 @ Ya ) @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % AND_upper1'
% 5.46/5.73 thf(fact_4784_AND__upper2,axiom,
% 5.46/5.73 ! [Y3: int,X4: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.73 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y3 ) @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % AND_upper2
% 5.46/5.73 thf(fact_4785_AND__upper1,axiom,
% 5.46/5.73 ! [X4: int,Y3: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.73 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y3 ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % AND_upper1
% 5.46/5.73 thf(fact_4786_AND__lower,axiom,
% 5.46/5.73 ! [X4: int,Y3: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.73 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X4 @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % AND_lower
% 5.46/5.73 thf(fact_4787_take__bit__int__less__eq__self__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.46/5.73 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_int_less_eq_self_iff
% 5.46/5.73 thf(fact_4788_take__bit__nonnegative,axiom,
% 5.46/5.73 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_nonnegative
% 5.46/5.73 thf(fact_4789_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,A: int,B2: int] :
% 5.46/5.73 ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.46/5.73 = ( bit_ri631733984087533419it_int @ N @ B2 ) )
% 5.46/5.73 = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % signed_take_bit_eq_iff_take_bit_eq
% 5.46/5.73 thf(fact_4790_not__take__bit__negative,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % not_take_bit_negative
% 5.46/5.73 thf(fact_4791_take__bit__int__greater__self__iff,axiom,
% 5.46/5.73 ! [K: int,N: nat] :
% 5.46/5.73 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.46/5.73 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_int_greater_self_iff
% 5.46/5.73 thf(fact_4792_signed__take__bit__take__bit,axiom,
% 5.46/5.73 ! [M: nat,N: nat,A: int] :
% 5.46/5.73 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.46/5.73 = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % signed_take_bit_take_bit
% 5.46/5.73 thf(fact_4793_take__bit__unset__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,M: nat,A: int] :
% 5.46/5.73 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.46/5.73 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_unset_bit_eq
% 5.46/5.73 thf(fact_4794_take__bit__unset__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,M: nat,A: nat] :
% 5.46/5.73 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.46/5.73 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.46/5.73 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_unset_bit_eq
% 5.46/5.73 thf(fact_4795_take__bit__set__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,M: nat,A: int] :
% 5.46/5.73 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.46/5.73 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_set_bit_eq
% 5.46/5.73 thf(fact_4796_take__bit__set__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,M: nat,A: nat] :
% 5.46/5.73 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.46/5.73 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.46/5.73 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_set_bit_eq
% 5.46/5.73 thf(fact_4797_take__bit__flip__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,M: nat,A: int] :
% 5.46/5.73 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.46/5.73 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_flip_bit_eq
% 5.46/5.73 thf(fact_4798_take__bit__flip__bit__eq,axiom,
% 5.46/5.73 ! [N: nat,M: nat,A: nat] :
% 5.46/5.73 ( ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.46/5.73 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.46/5.73 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.46/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.46/5.73 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_flip_bit_eq
% 5.46/5.73 thf(fact_4799_mask__nonnegative__int,axiom,
% 5.46/5.73 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_nonnegative_int
% 5.46/5.73 thf(fact_4800_not__mask__negative__int,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.46/5.73
% 5.46/5.73 % not_mask_negative_int
% 5.46/5.73 thf(fact_4801_real__div__sqrt,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( divide_divide_real @ X4 @ ( sqrt @ X4 ) )
% 5.46/5.73 = ( sqrt @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_div_sqrt
% 5.46/5.73 thf(fact_4802_sqrt__add__le__add__sqrt,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X4 @ Y3 ) ) @ ( plus_plus_real @ ( sqrt @ X4 ) @ ( sqrt @ Y3 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sqrt_add_le_add_sqrt
% 5.46/5.73 thf(fact_4803_take__bit__signed__take__bit,axiom,
% 5.46/5.73 ! [M: nat,N: nat,A: int] :
% 5.46/5.73 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 5.46/5.73 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_signed_take_bit
% 5.46/5.73 thf(fact_4804_le__real__sqrt__sumsq,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] : ( ord_less_eq_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y3 @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % le_real_sqrt_sumsq
% 5.46/5.73 thf(fact_4805_and__less__eq,axiom,
% 5.46/5.73 ! [L2: int,K: int] :
% 5.46/5.73 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.46/5.73 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_less_eq
% 5.46/5.73 thf(fact_4806_AND__upper1_H_H,axiom,
% 5.46/5.73 ! [Y3: int,Z: int,Ya: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.73 => ( ( ord_less_int @ Y3 @ Z )
% 5.46/5.73 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y3 @ Ya ) @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % AND_upper1''
% 5.46/5.73 thf(fact_4807_AND__upper2_H_H,axiom,
% 5.46/5.73 ! [Y3: int,Z: int,X4: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.73 => ( ( ord_less_int @ Y3 @ Z )
% 5.46/5.73 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X4 @ Y3 ) @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % AND_upper2''
% 5.46/5.73 thf(fact_4808_take__bit__decr__eq,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.73 != zero_zero_int )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.46/5.73 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_decr_eq
% 5.46/5.73 thf(fact_4809_real__of__int__div4,axiom,
% 5.46/5.73 ! [N: int,X4: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X4 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_of_int_div4
% 5.46/5.73 thf(fact_4810_real__of__int__div,axiom,
% 5.46/5.73 ! [D: int,N: int] :
% 5.46/5.73 ( ( dvd_dvd_int @ D @ N )
% 5.46/5.73 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 5.46/5.73 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_of_int_div
% 5.46/5.73 thf(fact_4811_less__mask,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.73 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % less_mask
% 5.46/5.73 thf(fact_4812_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.73 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.73 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_eq_mask_iff_exp_dvd
% 5.46/5.73 thf(fact_4813_even__and__iff,axiom,
% 5.46/5.73 ! [A: code_integer,B2: code_integer] :
% 5.46/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B2 ) )
% 5.46/5.73 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.73 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_and_iff
% 5.46/5.73 thf(fact_4814_even__and__iff,axiom,
% 5.46/5.73 ! [A: int,B2: int] :
% 5.46/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B2 ) )
% 5.46/5.73 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.73 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_and_iff
% 5.46/5.73 thf(fact_4815_even__and__iff,axiom,
% 5.46/5.73 ! [A: nat,B2: nat] :
% 5.46/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B2 ) )
% 5.46/5.73 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.73 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_and_iff
% 5.46/5.73 thf(fact_4816_sqrt2__less__2,axiom,
% 5.46/5.73 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % sqrt2_less_2
% 5.46/5.73 thf(fact_4817_of__int__nonneg,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.73 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_nonneg
% 5.46/5.73 thf(fact_4818_of__int__nonneg,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.73 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_nonneg
% 5.46/5.73 thf(fact_4819_of__int__nonneg,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.73 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_nonneg
% 5.46/5.73 thf(fact_4820_of__int__pos,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.73 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_pos
% 5.46/5.73 thf(fact_4821_of__int__pos,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.73 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_pos
% 5.46/5.73 thf(fact_4822_of__int__pos,axiom,
% 5.46/5.73 ! [Z: int] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.73 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_pos
% 5.46/5.73 thf(fact_4823_even__and__iff__int,axiom,
% 5.46/5.73 ! [K: int,L2: int] :
% 5.46/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.46/5.73 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.46/5.73 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_and_iff_int
% 5.46/5.73 thf(fact_4824_of__int__neg__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_neg_numeral
% 5.46/5.73 thf(fact_4825_of__int__neg__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_neg_numeral
% 5.46/5.73 thf(fact_4826_of__int__neg__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.73 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_neg_numeral
% 5.46/5.73 thf(fact_4827_of__int__neg__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_neg_numeral
% 5.46/5.73 thf(fact_4828_of__int__neg__numeral,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.73 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_neg_numeral
% 5.46/5.73 thf(fact_4829_int__le__real__less,axiom,
% 5.46/5.73 ( ord_less_eq_int
% 5.46/5.73 = ( ^ [N2: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % int_le_real_less
% 5.46/5.73 thf(fact_4830_int__less__real__le,axiom,
% 5.46/5.73 ( ord_less_int
% 5.46/5.73 = ( ^ [N2: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % int_less_real_le
% 5.46/5.73 thf(fact_4831_real__of__int__div__aux,axiom,
% 5.46/5.73 ! [X4: int,D: int] :
% 5.46/5.73 ( ( divide_divide_real @ ( ring_1_of_int_real @ X4 ) @ ( ring_1_of_int_real @ D ) )
% 5.46/5.73 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X4 @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X4 @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_of_int_div_aux
% 5.46/5.73 thf(fact_4832_take__bit__Suc__bit0,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.46/5.73 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_bit0
% 5.46/5.73 thf(fact_4833_take__bit__Suc__bit0,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.73 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_bit0
% 5.46/5.73 thf(fact_4834_take__bit__eq__mod,axiom,
% 5.46/5.73 ( bit_se1745604003318907178nteger
% 5.46/5.73 = ( ^ [N2: nat,A4: code_integer] : ( modulo364778990260209775nteger @ A4 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_eq_mod
% 5.46/5.73 thf(fact_4835_take__bit__eq__mod,axiom,
% 5.46/5.73 ( bit_se2923211474154528505it_int
% 5.46/5.73 = ( ^ [N2: nat,A4: int] : ( modulo_modulo_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_eq_mod
% 5.46/5.73 thf(fact_4836_take__bit__eq__mod,axiom,
% 5.46/5.73 ( bit_se2925701944663578781it_nat
% 5.46/5.73 = ( ^ [N2: nat,A4: nat] : ( modulo_modulo_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_eq_mod
% 5.46/5.73 thf(fact_4837_one__and__eq,axiom,
% 5.46/5.73 ! [A: code_integer] :
% 5.46/5.73 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 5.46/5.73 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_and_eq
% 5.46/5.73 thf(fact_4838_one__and__eq,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.46/5.73 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_and_eq
% 5.46/5.73 thf(fact_4839_one__and__eq,axiom,
% 5.46/5.73 ! [A: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.46/5.73 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_and_eq
% 5.46/5.73 thf(fact_4840_and__one__eq,axiom,
% 5.46/5.73 ! [A: code_integer] :
% 5.46/5.73 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 5.46/5.73 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_one_eq
% 5.46/5.73 thf(fact_4841_and__one__eq,axiom,
% 5.46/5.73 ! [A: int] :
% 5.46/5.73 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.46/5.73 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_one_eq
% 5.46/5.73 thf(fact_4842_and__one__eq,axiom,
% 5.46/5.73 ! [A: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.46/5.73 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_one_eq
% 5.46/5.73 thf(fact_4843_take__bit__nat__eq__self__iff,axiom,
% 5.46/5.73 ! [N: nat,M: nat] :
% 5.46/5.73 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.46/5.73 = M )
% 5.46/5.73 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_nat_eq_self_iff
% 5.46/5.73 thf(fact_4844_take__bit__nat__less__exp,axiom,
% 5.46/5.73 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_nat_less_exp
% 5.46/5.73 thf(fact_4845_take__bit__nat__eq__self,axiom,
% 5.46/5.73 ! [M: nat,N: nat] :
% 5.46/5.73 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.46/5.73 = M ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_nat_eq_self
% 5.46/5.73 thf(fact_4846_real__less__rsqrt,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 )
% 5.46/5.73 => ( ord_less_real @ X4 @ ( sqrt @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_less_rsqrt
% 5.46/5.73 thf(fact_4847_real__le__rsqrt,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 )
% 5.46/5.73 => ( ord_less_eq_real @ X4 @ ( sqrt @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_le_rsqrt
% 5.46/5.73 thf(fact_4848_sqrt__le__D,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ Y3 )
% 5.46/5.73 => ( ord_less_eq_real @ X4 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sqrt_le_D
% 5.46/5.73 thf(fact_4849_take__bit__nat__def,axiom,
% 5.46/5.73 ( bit_se2925701944663578781it_nat
% 5.46/5.73 = ( ^ [N2: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_nat_def
% 5.46/5.73 thf(fact_4850_take__bit__int__less__exp,axiom,
% 5.46/5.73 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_int_less_exp
% 5.46/5.73 thf(fact_4851_take__bit__int__def,axiom,
% 5.46/5.73 ( bit_se2923211474154528505it_int
% 5.46/5.73 = ( ^ [N2: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_int_def
% 5.46/5.73 thf(fact_4852_real__of__int__div2,axiom,
% 5.46/5.73 ! [N: int,X4: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X4 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X4 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_of_int_div2
% 5.46/5.73 thf(fact_4853_real__of__int__div3,axiom,
% 5.46/5.73 ! [N: int,X4: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X4 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X4 ) ) ) @ one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % real_of_int_div3
% 5.46/5.73 thf(fact_4854_take__bit__eq__0__iff,axiom,
% 5.46/5.73 ! [N: nat,A: code_integer] :
% 5.46/5.73 ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.46/5.73 = zero_z3403309356797280102nteger )
% 5.46/5.73 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_eq_0_iff
% 5.46/5.73 thf(fact_4855_take__bit__eq__0__iff,axiom,
% 5.46/5.73 ! [N: nat,A: int] :
% 5.46/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.46/5.73 = zero_zero_int )
% 5.46/5.73 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_eq_0_iff
% 5.46/5.73 thf(fact_4856_take__bit__eq__0__iff,axiom,
% 5.46/5.73 ! [N: nat,A: nat] :
% 5.46/5.73 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.46/5.73 = zero_zero_nat )
% 5.46/5.73 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_eq_0_iff
% 5.46/5.73 thf(fact_4857_take__bit__numeral__bit0,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.46/5.73 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_bit0
% 5.46/5.73 thf(fact_4858_take__bit__numeral__bit0,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.46/5.73 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_bit0
% 5.46/5.73 thf(fact_4859_take__bit__nat__less__self__iff,axiom,
% 5.46/5.73 ! [N: nat,M: nat] :
% 5.46/5.73 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.46/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_nat_less_self_iff
% 5.46/5.73 thf(fact_4860_real__sqrt__unique,axiom,
% 5.46/5.73 ! [Y3: real,X4: real] :
% 5.46/5.73 ( ( ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ( sqrt @ X4 )
% 5.46/5.73 = Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_unique
% 5.46/5.73 thf(fact_4861_real__le__lsqrt,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X4 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.73 => ( ord_less_eq_real @ ( sqrt @ X4 ) @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_le_lsqrt
% 5.46/5.73 thf(fact_4862_lemma__real__divide__sqrt__less,axiom,
% 5.46/5.73 ! [U: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ U )
% 5.46/5.73 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.46/5.73
% 5.46/5.73 % lemma_real_divide_sqrt_less
% 5.46/5.73 thf(fact_4863_Suc__mask__eq__exp,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.46/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_mask_eq_exp
% 5.46/5.73 thf(fact_4864_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.73 = Y3 )
% 5.46/5.73 => ( X4 = zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_sum_squares_eq_cancel2
% 5.46/5.73 thf(fact_4865_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.73 = X4 )
% 5.46/5.73 => ( Y3 = zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_sum_squares_eq_cancel
% 5.46/5.73 thf(fact_4866_mask__nat__less__exp,axiom,
% 5.46/5.73 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_nat_less_exp
% 5.46/5.73 thf(fact_4867_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.46/5.73 ! [A: real,C: real,B2: 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 @ B2 @ 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 @ B2 @ ( 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 ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_sum_squares_triangle_ineq
% 5.46/5.73 thf(fact_4868_real__sqrt__sum__squares__ge2,axiom,
% 5.46/5.73 ! [Y3: real,X4: real] : ( ord_less_eq_real @ Y3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_sum_squares_ge2
% 5.46/5.73 thf(fact_4869_real__sqrt__sum__squares__ge1,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] : ( ord_less_eq_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_sum_squares_ge1
% 5.46/5.73 thf(fact_4870_take__bit__Suc__minus__bit0,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.73 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_minus_bit0
% 5.46/5.73 thf(fact_4871_even__of__int__iff,axiom,
% 5.46/5.73 ! [K: int] :
% 5.46/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.46/5.73 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_of_int_iff
% 5.46/5.73 thf(fact_4872_even__of__int__iff,axiom,
% 5.46/5.73 ! [K: int] :
% 5.46/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.46/5.73 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % even_of_int_iff
% 5.46/5.73 thf(fact_4873_take__bit__int__greater__eq__self__iff,axiom,
% 5.46/5.73 ! [K: int,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.46/5.73 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_int_greater_eq_self_iff
% 5.46/5.73 thf(fact_4874_take__bit__int__less__self__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.46/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_int_less_self_iff
% 5.46/5.73 thf(fact_4875_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 5.46/5.73 = ( N = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_bit_operations_class.even_mask_iff
% 5.46/5.73 thf(fact_4876_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.46/5.73 = ( N = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_bit_operations_class.even_mask_iff
% 5.46/5.73 thf(fact_4877_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.73 = ( N = zero_zero_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % semiring_bit_operations_class.even_mask_iff
% 5.46/5.73 thf(fact_4878_real__less__lsqrt,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ( ord_less_real @ X4 @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.73 => ( ord_less_real @ ( sqrt @ X4 ) @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_less_lsqrt
% 5.46/5.73 thf(fact_4879_sqrt__sum__squares__le__sum,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sqrt_sum_squares_le_sum
% 5.46/5.73 thf(fact_4880_sqrt__even__pow2,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % sqrt_even_pow2
% 5.46/5.73 thf(fact_4881_take__bit__int__eq__self__iff,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.73 = K )
% 5.46/5.73 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.73 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_int_eq_self_iff
% 5.46/5.73 thf(fact_4882_take__bit__int__eq__self,axiom,
% 5.46/5.73 ! [K: int,N: nat] :
% 5.46/5.73 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.73 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.73 = K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_int_eq_self
% 5.46/5.73 thf(fact_4883_and__int__rec,axiom,
% 5.46/5.73 ( bit_se725231765392027082nd_int
% 5.46/5.73 = ( ^ [K3: int,L: int] :
% 5.46/5.73 ( plus_plus_int
% 5.46/5.73 @ ( zero_n2684676970156552555ol_int
% 5.46/5.73 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.46/5.73 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.46/5.73 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_int_rec
% 5.46/5.73 thf(fact_4884_mask__nat__def,axiom,
% 5.46/5.73 ( bit_se2002935070580805687sk_nat
% 5.46/5.73 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_nat_def
% 5.46/5.73 thf(fact_4885_take__bit__numeral__minus__bit0,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.73 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_minus_bit0
% 5.46/5.73 thf(fact_4886_mask__half__int,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.73 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_half_int
% 5.46/5.73 thf(fact_4887_take__bit__incr__eq,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.46/5.73 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.46/5.73 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_incr_eq
% 5.46/5.73 thf(fact_4888_mask__int__def,axiom,
% 5.46/5.73 ( bit_se2000444600071755411sk_int
% 5.46/5.73 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_int_def
% 5.46/5.73 thf(fact_4889_take__bit__Suc__minus__1__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_minus_1_eq
% 5.46/5.73 thf(fact_4890_take__bit__Suc__minus__1__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_minus_1_eq
% 5.46/5.73 thf(fact_4891_take__bit__Suc__bit1,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_bit1
% 5.46/5.73 thf(fact_4892_take__bit__Suc__bit1,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_bit1
% 5.46/5.73 thf(fact_4893_take__bit__numeral__minus__1__eq,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_minus_1_eq
% 5.46/5.73 thf(fact_4894_take__bit__numeral__minus__1__eq,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_minus_1_eq
% 5.46/5.73 thf(fact_4895_take__bit__Suc,axiom,
% 5.46/5.73 ! [N: nat,A: code_integer] :
% 5.46/5.73 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 5.46/5.73 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc
% 5.46/5.73 thf(fact_4896_take__bit__Suc,axiom,
% 5.46/5.73 ! [N: nat,A: int] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.46/5.73 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc
% 5.46/5.73 thf(fact_4897_take__bit__Suc,axiom,
% 5.46/5.73 ! [N: nat,A: nat] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 5.46/5.73 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc
% 5.46/5.73 thf(fact_4898_mask__eq__exp__minus__1,axiom,
% 5.46/5.73 ( bit_se2002935070580805687sk_nat
% 5.46/5.73 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_eq_exp_minus_1
% 5.46/5.73 thf(fact_4899_mask__eq__exp__minus__1,axiom,
% 5.46/5.73 ( bit_se2000444600071755411sk_int
% 5.46/5.73 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mask_eq_exp_minus_1
% 5.46/5.73 thf(fact_4900_real__sqrt__power__even,axiom,
% 5.46/5.73 ! [N: nat,X4: real] :
% 5.46/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( power_power_real @ ( sqrt @ X4 ) @ N )
% 5.46/5.73 = ( power_power_real @ X4 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_power_even
% 5.46/5.73 thf(fact_4901_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.46/5.73 ! [X4: real,Y3: real,Xa: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_sqrt_sum_squares_mult_ge_zero
% 5.46/5.73 thf(fact_4902_arith__geo__mean__sqrt,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X4 @ Y3 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % arith_geo_mean_sqrt
% 5.46/5.73 thf(fact_4903_take__bit__int__less__eq,axiom,
% 5.46/5.73 ! [N: nat,K: int] :
% 5.46/5.73 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.46/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.73 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_int_less_eq
% 5.46/5.73 thf(fact_4904_take__bit__int__greater__eq,axiom,
% 5.46/5.73 ! [K: int,N: nat] :
% 5.46/5.73 ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.73 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_int_greater_eq
% 5.46/5.73 thf(fact_4905_signed__take__bit__eq__take__bit__shift,axiom,
% 5.46/5.73 ( bit_ri631733984087533419it_int
% 5.46/5.73 = ( ^ [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 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % signed_take_bit_eq_take_bit_shift
% 5.46/5.73 thf(fact_4906_stable__imp__take__bit__eq,axiom,
% 5.46/5.73 ! [A: code_integer,N: nat] :
% 5.46/5.73 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.73 = A )
% 5.46/5.73 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.73 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.46/5.73 = zero_z3403309356797280102nteger ) )
% 5.46/5.73 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.73 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.46/5.73 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % stable_imp_take_bit_eq
% 5.46/5.73 thf(fact_4907_stable__imp__take__bit__eq,axiom,
% 5.46/5.73 ! [A: int,N: nat] :
% 5.46/5.73 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.73 = A )
% 5.46/5.73 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.46/5.73 = zero_zero_int ) )
% 5.46/5.73 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.46/5.73 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % stable_imp_take_bit_eq
% 5.46/5.73 thf(fact_4908_stable__imp__take__bit__eq,axiom,
% 5.46/5.73 ! [A: nat,N: nat] :
% 5.46/5.73 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.73 = A )
% 5.46/5.73 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.46/5.73 = zero_zero_nat ) )
% 5.46/5.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.46/5.73 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % stable_imp_take_bit_eq
% 5.46/5.73 thf(fact_4909_take__bit__numeral__bit1,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_bit1
% 5.46/5.73 thf(fact_4910_take__bit__numeral__bit1,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.46/5.73 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_bit1
% 5.46/5.73 thf(fact_4911_take__bit__minus__small__eq,axiom,
% 5.46/5.73 ! [K: int,N: nat] :
% 5.46/5.73 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.73 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.46/5.73 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_minus_small_eq
% 5.46/5.73 thf(fact_4912_one__le__exp__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X4 ) )
% 5.46/5.73 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_le_exp_iff
% 5.46/5.73 thf(fact_4913_exp__le__one__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( exp_real @ X4 ) @ one_one_real )
% 5.46/5.73 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_le_one_iff
% 5.46/5.73 thf(fact_4914_exp__less__one__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ ( exp_real @ X4 ) @ one_one_real )
% 5.46/5.73 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_less_one_iff
% 5.46/5.73 thf(fact_4915_one__less__exp__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ one_one_real @ ( exp_real @ X4 ) )
% 5.46/5.73 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % one_less_exp_iff
% 5.46/5.73 thf(fact_4916_real__exp__bound__lemma,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.73 => ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % real_exp_bound_lemma
% 5.46/5.73 thf(fact_4917_exp__bound,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.73 => ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_bound
% 5.46/5.73 thf(fact_4918_arsinh__real__aux,axiom,
% 5.46/5.73 ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % arsinh_real_aux
% 5.46/5.73 thf(fact_4919_exp__less__cancel__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y3 ) )
% 5.46/5.73 = ( ord_less_real @ X4 @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_less_cancel_iff
% 5.46/5.73 thf(fact_4920_exp__less__mono,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.73 => ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_less_mono
% 5.46/5.73 thf(fact_4921_exp__le__cancel__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( exp_real @ Y3 ) )
% 5.46/5.73 = ( ord_less_eq_real @ X4 @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_le_cancel_iff
% 5.46/5.73 thf(fact_4922_exp__zero,axiom,
% 5.46/5.73 ( ( exp_complex @ zero_zero_complex )
% 5.46/5.73 = one_one_complex ) ).
% 5.46/5.73
% 5.46/5.73 % exp_zero
% 5.46/5.73 thf(fact_4923_exp__zero,axiom,
% 5.46/5.73 ( ( exp_real @ zero_zero_real )
% 5.46/5.73 = one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % exp_zero
% 5.46/5.73 thf(fact_4924_exp__eq__one__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ( exp_real @ X4 )
% 5.46/5.73 = one_one_real )
% 5.46/5.73 = ( X4 = zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_eq_one_iff
% 5.46/5.73 thf(fact_4925_and__nat__numerals_I3_J,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % and_nat_numerals(3)
% 5.46/5.73 thf(fact_4926_and__nat__numerals_I1_J,axiom,
% 5.46/5.73 ! [Y3: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.46/5.73 = zero_zero_nat ) ).
% 5.46/5.73
% 5.46/5.73 % and_nat_numerals(1)
% 5.46/5.73 thf(fact_4927_and__nat__numerals_I2_J,axiom,
% 5.46/5.73 ! [Y3: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.46/5.73 = one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % and_nat_numerals(2)
% 5.46/5.73 thf(fact_4928_and__nat__numerals_I4_J,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = one_one_nat ) ).
% 5.46/5.73
% 5.46/5.73 % and_nat_numerals(4)
% 5.46/5.73 thf(fact_4929_Suc__0__and__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.73 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % Suc_0_and_eq
% 5.46/5.73 thf(fact_4930_and__Suc__0__eq,axiom,
% 5.46/5.73 ! [N: nat] :
% 5.46/5.73 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.73 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_Suc_0_eq
% 5.46/5.73 thf(fact_4931_exp__times__arg__commute,axiom,
% 5.46/5.73 ! [A3: complex] :
% 5.46/5.73 ( ( times_times_complex @ ( exp_complex @ A3 ) @ A3 )
% 5.46/5.73 = ( times_times_complex @ A3 @ ( exp_complex @ A3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_times_arg_commute
% 5.46/5.73 thf(fact_4932_exp__times__arg__commute,axiom,
% 5.46/5.73 ! [A3: real] :
% 5.46/5.73 ( ( times_times_real @ ( exp_real @ A3 ) @ A3 )
% 5.46/5.73 = ( times_times_real @ A3 @ ( exp_real @ A3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_times_arg_commute
% 5.46/5.73 thf(fact_4933_exp__less__cancel,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y3 ) )
% 5.46/5.73 => ( ord_less_real @ X4 @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_less_cancel
% 5.46/5.73 thf(fact_4934_and__nat__unfold,axiom,
% 5.46/5.73 ( bit_se727722235901077358nd_nat
% 5.46/5.73 = ( ^ [M6: nat,N2: nat] :
% 5.46/5.73 ( if_nat
% 5.46/5.73 @ ( ( M6 = zero_zero_nat )
% 5.46/5.73 | ( N2 = zero_zero_nat ) )
% 5.46/5.73 @ zero_zero_nat
% 5.46/5.73 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_nat_unfold
% 5.46/5.73 thf(fact_4935_and__nat__rec,axiom,
% 5.46/5.73 ( bit_se727722235901077358nd_nat
% 5.46/5.73 = ( ^ [M6: nat,N2: nat] :
% 5.46/5.73 ( plus_plus_nat
% 5.46/5.73 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.73 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.46/5.73 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.73 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % and_nat_rec
% 5.46/5.73 thf(fact_4936_mult__exp__exp,axiom,
% 5.46/5.73 ! [X4: complex,Y3: complex] :
% 5.46/5.73 ( ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y3 ) )
% 5.46/5.73 = ( exp_complex @ ( plus_plus_complex @ X4 @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mult_exp_exp
% 5.46/5.73 thf(fact_4937_mult__exp__exp,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ Y3 ) )
% 5.46/5.73 = ( exp_real @ ( plus_plus_real @ X4 @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % mult_exp_exp
% 5.46/5.73 thf(fact_4938_exp__add__commuting,axiom,
% 5.46/5.73 ! [X4: complex,Y3: complex] :
% 5.46/5.73 ( ( ( times_times_complex @ X4 @ Y3 )
% 5.46/5.73 = ( times_times_complex @ Y3 @ X4 ) )
% 5.46/5.73 => ( ( exp_complex @ ( plus_plus_complex @ X4 @ Y3 ) )
% 5.46/5.73 = ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_add_commuting
% 5.46/5.73 thf(fact_4939_exp__add__commuting,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ( times_times_real @ X4 @ Y3 )
% 5.46/5.73 = ( times_times_real @ Y3 @ X4 ) )
% 5.46/5.73 => ( ( exp_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.73 = ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_add_commuting
% 5.46/5.73 thf(fact_4940_exp__diff,axiom,
% 5.46/5.73 ! [X4: complex,Y3: complex] :
% 5.46/5.73 ( ( exp_complex @ ( minus_minus_complex @ X4 @ Y3 ) )
% 5.46/5.73 = ( divide1717551699836669952omplex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_diff
% 5.46/5.73 thf(fact_4941_exp__diff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( exp_real @ ( minus_minus_real @ X4 @ Y3 ) )
% 5.46/5.73 = ( divide_divide_real @ ( exp_real @ X4 ) @ ( exp_real @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_diff
% 5.46/5.73 thf(fact_4942_not__exp__less__zero,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ~ ( ord_less_real @ ( exp_real @ X4 ) @ zero_zero_real ) ).
% 5.46/5.73
% 5.46/5.73 % not_exp_less_zero
% 5.46/5.73 thf(fact_4943_exp__gt__zero,axiom,
% 5.46/5.73 ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_gt_zero
% 5.46/5.73 thf(fact_4944_exp__total,axiom,
% 5.46/5.73 ! [Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ? [X3: real] :
% 5.46/5.73 ( ( exp_real @ X3 )
% 5.46/5.73 = Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_total
% 5.46/5.73 thf(fact_4945_exp__ge__zero,axiom,
% 5.46/5.73 ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_ge_zero
% 5.46/5.73 thf(fact_4946_not__exp__le__zero,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ~ ( ord_less_eq_real @ ( exp_real @ X4 ) @ zero_zero_real ) ).
% 5.46/5.73
% 5.46/5.73 % not_exp_le_zero
% 5.46/5.73 thf(fact_4947_exp__minus__inverse,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ ( uminus_uminus_real @ X4 ) ) )
% 5.46/5.73 = one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % exp_minus_inverse
% 5.46/5.73 thf(fact_4948_exp__minus__inverse,axiom,
% 5.46/5.73 ! [X4: complex] :
% 5.46/5.73 ( ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X4 ) ) )
% 5.46/5.73 = one_one_complex ) ).
% 5.46/5.73
% 5.46/5.73 % exp_minus_inverse
% 5.46/5.73 thf(fact_4949_exp__gt__one,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_real @ one_one_real @ ( exp_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_gt_one
% 5.46/5.73 thf(fact_4950_exp__ge__add__one__self,axiom,
% 5.46/5.73 ! [X4: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( exp_real @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_ge_add_one_self
% 5.46/5.73 thf(fact_4951_exp__ge__add__one__self__aux,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( exp_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_ge_add_one_self_aux
% 5.46/5.73 thf(fact_4952_lemma__exp__total,axiom,
% 5.46/5.73 ! [Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ one_one_real @ Y3 )
% 5.46/5.73 => ? [X3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.46/5.73 & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y3 @ one_one_real ) )
% 5.46/5.73 & ( ( exp_real @ X3 )
% 5.46/5.73 = Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % lemma_exp_total
% 5.46/5.73 thf(fact_4953_exp__le,axiom,
% 5.46/5.73 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_le
% 5.46/5.73 thf(fact_4954_exp__double,axiom,
% 5.46/5.73 ! [Z: complex] :
% 5.46/5.73 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.46/5.73 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_double
% 5.46/5.73 thf(fact_4955_exp__double,axiom,
% 5.46/5.73 ! [Z: real] :
% 5.46/5.73 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.46/5.73 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_double
% 5.46/5.73 thf(fact_4956_exp__half__le2,axiom,
% 5.46/5.73 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_half_le2
% 5.46/5.73 thf(fact_4957_arcosh__1,axiom,
% 5.46/5.73 ( ( arcosh_real @ one_one_real )
% 5.46/5.73 = zero_zero_real ) ).
% 5.46/5.73
% 5.46/5.73 % arcosh_1
% 5.46/5.73 thf(fact_4958_floor__exists1,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ? [X3: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ X4 )
% 5.46/5.73 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.46/5.73 & ! [Y5: int] :
% 5.46/5.73 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y5 ) @ X4 )
% 5.46/5.73 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.46/5.73 => ( Y5 = X3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % floor_exists1
% 5.46/5.73 thf(fact_4959_floor__exists1,axiom,
% 5.46/5.73 ! [X4: rat] :
% 5.46/5.73 ? [X3: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X4 )
% 5.46/5.73 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.46/5.73 & ! [Y5: int] :
% 5.46/5.73 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X4 )
% 5.46/5.73 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.46/5.73 => ( Y5 = X3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % floor_exists1
% 5.46/5.73 thf(fact_4960_floor__exists,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ? [Z2: int] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X4 )
% 5.46/5.73 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % floor_exists
% 5.46/5.73 thf(fact_4961_floor__exists,axiom,
% 5.46/5.73 ! [X4: rat] :
% 5.46/5.73 ? [Z2: int] :
% 5.46/5.73 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X4 )
% 5.46/5.73 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % floor_exists
% 5.46/5.73 thf(fact_4962_take__bit__numeral__minus__bit1,axiom,
% 5.46/5.73 ! [L2: num,K: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.73 = ( 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 ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_numeral_minus_bit1
% 5.46/5.73 thf(fact_4963_take__bit__Suc__minus__bit1,axiom,
% 5.46/5.73 ! [N: nat,K: num] :
% 5.46/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.73 = ( 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 ) ) ).
% 5.46/5.73
% 5.46/5.73 % take_bit_Suc_minus_bit1
% 5.46/5.73 thf(fact_4964_tanh__real__altdef,axiom,
% 5.46/5.73 ( tanh_real
% 5.46/5.73 = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_altdef
% 5.46/5.73 thf(fact_4965_ln__one__minus__pos__lower__bound,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.73 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_one_minus_pos_lower_bound
% 5.46/5.73 thf(fact_4966_tanh__real__less__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y3 ) )
% 5.46/5.73 = ( ord_less_real @ X4 @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_less_iff
% 5.46/5.73 thf(fact_4967_tanh__real__le__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y3 ) )
% 5.46/5.73 = ( ord_less_eq_real @ X4 @ Y3 ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_le_iff
% 5.46/5.73 thf(fact_4968_ln__one,axiom,
% 5.46/5.73 ( ( ln_ln_real @ one_one_real )
% 5.46/5.73 = zero_zero_real ) ).
% 5.46/5.73
% 5.46/5.73 % ln_one
% 5.46/5.73 thf(fact_4969_ln__inj__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ( ( ln_ln_real @ X4 )
% 5.46/5.73 = ( ln_ln_real @ Y3 ) )
% 5.46/5.73 = ( X4 = Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_inj_iff
% 5.46/5.73 thf(fact_4970_ln__less__cancel__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ( ord_less_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y3 ) )
% 5.46/5.73 = ( ord_less_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_less_cancel_iff
% 5.46/5.73 thf(fact_4971_tanh__real__neg__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ ( tanh_real @ X4 ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_neg_iff
% 5.46/5.73 thf(fact_4972_tanh__real__pos__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X4 ) )
% 5.46/5.73 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_pos_iff
% 5.46/5.73 thf(fact_4973_tanh__real__nonpos__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( tanh_real @ X4 ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_nonpos_iff
% 5.46/5.73 thf(fact_4974_tanh__real__nonneg__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X4 ) )
% 5.46/5.73 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_nonneg_iff
% 5.46/5.73 thf(fact_4975_pred__numeral__inc,axiom,
% 5.46/5.73 ! [K: num] :
% 5.46/5.73 ( ( pred_numeral @ ( inc @ K ) )
% 5.46/5.73 = ( numeral_numeral_nat @ K ) ) ).
% 5.46/5.73
% 5.46/5.73 % pred_numeral_inc
% 5.46/5.73 thf(fact_4976_ln__le__cancel__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y3 ) )
% 5.46/5.73 = ( ord_less_eq_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_le_cancel_iff
% 5.46/5.73 thf(fact_4977_ln__eq__zero__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ( ln_ln_real @ X4 )
% 5.46/5.73 = zero_zero_real )
% 5.46/5.73 = ( X4 = one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_eq_zero_iff
% 5.46/5.73 thf(fact_4978_ln__gt__zero__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 5.46/5.73 = ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_gt_zero_iff
% 5.46/5.73 thf(fact_4979_ln__less__zero__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_real @ ( ln_ln_real @ X4 ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_less_zero_iff
% 5.46/5.73 thf(fact_4980_exp__ln,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( exp_real @ ( ln_ln_real @ X4 ) )
% 5.46/5.73 = X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_ln
% 5.46/5.73 thf(fact_4981_exp__ln__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ( exp_real @ ( ln_ln_real @ X4 ) )
% 5.46/5.73 = X4 )
% 5.46/5.73 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % exp_ln_iff
% 5.46/5.73 thf(fact_4982_ln__le__zero__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ zero_zero_real )
% 5.46/5.73 = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_le_zero_iff
% 5.46/5.73 thf(fact_4983_ln__ge__zero__iff,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 5.46/5.73 = ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_ge_zero_iff
% 5.46/5.73 thf(fact_4984_add__neg__numeral__special_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.73 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_neg_numeral_special(5)
% 5.46/5.73 thf(fact_4985_add__neg__numeral__special_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_neg_numeral_special(5)
% 5.46/5.73 thf(fact_4986_add__neg__numeral__special_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.46/5.73 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_neg_numeral_special(5)
% 5.46/5.73 thf(fact_4987_add__neg__numeral__special_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_neg_numeral_special(5)
% 5.46/5.73 thf(fact_4988_add__neg__numeral__special_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.73 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_neg_numeral_special(5)
% 5.46/5.73 thf(fact_4989_add__neg__numeral__special_I6_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.73 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_neg_numeral_special(6)
% 5.46/5.73 thf(fact_4990_add__neg__numeral__special_I6_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_neg_numeral_special(6)
% 5.46/5.73 thf(fact_4991_add__neg__numeral__special_I6_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.73 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_neg_numeral_special(6)
% 5.46/5.73 thf(fact_4992_add__neg__numeral__special_I6_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_neg_numeral_special(6)
% 5.46/5.73 thf(fact_4993_add__neg__numeral__special_I6_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.73 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_neg_numeral_special(6)
% 5.46/5.73 thf(fact_4994_diff__numeral__special_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.73 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_special(5)
% 5.46/5.73 thf(fact_4995_diff__numeral__special_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.73 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_special(5)
% 5.46/5.73 thf(fact_4996_diff__numeral__special_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 5.46/5.73 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_special(5)
% 5.46/5.73 thf(fact_4997_diff__numeral__special_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.73 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_special(5)
% 5.46/5.73 thf(fact_4998_diff__numeral__special_I5_J,axiom,
% 5.46/5.73 ! [N: num] :
% 5.46/5.73 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 5.46/5.73 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_special(5)
% 5.46/5.73 thf(fact_4999_diff__numeral__special_I6_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.73 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_special(6)
% 5.46/5.73 thf(fact_5000_diff__numeral__special_I6_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.73 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_special(6)
% 5.46/5.73 thf(fact_5001_diff__numeral__special_I6_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.73 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_special(6)
% 5.46/5.73 thf(fact_5002_diff__numeral__special_I6_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.73 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_special(6)
% 5.46/5.73 thf(fact_5003_diff__numeral__special_I6_J,axiom,
% 5.46/5.73 ! [M: num] :
% 5.46/5.73 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.73 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % diff_numeral_special(6)
% 5.46/5.73 thf(fact_5004_num__induct,axiom,
% 5.46/5.73 ! [P: num > $o,X4: num] :
% 5.46/5.73 ( ( P @ one )
% 5.46/5.73 => ( ! [X3: num] :
% 5.46/5.73 ( ( P @ X3 )
% 5.46/5.73 => ( P @ ( inc @ X3 ) ) )
% 5.46/5.73 => ( P @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % num_induct
% 5.46/5.73 thf(fact_5005_add__inc,axiom,
% 5.46/5.73 ! [X4: num,Y3: num] :
% 5.46/5.73 ( ( plus_plus_num @ X4 @ ( inc @ Y3 ) )
% 5.46/5.73 = ( inc @ ( plus_plus_num @ X4 @ Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_inc
% 5.46/5.73 thf(fact_5006_ln__less__self,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_less_self
% 5.46/5.73 thf(fact_5007_tanh__real__lt__1,axiom,
% 5.46/5.73 ! [X4: real] : ( ord_less_real @ ( tanh_real @ X4 ) @ one_one_real ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_lt_1
% 5.46/5.73 thf(fact_5008_inc_Osimps_I1_J,axiom,
% 5.46/5.73 ( ( inc @ one )
% 5.46/5.73 = ( bit0 @ one ) ) ).
% 5.46/5.73
% 5.46/5.73 % inc.simps(1)
% 5.46/5.73 thf(fact_5009_inc_Osimps_I2_J,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( inc @ ( bit0 @ X4 ) )
% 5.46/5.73 = ( bit1 @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % inc.simps(2)
% 5.46/5.73 thf(fact_5010_inc_Osimps_I3_J,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( inc @ ( bit1 @ X4 ) )
% 5.46/5.73 = ( bit0 @ ( inc @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % inc.simps(3)
% 5.46/5.73 thf(fact_5011_ln__bound,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_bound
% 5.46/5.73 thf(fact_5012_ln__gt__zero,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.73 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_gt_zero
% 5.46/5.73 thf(fact_5013_ln__less__zero,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.73 => ( ord_less_real @ ( ln_ln_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_less_zero
% 5.46/5.73 thf(fact_5014_ln__gt__zero__imp__gt__one,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_gt_zero_imp_gt_one
% 5.46/5.73 thf(fact_5015_ln__ge__zero,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.46/5.73 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_ge_zero
% 5.46/5.73 thf(fact_5016_add__One,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( plus_plus_num @ X4 @ one )
% 5.46/5.73 = ( inc @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % add_One
% 5.46/5.73 thf(fact_5017_mult__inc,axiom,
% 5.46/5.73 ! [X4: num,Y3: num] :
% 5.46/5.73 ( ( times_times_num @ X4 @ ( inc @ Y3 ) )
% 5.46/5.73 = ( plus_plus_num @ ( times_times_num @ X4 @ Y3 ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % mult_inc
% 5.46/5.73 thf(fact_5018_tanh__real__gt__neg1,axiom,
% 5.46/5.73 ! [X4: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_real_gt_neg1
% 5.46/5.73 thf(fact_5019_ln__ge__zero__imp__ge__one,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_ge_zero_imp_ge_one
% 5.46/5.73 thf(fact_5020_ln__add__one__self__le__self,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_add_one_self_le_self
% 5.46/5.73 thf(fact_5021_ln__mult,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ( ln_ln_real @ ( times_times_real @ X4 @ Y3 ) )
% 5.46/5.73 = ( plus_plus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y3 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_mult
% 5.46/5.73 thf(fact_5022_ln__eq__minus__one,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ( ln_ln_real @ X4 )
% 5.46/5.73 = ( minus_minus_real @ X4 @ one_one_real ) )
% 5.46/5.73 => ( X4 = one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_eq_minus_one
% 5.46/5.73 thf(fact_5023_ln__div,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ( ln_ln_real @ ( divide_divide_real @ X4 @ Y3 ) )
% 5.46/5.73 = ( minus_minus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y3 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_div
% 5.46/5.73 thf(fact_5024_ln__ge__iff,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ Y3 @ ( ln_ln_real @ X4 ) )
% 5.46/5.73 = ( ord_less_eq_real @ ( exp_real @ Y3 ) @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_ge_iff
% 5.46/5.73 thf(fact_5025_ln__x__over__x__mono,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.73 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y3 ) @ Y3 ) @ ( divide_divide_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_x_over_x_mono
% 5.46/5.73 thf(fact_5026_numeral__inc,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( numera6690914467698888265omplex @ ( inc @ X4 ) )
% 5.46/5.73 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X4 ) @ one_one_complex ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_inc
% 5.46/5.73 thf(fact_5027_numeral__inc,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( numeral_numeral_real @ ( inc @ X4 ) )
% 5.46/5.73 = ( plus_plus_real @ ( numeral_numeral_real @ X4 ) @ one_one_real ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_inc
% 5.46/5.73 thf(fact_5028_numeral__inc,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( numeral_numeral_rat @ ( inc @ X4 ) )
% 5.46/5.73 = ( plus_plus_rat @ ( numeral_numeral_rat @ X4 ) @ one_one_rat ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_inc
% 5.46/5.73 thf(fact_5029_numeral__inc,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( numeral_numeral_nat @ ( inc @ X4 ) )
% 5.46/5.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ X4 ) @ one_one_nat ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_inc
% 5.46/5.73 thf(fact_5030_numeral__inc,axiom,
% 5.46/5.73 ! [X4: num] :
% 5.46/5.73 ( ( numeral_numeral_int @ ( inc @ X4 ) )
% 5.46/5.73 = ( plus_plus_int @ ( numeral_numeral_int @ X4 ) @ one_one_int ) ) ).
% 5.46/5.73
% 5.46/5.73 % numeral_inc
% 5.46/5.73 thf(fact_5031_ln__2__less__1,axiom,
% 5.46/5.73 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.46/5.73
% 5.46/5.73 % ln_2_less_1
% 5.46/5.73 thf(fact_5032_ln__le__minus__one,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_le_minus_one
% 5.46/5.73 thf(fact_5033_ln__diff__le,axiom,
% 5.46/5.73 ! [X4: real,Y3: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.73 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y3 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X4 @ Y3 ) @ Y3 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_diff_le
% 5.46/5.73 thf(fact_5034_ln__add__one__self__le__self2,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.73 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_add_one_self_le_self2
% 5.46/5.73 thf(fact_5035_tanh__ln__real,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( tanh_real @ ( ln_ln_real @ X4 ) )
% 5.46/5.73 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_ln_real
% 5.46/5.73 thf(fact_5036_arcosh__real__def,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.46/5.73 => ( ( arcosh_real @ X4 )
% 5.46/5.73 = ( ln_ln_real @ ( plus_plus_real @ X4 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % arcosh_real_def
% 5.46/5.73 thf(fact_5037_ln__one__minus__pos__upper__bound,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.73 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X4 ) ) @ ( uminus_uminus_real @ X4 ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_one_minus_pos_upper_bound
% 5.46/5.73 thf(fact_5038_ln__sqrt,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ln_ln_real @ ( sqrt @ X4 ) )
% 5.46/5.73 = ( divide_divide_real @ ( ln_ln_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_sqrt
% 5.46/5.73 thf(fact_5039_exists__least__lemma,axiom,
% 5.46/5.73 ! [P: nat > $o] :
% 5.46/5.73 ( ~ ( P @ zero_zero_nat )
% 5.46/5.73 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.46/5.73 => ? [N4: nat] :
% 5.46/5.73 ( ~ ( P @ N4 )
% 5.46/5.73 & ( P @ ( suc @ N4 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % exists_least_lemma
% 5.46/5.73 thf(fact_5040_ex__le__of__int,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ? [Z2: int] : ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % ex_le_of_int
% 5.46/5.73 thf(fact_5041_ex__le__of__int,axiom,
% 5.46/5.73 ! [X4: rat] :
% 5.46/5.73 ? [Z2: int] : ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % ex_le_of_int
% 5.46/5.73 thf(fact_5042_ex__of__int__less,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X4 ) ).
% 5.46/5.73
% 5.46/5.73 % ex_of_int_less
% 5.46/5.73 thf(fact_5043_ex__of__int__less,axiom,
% 5.46/5.73 ! [X4: rat] :
% 5.46/5.73 ? [Z2: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X4 ) ).
% 5.46/5.73
% 5.46/5.73 % ex_of_int_less
% 5.46/5.73 thf(fact_5044_ex__less__of__int,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ? [Z2: int] : ( ord_less_real @ X4 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % ex_less_of_int
% 5.46/5.73 thf(fact_5045_ex__less__of__int,axiom,
% 5.46/5.73 ! [X4: rat] :
% 5.46/5.73 ? [Z2: int] : ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.46/5.73
% 5.46/5.73 % ex_less_of_int
% 5.46/5.73 thf(fact_5046_tanh__altdef,axiom,
% 5.46/5.73 ( tanh_real
% 5.46/5.73 = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_altdef
% 5.46/5.73 thf(fact_5047_tanh__altdef,axiom,
% 5.46/5.73 ( tanh_complex
% 5.46/5.73 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % tanh_altdef
% 5.46/5.73 thf(fact_5048_ln__one__plus__pos__lower__bound,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.73 => ( ord_less_eq_real @ ( minus_minus_real @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % ln_one_plus_pos_lower_bound
% 5.46/5.73 thf(fact_5049_artanh__def,axiom,
% 5.46/5.73 ( artanh_real
% 5.46/5.73 = ( ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X ) @ ( minus_minus_real @ one_one_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % artanh_def
% 5.46/5.73 thf(fact_5050_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.73 => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.73 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.46/5.73 thf(fact_5051_round__unique,axiom,
% 5.46/5.73 ! [X4: real,Y3: int] :
% 5.46/5.73 ( ( ord_less_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y3 ) )
% 5.46/5.73 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y3 ) @ ( plus_plus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.73 => ( ( archim8280529875227126926d_real @ X4 )
% 5.46/5.73 = Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % round_unique
% 5.46/5.73 thf(fact_5052_round__unique,axiom,
% 5.46/5.73 ! [X4: rat,Y3: int] :
% 5.46/5.73 ( ( ord_less_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y3 ) )
% 5.46/5.73 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y3 ) @ ( plus_plus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.73 => ( ( archim7778729529865785530nd_rat @ X4 )
% 5.46/5.73 = Y3 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % round_unique
% 5.46/5.73 thf(fact_5053_arsinh__real__def,axiom,
% 5.46/5.73 ( arsinh_real
% 5.46/5.73 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % arsinh_real_def
% 5.46/5.73 thf(fact_5054_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.46/5.73 ! [X4: real] :
% 5.46/5.73 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.73 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % abs_ln_one_plus_x_minus_x_bound
% 5.46/5.73 thf(fact_5055_of__int__round__gt,axiom,
% 5.46/5.73 ! [X4: real] : ( ord_less_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_round_gt
% 5.46/5.73 thf(fact_5056_of__int__round__gt,axiom,
% 5.46/5.73 ! [X4: rat] : ( ord_less_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_round_gt
% 5.46/5.73 thf(fact_5057_of__int__round__ge,axiom,
% 5.46/5.73 ! [X4: real] : ( ord_less_eq_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_round_ge
% 5.46/5.73 thf(fact_5058_of__int__round__ge,axiom,
% 5.46/5.73 ! [X4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) ) ).
% 5.46/5.73
% 5.46/5.73 % of_int_round_ge
% 5.46/5.73 thf(fact_5059_abs__abs,axiom,
% 5.46/5.73 ! [A: real] :
% 5.46/5.73 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.46/5.73 = ( abs_abs_real @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_abs
% 5.46/5.74 thf(fact_5060_abs__abs,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.46/5.74 = ( abs_abs_int @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_abs
% 5.46/5.74 thf(fact_5061_abs__abs,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.46/5.74 = ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_abs
% 5.46/5.74 thf(fact_5062_abs__abs,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.46/5.74 = ( abs_abs_rat @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_abs
% 5.46/5.74 thf(fact_5063_abs__idempotent,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.46/5.74 = ( abs_abs_real @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_idempotent
% 5.46/5.74 thf(fact_5064_abs__idempotent,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.46/5.74 = ( abs_abs_int @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_idempotent
% 5.46/5.74 thf(fact_5065_abs__idempotent,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.46/5.74 = ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_idempotent
% 5.46/5.74 thf(fact_5066_abs__idempotent,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.46/5.74 = ( abs_abs_rat @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_idempotent
% 5.46/5.74 thf(fact_5067_abs__0,axiom,
% 5.46/5.74 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.46/5.74 = zero_z3403309356797280102nteger ) ).
% 5.46/5.74
% 5.46/5.74 % abs_0
% 5.46/5.74 thf(fact_5068_abs__0,axiom,
% 5.46/5.74 ( ( abs_abs_real @ zero_zero_real )
% 5.46/5.74 = zero_zero_real ) ).
% 5.46/5.74
% 5.46/5.74 % abs_0
% 5.46/5.74 thf(fact_5069_abs__0,axiom,
% 5.46/5.74 ( ( abs_abs_rat @ zero_zero_rat )
% 5.46/5.74 = zero_zero_rat ) ).
% 5.46/5.74
% 5.46/5.74 % abs_0
% 5.46/5.74 thf(fact_5070_abs__0,axiom,
% 5.46/5.74 ( ( abs_abs_int @ zero_zero_int )
% 5.46/5.74 = zero_zero_int ) ).
% 5.46/5.74
% 5.46/5.74 % abs_0
% 5.46/5.74 thf(fact_5071_abs__0__eq,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( zero_z3403309356797280102nteger
% 5.46/5.74 = ( abs_abs_Code_integer @ A ) )
% 5.46/5.74 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_0_eq
% 5.46/5.74 thf(fact_5072_abs__0__eq,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( zero_zero_real
% 5.46/5.74 = ( abs_abs_real @ A ) )
% 5.46/5.74 = ( A = zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_0_eq
% 5.46/5.74 thf(fact_5073_abs__0__eq,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( zero_zero_rat
% 5.46/5.74 = ( abs_abs_rat @ A ) )
% 5.46/5.74 = ( A = zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_0_eq
% 5.46/5.74 thf(fact_5074_abs__0__eq,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( zero_zero_int
% 5.46/5.74 = ( abs_abs_int @ A ) )
% 5.46/5.74 = ( A = zero_zero_int ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_0_eq
% 5.46/5.74 thf(fact_5075_abs__eq__0,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( ( abs_abs_Code_integer @ A )
% 5.46/5.74 = zero_z3403309356797280102nteger )
% 5.46/5.74 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_0
% 5.46/5.74 thf(fact_5076_abs__eq__0,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( ( abs_abs_real @ A )
% 5.46/5.74 = zero_zero_real )
% 5.46/5.74 = ( A = zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_0
% 5.46/5.74 thf(fact_5077_abs__eq__0,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( ( abs_abs_rat @ A )
% 5.46/5.74 = zero_zero_rat )
% 5.46/5.74 = ( A = zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_0
% 5.46/5.74 thf(fact_5078_abs__eq__0,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( ( abs_abs_int @ A )
% 5.46/5.74 = zero_zero_int )
% 5.46/5.74 = ( A = zero_zero_int ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_0
% 5.46/5.74 thf(fact_5079_abs__zero,axiom,
% 5.46/5.74 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.46/5.74 = zero_z3403309356797280102nteger ) ).
% 5.46/5.74
% 5.46/5.74 % abs_zero
% 5.46/5.74 thf(fact_5080_abs__zero,axiom,
% 5.46/5.74 ( ( abs_abs_real @ zero_zero_real )
% 5.46/5.74 = zero_zero_real ) ).
% 5.46/5.74
% 5.46/5.74 % abs_zero
% 5.46/5.74 thf(fact_5081_abs__zero,axiom,
% 5.46/5.74 ( ( abs_abs_rat @ zero_zero_rat )
% 5.46/5.74 = zero_zero_rat ) ).
% 5.46/5.74
% 5.46/5.74 % abs_zero
% 5.46/5.74 thf(fact_5082_abs__zero,axiom,
% 5.46/5.74 ( ( abs_abs_int @ zero_zero_int )
% 5.46/5.74 = zero_zero_int ) ).
% 5.46/5.74
% 5.46/5.74 % abs_zero
% 5.46/5.74 thf(fact_5083_abs__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.74 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_numeral
% 5.46/5.74 thf(fact_5084_abs__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.46/5.74 = ( numeral_numeral_real @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_numeral
% 5.46/5.74 thf(fact_5085_abs__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.46/5.74 = ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_numeral
% 5.46/5.74 thf(fact_5086_abs__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.46/5.74 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_numeral
% 5.46/5.74 thf(fact_5087_abs__mult__self__eq,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.46/5.74 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_self_eq
% 5.46/5.74 thf(fact_5088_abs__mult__self__eq,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.46/5.74 = ( times_times_real @ A @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_self_eq
% 5.46/5.74 thf(fact_5089_abs__mult__self__eq,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.46/5.74 = ( times_times_rat @ A @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_self_eq
% 5.46/5.74 thf(fact_5090_abs__mult__self__eq,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.46/5.74 = ( times_times_int @ A @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_self_eq
% 5.46/5.74 thf(fact_5091_abs__1,axiom,
% 5.46/5.74 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.46/5.74 = one_one_Code_integer ) ).
% 5.46/5.74
% 5.46/5.74 % abs_1
% 5.46/5.74 thf(fact_5092_abs__1,axiom,
% 5.46/5.74 ( ( abs_abs_complex @ one_one_complex )
% 5.46/5.74 = one_one_complex ) ).
% 5.46/5.74
% 5.46/5.74 % abs_1
% 5.46/5.74 thf(fact_5093_abs__1,axiom,
% 5.46/5.74 ( ( abs_abs_real @ one_one_real )
% 5.46/5.74 = one_one_real ) ).
% 5.46/5.74
% 5.46/5.74 % abs_1
% 5.46/5.74 thf(fact_5094_abs__1,axiom,
% 5.46/5.74 ( ( abs_abs_rat @ one_one_rat )
% 5.46/5.74 = one_one_rat ) ).
% 5.46/5.74
% 5.46/5.74 % abs_1
% 5.46/5.74 thf(fact_5095_abs__1,axiom,
% 5.46/5.74 ( ( abs_abs_int @ one_one_int )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % abs_1
% 5.46/5.74 thf(fact_5096_abs__add__abs,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) )
% 5.46/5.74 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_add_abs
% 5.46/5.74 thf(fact_5097_abs__add__abs,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) )
% 5.46/5.74 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_add_abs
% 5.46/5.74 thf(fact_5098_abs__add__abs,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) )
% 5.46/5.74 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_add_abs
% 5.46/5.74 thf(fact_5099_abs__add__abs,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) )
% 5.46/5.74 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_add_abs
% 5.46/5.74 thf(fact_5100_abs__divide,axiom,
% 5.46/5.74 ! [A: complex,B2: complex] :
% 5.46/5.74 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.74 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_divide
% 5.46/5.74 thf(fact_5101_abs__divide,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( abs_abs_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.74 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_divide
% 5.46/5.74 thf(fact_5102_abs__divide,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B2 ) )
% 5.46/5.74 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_divide
% 5.46/5.74 thf(fact_5103_abs__minus,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.74 = ( abs_abs_real @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus
% 5.46/5.74 thf(fact_5104_abs__minus,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.74 = ( abs_abs_int @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus
% 5.46/5.74 thf(fact_5105_abs__minus,axiom,
% 5.46/5.74 ! [A: complex] :
% 5.46/5.74 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.74 = ( abs_abs_complex @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus
% 5.46/5.74 thf(fact_5106_abs__minus,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.74 = ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus
% 5.46/5.74 thf(fact_5107_abs__minus,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.74 = ( abs_abs_rat @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus
% 5.46/5.74 thf(fact_5108_abs__minus__cancel,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.74 = ( abs_abs_real @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_cancel
% 5.46/5.74 thf(fact_5109_abs__minus__cancel,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.74 = ( abs_abs_int @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_cancel
% 5.46/5.74 thf(fact_5110_abs__minus__cancel,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.74 = ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_cancel
% 5.46/5.74 thf(fact_5111_abs__minus__cancel,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.74 = ( abs_abs_rat @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_cancel
% 5.46/5.74 thf(fact_5112_abs__dvd__iff,axiom,
% 5.46/5.74 ! [M: real,K: real] :
% 5.46/5.74 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.46/5.74 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_dvd_iff
% 5.46/5.74 thf(fact_5113_abs__dvd__iff,axiom,
% 5.46/5.74 ! [M: int,K: int] :
% 5.46/5.74 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.46/5.74 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_dvd_iff
% 5.46/5.74 thf(fact_5114_abs__dvd__iff,axiom,
% 5.46/5.74 ! [M: code_integer,K: code_integer] :
% 5.46/5.74 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.46/5.74 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_dvd_iff
% 5.46/5.74 thf(fact_5115_abs__dvd__iff,axiom,
% 5.46/5.74 ! [M: rat,K: rat] :
% 5.46/5.74 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 5.46/5.74 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_dvd_iff
% 5.46/5.74 thf(fact_5116_dvd__abs__iff,axiom,
% 5.46/5.74 ! [M: real,K: real] :
% 5.46/5.74 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.46/5.74 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % dvd_abs_iff
% 5.46/5.74 thf(fact_5117_dvd__abs__iff,axiom,
% 5.46/5.74 ! [M: int,K: int] :
% 5.46/5.74 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.46/5.74 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % dvd_abs_iff
% 5.46/5.74 thf(fact_5118_dvd__abs__iff,axiom,
% 5.46/5.74 ! [M: code_integer,K: code_integer] :
% 5.46/5.74 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.46/5.74 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % dvd_abs_iff
% 5.46/5.74 thf(fact_5119_dvd__abs__iff,axiom,
% 5.46/5.74 ! [M: rat,K: rat] :
% 5.46/5.74 ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 5.46/5.74 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % dvd_abs_iff
% 5.46/5.74 thf(fact_5120_abs__bool__eq,axiom,
% 5.46/5.74 ! [P: $o] :
% 5.46/5.74 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.46/5.74 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_bool_eq
% 5.46/5.74 thf(fact_5121_abs__bool__eq,axiom,
% 5.46/5.74 ! [P: $o] :
% 5.46/5.74 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.46/5.74 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_bool_eq
% 5.46/5.74 thf(fact_5122_abs__bool__eq,axiom,
% 5.46/5.74 ! [P: $o] :
% 5.46/5.74 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.46/5.74 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_bool_eq
% 5.46/5.74 thf(fact_5123_abs__bool__eq,axiom,
% 5.46/5.74 ! [P: $o] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.46/5.74 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_bool_eq
% 5.46/5.74 thf(fact_5124_abs__le__zero__iff,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.46/5.74 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_zero_iff
% 5.46/5.74 thf(fact_5125_abs__le__zero__iff,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.46/5.74 = ( A = zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_zero_iff
% 5.46/5.74 thf(fact_5126_abs__le__zero__iff,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.46/5.74 = ( A = zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_zero_iff
% 5.46/5.74 thf(fact_5127_abs__le__zero__iff,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.46/5.74 = ( A = zero_zero_int ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_zero_iff
% 5.46/5.74 thf(fact_5128_abs__le__self__iff,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.46/5.74 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_self_iff
% 5.46/5.74 thf(fact_5129_abs__le__self__iff,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.46/5.74 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_self_iff
% 5.46/5.74 thf(fact_5130_abs__le__self__iff,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.46/5.74 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_self_iff
% 5.46/5.74 thf(fact_5131_abs__le__self__iff,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.46/5.74 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_self_iff
% 5.46/5.74 thf(fact_5132_abs__of__nonneg,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.74 => ( ( abs_abs_Code_integer @ A )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nonneg
% 5.46/5.74 thf(fact_5133_abs__of__nonneg,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.74 => ( ( abs_abs_real @ A )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nonneg
% 5.46/5.74 thf(fact_5134_abs__of__nonneg,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.74 => ( ( abs_abs_rat @ A )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nonneg
% 5.46/5.74 thf(fact_5135_abs__of__nonneg,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.74 => ( ( abs_abs_int @ A )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nonneg
% 5.46/5.74 thf(fact_5136_zero__less__abs__iff,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.46/5.74 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_abs_iff
% 5.46/5.74 thf(fact_5137_zero__less__abs__iff,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.46/5.74 = ( A != zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_abs_iff
% 5.46/5.74 thf(fact_5138_zero__less__abs__iff,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.46/5.74 = ( A != zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_abs_iff
% 5.46/5.74 thf(fact_5139_zero__less__abs__iff,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.46/5.74 = ( A != zero_zero_int ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_abs_iff
% 5.46/5.74 thf(fact_5140_abs__neg__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.74 = ( numeral_numeral_real @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_neg_numeral
% 5.46/5.74 thf(fact_5141_abs__neg__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.74 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_neg_numeral
% 5.46/5.74 thf(fact_5142_abs__neg__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.74 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_neg_numeral
% 5.46/5.74 thf(fact_5143_abs__neg__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.74 = ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_neg_numeral
% 5.46/5.74 thf(fact_5144_abs__neg__one,axiom,
% 5.46/5.74 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.74 = one_one_real ) ).
% 5.46/5.74
% 5.46/5.74 % abs_neg_one
% 5.46/5.74 thf(fact_5145_abs__neg__one,axiom,
% 5.46/5.74 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % abs_neg_one
% 5.46/5.74 thf(fact_5146_abs__neg__one,axiom,
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.74 = one_one_Code_integer ) ).
% 5.46/5.74
% 5.46/5.74 % abs_neg_one
% 5.46/5.74 thf(fact_5147_abs__neg__one,axiom,
% 5.46/5.74 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.74 = one_one_rat ) ).
% 5.46/5.74
% 5.46/5.74 % abs_neg_one
% 5.46/5.74 thf(fact_5148_abs__power__minus,axiom,
% 5.46/5.74 ! [A: real,N: nat] :
% 5.46/5.74 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.46/5.74 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_power_minus
% 5.46/5.74 thf(fact_5149_abs__power__minus,axiom,
% 5.46/5.74 ! [A: int,N: nat] :
% 5.46/5.74 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.46/5.74 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_power_minus
% 5.46/5.74 thf(fact_5150_abs__power__minus,axiom,
% 5.46/5.74 ! [A: code_integer,N: nat] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.46/5.74 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_power_minus
% 5.46/5.74 thf(fact_5151_abs__power__minus,axiom,
% 5.46/5.74 ! [A: rat,N: nat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.46/5.74 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_power_minus
% 5.46/5.74 thf(fact_5152_real__sqrt__abs2,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( sqrt @ ( times_times_real @ X4 @ X4 ) )
% 5.46/5.74 = ( abs_abs_real @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_sqrt_abs2
% 5.46/5.74 thf(fact_5153_real__sqrt__mult__self,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.46/5.74 = ( abs_abs_real @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_sqrt_mult_self
% 5.46/5.74 thf(fact_5154_round__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.46/5.74 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % round_numeral
% 5.46/5.74 thf(fact_5155_round__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.46/5.74 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % round_numeral
% 5.46/5.74 thf(fact_5156_round__1,axiom,
% 5.46/5.74 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % round_1
% 5.46/5.74 thf(fact_5157_round__1,axiom,
% 5.46/5.74 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % round_1
% 5.46/5.74 thf(fact_5158_zero__le__divide__abs__iff,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B2 ) ) )
% 5.46/5.74 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.74 | ( B2 = zero_zero_real ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_le_divide_abs_iff
% 5.46/5.74 thf(fact_5159_zero__le__divide__abs__iff,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B2 ) ) )
% 5.46/5.74 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.74 | ( B2 = zero_zero_rat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_le_divide_abs_iff
% 5.46/5.74 thf(fact_5160_divide__le__0__abs__iff,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B2 ) ) @ zero_zero_real )
% 5.46/5.74 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.74 | ( B2 = zero_zero_real ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % divide_le_0_abs_iff
% 5.46/5.74 thf(fact_5161_divide__le__0__abs__iff,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B2 ) ) @ zero_zero_rat )
% 5.46/5.74 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.74 | ( B2 = zero_zero_rat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % divide_le_0_abs_iff
% 5.46/5.74 thf(fact_5162_abs__of__nonpos,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.74 => ( ( abs_abs_real @ A )
% 5.46/5.74 = ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nonpos
% 5.46/5.74 thf(fact_5163_abs__of__nonpos,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.46/5.74 => ( ( abs_abs_Code_integer @ A )
% 5.46/5.74 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nonpos
% 5.46/5.74 thf(fact_5164_abs__of__nonpos,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.46/5.74 => ( ( abs_abs_rat @ A )
% 5.46/5.74 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nonpos
% 5.46/5.74 thf(fact_5165_abs__of__nonpos,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.46/5.74 => ( ( abs_abs_int @ A )
% 5.46/5.74 = ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nonpos
% 5.46/5.74 thf(fact_5166_artanh__minus__real,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.74 => ( ( artanh_real @ ( uminus_uminus_real @ X4 ) )
% 5.46/5.74 = ( uminus_uminus_real @ ( artanh_real @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % artanh_minus_real
% 5.46/5.74 thf(fact_5167_zero__less__power__abs__iff,axiom,
% 5.46/5.74 ! [A: code_integer,N: nat] :
% 5.46/5.74 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.46/5.74 = ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_power_abs_iff
% 5.46/5.74 thf(fact_5168_zero__less__power__abs__iff,axiom,
% 5.46/5.74 ! [A: real,N: nat] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.46/5.74 = ( ( A != zero_zero_real )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_power_abs_iff
% 5.46/5.74 thf(fact_5169_zero__less__power__abs__iff,axiom,
% 5.46/5.74 ! [A: rat,N: nat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.46/5.74 = ( ( A != zero_zero_rat )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_power_abs_iff
% 5.46/5.74 thf(fact_5170_zero__less__power__abs__iff,axiom,
% 5.46/5.74 ! [A: int,N: nat] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.46/5.74 = ( ( A != zero_zero_int )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_power_abs_iff
% 5.46/5.74 thf(fact_5171_abs__power2,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_power2
% 5.46/5.74 thf(fact_5172_abs__power2,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_power2
% 5.46/5.74 thf(fact_5173_abs__power2,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_power2
% 5.46/5.74 thf(fact_5174_abs__power2,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_power2
% 5.46/5.74 thf(fact_5175_power2__abs,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.74 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power2_abs
% 5.46/5.74 thf(fact_5176_power2__abs,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.74 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power2_abs
% 5.46/5.74 thf(fact_5177_power2__abs,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.74 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power2_abs
% 5.46/5.74 thf(fact_5178_power2__abs,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.74 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power2_abs
% 5.46/5.74 thf(fact_5179_round__neg__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % round_neg_numeral
% 5.46/5.74 thf(fact_5180_round__neg__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.46/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % round_neg_numeral
% 5.46/5.74 thf(fact_5181_power__even__abs__numeral,axiom,
% 5.46/5.74 ! [W: num,A: code_integer] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.74 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.74 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_even_abs_numeral
% 5.46/5.74 thf(fact_5182_power__even__abs__numeral,axiom,
% 5.46/5.74 ! [W: num,A: rat] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.74 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.74 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_even_abs_numeral
% 5.46/5.74 thf(fact_5183_power__even__abs__numeral,axiom,
% 5.46/5.74 ! [W: num,A: real] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.74 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.74 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_even_abs_numeral
% 5.46/5.74 thf(fact_5184_power__even__abs__numeral,axiom,
% 5.46/5.74 ! [W: num,A: int] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.74 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.46/5.74 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_even_abs_numeral
% 5.46/5.74 thf(fact_5185_real__sqrt__abs,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( sqrt @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( abs_abs_real @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_sqrt_abs
% 5.46/5.74 thf(fact_5186_abs__ge__self,axiom,
% 5.46/5.74 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_self
% 5.46/5.74 thf(fact_5187_abs__ge__self,axiom,
% 5.46/5.74 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_self
% 5.46/5.74 thf(fact_5188_abs__ge__self,axiom,
% 5.46/5.74 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_self
% 5.46/5.74 thf(fact_5189_abs__ge__self,axiom,
% 5.46/5.74 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_self
% 5.46/5.74 thf(fact_5190_abs__le__D1,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B2 )
% 5.46/5.74 => ( ord_less_eq_real @ A @ B2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_D1
% 5.46/5.74 thf(fact_5191_abs__le__D1,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B2 )
% 5.46/5.74 => ( ord_le3102999989581377725nteger @ A @ B2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_D1
% 5.46/5.74 thf(fact_5192_abs__le__D1,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B2 )
% 5.46/5.74 => ( ord_less_eq_rat @ A @ B2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_D1
% 5.46/5.74 thf(fact_5193_abs__le__D1,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B2 )
% 5.46/5.74 => ( ord_less_eq_int @ A @ B2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_D1
% 5.46/5.74 thf(fact_5194_abs__eq__0__iff,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( ( abs_abs_Code_integer @ A )
% 5.46/5.74 = zero_z3403309356797280102nteger )
% 5.46/5.74 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_0_iff
% 5.46/5.74 thf(fact_5195_abs__eq__0__iff,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( ( abs_abs_real @ A )
% 5.46/5.74 = zero_zero_real )
% 5.46/5.74 = ( A = zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_0_iff
% 5.46/5.74 thf(fact_5196_abs__eq__0__iff,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( ( abs_abs_rat @ A )
% 5.46/5.74 = zero_zero_rat )
% 5.46/5.74 = ( A = zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_0_iff
% 5.46/5.74 thf(fact_5197_abs__eq__0__iff,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( ( abs_abs_int @ A )
% 5.46/5.74 = zero_zero_int )
% 5.46/5.74 = ( A = zero_zero_int ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_0_iff
% 5.46/5.74 thf(fact_5198_abs__mult,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B2 ) )
% 5.46/5.74 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult
% 5.46/5.74 thf(fact_5199_abs__mult,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( abs_abs_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.74 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult
% 5.46/5.74 thf(fact_5200_abs__mult,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.74 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult
% 5.46/5.74 thf(fact_5201_abs__mult,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( abs_abs_int @ ( times_times_int @ A @ B2 ) )
% 5.46/5.74 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult
% 5.46/5.74 thf(fact_5202_abs__one,axiom,
% 5.46/5.74 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.46/5.74 = one_one_Code_integer ) ).
% 5.46/5.74
% 5.46/5.74 % abs_one
% 5.46/5.74 thf(fact_5203_abs__one,axiom,
% 5.46/5.74 ( ( abs_abs_real @ one_one_real )
% 5.46/5.74 = one_one_real ) ).
% 5.46/5.74
% 5.46/5.74 % abs_one
% 5.46/5.74 thf(fact_5204_abs__one,axiom,
% 5.46/5.74 ( ( abs_abs_rat @ one_one_rat )
% 5.46/5.74 = one_one_rat ) ).
% 5.46/5.74
% 5.46/5.74 % abs_one
% 5.46/5.74 thf(fact_5205_abs__one,axiom,
% 5.46/5.74 ( ( abs_abs_int @ one_one_int )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % abs_one
% 5.46/5.74 thf(fact_5206_abs__minus__commute,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B2 ) )
% 5.46/5.74 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B2 @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_commute
% 5.46/5.74 thf(fact_5207_abs__minus__commute,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( abs_abs_real @ ( minus_minus_real @ A @ B2 ) )
% 5.46/5.74 = ( abs_abs_real @ ( minus_minus_real @ B2 @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_commute
% 5.46/5.74 thf(fact_5208_abs__minus__commute,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B2 ) )
% 5.46/5.74 = ( abs_abs_rat @ ( minus_minus_rat @ B2 @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_commute
% 5.46/5.74 thf(fact_5209_abs__minus__commute,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( abs_abs_int @ ( minus_minus_int @ A @ B2 ) )
% 5.46/5.74 = ( abs_abs_int @ ( minus_minus_int @ B2 @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_commute
% 5.46/5.74 thf(fact_5210_abs__eq__iff,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] :
% 5.46/5.74 ( ( ( abs_abs_real @ X4 )
% 5.46/5.74 = ( abs_abs_real @ Y3 ) )
% 5.46/5.74 = ( ( X4 = Y3 )
% 5.46/5.74 | ( X4
% 5.46/5.74 = ( uminus_uminus_real @ Y3 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_iff
% 5.46/5.74 thf(fact_5211_abs__eq__iff,axiom,
% 5.46/5.74 ! [X4: int,Y3: int] :
% 5.46/5.74 ( ( ( abs_abs_int @ X4 )
% 5.46/5.74 = ( abs_abs_int @ Y3 ) )
% 5.46/5.74 = ( ( X4 = Y3 )
% 5.46/5.74 | ( X4
% 5.46/5.74 = ( uminus_uminus_int @ Y3 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_iff
% 5.46/5.74 thf(fact_5212_abs__eq__iff,axiom,
% 5.46/5.74 ! [X4: code_integer,Y3: code_integer] :
% 5.46/5.74 ( ( ( abs_abs_Code_integer @ X4 )
% 5.46/5.74 = ( abs_abs_Code_integer @ Y3 ) )
% 5.46/5.74 = ( ( X4 = Y3 )
% 5.46/5.74 | ( X4
% 5.46/5.74 = ( uminus1351360451143612070nteger @ Y3 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_iff
% 5.46/5.74 thf(fact_5213_abs__eq__iff,axiom,
% 5.46/5.74 ! [X4: rat,Y3: rat] :
% 5.46/5.74 ( ( ( abs_abs_rat @ X4 )
% 5.46/5.74 = ( abs_abs_rat @ Y3 ) )
% 5.46/5.74 = ( ( X4 = Y3 )
% 5.46/5.74 | ( X4
% 5.46/5.74 = ( uminus_uminus_rat @ Y3 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_iff
% 5.46/5.74 thf(fact_5214_power__abs,axiom,
% 5.46/5.74 ! [A: code_integer,N: nat] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.46/5.74 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_abs
% 5.46/5.74 thf(fact_5215_power__abs,axiom,
% 5.46/5.74 ! [A: rat,N: nat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 5.46/5.74 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_abs
% 5.46/5.74 thf(fact_5216_power__abs,axiom,
% 5.46/5.74 ! [A: real,N: nat] :
% 5.46/5.74 ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 5.46/5.74 = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_abs
% 5.46/5.74 thf(fact_5217_power__abs,axiom,
% 5.46/5.74 ! [A: int,N: nat] :
% 5.46/5.74 ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 5.46/5.74 = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_abs
% 5.46/5.74 thf(fact_5218_dvd__if__abs__eq,axiom,
% 5.46/5.74 ! [L2: real,K: real] :
% 5.46/5.74 ( ( ( abs_abs_real @ L2 )
% 5.46/5.74 = ( abs_abs_real @ K ) )
% 5.46/5.74 => ( dvd_dvd_real @ L2 @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % dvd_if_abs_eq
% 5.46/5.74 thf(fact_5219_dvd__if__abs__eq,axiom,
% 5.46/5.74 ! [L2: int,K: int] :
% 5.46/5.74 ( ( ( abs_abs_int @ L2 )
% 5.46/5.74 = ( abs_abs_int @ K ) )
% 5.46/5.74 => ( dvd_dvd_int @ L2 @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % dvd_if_abs_eq
% 5.46/5.74 thf(fact_5220_dvd__if__abs__eq,axiom,
% 5.46/5.74 ! [L2: code_integer,K: code_integer] :
% 5.46/5.74 ( ( ( abs_abs_Code_integer @ L2 )
% 5.46/5.74 = ( abs_abs_Code_integer @ K ) )
% 5.46/5.74 => ( dvd_dvd_Code_integer @ L2 @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % dvd_if_abs_eq
% 5.46/5.74 thf(fact_5221_dvd__if__abs__eq,axiom,
% 5.46/5.74 ! [L2: rat,K: rat] :
% 5.46/5.74 ( ( ( abs_abs_rat @ L2 )
% 5.46/5.74 = ( abs_abs_rat @ K ) )
% 5.46/5.74 => ( dvd_dvd_rat @ L2 @ K ) ) ).
% 5.46/5.74
% 5.46/5.74 % dvd_if_abs_eq
% 5.46/5.74 thf(fact_5222_round__diff__minimal,axiom,
% 5.46/5.74 ! [Z: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % round_diff_minimal
% 5.46/5.74 thf(fact_5223_round__diff__minimal,axiom,
% 5.46/5.74 ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % round_diff_minimal
% 5.46/5.74 thf(fact_5224_abs__ge__zero,axiom,
% 5.46/5.74 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_zero
% 5.46/5.74 thf(fact_5225_abs__ge__zero,axiom,
% 5.46/5.74 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_zero
% 5.46/5.74 thf(fact_5226_abs__ge__zero,axiom,
% 5.46/5.74 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_zero
% 5.46/5.74 thf(fact_5227_abs__ge__zero,axiom,
% 5.46/5.74 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_zero
% 5.46/5.74 thf(fact_5228_abs__not__less__zero,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.46/5.74
% 5.46/5.74 % abs_not_less_zero
% 5.46/5.74 thf(fact_5229_abs__not__less__zero,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.46/5.74
% 5.46/5.74 % abs_not_less_zero
% 5.46/5.74 thf(fact_5230_abs__not__less__zero,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.46/5.74
% 5.46/5.74 % abs_not_less_zero
% 5.46/5.74 thf(fact_5231_abs__not__less__zero,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.46/5.74
% 5.46/5.74 % abs_not_less_zero
% 5.46/5.74 thf(fact_5232_abs__of__pos,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.74 => ( ( abs_abs_Code_integer @ A )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_pos
% 5.46/5.74 thf(fact_5233_abs__of__pos,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.74 => ( ( abs_abs_real @ A )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_pos
% 5.46/5.74 thf(fact_5234_abs__of__pos,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.74 => ( ( abs_abs_rat @ A )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_pos
% 5.46/5.74 thf(fact_5235_abs__of__pos,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.74 => ( ( abs_abs_int @ A )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_pos
% 5.46/5.74 thf(fact_5236_abs__triangle__ineq,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B2 ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq
% 5.46/5.74 thf(fact_5237_abs__triangle__ineq,axiom,
% 5.46/5.74 ! [A: real,B2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B2 ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq
% 5.46/5.74 thf(fact_5238_abs__triangle__ineq,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B2 ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq
% 5.46/5.74 thf(fact_5239_abs__triangle__ineq,axiom,
% 5.46/5.74 ! [A: int,B2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B2 ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq
% 5.46/5.74 thf(fact_5240_abs__mult__less,axiom,
% 5.46/5.74 ! [A: code_integer,C: code_integer,B2: code_integer,D: code_integer] :
% 5.46/5.74 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.46/5.74 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B2 ) @ D )
% 5.46/5.74 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_less
% 5.46/5.74 thf(fact_5241_abs__mult__less,axiom,
% 5.46/5.74 ! [A: real,C: real,B2: real,D: real] :
% 5.46/5.74 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.46/5.74 => ( ( ord_less_real @ ( abs_abs_real @ B2 ) @ D )
% 5.46/5.74 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_less
% 5.46/5.74 thf(fact_5242_abs__mult__less,axiom,
% 5.46/5.74 ! [A: rat,C: rat,B2: rat,D: rat] :
% 5.46/5.74 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.46/5.74 => ( ( ord_less_rat @ ( abs_abs_rat @ B2 ) @ D )
% 5.46/5.74 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_less
% 5.46/5.74 thf(fact_5243_abs__mult__less,axiom,
% 5.46/5.74 ! [A: int,C: int,B2: int,D: int] :
% 5.46/5.74 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.46/5.74 => ( ( ord_less_int @ ( abs_abs_int @ B2 ) @ D )
% 5.46/5.74 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_less
% 5.46/5.74 thf(fact_5244_abs__triangle__ineq2,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq2
% 5.46/5.74 thf(fact_5245_abs__triangle__ineq2,axiom,
% 5.46/5.74 ! [A: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq2
% 5.46/5.74 thf(fact_5246_abs__triangle__ineq2,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq2
% 5.46/5.74 thf(fact_5247_abs__triangle__ineq2,axiom,
% 5.46/5.74 ! [A: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq2
% 5.46/5.74 thf(fact_5248_abs__triangle__ineq3,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq3
% 5.46/5.74 thf(fact_5249_abs__triangle__ineq3,axiom,
% 5.46/5.74 ! [A: real,B2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq3
% 5.46/5.74 thf(fact_5250_abs__triangle__ineq3,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq3
% 5.46/5.74 thf(fact_5251_abs__triangle__ineq3,axiom,
% 5.46/5.74 ! [A: int,B2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq3
% 5.46/5.74 thf(fact_5252_abs__triangle__ineq2__sym,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B2 @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq2_sym
% 5.46/5.74 thf(fact_5253_abs__triangle__ineq2__sym,axiom,
% 5.46/5.74 ! [A: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) @ ( abs_abs_real @ ( minus_minus_real @ B2 @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq2_sym
% 5.46/5.74 thf(fact_5254_abs__triangle__ineq2__sym,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B2 @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq2_sym
% 5.46/5.74 thf(fact_5255_abs__triangle__ineq2__sym,axiom,
% 5.46/5.74 ! [A: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) @ ( abs_abs_int @ ( minus_minus_int @ B2 @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq2_sym
% 5.46/5.74 thf(fact_5256_nonzero__abs__divide,axiom,
% 5.46/5.74 ! [B2: real,A: real] :
% 5.46/5.74 ( ( B2 != zero_zero_real )
% 5.46/5.74 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.74 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % nonzero_abs_divide
% 5.46/5.74 thf(fact_5257_nonzero__abs__divide,axiom,
% 5.46/5.74 ! [B2: rat,A: rat] :
% 5.46/5.74 ( ( B2 != zero_zero_rat )
% 5.46/5.74 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B2 ) )
% 5.46/5.74 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % nonzero_abs_divide
% 5.46/5.74 thf(fact_5258_abs__ge__minus__self,axiom,
% 5.46/5.74 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_minus_self
% 5.46/5.74 thf(fact_5259_abs__ge__minus__self,axiom,
% 5.46/5.74 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_minus_self
% 5.46/5.74 thf(fact_5260_abs__ge__minus__self,axiom,
% 5.46/5.74 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_minus_self
% 5.46/5.74 thf(fact_5261_abs__ge__minus__self,axiom,
% 5.46/5.74 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ge_minus_self
% 5.46/5.74 thf(fact_5262_abs__le__iff,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B2 )
% 5.46/5.74 = ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.74 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_iff
% 5.46/5.74 thf(fact_5263_abs__le__iff,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B2 )
% 5.46/5.74 = ( ( ord_le3102999989581377725nteger @ A @ B2 )
% 5.46/5.74 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_iff
% 5.46/5.74 thf(fact_5264_abs__le__iff,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B2 )
% 5.46/5.74 = ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.74 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_iff
% 5.46/5.74 thf(fact_5265_abs__le__iff,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B2 )
% 5.46/5.74 = ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.74 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_iff
% 5.46/5.74 thf(fact_5266_abs__le__D2,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B2 )
% 5.46/5.74 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_D2
% 5.46/5.74 thf(fact_5267_abs__le__D2,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B2 )
% 5.46/5.74 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_D2
% 5.46/5.74 thf(fact_5268_abs__le__D2,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B2 )
% 5.46/5.74 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_D2
% 5.46/5.74 thf(fact_5269_abs__le__D2,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B2 )
% 5.46/5.74 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_D2
% 5.46/5.74 thf(fact_5270_abs__leI,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B2 )
% 5.46/5.74 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_leI
% 5.46/5.74 thf(fact_5271_abs__leI,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ A @ B2 )
% 5.46/5.74 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 )
% 5.46/5.74 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_leI
% 5.46/5.74 thf(fact_5272_abs__leI,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.74 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B2 )
% 5.46/5.74 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_leI
% 5.46/5.74 thf(fact_5273_abs__leI,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.74 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B2 )
% 5.46/5.74 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_leI
% 5.46/5.74 thf(fact_5274_abs__less__iff,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B2 )
% 5.46/5.74 = ( ( ord_less_real @ A @ B2 )
% 5.46/5.74 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_less_iff
% 5.46/5.74 thf(fact_5275_abs__less__iff,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B2 )
% 5.46/5.74 = ( ( ord_less_int @ A @ B2 )
% 5.46/5.74 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_less_iff
% 5.46/5.74 thf(fact_5276_abs__less__iff,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B2 )
% 5.46/5.74 = ( ( ord_le6747313008572928689nteger @ A @ B2 )
% 5.46/5.74 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_less_iff
% 5.46/5.74 thf(fact_5277_abs__less__iff,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B2 )
% 5.46/5.74 = ( ( ord_less_rat @ A @ B2 )
% 5.46/5.74 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_less_iff
% 5.46/5.74 thf(fact_5278_dense__eq0__I,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ! [E2: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.46/5.74 => ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ E2 ) )
% 5.46/5.74 => ( X4 = zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % dense_eq0_I
% 5.46/5.74 thf(fact_5279_dense__eq0__I,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ! [E2: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.46/5.74 => ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ E2 ) )
% 5.46/5.74 => ( X4 = zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % dense_eq0_I
% 5.46/5.74 thf(fact_5280_abs__eq__mult,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.74 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.46/5.74 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.46/5.74 | ( ord_le3102999989581377725nteger @ B2 @ zero_z3403309356797280102nteger ) ) )
% 5.46/5.74 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B2 ) )
% 5.46/5.74 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_mult
% 5.46/5.74 thf(fact_5281_abs__eq__mult,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.74 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.46/5.74 & ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.74 | ( ord_less_eq_real @ B2 @ zero_zero_real ) ) )
% 5.46/5.74 => ( ( abs_abs_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.74 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_mult
% 5.46/5.74 thf(fact_5282_abs__eq__mult,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.74 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.46/5.74 & ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.74 | ( ord_less_eq_rat @ B2 @ zero_zero_rat ) ) )
% 5.46/5.74 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.74 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_mult
% 5.46/5.74 thf(fact_5283_abs__eq__mult,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.74 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.46/5.74 & ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.74 | ( ord_less_eq_int @ B2 @ zero_zero_int ) ) )
% 5.46/5.74 => ( ( abs_abs_int @ ( times_times_int @ A @ B2 ) )
% 5.46/5.74 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_mult
% 5.46/5.74 thf(fact_5284_abs__mult__pos,axiom,
% 5.46/5.74 ! [X4: code_integer,Y3: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 5.46/5.74 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y3 ) @ X4 )
% 5.46/5.74 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y3 @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_pos
% 5.46/5.74 thf(fact_5285_abs__mult__pos,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( times_times_real @ ( abs_abs_real @ Y3 ) @ X4 )
% 5.46/5.74 = ( abs_abs_real @ ( times_times_real @ Y3 @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_pos
% 5.46/5.74 thf(fact_5286_abs__mult__pos,axiom,
% 5.46/5.74 ! [X4: rat,Y3: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.74 => ( ( times_times_rat @ ( abs_abs_rat @ Y3 ) @ X4 )
% 5.46/5.74 = ( abs_abs_rat @ ( times_times_rat @ Y3 @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_pos
% 5.46/5.74 thf(fact_5287_abs__mult__pos,axiom,
% 5.46/5.74 ! [X4: int,Y3: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.74 => ( ( times_times_int @ ( abs_abs_int @ Y3 ) @ X4 )
% 5.46/5.74 = ( abs_abs_int @ ( times_times_int @ Y3 @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mult_pos
% 5.46/5.74 thf(fact_5288_abs__minus__le__zero,axiom,
% 5.46/5.74 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_le_zero
% 5.46/5.74 thf(fact_5289_abs__minus__le__zero,axiom,
% 5.46/5.74 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_le_zero
% 5.46/5.74 thf(fact_5290_abs__minus__le__zero,axiom,
% 5.46/5.74 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_le_zero
% 5.46/5.74 thf(fact_5291_abs__minus__le__zero,axiom,
% 5.46/5.74 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.46/5.74
% 5.46/5.74 % abs_minus_le_zero
% 5.46/5.74 thf(fact_5292_eq__abs__iff_H,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( A
% 5.46/5.74 = ( abs_abs_real @ B2 ) )
% 5.46/5.74 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.74 & ( ( B2 = A )
% 5.46/5.74 | ( B2
% 5.46/5.74 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % eq_abs_iff'
% 5.46/5.74 thf(fact_5293_eq__abs__iff_H,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( A
% 5.46/5.74 = ( abs_abs_Code_integer @ B2 ) )
% 5.46/5.74 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.74 & ( ( B2 = A )
% 5.46/5.74 | ( B2
% 5.46/5.74 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % eq_abs_iff'
% 5.46/5.74 thf(fact_5294_eq__abs__iff_H,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( A
% 5.46/5.74 = ( abs_abs_rat @ B2 ) )
% 5.46/5.74 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.74 & ( ( B2 = A )
% 5.46/5.74 | ( B2
% 5.46/5.74 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % eq_abs_iff'
% 5.46/5.74 thf(fact_5295_eq__abs__iff_H,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( A
% 5.46/5.74 = ( abs_abs_int @ B2 ) )
% 5.46/5.74 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.46/5.74 & ( ( B2 = A )
% 5.46/5.74 | ( B2
% 5.46/5.74 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % eq_abs_iff'
% 5.46/5.74 thf(fact_5296_abs__eq__iff_H,axiom,
% 5.46/5.74 ! [A: real,B2: real] :
% 5.46/5.74 ( ( ( abs_abs_real @ A )
% 5.46/5.74 = B2 )
% 5.46/5.74 = ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.74 & ( ( A = B2 )
% 5.46/5.74 | ( A
% 5.46/5.74 = ( uminus_uminus_real @ B2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_iff'
% 5.46/5.74 thf(fact_5297_abs__eq__iff_H,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( ( abs_abs_Code_integer @ A )
% 5.46/5.74 = B2 )
% 5.46/5.74 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B2 )
% 5.46/5.74 & ( ( A = B2 )
% 5.46/5.74 | ( A
% 5.46/5.74 = ( uminus1351360451143612070nteger @ B2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_iff'
% 5.46/5.74 thf(fact_5298_abs__eq__iff_H,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] :
% 5.46/5.74 ( ( ( abs_abs_rat @ A )
% 5.46/5.74 = B2 )
% 5.46/5.74 = ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.74 & ( ( A = B2 )
% 5.46/5.74 | ( A
% 5.46/5.74 = ( uminus_uminus_rat @ B2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_iff'
% 5.46/5.74 thf(fact_5299_abs__eq__iff_H,axiom,
% 5.46/5.74 ! [A: int,B2: int] :
% 5.46/5.74 ( ( ( abs_abs_int @ A )
% 5.46/5.74 = B2 )
% 5.46/5.74 = ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.74 & ( ( A = B2 )
% 5.46/5.74 | ( A
% 5.46/5.74 = ( uminus_uminus_int @ B2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_eq_iff'
% 5.46/5.74 thf(fact_5300_abs__div__pos,axiom,
% 5.46/5.74 ! [Y3: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.74 => ( ( divide_divide_real @ ( abs_abs_real @ X4 ) @ Y3 )
% 5.46/5.74 = ( abs_abs_real @ ( divide_divide_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_div_pos
% 5.46/5.74 thf(fact_5301_abs__div__pos,axiom,
% 5.46/5.74 ! [Y3: rat,X4: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ Y3 )
% 5.46/5.74 => ( ( divide_divide_rat @ ( abs_abs_rat @ X4 ) @ Y3 )
% 5.46/5.74 = ( abs_abs_rat @ ( divide_divide_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_div_pos
% 5.46/5.74 thf(fact_5302_zero__le__power__abs,axiom,
% 5.46/5.74 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_le_power_abs
% 5.46/5.74 thf(fact_5303_zero__le__power__abs,axiom,
% 5.46/5.74 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_le_power_abs
% 5.46/5.74 thf(fact_5304_zero__le__power__abs,axiom,
% 5.46/5.74 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_le_power_abs
% 5.46/5.74 thf(fact_5305_zero__le__power__abs,axiom,
% 5.46/5.74 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_le_power_abs
% 5.46/5.74 thf(fact_5306_abs__if,axiom,
% 5.46/5.74 ( abs_abs_real
% 5.46/5.74 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_if
% 5.46/5.74 thf(fact_5307_abs__if,axiom,
% 5.46/5.74 ( abs_abs_int
% 5.46/5.74 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_if
% 5.46/5.74 thf(fact_5308_abs__if,axiom,
% 5.46/5.74 ( abs_abs_Code_integer
% 5.46/5.74 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_if
% 5.46/5.74 thf(fact_5309_abs__if,axiom,
% 5.46/5.74 ( abs_abs_rat
% 5.46/5.74 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_if
% 5.46/5.74 thf(fact_5310_abs__if__raw,axiom,
% 5.46/5.74 ( abs_abs_real
% 5.46/5.74 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_if_raw
% 5.46/5.74 thf(fact_5311_abs__if__raw,axiom,
% 5.46/5.74 ( abs_abs_int
% 5.46/5.74 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_if_raw
% 5.46/5.74 thf(fact_5312_abs__if__raw,axiom,
% 5.46/5.74 ( abs_abs_Code_integer
% 5.46/5.74 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_if_raw
% 5.46/5.74 thf(fact_5313_abs__if__raw,axiom,
% 5.46/5.74 ( abs_abs_rat
% 5.46/5.74 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_if_raw
% 5.46/5.74 thf(fact_5314_abs__of__neg,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.74 => ( ( abs_abs_real @ A )
% 5.46/5.74 = ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_neg
% 5.46/5.74 thf(fact_5315_abs__of__neg,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.74 => ( ( abs_abs_int @ A )
% 5.46/5.74 = ( uminus_uminus_int @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_neg
% 5.46/5.74 thf(fact_5316_abs__of__neg,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.46/5.74 => ( ( abs_abs_Code_integer @ A )
% 5.46/5.74 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_neg
% 5.46/5.74 thf(fact_5317_abs__of__neg,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.74 => ( ( abs_abs_rat @ A )
% 5.46/5.74 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_neg
% 5.46/5.74 thf(fact_5318_abs__triangle__ineq4,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B2 ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq4
% 5.46/5.74 thf(fact_5319_abs__triangle__ineq4,axiom,
% 5.46/5.74 ! [A: real,B2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B2 ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq4
% 5.46/5.74 thf(fact_5320_abs__triangle__ineq4,axiom,
% 5.46/5.74 ! [A: rat,B2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B2 ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq4
% 5.46/5.74 thf(fact_5321_abs__triangle__ineq4,axiom,
% 5.46/5.74 ! [A: int,B2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B2 ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_triangle_ineq4
% 5.46/5.74 thf(fact_5322_abs__diff__triangle__ineq,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B2 ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B2 @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_triangle_ineq
% 5.46/5.74 thf(fact_5323_abs__diff__triangle__ineq,axiom,
% 5.46/5.74 ! [A: real,B2: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B2 @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_triangle_ineq
% 5.46/5.74 thf(fact_5324_abs__diff__triangle__ineq,axiom,
% 5.46/5.74 ! [A: rat,B2: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B2 ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B2 @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_triangle_ineq
% 5.46/5.74 thf(fact_5325_abs__diff__triangle__ineq,axiom,
% 5.46/5.74 ! [A: int,B2: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B2 ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B2 @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_triangle_ineq
% 5.46/5.74 thf(fact_5326_abs__diff__le__iff,axiom,
% 5.46/5.74 ! [X4: code_integer,A: code_integer,R2: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ A ) ) @ R2 )
% 5.46/5.74 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X4 )
% 5.46/5.74 & ( ord_le3102999989581377725nteger @ X4 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_le_iff
% 5.46/5.74 thf(fact_5327_abs__diff__le__iff,axiom,
% 5.46/5.74 ! [X4: real,A: real,R2: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ A ) ) @ R2 )
% 5.46/5.74 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X4 )
% 5.46/5.74 & ( ord_less_eq_real @ X4 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_le_iff
% 5.46/5.74 thf(fact_5328_abs__diff__le__iff,axiom,
% 5.46/5.74 ! [X4: rat,A: rat,R2: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ A ) ) @ R2 )
% 5.46/5.74 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X4 )
% 5.46/5.74 & ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_le_iff
% 5.46/5.74 thf(fact_5329_abs__diff__le__iff,axiom,
% 5.46/5.74 ! [X4: int,A: int,R2: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ A ) ) @ R2 )
% 5.46/5.74 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X4 )
% 5.46/5.74 & ( ord_less_eq_int @ X4 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_le_iff
% 5.46/5.74 thf(fact_5330_abs__diff__less__iff,axiom,
% 5.46/5.74 ! [X4: code_integer,A: code_integer,R2: code_integer] :
% 5.46/5.74 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ A ) ) @ R2 )
% 5.46/5.74 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X4 )
% 5.46/5.74 & ( ord_le6747313008572928689nteger @ X4 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_less_iff
% 5.46/5.74 thf(fact_5331_abs__diff__less__iff,axiom,
% 5.46/5.74 ! [X4: real,A: real,R2: real] :
% 5.46/5.74 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ A ) ) @ R2 )
% 5.46/5.74 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X4 )
% 5.46/5.74 & ( ord_less_real @ X4 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_less_iff
% 5.46/5.74 thf(fact_5332_abs__diff__less__iff,axiom,
% 5.46/5.74 ! [X4: rat,A: rat,R2: rat] :
% 5.46/5.74 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ A ) ) @ R2 )
% 5.46/5.74 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X4 )
% 5.46/5.74 & ( ord_less_rat @ X4 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_less_iff
% 5.46/5.74 thf(fact_5333_abs__diff__less__iff,axiom,
% 5.46/5.74 ! [X4: int,A: int,R2: int] :
% 5.46/5.74 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ A ) ) @ R2 )
% 5.46/5.74 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X4 )
% 5.46/5.74 & ( ord_less_int @ X4 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_diff_less_iff
% 5.46/5.74 thf(fact_5334_round__mono,axiom,
% 5.46/5.74 ! [X4: rat,Y3: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.74 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X4 ) @ ( archim7778729529865785530nd_rat @ Y3 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % round_mono
% 5.46/5.74 thf(fact_5335_abs__real__def,axiom,
% 5.46/5.74 ( abs_abs_real
% 5.46/5.74 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_real_def
% 5.46/5.74 thf(fact_5336_lemma__interval__lt,axiom,
% 5.46/5.74 ! [A: real,X4: real,B2: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ X4 )
% 5.46/5.74 => ( ( ord_less_real @ X4 @ B2 )
% 5.46/5.74 => ? [D3: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.74 & ! [Y5: real] :
% 5.46/5.74 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y5 ) ) @ D3 )
% 5.46/5.74 => ( ( ord_less_real @ A @ Y5 )
% 5.46/5.74 & ( ord_less_real @ Y5 @ B2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % lemma_interval_lt
% 5.46/5.74 thf(fact_5337_sin__bound__lemma,axiom,
% 5.46/5.74 ! [X4: real,Y3: real,U: real,V: real] :
% 5.46/5.74 ( ( X4 = Y3 )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.46/5.74 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X4 @ U ) @ Y3 ) ) @ V ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % sin_bound_lemma
% 5.46/5.74 thf(fact_5338_abs__add__one__gt__zero,axiom,
% 5.46/5.74 ! [X4: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_add_one_gt_zero
% 5.46/5.74 thf(fact_5339_abs__add__one__gt__zero,axiom,
% 5.46/5.74 ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_add_one_gt_zero
% 5.46/5.74 thf(fact_5340_abs__add__one__gt__zero,axiom,
% 5.46/5.74 ! [X4: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_add_one_gt_zero
% 5.46/5.74 thf(fact_5341_abs__add__one__gt__zero,axiom,
% 5.46/5.74 ! [X4: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_add_one_gt_zero
% 5.46/5.74 thf(fact_5342_of__int__leD,axiom,
% 5.46/5.74 ! [N: int,X4: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X4 )
% 5.46/5.74 => ( ( N = zero_zero_int )
% 5.46/5.74 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_leD
% 5.46/5.74 thf(fact_5343_of__int__leD,axiom,
% 5.46/5.74 ! [N: int,X4: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X4 )
% 5.46/5.74 => ( ( N = zero_zero_int )
% 5.46/5.74 | ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_leD
% 5.46/5.74 thf(fact_5344_of__int__leD,axiom,
% 5.46/5.74 ! [N: int,X4: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X4 )
% 5.46/5.74 => ( ( N = zero_zero_int )
% 5.46/5.74 | ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_leD
% 5.46/5.74 thf(fact_5345_of__int__leD,axiom,
% 5.46/5.74 ! [N: int,X4: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X4 )
% 5.46/5.74 => ( ( N = zero_zero_int )
% 5.46/5.74 | ( ord_less_eq_int @ one_one_int @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_leD
% 5.46/5.74 thf(fact_5346_of__int__lessD,axiom,
% 5.46/5.74 ! [N: int,X4: code_integer] :
% 5.46/5.74 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X4 )
% 5.46/5.74 => ( ( N = zero_zero_int )
% 5.46/5.74 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_lessD
% 5.46/5.74 thf(fact_5347_of__int__lessD,axiom,
% 5.46/5.74 ! [N: int,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X4 )
% 5.46/5.74 => ( ( N = zero_zero_int )
% 5.46/5.74 | ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_lessD
% 5.46/5.74 thf(fact_5348_of__int__lessD,axiom,
% 5.46/5.74 ! [N: int,X4: rat] :
% 5.46/5.74 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X4 )
% 5.46/5.74 => ( ( N = zero_zero_int )
% 5.46/5.74 | ( ord_less_rat @ one_one_rat @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_lessD
% 5.46/5.74 thf(fact_5349_of__int__lessD,axiom,
% 5.46/5.74 ! [N: int,X4: int] :
% 5.46/5.74 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X4 )
% 5.46/5.74 => ( ( N = zero_zero_int )
% 5.46/5.74 | ( ord_less_int @ one_one_int @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_lessD
% 5.46/5.74 thf(fact_5350_lemma__interval,axiom,
% 5.46/5.74 ! [A: real,X4: real,B2: real] :
% 5.46/5.74 ( ( ord_less_real @ A @ X4 )
% 5.46/5.74 => ( ( ord_less_real @ X4 @ B2 )
% 5.46/5.74 => ? [D3: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.74 & ! [Y5: real] :
% 5.46/5.74 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y5 ) ) @ D3 )
% 5.46/5.74 => ( ( ord_less_eq_real @ A @ Y5 )
% 5.46/5.74 & ( ord_less_eq_real @ Y5 @ B2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % lemma_interval
% 5.46/5.74 thf(fact_5351_of__int__round__abs__le,axiom,
% 5.46/5.74 ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) @ X4 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_round_abs_le
% 5.46/5.74 thf(fact_5352_of__int__round__abs__le,axiom,
% 5.46/5.74 ! [X4: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) @ X4 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_round_abs_le
% 5.46/5.74 thf(fact_5353_round__unique_H,axiom,
% 5.46/5.74 ! [X4: real,N: int] :
% 5.46/5.74 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.74 => ( ( archim8280529875227126926d_real @ X4 )
% 5.46/5.74 = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % round_unique'
% 5.46/5.74 thf(fact_5354_round__unique_H,axiom,
% 5.46/5.74 ! [X4: rat,N: int] :
% 5.46/5.74 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 => ( ( archim7778729529865785530nd_rat @ X4 )
% 5.46/5.74 = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % round_unique'
% 5.46/5.74 thf(fact_5355_abs__le__square__iff,axiom,
% 5.46/5.74 ! [X4: code_integer,Y3: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ ( abs_abs_Code_integer @ Y3 ) )
% 5.46/5.74 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_square_iff
% 5.46/5.74 thf(fact_5356_abs__le__square__iff,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ Y3 ) )
% 5.46/5.74 = ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_square_iff
% 5.46/5.74 thf(fact_5357_abs__le__square__iff,axiom,
% 5.46/5.74 ! [X4: rat,Y3: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ ( abs_abs_rat @ Y3 ) )
% 5.46/5.74 = ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_square_iff
% 5.46/5.74 thf(fact_5358_abs__le__square__iff,axiom,
% 5.46/5.74 ! [X4: int,Y3: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ ( abs_abs_int @ Y3 ) )
% 5.46/5.74 = ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_le_square_iff
% 5.46/5.74 thf(fact_5359_abs__square__eq__1,axiom,
% 5.46/5.74 ! [X4: code_integer] :
% 5.46/5.74 ( ( ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.74 = one_one_Code_integer )
% 5.46/5.74 = ( ( abs_abs_Code_integer @ X4 )
% 5.46/5.74 = one_one_Code_integer ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_eq_1
% 5.46/5.74 thf(fact_5360_abs__square__eq__1,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.74 = one_one_rat )
% 5.46/5.74 = ( ( abs_abs_rat @ X4 )
% 5.46/5.74 = one_one_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_eq_1
% 5.46/5.74 thf(fact_5361_abs__square__eq__1,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.74 = one_one_real )
% 5.46/5.74 = ( ( abs_abs_real @ X4 )
% 5.46/5.74 = one_one_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_eq_1
% 5.46/5.74 thf(fact_5362_abs__square__eq__1,axiom,
% 5.46/5.74 ! [X4: int] :
% 5.46/5.74 ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.74 = one_one_int )
% 5.46/5.74 = ( ( abs_abs_int @ X4 )
% 5.46/5.74 = one_one_int ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_eq_1
% 5.46/5.74 thf(fact_5363_power__even__abs,axiom,
% 5.46/5.74 ! [N: nat,A: code_integer] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 5.46/5.74 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_even_abs
% 5.46/5.74 thf(fact_5364_power__even__abs,axiom,
% 5.46/5.74 ! [N: nat,A: rat] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 5.46/5.74 = ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_even_abs
% 5.46/5.74 thf(fact_5365_power__even__abs,axiom,
% 5.46/5.74 ! [N: nat,A: real] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 5.46/5.74 = ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_even_abs
% 5.46/5.74 thf(fact_5366_power__even__abs,axiom,
% 5.46/5.74 ! [N: nat,A: int] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 5.46/5.74 = ( power_power_int @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_even_abs
% 5.46/5.74 thf(fact_5367_power2__le__iff__abs__le,axiom,
% 5.46/5.74 ! [Y3: code_integer,X4: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y3 )
% 5.46/5.74 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ Y3 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power2_le_iff_abs_le
% 5.46/5.74 thf(fact_5368_power2__le__iff__abs__le,axiom,
% 5.46/5.74 ! [Y3: real,X4: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ Y3 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power2_le_iff_abs_le
% 5.46/5.74 thf(fact_5369_power2__le__iff__abs__le,axiom,
% 5.46/5.74 ! [Y3: rat,X4: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ Y3 )
% 5.46/5.74 => ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ Y3 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power2_le_iff_abs_le
% 5.46/5.74 thf(fact_5370_power2__le__iff__abs__le,axiom,
% 5.46/5.74 ! [Y3: int,X4: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.74 => ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ Y3 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power2_le_iff_abs_le
% 5.46/5.74 thf(fact_5371_abs__square__le__1,axiom,
% 5.46/5.74 ! [X4: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.46/5.74 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_le_1
% 5.46/5.74 thf(fact_5372_abs__square__le__1,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.46/5.74 = ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_le_1
% 5.46/5.74 thf(fact_5373_abs__square__le__1,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.46/5.74 = ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_le_1
% 5.46/5.74 thf(fact_5374_abs__square__le__1,axiom,
% 5.46/5.74 ! [X4: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.46/5.74 = ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ one_one_int ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_le_1
% 5.46/5.74 thf(fact_5375_abs__square__less__1,axiom,
% 5.46/5.74 ! [X4: code_integer] :
% 5.46/5.74 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.46/5.74 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_less_1
% 5.46/5.74 thf(fact_5376_abs__square__less__1,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.46/5.74 = ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_less_1
% 5.46/5.74 thf(fact_5377_abs__square__less__1,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.46/5.74 = ( ord_less_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_less_1
% 5.46/5.74 thf(fact_5378_abs__square__less__1,axiom,
% 5.46/5.74 ! [X4: int] :
% 5.46/5.74 ( ( ord_less_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.46/5.74 = ( ord_less_int @ ( abs_abs_int @ X4 ) @ one_one_int ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_square_less_1
% 5.46/5.74 thf(fact_5379_power__mono__even,axiom,
% 5.46/5.74 ! [N: nat,A: code_integer,B2: code_integer] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) )
% 5.46/5.74 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B2 @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_mono_even
% 5.46/5.74 thf(fact_5380_power__mono__even,axiom,
% 5.46/5.74 ! [N: nat,A: real,B2: real] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) )
% 5.46/5.74 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B2 @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_mono_even
% 5.46/5.74 thf(fact_5381_power__mono__even,axiom,
% 5.46/5.74 ! [N: nat,A: rat,B2: rat] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) )
% 5.46/5.74 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B2 @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_mono_even
% 5.46/5.74 thf(fact_5382_power__mono__even,axiom,
% 5.46/5.74 ! [N: nat,A: int,B2: int] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) )
% 5.46/5.74 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B2 @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % power_mono_even
% 5.46/5.74 thf(fact_5383_sqrt__ge__absD,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( sqrt @ Y3 ) )
% 5.46/5.74 => ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y3 ) ) ).
% 5.46/5.74
% 5.46/5.74 % sqrt_ge_absD
% 5.46/5.74 thf(fact_5384_real__sqrt__ge__abs1,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_sqrt_ge_abs1
% 5.46/5.74 thf(fact_5385_real__sqrt__ge__abs2,axiom,
% 5.46/5.74 ! [Y3: real,X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_sqrt_ge_abs2
% 5.46/5.74 thf(fact_5386_sqrt__sum__squares__le__sum__abs,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ Y3 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % sqrt_sum_squares_le_sum_abs
% 5.46/5.74 thf(fact_5387_cos__x__y__le__one,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.46/5.74
% 5.46/5.74 % cos_x_y_le_one
% 5.46/5.74 thf(fact_5388_real__sqrt__sum__squares__less,axiom,
% 5.46/5.74 ! [X4: real,U: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 => ( ( ord_less_real @ ( abs_abs_real @ Y3 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_sqrt_sum_squares_less
% 5.46/5.74 thf(fact_5389_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.74 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.46/5.74 thf(fact_5390_of__int__round__le,axiom,
% 5.46/5.74 ! [X4: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) @ ( plus_plus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_round_le
% 5.46/5.74 thf(fact_5391_of__int__round__le,axiom,
% 5.46/5.74 ! [X4: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) @ ( plus_plus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_round_le
% 5.46/5.74 thf(fact_5392_abs__sqrt__wlog,axiom,
% 5.46/5.74 ! [P: code_integer > code_integer > $o,X4: code_integer] :
% 5.46/5.74 ( ! [X3: code_integer] :
% 5.46/5.74 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 5.46/5.74 => ( P @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 => ( P @ ( abs_abs_Code_integer @ X4 ) @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_sqrt_wlog
% 5.46/5.74 thf(fact_5393_abs__sqrt__wlog,axiom,
% 5.46/5.74 ! [P: real > real > $o,X4: real] :
% 5.46/5.74 ( ! [X3: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.46/5.74 => ( P @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 => ( P @ ( abs_abs_real @ X4 ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_sqrt_wlog
% 5.46/5.74 thf(fact_5394_abs__sqrt__wlog,axiom,
% 5.46/5.74 ! [P: rat > rat > $o,X4: rat] :
% 5.46/5.74 ( ! [X3: rat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.46/5.74 => ( P @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 => ( P @ ( abs_abs_rat @ X4 ) @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_sqrt_wlog
% 5.46/5.74 thf(fact_5395_abs__sqrt__wlog,axiom,
% 5.46/5.74 ! [P: int > int > $o,X4: int] :
% 5.46/5.74 ( ! [X3: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.46/5.74 => ( P @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.74 => ( P @ ( abs_abs_int @ X4 ) @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_sqrt_wlog
% 5.46/5.74 thf(fact_5396_arctan__double,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.74 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X4 ) )
% 5.46/5.74 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % arctan_double
% 5.46/5.74 thf(fact_5397_arctan__half,axiom,
% 5.46/5.74 ( arctan
% 5.46/5.74 = ( ^ [X: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % arctan_half
% 5.46/5.74 thf(fact_5398_log__base__10__eq1,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.74 = ( 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 @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_base_10_eq1
% 5.46/5.74 thf(fact_5399_signed__take__bit__eq__take__bit__minus,axiom,
% 5.46/5.74 ( bit_ri631733984087533419it_int
% 5.46/5.74 = ( ^ [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 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % signed_take_bit_eq_take_bit_minus
% 5.46/5.74 thf(fact_5400_log__base__10__eq2,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.74 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_base_10_eq2
% 5.46/5.74 thf(fact_5401_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.46/5.74 ! [X4: real,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.74 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X4 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % exp_ge_one_minus_x_over_n_power_n
% 5.46/5.74 thf(fact_5402_of__nat__eq__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ( semiri8010041392384452111omplex @ M )
% 5.46/5.74 = ( semiri8010041392384452111omplex @ N ) )
% 5.46/5.74 = ( M = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_iff
% 5.46/5.74 thf(fact_5403_of__nat__eq__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ( semiri5074537144036343181t_real @ M )
% 5.46/5.74 = ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.74 = ( M = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_iff
% 5.46/5.74 thf(fact_5404_of__nat__eq__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ( semiri681578069525770553at_rat @ M )
% 5.46/5.74 = ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.74 = ( M = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_iff
% 5.46/5.74 thf(fact_5405_of__nat__eq__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.46/5.74 = ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.74 = ( M = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_iff
% 5.46/5.74 thf(fact_5406_of__nat__eq__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ( semiri1314217659103216013at_int @ M )
% 5.46/5.74 = ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 = ( M = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_iff
% 5.46/5.74 thf(fact_5407_abs__of__nat,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.46/5.74 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nat
% 5.46/5.74 thf(fact_5408_abs__of__nat,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.74 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nat
% 5.46/5.74 thf(fact_5409_abs__of__nat,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.74 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nat
% 5.46/5.74 thf(fact_5410_abs__of__nat,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_of_nat
% 5.46/5.74 thf(fact_5411_of__nat__eq__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( ( semiri8010041392384452111omplex @ M )
% 5.46/5.74 = zero_zero_complex )
% 5.46/5.74 = ( M = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_0_iff
% 5.46/5.74 thf(fact_5412_of__nat__eq__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( ( semiri5074537144036343181t_real @ M )
% 5.46/5.74 = zero_zero_real )
% 5.46/5.74 = ( M = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_0_iff
% 5.46/5.74 thf(fact_5413_of__nat__eq__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( ( semiri681578069525770553at_rat @ M )
% 5.46/5.74 = zero_zero_rat )
% 5.46/5.74 = ( M = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_0_iff
% 5.46/5.74 thf(fact_5414_of__nat__eq__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.46/5.74 = zero_zero_nat )
% 5.46/5.74 = ( M = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_0_iff
% 5.46/5.74 thf(fact_5415_of__nat__eq__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( ( semiri1314217659103216013at_int @ M )
% 5.46/5.74 = zero_zero_int )
% 5.46/5.74 = ( M = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_0_iff
% 5.46/5.74 thf(fact_5416_of__nat__0__eq__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( zero_zero_complex
% 5.46/5.74 = ( semiri8010041392384452111omplex @ N ) )
% 5.46/5.74 = ( zero_zero_nat = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_eq_iff
% 5.46/5.74 thf(fact_5417_of__nat__0__eq__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( zero_zero_real
% 5.46/5.74 = ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.74 = ( zero_zero_nat = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_eq_iff
% 5.46/5.74 thf(fact_5418_of__nat__0__eq__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( zero_zero_rat
% 5.46/5.74 = ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.74 = ( zero_zero_nat = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_eq_iff
% 5.46/5.74 thf(fact_5419_of__nat__0__eq__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( zero_zero_nat
% 5.46/5.74 = ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.74 = ( zero_zero_nat = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_eq_iff
% 5.46/5.74 thf(fact_5420_of__nat__0__eq__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( zero_zero_int
% 5.46/5.74 = ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 = ( zero_zero_nat = N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_eq_iff
% 5.46/5.74 thf(fact_5421_of__nat__0,axiom,
% 5.46/5.74 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.46/5.74 = zero_zero_complex ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0
% 5.46/5.74 thf(fact_5422_of__nat__0,axiom,
% 5.46/5.74 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.46/5.74 = zero_zero_real ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0
% 5.46/5.74 thf(fact_5423_of__nat__0,axiom,
% 5.46/5.74 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.46/5.74 = zero_zero_rat ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0
% 5.46/5.74 thf(fact_5424_of__nat__0,axiom,
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.46/5.74 = zero_zero_nat ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0
% 5.46/5.74 thf(fact_5425_of__nat__0,axiom,
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.46/5.74 = zero_zero_int ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0
% 5.46/5.74 thf(fact_5426_of__nat__less__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.74 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_iff
% 5.46/5.74 thf(fact_5427_of__nat__less__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.74 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_iff
% 5.46/5.74 thf(fact_5428_of__nat__less__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.74 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_iff
% 5.46/5.74 thf(fact_5429_of__nat__less__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_iff
% 5.46/5.74 thf(fact_5430_of__nat__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_numeral
% 5.46/5.74 thf(fact_5431_of__nat__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( numeral_numeral_real @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_numeral
% 5.46/5.74 thf(fact_5432_of__nat__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( numeral_numeral_rat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_numeral
% 5.46/5.74 thf(fact_5433_of__nat__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( numeral_numeral_nat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_numeral
% 5.46/5.74 thf(fact_5434_of__nat__numeral,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_numeral
% 5.46/5.74 thf(fact_5435_of__nat__le__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.74 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_iff
% 5.46/5.74 thf(fact_5436_of__nat__le__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.74 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_iff
% 5.46/5.74 thf(fact_5437_of__nat__le__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.74 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_iff
% 5.46/5.74 thf(fact_5438_of__nat__le__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_iff
% 5.46/5.74 thf(fact_5439_of__nat__add,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.74 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_add
% 5.46/5.74 thf(fact_5440_of__nat__add,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.74 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_add
% 5.46/5.74 thf(fact_5441_of__nat__add,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.74 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_add
% 5.46/5.74 thf(fact_5442_of__nat__add,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.74 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_add
% 5.46/5.74 thf(fact_5443_of__nat__add,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.74 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_add
% 5.46/5.74 thf(fact_5444_of__nat__mult,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 5.46/5.74 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mult
% 5.46/5.74 thf(fact_5445_of__nat__mult,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.46/5.74 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mult
% 5.46/5.74 thf(fact_5446_of__nat__mult,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.46/5.74 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mult
% 5.46/5.74 thf(fact_5447_of__nat__mult,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.46/5.74 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mult
% 5.46/5.74 thf(fact_5448_of__nat__mult,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.46/5.74 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mult
% 5.46/5.74 thf(fact_5449_of__nat__1,axiom,
% 5.46/5.74 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.46/5.74 = one_one_complex ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_1
% 5.46/5.74 thf(fact_5450_of__nat__1,axiom,
% 5.46/5.74 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.46/5.74 = one_one_real ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_1
% 5.46/5.74 thf(fact_5451_of__nat__1,axiom,
% 5.46/5.74 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.46/5.74 = one_one_rat ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_1
% 5.46/5.74 thf(fact_5452_of__nat__1,axiom,
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.46/5.74 = one_one_nat ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_1
% 5.46/5.74 thf(fact_5453_of__nat__1,axiom,
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_1
% 5.46/5.74 thf(fact_5454_of__nat__1__eq__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( one_one_complex
% 5.46/5.74 = ( semiri8010041392384452111omplex @ N ) )
% 5.46/5.74 = ( N = one_one_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_1_eq_iff
% 5.46/5.74 thf(fact_5455_of__nat__1__eq__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( one_one_real
% 5.46/5.74 = ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.74 = ( N = one_one_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_1_eq_iff
% 5.46/5.74 thf(fact_5456_of__nat__1__eq__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( one_one_rat
% 5.46/5.74 = ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.74 = ( N = one_one_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_1_eq_iff
% 5.46/5.74 thf(fact_5457_of__nat__1__eq__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( one_one_nat
% 5.46/5.74 = ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.74 = ( N = one_one_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_1_eq_iff
% 5.46/5.74 thf(fact_5458_of__nat__1__eq__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( one_one_int
% 5.46/5.74 = ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 = ( N = one_one_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_1_eq_iff
% 5.46/5.74 thf(fact_5459_of__nat__eq__1__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ( semiri8010041392384452111omplex @ N )
% 5.46/5.74 = one_one_complex )
% 5.46/5.74 = ( N = one_one_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_1_iff
% 5.46/5.74 thf(fact_5460_of__nat__eq__1__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ( semiri5074537144036343181t_real @ N )
% 5.46/5.74 = one_one_real )
% 5.46/5.74 = ( N = one_one_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_1_iff
% 5.46/5.74 thf(fact_5461_of__nat__eq__1__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ( semiri681578069525770553at_rat @ N )
% 5.46/5.74 = one_one_rat )
% 5.46/5.74 = ( N = one_one_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_1_iff
% 5.46/5.74 thf(fact_5462_of__nat__eq__1__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.46/5.74 = one_one_nat )
% 5.46/5.74 = ( N = one_one_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_1_iff
% 5.46/5.74 thf(fact_5463_of__nat__eq__1__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ( semiri1314217659103216013at_int @ N )
% 5.46/5.74 = one_one_int )
% 5.46/5.74 = ( N = one_one_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_1_iff
% 5.46/5.74 thf(fact_5464_of__nat__power,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 5.46/5.74 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power
% 5.46/5.74 thf(fact_5465_of__nat__power,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 5.46/5.74 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power
% 5.46/5.74 thf(fact_5466_of__nat__power,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 5.46/5.74 = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power
% 5.46/5.74 thf(fact_5467_of__nat__power,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 5.46/5.74 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power
% 5.46/5.74 thf(fact_5468_of__nat__power,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 5.46/5.74 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power
% 5.46/5.74 thf(fact_5469_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B2 ) @ W )
% 5.46/5.74 = ( semiri8010041392384452111omplex @ X4 ) )
% 5.46/5.74 = ( ( power_power_nat @ B2 @ W )
% 5.46/5.74 = X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5470_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W )
% 5.46/5.74 = ( semiri5074537144036343181t_real @ X4 ) )
% 5.46/5.74 = ( ( power_power_nat @ B2 @ W )
% 5.46/5.74 = X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5471_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B2 ) @ W )
% 5.46/5.74 = ( semiri681578069525770553at_rat @ X4 ) )
% 5.46/5.74 = ( ( power_power_nat @ B2 @ W )
% 5.46/5.74 = X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5472_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W )
% 5.46/5.74 = ( semiri1316708129612266289at_nat @ X4 ) )
% 5.46/5.74 = ( ( power_power_nat @ B2 @ W )
% 5.46/5.74 = X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5473_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W )
% 5.46/5.74 = ( semiri1314217659103216013at_int @ X4 ) )
% 5.46/5.74 = ( ( power_power_nat @ B2 @ W )
% 5.46/5.74 = X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_eq_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5474_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ( semiri8010041392384452111omplex @ X4 )
% 5.46/5.74 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B2 ) @ W ) )
% 5.46/5.74 = ( X4
% 5.46/5.74 = ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_eq_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5475_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ( semiri5074537144036343181t_real @ X4 )
% 5.46/5.74 = ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W ) )
% 5.46/5.74 = ( X4
% 5.46/5.74 = ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_eq_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5476_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ( semiri681578069525770553at_rat @ X4 )
% 5.46/5.74 = ( power_power_rat @ ( semiri681578069525770553at_rat @ B2 ) @ W ) )
% 5.46/5.74 = ( X4
% 5.46/5.74 = ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_eq_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5477_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ( semiri1316708129612266289at_nat @ X4 )
% 5.46/5.74 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W ) )
% 5.46/5.74 = ( X4
% 5.46/5.74 = ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_eq_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5478_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ( semiri1314217659103216013at_int @ X4 )
% 5.46/5.74 = ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W ) )
% 5.46/5.74 = ( X4
% 5.46/5.74 = ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_eq_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5479_zabs__less__one__iff,axiom,
% 5.46/5.74 ! [Z: int] :
% 5.46/5.74 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.46/5.74 = ( Z = zero_zero_int ) ) ).
% 5.46/5.74
% 5.46/5.74 % zabs_less_one_iff
% 5.46/5.74 thf(fact_5480_log__one,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( log @ A @ one_one_real )
% 5.46/5.74 = zero_zero_real ) ).
% 5.46/5.74
% 5.46/5.74 % log_one
% 5.46/5.74 thf(fact_5481_arctan__less__zero__iff,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_real @ ( arctan @ X4 ) @ zero_zero_real )
% 5.46/5.74 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % arctan_less_zero_iff
% 5.46/5.74 thf(fact_5482_zero__less__arctan__iff,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X4 ) )
% 5.46/5.74 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_arctan_iff
% 5.46/5.74 thf(fact_5483_zero__le__arctan__iff,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_le_arctan_iff
% 5.46/5.74 thf(fact_5484_arctan__le__zero__iff,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( arctan @ X4 ) @ zero_zero_real )
% 5.46/5.74 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % arctan_le_zero_iff
% 5.46/5.74 thf(fact_5485_of__nat__of__bool,axiom,
% 5.46/5.74 ! [P: $o] :
% 5.46/5.74 ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.74 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_of_bool
% 5.46/5.74 thf(fact_5486_of__nat__of__bool,axiom,
% 5.46/5.74 ! [P: $o] :
% 5.46/5.74 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.74 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_of_bool
% 5.46/5.74 thf(fact_5487_of__nat__of__bool,axiom,
% 5.46/5.74 ! [P: $o] :
% 5.46/5.74 ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.74 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_of_bool
% 5.46/5.74 thf(fact_5488_of__nat__of__bool,axiom,
% 5.46/5.74 ! [P: $o] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.74 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_of_bool
% 5.46/5.74 thf(fact_5489_of__nat__of__bool,axiom,
% 5.46/5.74 ! [P: $o] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.74 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_of_bool
% 5.46/5.74 thf(fact_5490_of__nat__of__bool,axiom,
% 5.46/5.74 ! [P: $o] :
% 5.46/5.74 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.46/5.74 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_of_bool
% 5.46/5.74 thf(fact_5491_of__nat__le__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.46/5.74 = ( M = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_0_iff
% 5.46/5.74 thf(fact_5492_of__nat__le__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.46/5.74 = ( M = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_0_iff
% 5.46/5.74 thf(fact_5493_of__nat__le__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.46/5.74 = ( M = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_0_iff
% 5.46/5.74 thf(fact_5494_of__nat__le__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.46/5.74 = ( M = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_0_iff
% 5.46/5.74 thf(fact_5495_of__nat__Suc,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.46/5.74 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_Suc
% 5.46/5.74 thf(fact_5496_of__nat__Suc,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.46/5.74 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_Suc
% 5.46/5.74 thf(fact_5497_of__nat__Suc,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.46/5.74 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_Suc
% 5.46/5.74 thf(fact_5498_of__nat__Suc,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.46/5.74 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_Suc
% 5.46/5.74 thf(fact_5499_of__nat__Suc,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.46/5.74 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_Suc
% 5.46/5.74 thf(fact_5500_bit__numeral__Bit0__Suc__iff,axiom,
% 5.46/5.74 ! [M: num,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( suc @ N ) )
% 5.46/5.74 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_Bit0_Suc_iff
% 5.46/5.74 thf(fact_5501_bit__numeral__Bit0__Suc__iff,axiom,
% 5.46/5.74 ! [M: num,N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( suc @ N ) )
% 5.46/5.74 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_Bit0_Suc_iff
% 5.46/5.74 thf(fact_5502_bit__numeral__Bit1__Suc__iff,axiom,
% 5.46/5.74 ! [M: num,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( suc @ N ) )
% 5.46/5.74 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_Bit1_Suc_iff
% 5.46/5.74 thf(fact_5503_bit__numeral__Bit1__Suc__iff,axiom,
% 5.46/5.74 ! [M: num,N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( suc @ N ) )
% 5.46/5.74 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_Bit1_Suc_iff
% 5.46/5.74 thf(fact_5504_log__eq__one,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.74 => ( ( A != one_one_real )
% 5.46/5.74 => ( ( log @ A @ A )
% 5.46/5.74 = one_one_real ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_eq_one
% 5.46/5.74 thf(fact_5505_log__less__cancel__iff,axiom,
% 5.46/5.74 ! [A: real,X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.74 => ( ( ord_less_real @ ( log @ A @ X4 ) @ ( log @ A @ Y3 ) )
% 5.46/5.74 = ( ord_less_real @ X4 @ Y3 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_less_cancel_iff
% 5.46/5.74 thf(fact_5506_log__less__one__cancel__iff,axiom,
% 5.46/5.74 ! [A: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_real @ ( log @ A @ X4 ) @ one_one_real )
% 5.46/5.74 = ( ord_less_real @ X4 @ A ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_less_one_cancel_iff
% 5.46/5.74 thf(fact_5507_one__less__log__cancel__iff,axiom,
% 5.46/5.74 ! [A: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X4 ) )
% 5.46/5.74 = ( ord_less_real @ A @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % one_less_log_cancel_iff
% 5.46/5.74 thf(fact_5508_log__less__zero__cancel__iff,axiom,
% 5.46/5.74 ! [A: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_real @ ( log @ A @ X4 ) @ zero_zero_real )
% 5.46/5.74 = ( ord_less_real @ X4 @ one_one_real ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_less_zero_cancel_iff
% 5.46/5.74 thf(fact_5509_zero__less__log__cancel__iff,axiom,
% 5.46/5.74 ! [A: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X4 ) )
% 5.46/5.74 = ( ord_less_real @ one_one_real @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_log_cancel_iff
% 5.46/5.74 thf(fact_5510_signed__take__bit__nonnegative__iff,axiom,
% 5.46/5.74 ! [N: nat,K: int] :
% 5.46/5.74 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.46/5.74 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % signed_take_bit_nonnegative_iff
% 5.46/5.74 thf(fact_5511_signed__take__bit__negative__iff,axiom,
% 5.46/5.74 ! [N: nat,K: int] :
% 5.46/5.74 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.74 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % signed_take_bit_negative_iff
% 5.46/5.74 thf(fact_5512_of__nat__0__less__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.74 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_less_iff
% 5.46/5.74 thf(fact_5513_of__nat__0__less__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.74 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_less_iff
% 5.46/5.74 thf(fact_5514_of__nat__0__less__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.74 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_less_iff
% 5.46/5.74 thf(fact_5515_of__nat__0__less__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_less_iff
% 5.46/5.74 thf(fact_5516_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 5.46/5.74 = ( ord_less_nat @ ( power_power_nat @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5517_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B2 ) @ W ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_nat @ ( power_power_nat @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5518_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 5.46/5.74 = ( ord_less_nat @ ( power_power_nat @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5519_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 5.46/5.74 = ( ord_less_nat @ ( power_power_nat @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5520_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W ) )
% 5.46/5.74 = ( ord_less_nat @ X4 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_less_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5521_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B2 ) @ W ) )
% 5.46/5.74 = ( ord_less_nat @ X4 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_less_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5522_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W ) )
% 5.46/5.74 = ( ord_less_nat @ X4 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_less_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5523_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W ) )
% 5.46/5.74 = ( ord_less_nat @ X4 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_less_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5524_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [Y3: nat,X4: num,N: nat] :
% 5.46/5.74 ( ( ( semiri8010041392384452111omplex @ Y3 )
% 5.46/5.74 = ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N ) )
% 5.46/5.74 = ( Y3
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_eq_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5525_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [Y3: nat,X4: num,N: nat] :
% 5.46/5.74 ( ( ( semiri5074537144036343181t_real @ Y3 )
% 5.46/5.74 = ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N ) )
% 5.46/5.74 = ( Y3
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_eq_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5526_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [Y3: nat,X4: num,N: nat] :
% 5.46/5.74 ( ( ( semiri681578069525770553at_rat @ Y3 )
% 5.46/5.74 = ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N ) )
% 5.46/5.74 = ( Y3
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_eq_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5527_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [Y3: nat,X4: num,N: nat] :
% 5.46/5.74 ( ( ( semiri1316708129612266289at_nat @ Y3 )
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) )
% 5.46/5.74 = ( Y3
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_eq_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5528_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [Y3: nat,X4: num,N: nat] :
% 5.46/5.74 ( ( ( semiri1314217659103216013at_int @ Y3 )
% 5.46/5.74 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) )
% 5.46/5.74 = ( Y3
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_eq_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5529_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: num,N: nat,Y3: nat] :
% 5.46/5.74 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N )
% 5.46/5.74 = ( semiri8010041392384452111omplex @ Y3 ) )
% 5.46/5.74 = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N )
% 5.46/5.74 = Y3 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_eq_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5530_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: num,N: nat,Y3: nat] :
% 5.46/5.74 ( ( ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N )
% 5.46/5.74 = ( semiri5074537144036343181t_real @ Y3 ) )
% 5.46/5.74 = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N )
% 5.46/5.74 = Y3 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_eq_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5531_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: num,N: nat,Y3: nat] :
% 5.46/5.74 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N )
% 5.46/5.74 = ( semiri681578069525770553at_rat @ Y3 ) )
% 5.46/5.74 = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N )
% 5.46/5.74 = Y3 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_eq_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5532_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: num,N: nat,Y3: nat] :
% 5.46/5.74 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N )
% 5.46/5.74 = ( semiri1316708129612266289at_nat @ Y3 ) )
% 5.46/5.74 = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N )
% 5.46/5.74 = Y3 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_eq_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5533_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: num,N: nat,Y3: nat] :
% 5.46/5.74 ( ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N )
% 5.46/5.74 = ( semiri1314217659103216013at_int @ Y3 ) )
% 5.46/5.74 = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N )
% 5.46/5.74 = Y3 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_eq_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5534_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5535_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B2 ) @ W ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5536_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5537_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.46/5.74 ! [B2: nat,W: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_nat @ ( power_power_nat @ B2 @ W ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_of_nat_power_cancel_iff
% 5.46/5.74 thf(fact_5538_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B2 ) @ W ) )
% 5.46/5.74 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_le_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5539_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B2 ) @ W ) )
% 5.46/5.74 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_le_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5540_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B2 ) @ W ) )
% 5.46/5.74 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_le_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5541_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,B2: nat,W: nat] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B2 ) @ W ) )
% 5.46/5.74 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B2 @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_power_le_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5542_numeral__less__real__of__nat__iff,axiom,
% 5.46/5.74 ! [W: num,N: nat] :
% 5.46/5.74 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.74 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_less_real_of_nat_iff
% 5.46/5.74 thf(fact_5543_real__of__nat__less__numeral__iff,axiom,
% 5.46/5.74 ! [N: nat,W: num] :
% 5.46/5.74 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 5.46/5.74 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_less_numeral_iff
% 5.46/5.74 thf(fact_5544_numeral__le__real__of__nat__iff,axiom,
% 5.46/5.74 ! [N: num,M: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.46/5.74 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_le_real_of_nat_iff
% 5.46/5.74 thf(fact_5545_zero__le__log__cancel__iff,axiom,
% 5.46/5.74 ! [A: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_le_log_cancel_iff
% 5.46/5.74 thf(fact_5546_log__le__zero__cancel__iff,axiom,
% 5.46/5.74 ! [A: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ zero_zero_real )
% 5.46/5.74 = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_le_zero_cancel_iff
% 5.46/5.74 thf(fact_5547_one__le__log__cancel__iff,axiom,
% 5.46/5.74 ! [A: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_real @ A @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % one_le_log_cancel_iff
% 5.46/5.74 thf(fact_5548_log__le__one__cancel__iff,axiom,
% 5.46/5.74 ! [A: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ one_one_real )
% 5.46/5.74 = ( ord_less_eq_real @ X4 @ A ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_le_one_cancel_iff
% 5.46/5.74 thf(fact_5549_log__le__cancel__iff,axiom,
% 5.46/5.74 ! [A: real,X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ ( log @ A @ Y3 ) )
% 5.46/5.74 = ( ord_less_eq_real @ X4 @ Y3 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_le_cancel_iff
% 5.46/5.74 thf(fact_5550_bit__numeral__simps_I2_J,axiom,
% 5.46/5.74 ! [W: num,N: num] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_simps(2)
% 5.46/5.74 thf(fact_5551_bit__numeral__simps_I2_J,axiom,
% 5.46/5.74 ! [W: num,N: num] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_simps(2)
% 5.46/5.74 thf(fact_5552_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.46/5.74 ! [W: num,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.46/5.74 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_minus_numeral_Bit0_Suc_iff
% 5.46/5.74 thf(fact_5553_bit__numeral__simps_I3_J,axiom,
% 5.46/5.74 ! [W: num,N: num] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_simps(3)
% 5.46/5.74 thf(fact_5554_bit__numeral__simps_I3_J,axiom,
% 5.46/5.74 ! [W: num,N: num] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_simps(3)
% 5.46/5.74 thf(fact_5555_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.46/5.74 ! [W: num,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.46/5.74 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_minus_numeral_Bit1_Suc_iff
% 5.46/5.74 thf(fact_5556_of__nat__zero__less__power__iff,axiom,
% 5.46/5.74 ! [X4: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X4 ) @ N ) )
% 5.46/5.74 = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_zero_less_power_iff
% 5.46/5.74 thf(fact_5557_of__nat__zero__less__power__iff,axiom,
% 5.46/5.74 ! [X4: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X4 ) @ N ) )
% 5.46/5.74 = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_zero_less_power_iff
% 5.46/5.74 thf(fact_5558_of__nat__zero__less__power__iff,axiom,
% 5.46/5.74 ! [X4: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ N ) )
% 5.46/5.74 = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_zero_less_power_iff
% 5.46/5.74 thf(fact_5559_of__nat__zero__less__power__iff,axiom,
% 5.46/5.74 ! [X4: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X4 ) @ N ) )
% 5.46/5.74 = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_zero_less_power_iff
% 5.46/5.74 thf(fact_5560_bit__0,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 5.46/5.74 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_0
% 5.46/5.74 thf(fact_5561_bit__0,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 5.46/5.74 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_0
% 5.46/5.74 thf(fact_5562_bit__0,axiom,
% 5.46/5.74 ! [A: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 5.46/5.74 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_0
% 5.46/5.74 thf(fact_5563_log__pow__cancel,axiom,
% 5.46/5.74 ! [A: real,B2: nat] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.74 => ( ( A != one_one_real )
% 5.46/5.74 => ( ( log @ A @ ( power_power_real @ A @ B2 ) )
% 5.46/5.74 = ( semiri5074537144036343181t_real @ B2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_pow_cancel
% 5.46/5.74 thf(fact_5564_bit__minus__numeral__int_I1_J,axiom,
% 5.46/5.74 ! [W: num,N: num] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_minus_numeral_int(1)
% 5.46/5.74 thf(fact_5565_bit__minus__numeral__int_I2_J,axiom,
% 5.46/5.74 ! [W: num,N: num] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.74 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_minus_numeral_int(2)
% 5.46/5.74 thf(fact_5566_even__of__nat,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.46/5.74 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % even_of_nat
% 5.46/5.74 thf(fact_5567_even__of__nat,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.74 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % even_of_nat
% 5.46/5.74 thf(fact_5568_even__of__nat,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % even_of_nat
% 5.46/5.74 thf(fact_5569_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [I: num,N: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 5.46/5.74 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_less_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5570_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [I: num,N: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_less_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5571_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [I: num,N: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 5.46/5.74 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_less_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5572_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [I: num,N: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 5.46/5.74 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_less_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5573_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,I: num,N: nat] :
% 5.46/5.74 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.46/5.74 = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5574_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,I: num,N: nat] :
% 5.46/5.74 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.46/5.74 = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5575_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,I: num,N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.46/5.74 = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5576_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,I: num,N: nat] :
% 5.46/5.74 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.46/5.74 = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5577_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [I: num,N: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_le_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5578_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [I: num,N: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_le_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5579_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [I: num,N: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_le_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5580_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.46/5.74 ! [I: num,N: nat,X4: nat] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_power_le_of_nat_cancel_iff
% 5.46/5.74 thf(fact_5581_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,I: num,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.46/5.74 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5582_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,I: num,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.46/5.74 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5583_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,I: num,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.46/5.74 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5584_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.46/5.74 ! [X4: nat,I: num,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.46/5.74 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_le_numeral_power_cancel_iff
% 5.46/5.74 thf(fact_5585_bit__mod__2__iff,axiom,
% 5.46/5.74 ! [A: code_integer,N: nat] :
% 5.46/5.74 ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N )
% 5.46/5.74 = ( ( N = zero_zero_nat )
% 5.46/5.74 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_mod_2_iff
% 5.46/5.74 thf(fact_5586_bit__mod__2__iff,axiom,
% 5.46/5.74 ! [A: int,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N )
% 5.46/5.74 = ( ( N = zero_zero_nat )
% 5.46/5.74 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_mod_2_iff
% 5.46/5.74 thf(fact_5587_bit__mod__2__iff,axiom,
% 5.46/5.74 ! [A: nat,N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.46/5.74 = ( ( N = zero_zero_nat )
% 5.46/5.74 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_mod_2_iff
% 5.46/5.74 thf(fact_5588_bit__numeral__iff,axiom,
% 5.46/5.74 ! [M: num,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N )
% 5.46/5.74 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_iff
% 5.46/5.74 thf(fact_5589_bit__numeral__iff,axiom,
% 5.46/5.74 ! [M: num,N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N )
% 5.46/5.74 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_iff
% 5.46/5.74 thf(fact_5590_bit__of__nat__iff__bit,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M ) @ N )
% 5.46/5.74 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_of_nat_iff_bit
% 5.46/5.74 thf(fact_5591_bit__of__nat__iff__bit,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M ) @ N )
% 5.46/5.74 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_of_nat_iff_bit
% 5.46/5.74 thf(fact_5592_bit__disjunctive__add__iff,axiom,
% 5.46/5.74 ! [A: int,B2: int,N: nat] :
% 5.46/5.74 ( ! [N4: nat] :
% 5.46/5.74 ( ~ ( bit_se1146084159140164899it_int @ A @ N4 )
% 5.46/5.74 | ~ ( bit_se1146084159140164899it_int @ B2 @ N4 ) )
% 5.46/5.74 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B2 ) @ N )
% 5.46/5.74 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.46/5.74 | ( bit_se1146084159140164899it_int @ B2 @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_disjunctive_add_iff
% 5.46/5.74 thf(fact_5593_bit__disjunctive__add__iff,axiom,
% 5.46/5.74 ! [A: nat,B2: nat,N: nat] :
% 5.46/5.74 ( ! [N4: nat] :
% 5.46/5.74 ( ~ ( bit_se1148574629649215175it_nat @ A @ N4 )
% 5.46/5.74 | ~ ( bit_se1148574629649215175it_nat @ B2 @ N4 ) )
% 5.46/5.74 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B2 ) @ N )
% 5.46/5.74 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.46/5.74 | ( bit_se1148574629649215175it_nat @ B2 @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_disjunctive_add_iff
% 5.46/5.74 thf(fact_5594_real__arch__simple,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ? [N4: nat] : ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ N4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_arch_simple
% 5.46/5.74 thf(fact_5595_real__arch__simple,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ? [N4: nat] : ( ord_less_eq_rat @ X4 @ ( semiri681578069525770553at_rat @ N4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_arch_simple
% 5.46/5.74 thf(fact_5596_reals__Archimedean2,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ? [N4: nat] : ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ N4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % reals_Archimedean2
% 5.46/5.74 thf(fact_5597_reals__Archimedean2,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ? [N4: nat] : ( ord_less_rat @ X4 @ ( semiri681578069525770553at_rat @ N4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % reals_Archimedean2
% 5.46/5.74 thf(fact_5598_mult__of__nat__commute,axiom,
% 5.46/5.74 ! [X4: nat,Y3: complex] :
% 5.46/5.74 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X4 ) @ Y3 )
% 5.46/5.74 = ( times_times_complex @ Y3 @ ( semiri8010041392384452111omplex @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mult_of_nat_commute
% 5.46/5.74 thf(fact_5599_mult__of__nat__commute,axiom,
% 5.46/5.74 ! [X4: nat,Y3: real] :
% 5.46/5.74 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ Y3 )
% 5.46/5.74 = ( times_times_real @ Y3 @ ( semiri5074537144036343181t_real @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mult_of_nat_commute
% 5.46/5.74 thf(fact_5600_mult__of__nat__commute,axiom,
% 5.46/5.74 ! [X4: nat,Y3: rat] :
% 5.46/5.74 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X4 ) @ Y3 )
% 5.46/5.74 = ( times_times_rat @ Y3 @ ( semiri681578069525770553at_rat @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mult_of_nat_commute
% 5.46/5.74 thf(fact_5601_mult__of__nat__commute,axiom,
% 5.46/5.74 ! [X4: nat,Y3: nat] :
% 5.46/5.74 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ Y3 )
% 5.46/5.74 = ( times_times_nat @ Y3 @ ( semiri1316708129612266289at_nat @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mult_of_nat_commute
% 5.46/5.74 thf(fact_5602_mult__of__nat__commute,axiom,
% 5.46/5.74 ! [X4: nat,Y3: int] :
% 5.46/5.74 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X4 ) @ Y3 )
% 5.46/5.74 = ( times_times_int @ Y3 @ ( semiri1314217659103216013at_int @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mult_of_nat_commute
% 5.46/5.74 thf(fact_5603_bit__and__iff,axiom,
% 5.46/5.74 ! [A: int,B2: int,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ A @ B2 ) @ N )
% 5.46/5.74 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.46/5.74 & ( bit_se1146084159140164899it_int @ B2 @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_and_iff
% 5.46/5.74 thf(fact_5604_bit__and__iff,axiom,
% 5.46/5.74 ! [A: nat,B2: nat,N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( bit_se727722235901077358nd_nat @ A @ B2 ) @ N )
% 5.46/5.74 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.46/5.74 & ( bit_se1148574629649215175it_nat @ B2 @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_and_iff
% 5.46/5.74 thf(fact_5605_bit__and__int__iff,axiom,
% 5.46/5.74 ! [K: int,L2: int,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N )
% 5.46/5.74 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.46/5.74 & ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_and_int_iff
% 5.46/5.74 thf(fact_5606_arctan__less__iff,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_real @ ( arctan @ X4 ) @ ( arctan @ Y3 ) )
% 5.46/5.74 = ( ord_less_real @ X4 @ Y3 ) ) ).
% 5.46/5.74
% 5.46/5.74 % arctan_less_iff
% 5.46/5.74 thf(fact_5607_arctan__monotone,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.74 => ( ord_less_real @ ( arctan @ X4 ) @ ( arctan @ Y3 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % arctan_monotone
% 5.46/5.74 thf(fact_5608_arctan__le__iff,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( arctan @ X4 ) @ ( arctan @ Y3 ) )
% 5.46/5.74 = ( ord_less_eq_real @ X4 @ Y3 ) ) ).
% 5.46/5.74
% 5.46/5.74 % arctan_le_iff
% 5.46/5.74 thf(fact_5609_arctan__monotone_H,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.74 => ( ord_less_eq_real @ ( arctan @ X4 ) @ ( arctan @ Y3 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % arctan_monotone'
% 5.46/5.74 thf(fact_5610_bit__unset__bit__iff,axiom,
% 5.46/5.74 ! [M: nat,A: int,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( bit_se4203085406695923979it_int @ M @ A ) @ N )
% 5.46/5.74 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.46/5.74 & ( M != N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_unset_bit_iff
% 5.46/5.74 thf(fact_5611_bit__unset__bit__iff,axiom,
% 5.46/5.74 ! [M: nat,A: nat,N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( bit_se4205575877204974255it_nat @ M @ A ) @ N )
% 5.46/5.74 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.46/5.74 & ( M != N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_unset_bit_iff
% 5.46/5.74 thf(fact_5612_less__log__of__power,axiom,
% 5.46/5.74 ! [B2: real,N: nat,M: real] :
% 5.46/5.74 ( ( ord_less_real @ ( power_power_real @ B2 @ N ) @ M )
% 5.46/5.74 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.74 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B2 @ M ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % less_log_of_power
% 5.46/5.74 thf(fact_5613_log__of__power__eq,axiom,
% 5.46/5.74 ! [M: nat,B2: real,N: nat] :
% 5.46/5.74 ( ( ( semiri5074537144036343181t_real @ M )
% 5.46/5.74 = ( power_power_real @ B2 @ N ) )
% 5.46/5.74 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.74 => ( ( semiri5074537144036343181t_real @ N )
% 5.46/5.74 = ( log @ B2 @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_of_power_eq
% 5.46/5.74 thf(fact_5614_of__nat__less__of__int__iff,axiom,
% 5.46/5.74 ! [N: nat,X4: int] :
% 5.46/5.74 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X4 ) )
% 5.46/5.74 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_of_int_iff
% 5.46/5.74 thf(fact_5615_of__nat__less__of__int__iff,axiom,
% 5.46/5.74 ! [N: nat,X4: int] :
% 5.46/5.74 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_of_int_iff
% 5.46/5.74 thf(fact_5616_of__nat__less__of__int__iff,axiom,
% 5.46/5.74 ! [N: nat,X4: int] :
% 5.46/5.74 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X4 ) )
% 5.46/5.74 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_of_int_iff
% 5.46/5.74 thf(fact_5617_le__log__of__power,axiom,
% 5.46/5.74 ! [B2: real,N: nat,M: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( power_power_real @ B2 @ N ) @ M )
% 5.46/5.74 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.74 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B2 @ M ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % le_log_of_power
% 5.46/5.74 thf(fact_5618_log__base__pow,axiom,
% 5.46/5.74 ! [A: real,N: nat,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.74 => ( ( log @ ( power_power_real @ A @ N ) @ X4 )
% 5.46/5.74 = ( divide_divide_real @ ( log @ A @ X4 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_base_pow
% 5.46/5.74 thf(fact_5619_log__nat__power,axiom,
% 5.46/5.74 ! [X4: real,B2: real,N: nat] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( log @ B2 @ ( power_power_real @ X4 @ N ) )
% 5.46/5.74 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B2 @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_nat_power
% 5.46/5.74 thf(fact_5620_not__bit__1__Suc,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % not_bit_1_Suc
% 5.46/5.74 thf(fact_5621_not__bit__1__Suc,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % not_bit_1_Suc
% 5.46/5.74 thf(fact_5622_bit__1__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ one_one_int @ N )
% 5.46/5.74 = ( N = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_1_iff
% 5.46/5.74 thf(fact_5623_bit__1__iff,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N )
% 5.46/5.74 = ( N = zero_zero_nat ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_1_iff
% 5.46/5.74 thf(fact_5624_bit__numeral__simps_I1_J,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_simps(1)
% 5.46/5.74 thf(fact_5625_bit__numeral__simps_I1_J,axiom,
% 5.46/5.74 ! [N: num] :
% 5.46/5.74 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_numeral_simps(1)
% 5.46/5.74 thf(fact_5626_of__nat__0__le__iff,axiom,
% 5.46/5.74 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_le_iff
% 5.46/5.74 thf(fact_5627_of__nat__0__le__iff,axiom,
% 5.46/5.74 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_le_iff
% 5.46/5.74 thf(fact_5628_of__nat__0__le__iff,axiom,
% 5.46/5.74 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_le_iff
% 5.46/5.74 thf(fact_5629_of__nat__0__le__iff,axiom,
% 5.46/5.74 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_0_le_iff
% 5.46/5.74 thf(fact_5630_of__nat__less__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_0_iff
% 5.46/5.74 thf(fact_5631_of__nat__less__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_0_iff
% 5.46/5.74 thf(fact_5632_of__nat__less__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_0_iff
% 5.46/5.74 thf(fact_5633_of__nat__less__0__iff,axiom,
% 5.46/5.74 ! [M: nat] :
% 5.46/5.74 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_0_iff
% 5.46/5.74 thf(fact_5634_bit__take__bit__iff,axiom,
% 5.46/5.74 ! [M: nat,A: int,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N )
% 5.46/5.74 = ( ( ord_less_nat @ N @ M )
% 5.46/5.74 & ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_take_bit_iff
% 5.46/5.74 thf(fact_5635_bit__take__bit__iff,axiom,
% 5.46/5.74 ! [M: nat,A: nat,N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N )
% 5.46/5.74 = ( ( ord_less_nat @ N @ M )
% 5.46/5.74 & ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_take_bit_iff
% 5.46/5.74 thf(fact_5636_of__nat__neq__0,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.46/5.74 != zero_zero_complex ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_neq_0
% 5.46/5.74 thf(fact_5637_of__nat__neq__0,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.46/5.74 != zero_zero_real ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_neq_0
% 5.46/5.74 thf(fact_5638_of__nat__neq__0,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.46/5.74 != zero_zero_rat ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_neq_0
% 5.46/5.74 thf(fact_5639_of__nat__neq__0,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.46/5.74 != zero_zero_nat ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_neq_0
% 5.46/5.74 thf(fact_5640_of__nat__neq__0,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.46/5.74 != zero_zero_int ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_neq_0
% 5.46/5.74 thf(fact_5641_bit__of__bool__iff,axiom,
% 5.46/5.74 ! [B2: $o,N: nat] :
% 5.46/5.74 ( ( bit_se9216721137139052372nteger @ ( zero_n356916108424825756nteger @ B2 ) @ N )
% 5.46/5.74 = ( B2
% 5.46/5.74 & ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_of_bool_iff
% 5.46/5.74 thf(fact_5642_bit__of__bool__iff,axiom,
% 5.46/5.74 ! [B2: $o,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ N )
% 5.46/5.74 = ( B2
% 5.46/5.74 & ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_of_bool_iff
% 5.46/5.74 thf(fact_5643_bit__of__bool__iff,axiom,
% 5.46/5.74 ! [B2: $o,N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ N )
% 5.46/5.74 = ( B2
% 5.46/5.74 & ( N = zero_zero_nat ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_of_bool_iff
% 5.46/5.74 thf(fact_5644_div__mult2__eq_H,axiom,
% 5.46/5.74 ! [A: nat,M: nat,N: nat] :
% 5.46/5.74 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.46/5.74 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % div_mult2_eq'
% 5.46/5.74 thf(fact_5645_div__mult2__eq_H,axiom,
% 5.46/5.74 ! [A: int,M: nat,N: nat] :
% 5.46/5.74 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.74 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % div_mult2_eq'
% 5.46/5.74 thf(fact_5646_less__imp__of__nat__less,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ M @ N )
% 5.46/5.74 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % less_imp_of_nat_less
% 5.46/5.74 thf(fact_5647_less__imp__of__nat__less,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ M @ N )
% 5.46/5.74 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % less_imp_of_nat_less
% 5.46/5.74 thf(fact_5648_less__imp__of__nat__less,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ M @ N )
% 5.46/5.74 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % less_imp_of_nat_less
% 5.46/5.74 thf(fact_5649_less__imp__of__nat__less,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ M @ N )
% 5.46/5.74 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % less_imp_of_nat_less
% 5.46/5.74 thf(fact_5650_of__nat__less__imp__less,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.74 => ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_imp_less
% 5.46/5.74 thf(fact_5651_of__nat__less__imp__less,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.74 => ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_imp_less
% 5.46/5.74 thf(fact_5652_of__nat__less__imp__less,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.74 => ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_imp_less
% 5.46/5.74 thf(fact_5653_of__nat__less__imp__less,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 => ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_imp_less
% 5.46/5.74 thf(fact_5654_of__nat__mono,axiom,
% 5.46/5.74 ! [I: nat,J: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.74 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mono
% 5.46/5.74 thf(fact_5655_of__nat__mono,axiom,
% 5.46/5.74 ! [I: nat,J: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.74 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mono
% 5.46/5.74 thf(fact_5656_of__nat__mono,axiom,
% 5.46/5.74 ! [I: nat,J: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.74 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mono
% 5.46/5.74 thf(fact_5657_of__nat__mono,axiom,
% 5.46/5.74 ! [I: nat,J: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.74 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mono
% 5.46/5.74 thf(fact_5658_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.74 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.46/5.74 thf(fact_5659_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.74 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.46/5.74 thf(fact_5660_log__def,axiom,
% 5.46/5.74 ( log
% 5.46/5.74 = ( ^ [A4: real,X: real] : ( divide_divide_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ A4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_def
% 5.46/5.74 thf(fact_5661_of__nat__dvd__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.46/5.74 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_dvd_iff
% 5.46/5.74 thf(fact_5662_of__nat__dvd__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.46/5.74 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_dvd_iff
% 5.46/5.74 thf(fact_5663_of__nat__dvd__iff,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.74 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_dvd_iff
% 5.46/5.74 thf(fact_5664_signed__take__bit__eq__if__positive,axiom,
% 5.46/5.74 ! [A: int,N: nat] :
% 5.46/5.74 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 5.46/5.74 => ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.46/5.74 = ( bit_se2923211474154528505it_int @ N @ A ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % signed_take_bit_eq_if_positive
% 5.46/5.74 thf(fact_5665_abs__zmult__eq__1,axiom,
% 5.46/5.74 ! [M: int,N: int] :
% 5.46/5.74 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 5.46/5.74 = one_one_int )
% 5.46/5.74 => ( ( abs_abs_int @ M )
% 5.46/5.74 = one_one_int ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_zmult_eq_1
% 5.46/5.74 thf(fact_5666_of__nat__mod,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.74 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mod
% 5.46/5.74 thf(fact_5667_of__nat__mod,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.74 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mod
% 5.46/5.74 thf(fact_5668_of__nat__mod,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 5.46/5.74 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mod
% 5.46/5.74 thf(fact_5669_abs__div,axiom,
% 5.46/5.74 ! [Y3: int,X4: int] :
% 5.46/5.74 ( ( dvd_dvd_int @ Y3 @ X4 )
% 5.46/5.74 => ( ( abs_abs_int @ ( divide_divide_int @ X4 @ Y3 ) )
% 5.46/5.74 = ( divide_divide_int @ ( abs_abs_int @ X4 ) @ ( abs_abs_int @ Y3 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_div
% 5.46/5.74 thf(fact_5670_log2__of__power__eq,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( M
% 5.46/5.74 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.74 => ( ( semiri5074537144036343181t_real @ N )
% 5.46/5.74 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log2_of_power_eq
% 5.46/5.74 thf(fact_5671_log__of__power__less,axiom,
% 5.46/5.74 ! [M: nat,B2: real,N: nat] :
% 5.46/5.74 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B2 @ N ) )
% 5.46/5.74 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.74 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.74 => ( ord_less_real @ ( log @ B2 @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_of_power_less
% 5.46/5.74 thf(fact_5672_take__bit__of__nat,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.46/5.74 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % take_bit_of_nat
% 5.46/5.74 thf(fact_5673_take__bit__of__nat,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.46/5.74 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % take_bit_of_nat
% 5.46/5.74 thf(fact_5674_of__nat__and__eq,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.46/5.74 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_and_eq
% 5.46/5.74 thf(fact_5675_of__nat__and__eq,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.46/5.74 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_and_eq
% 5.46/5.74 thf(fact_5676_of__nat__mask__eq,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.46/5.74 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mask_eq
% 5.46/5.74 thf(fact_5677_of__nat__mask__eq,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.46/5.74 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_mask_eq
% 5.46/5.74 thf(fact_5678_log__of__power__le,axiom,
% 5.46/5.74 ! [M: nat,B2: real,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B2 @ N ) )
% 5.46/5.74 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.74 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.74 => ( ord_less_eq_real @ ( log @ B2 @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_of_power_le
% 5.46/5.74 thf(fact_5679_ex__less__of__nat__mult,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ? [N4: nat] : ( ord_less_real @ Y3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % ex_less_of_nat_mult
% 5.46/5.74 thf(fact_5680_ex__less__of__nat__mult,axiom,
% 5.46/5.74 ! [X4: rat,Y3: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.46/5.74 => ? [N4: nat] : ( ord_less_rat @ Y3 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N4 ) @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % ex_less_of_nat_mult
% 5.46/5.74 thf(fact_5681_of__nat__diff,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.74 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.74 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_diff
% 5.46/5.74 thf(fact_5682_of__nat__diff,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.74 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.74 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_diff
% 5.46/5.74 thf(fact_5683_of__nat__diff,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.74 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.74 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_diff
% 5.46/5.74 thf(fact_5684_of__nat__diff,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.74 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.74 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_diff
% 5.46/5.74 thf(fact_5685_of__nat__diff,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.74 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.46/5.74 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_diff
% 5.46/5.74 thf(fact_5686_bit__not__int__iff_H,axiom,
% 5.46/5.74 ! [K: int,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.46/5.74 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_not_int_iff'
% 5.46/5.74 thf(fact_5687_exp__of__nat__mult,axiom,
% 5.46/5.74 ! [N: nat,X4: complex] :
% 5.46/5.74 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X4 ) )
% 5.46/5.74 = ( power_power_complex @ ( exp_complex @ X4 ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % exp_of_nat_mult
% 5.46/5.74 thf(fact_5688_exp__of__nat__mult,axiom,
% 5.46/5.74 ! [N: nat,X4: real] :
% 5.46/5.74 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X4 ) )
% 5.46/5.74 = ( power_power_real @ ( exp_real @ X4 ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % exp_of_nat_mult
% 5.46/5.74 thf(fact_5689_exp__of__nat2__mult,axiom,
% 5.46/5.74 ! [X4: complex,N: nat] :
% 5.46/5.74 ( ( exp_complex @ ( times_times_complex @ X4 @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.46/5.74 = ( power_power_complex @ ( exp_complex @ X4 ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % exp_of_nat2_mult
% 5.46/5.74 thf(fact_5690_exp__of__nat2__mult,axiom,
% 5.46/5.74 ! [X4: real,N: nat] :
% 5.46/5.74 ( ( exp_real @ ( times_times_real @ X4 @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.74 = ( power_power_real @ ( exp_real @ X4 ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % exp_of_nat2_mult
% 5.46/5.74 thf(fact_5691_zabs__def,axiom,
% 5.46/5.74 ( abs_abs_int
% 5.46/5.74 = ( ^ [I2: int] : ( if_int @ ( ord_less_int @ I2 @ zero_zero_int ) @ ( uminus_uminus_int @ I2 ) @ I2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % zabs_def
% 5.46/5.74 thf(fact_5692_reals__Archimedean3,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ! [Y5: real] :
% 5.46/5.74 ? [N4: nat] : ( ord_less_real @ Y5 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % reals_Archimedean3
% 5.46/5.74 thf(fact_5693_log__ln,axiom,
% 5.46/5.74 ( ln_ln_real
% 5.46/5.74 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_ln
% 5.46/5.74 thf(fact_5694_real__of__nat__div4,axiom,
% 5.46/5.74 ! [N: nat,X4: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X4 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_div4
% 5.46/5.74 thf(fact_5695_abs__mod__less,axiom,
% 5.46/5.74 ! [L2: int,K: int] :
% 5.46/5.74 ( ( L2 != zero_zero_int )
% 5.46/5.74 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % abs_mod_less
% 5.46/5.74 thf(fact_5696_real__of__nat__div,axiom,
% 5.46/5.74 ! [D: nat,N: nat] :
% 5.46/5.74 ( ( dvd_dvd_nat @ D @ N )
% 5.46/5.74 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 5.46/5.74 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_div
% 5.46/5.74 thf(fact_5697_less__log2__of__power,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.46/5.74 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % less_log2_of_power
% 5.46/5.74 thf(fact_5698_le__log2__of__power,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.46/5.74 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % le_log2_of_power
% 5.46/5.74 thf(fact_5699_flip__bit__eq__if,axiom,
% 5.46/5.74 ( bit_se2159334234014336723it_int
% 5.46/5.74 = ( ^ [N2: nat,A4: int] : ( if_nat_int_int @ ( bit_se1146084159140164899it_int @ A4 @ N2 ) @ bit_se4203085406695923979it_int @ bit_se7879613467334960850it_int @ N2 @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % flip_bit_eq_if
% 5.46/5.74 thf(fact_5700_flip__bit__eq__if,axiom,
% 5.46/5.74 ( bit_se2161824704523386999it_nat
% 5.46/5.74 = ( ^ [N2: nat,A4: nat] : ( if_nat_nat_nat @ ( bit_se1148574629649215175it_nat @ A4 @ N2 ) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ N2 @ A4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % flip_bit_eq_if
% 5.46/5.74 thf(fact_5701_log2__of__power__less,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.74 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.74 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log2_of_power_less
% 5.46/5.74 thf(fact_5702_log__base__change,axiom,
% 5.46/5.74 ! [A: real,B2: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.74 => ( ( A != one_one_real )
% 5.46/5.74 => ( ( log @ B2 @ X4 )
% 5.46/5.74 = ( divide_divide_real @ ( log @ A @ X4 ) @ ( log @ A @ B2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_base_change
% 5.46/5.74 thf(fact_5703_mod__mult2__eq_H,axiom,
% 5.46/5.74 ! [A: code_integer,M: nat,N: nat] :
% 5.46/5.74 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.46/5.74 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mod_mult2_eq'
% 5.46/5.74 thf(fact_5704_mod__mult2__eq_H,axiom,
% 5.46/5.74 ! [A: nat,M: nat,N: nat] :
% 5.46/5.74 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.46/5.74 = ( 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 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mod_mult2_eq'
% 5.46/5.74 thf(fact_5705_mod__mult2__eq_H,axiom,
% 5.46/5.74 ! [A: int,M: nat,N: nat] :
% 5.46/5.74 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.74 = ( 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 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % mod_mult2_eq'
% 5.46/5.74 thf(fact_5706_bit__imp__take__bit__positive,axiom,
% 5.46/5.74 ! [N: nat,M: nat,K: int] :
% 5.46/5.74 ( ( ord_less_nat @ N @ M )
% 5.46/5.74 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.46/5.74 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_imp_take_bit_positive
% 5.46/5.74 thf(fact_5707_field__char__0__class_Oof__nat__div,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.74 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % field_char_0_class.of_nat_div
% 5.46/5.74 thf(fact_5708_field__char__0__class_Oof__nat__div,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.74 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % field_char_0_class.of_nat_div
% 5.46/5.74 thf(fact_5709_field__char__0__class_Oof__nat__div,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.46/5.74 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % field_char_0_class.of_nat_div
% 5.46/5.74 thf(fact_5710_bit__concat__bit__iff,axiom,
% 5.46/5.74 ! [M: nat,K: int,L2: int,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 5.46/5.74 = ( ( ( ord_less_nat @ N @ M )
% 5.46/5.74 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.46/5.74 | ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.74 & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_concat_bit_iff
% 5.46/5.74 thf(fact_5711_nat__less__real__le,axiom,
% 5.46/5.74 ( ord_less_nat
% 5.46/5.74 = ( ^ [N2: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % nat_less_real_le
% 5.46/5.74 thf(fact_5712_nat__le__real__less,axiom,
% 5.46/5.74 ( ord_less_eq_nat
% 5.46/5.74 = ( ^ [N2: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % nat_le_real_less
% 5.46/5.74 thf(fact_5713_zdvd__mult__cancel1,axiom,
% 5.46/5.74 ! [M: int,N: int] :
% 5.46/5.74 ( ( M != zero_zero_int )
% 5.46/5.74 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 5.46/5.74 = ( ( abs_abs_int @ N )
% 5.46/5.74 = one_one_int ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % zdvd_mult_cancel1
% 5.46/5.74 thf(fact_5714_log2__of__power__le,axiom,
% 5.46/5.74 ! [M: nat,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.74 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.74 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log2_of_power_le
% 5.46/5.74 thf(fact_5715_real__of__nat__div__aux,axiom,
% 5.46/5.74 ! [X4: nat,D: nat] :
% 5.46/5.74 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.46/5.74 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X4 @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X4 @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_div_aux
% 5.46/5.74 thf(fact_5716_signed__take__bit__eq__concat__bit,axiom,
% 5.46/5.74 ( bit_ri631733984087533419it_int
% 5.46/5.74 = ( ^ [N2: nat,K3: int] : ( bit_concat_bit @ N2 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % signed_take_bit_eq_concat_bit
% 5.46/5.74 thf(fact_5717_exp__eq__0__imp__not__bit,axiom,
% 5.46/5.74 ! [N: nat,A: int] :
% 5.46/5.74 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 = zero_zero_int )
% 5.46/5.74 => ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % exp_eq_0_imp_not_bit
% 5.46/5.74 thf(fact_5718_exp__eq__0__imp__not__bit,axiom,
% 5.46/5.74 ! [N: nat,A: nat] :
% 5.46/5.74 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 = zero_zero_nat )
% 5.46/5.74 => ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % exp_eq_0_imp_not_bit
% 5.46/5.74 thf(fact_5719_bit__Suc,axiom,
% 5.46/5.74 ! [A: int,N: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N ) )
% 5.46/5.74 = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_Suc
% 5.46/5.74 thf(fact_5720_bit__Suc,axiom,
% 5.46/5.74 ! [A: nat,N: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N ) )
% 5.46/5.74 = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_Suc
% 5.46/5.74 thf(fact_5721_stable__imp__bit__iff__odd,axiom,
% 5.46/5.74 ! [A: code_integer,N: nat] :
% 5.46/5.74 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.74 = A )
% 5.46/5.74 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.46/5.74 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % stable_imp_bit_iff_odd
% 5.46/5.74 thf(fact_5722_stable__imp__bit__iff__odd,axiom,
% 5.46/5.74 ! [A: int,N: nat] :
% 5.46/5.74 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.74 = A )
% 5.46/5.74 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.46/5.74 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % stable_imp_bit_iff_odd
% 5.46/5.74 thf(fact_5723_stable__imp__bit__iff__odd,axiom,
% 5.46/5.74 ! [A: nat,N: nat] :
% 5.46/5.74 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.74 = A )
% 5.46/5.74 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.46/5.74 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % stable_imp_bit_iff_odd
% 5.46/5.74 thf(fact_5724_bit__iff__idd__imp__stable,axiom,
% 5.46/5.74 ! [A: code_integer] :
% 5.46/5.74 ( ! [N4: nat] :
% 5.46/5.74 ( ( bit_se9216721137139052372nteger @ A @ N4 )
% 5.46/5.74 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.46/5.74 => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_iff_idd_imp_stable
% 5.46/5.74 thf(fact_5725_bit__iff__idd__imp__stable,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ! [N4: nat] :
% 5.46/5.74 ( ( bit_se1146084159140164899it_int @ A @ N4 )
% 5.46/5.74 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.46/5.74 => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_iff_idd_imp_stable
% 5.46/5.74 thf(fact_5726_bit__iff__idd__imp__stable,axiom,
% 5.46/5.74 ! [A: nat] :
% 5.46/5.74 ( ! [N4: nat] :
% 5.46/5.74 ( ( bit_se1148574629649215175it_nat @ A @ N4 )
% 5.46/5.74 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.46/5.74 => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.74 = A ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_iff_idd_imp_stable
% 5.46/5.74 thf(fact_5727_log__mult,axiom,
% 5.46/5.74 ! [A: real,X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.74 => ( ( A != one_one_real )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.74 => ( ( log @ A @ ( times_times_real @ X4 @ Y3 ) )
% 5.46/5.74 = ( plus_plus_real @ ( log @ A @ X4 ) @ ( log @ A @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_mult
% 5.46/5.74 thf(fact_5728_nat__approx__posE,axiom,
% 5.46/5.74 ! [E: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.74 => ~ ! [N4: nat] :
% 5.46/5.74 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ E ) ) ).
% 5.46/5.74
% 5.46/5.74 % nat_approx_posE
% 5.46/5.74 thf(fact_5729_nat__approx__posE,axiom,
% 5.46/5.74 ! [E: rat] :
% 5.46/5.74 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.46/5.74 => ~ ! [N4: nat] :
% 5.46/5.74 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N4 ) ) ) @ E ) ) ).
% 5.46/5.74
% 5.46/5.74 % nat_approx_posE
% 5.46/5.74 thf(fact_5730_of__nat__less__two__power,axiom,
% 5.46/5.74 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_two_power
% 5.46/5.74 thf(fact_5731_of__nat__less__two__power,axiom,
% 5.46/5.74 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_two_power
% 5.46/5.74 thf(fact_5732_of__nat__less__two__power,axiom,
% 5.46/5.74 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_nat_less_two_power
% 5.46/5.74 thf(fact_5733_int__bit__bound,axiom,
% 5.46/5.74 ! [K: int] :
% 5.46/5.74 ~ ! [N4: nat] :
% 5.46/5.74 ( ! [M5: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N4 @ M5 )
% 5.46/5.74 => ( ( bit_se1146084159140164899it_int @ K @ M5 )
% 5.46/5.74 = ( bit_se1146084159140164899it_int @ K @ N4 ) ) )
% 5.46/5.74 => ~ ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.46/5.74 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N4 @ one_one_nat ) )
% 5.46/5.74 = ( ~ ( bit_se1146084159140164899it_int @ K @ N4 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % int_bit_bound
% 5.46/5.74 thf(fact_5734_log__divide,axiom,
% 5.46/5.74 ! [A: real,X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.74 => ( ( A != one_one_real )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.74 => ( ( log @ A @ ( divide_divide_real @ X4 @ Y3 ) )
% 5.46/5.74 = ( minus_minus_real @ ( log @ A @ X4 ) @ ( log @ A @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_divide
% 5.46/5.74 thf(fact_5735_inverse__of__nat__le,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.74 => ( ( N != zero_zero_nat )
% 5.46/5.74 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % inverse_of_nat_le
% 5.46/5.74 thf(fact_5736_inverse__of__nat__le,axiom,
% 5.46/5.74 ! [N: nat,M: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.74 => ( ( N != zero_zero_nat )
% 5.46/5.74 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % inverse_of_nat_le
% 5.46/5.74 thf(fact_5737_exp__divide__power__eq,axiom,
% 5.46/5.74 ! [N: nat,X4: complex] :
% 5.46/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.74 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X4 @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.46/5.74 = ( exp_complex @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % exp_divide_power_eq
% 5.46/5.74 thf(fact_5738_exp__divide__power__eq,axiom,
% 5.46/5.74 ! [N: nat,X4: real] :
% 5.46/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.74 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.46/5.74 = ( exp_real @ X4 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % exp_divide_power_eq
% 5.46/5.74 thf(fact_5739_even__abs__add__iff,axiom,
% 5.46/5.74 ! [K: int,L2: int] :
% 5.46/5.74 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 5.46/5.74 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % even_abs_add_iff
% 5.46/5.74 thf(fact_5740_even__add__abs__iff,axiom,
% 5.46/5.74 ! [K: int,L2: int] :
% 5.46/5.74 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 5.46/5.74 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % even_add_abs_iff
% 5.46/5.74 thf(fact_5741_real__archimedian__rdiv__eq__0,axiom,
% 5.46/5.74 ! [X4: real,C: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.46/5.74 => ( ! [M4: nat] :
% 5.46/5.74 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 5.46/5.74 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X4 ) @ C ) )
% 5.46/5.74 => ( X4 = zero_zero_real ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_archimedian_rdiv_eq_0
% 5.46/5.74 thf(fact_5742_real__of__nat__div2,axiom,
% 5.46/5.74 ! [N: nat,X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X4 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_div2
% 5.46/5.74 thf(fact_5743_real__of__nat__div3,axiom,
% 5.46/5.74 ! [N: nat,X4: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X4 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X4 ) ) ) @ one_one_real ) ).
% 5.46/5.74
% 5.46/5.74 % real_of_nat_div3
% 5.46/5.74 thf(fact_5744_ln__realpow,axiom,
% 5.46/5.74 ! [X4: real,N: nat] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( ln_ln_real @ ( power_power_real @ X4 @ N ) )
% 5.46/5.74 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % ln_realpow
% 5.46/5.74 thf(fact_5745_bit__iff__odd,axiom,
% 5.46/5.74 ( bit_se9216721137139052372nteger
% 5.46/5.74 = ( ^ [A4: code_integer,N2: nat] :
% 5.46/5.74 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A4 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_iff_odd
% 5.46/5.74 thf(fact_5746_bit__iff__odd,axiom,
% 5.46/5.74 ( bit_se1146084159140164899it_int
% 5.46/5.74 = ( ^ [A4: int,N2: nat] :
% 5.46/5.74 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_iff_odd
% 5.46/5.74 thf(fact_5747_bit__iff__odd,axiom,
% 5.46/5.74 ( bit_se1148574629649215175it_nat
% 5.46/5.74 = ( ^ [A4: nat,N2: nat] :
% 5.46/5.74 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_iff_odd
% 5.46/5.74 thf(fact_5748_and__exp__eq__0__iff__not__bit,axiom,
% 5.46/5.74 ! [A: int,N: nat] :
% 5.46/5.74 ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.74 = zero_zero_int )
% 5.46/5.74 = ( ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % and_exp_eq_0_iff_not_bit
% 5.46/5.74 thf(fact_5749_and__exp__eq__0__iff__not__bit,axiom,
% 5.46/5.74 ! [A: nat,N: nat] :
% 5.46/5.74 ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.74 = zero_zero_nat )
% 5.46/5.74 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % and_exp_eq_0_iff_not_bit
% 5.46/5.74 thf(fact_5750_log__eq__div__ln__mult__log,axiom,
% 5.46/5.74 ! [A: real,B2: real,X4: real] :
% 5.46/5.74 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.74 => ( ( A != one_one_real )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.74 => ( ( B2 != one_one_real )
% 5.46/5.74 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ( log @ A @ X4 )
% 5.46/5.74 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B2 ) @ ( ln_ln_real @ A ) ) @ ( log @ B2 @ X4 ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % log_eq_div_ln_mult_log
% 5.46/5.74 thf(fact_5751_bit__int__def,axiom,
% 5.46/5.74 ( bit_se1146084159140164899it_int
% 5.46/5.74 = ( ^ [K3: int,N2: nat] :
% 5.46/5.74 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_int_def
% 5.46/5.74 thf(fact_5752_nat__intermed__int__val,axiom,
% 5.46/5.74 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.46/5.74 ( ! [I3: nat] :
% 5.46/5.74 ( ( ( ord_less_eq_nat @ M @ I3 )
% 5.46/5.74 & ( ord_less_nat @ I3 @ N ) )
% 5.46/5.74 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.46/5.74 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.74 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.46/5.74 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.46/5.74 => ? [I3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ M @ I3 )
% 5.46/5.74 & ( ord_less_eq_nat @ I3 @ N )
% 5.46/5.74 & ( ( F @ I3 )
% 5.46/5.74 = K ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % nat_intermed_int_val
% 5.46/5.74 thf(fact_5753_decr__lemma,axiom,
% 5.46/5.74 ! [D: int,X4: int,Z: int] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ D )
% 5.46/5.74 => ( ord_less_int @ ( minus_minus_int @ X4 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.46/5.74
% 5.46/5.74 % decr_lemma
% 5.46/5.74 thf(fact_5754_incr__lemma,axiom,
% 5.46/5.74 ! [D: int,Z: int,X4: int] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ D )
% 5.46/5.74 => ( ord_less_int @ Z @ ( plus_plus_int @ X4 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % incr_lemma
% 5.46/5.74 thf(fact_5755_linear__plus__1__le__power,axiom,
% 5.46/5.74 ! [X4: real,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.74 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X4 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X4 @ one_one_real ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % linear_plus_1_le_power
% 5.46/5.74 thf(fact_5756_Bernoulli__inequality,axiom,
% 5.46/5.74 ! [X4: real,N: nat] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.74 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X4 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X4 ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Bernoulli_inequality
% 5.46/5.74 thf(fact_5757_even__bit__succ__iff,axiom,
% 5.46/5.74 ! [A: code_integer,N: nat] :
% 5.46/5.74 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.74 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N )
% 5.46/5.74 = ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % even_bit_succ_iff
% 5.46/5.74 thf(fact_5758_even__bit__succ__iff,axiom,
% 5.46/5.74 ! [A: int,N: nat] :
% 5.46/5.74 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.74 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N )
% 5.46/5.74 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % even_bit_succ_iff
% 5.46/5.74 thf(fact_5759_even__bit__succ__iff,axiom,
% 5.46/5.74 ! [A: nat,N: nat] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.74 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N )
% 5.46/5.74 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % even_bit_succ_iff
% 5.46/5.74 thf(fact_5760_odd__bit__iff__bit__pred,axiom,
% 5.46/5.74 ! [A: code_integer,N: nat] :
% 5.46/5.74 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.74 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.46/5.74 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % odd_bit_iff_bit_pred
% 5.46/5.74 thf(fact_5761_odd__bit__iff__bit__pred,axiom,
% 5.46/5.74 ! [A: int,N: nat] :
% 5.46/5.74 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.74 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.46/5.74 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % odd_bit_iff_bit_pred
% 5.46/5.74 thf(fact_5762_odd__bit__iff__bit__pred,axiom,
% 5.46/5.74 ! [A: nat,N: nat] :
% 5.46/5.74 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.74 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.46/5.74 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N )
% 5.46/5.74 | ( N = zero_zero_nat ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % odd_bit_iff_bit_pred
% 5.46/5.74 thf(fact_5763_nat__ivt__aux,axiom,
% 5.46/5.74 ! [N: nat,F: nat > int,K: int] :
% 5.46/5.74 ( ! [I3: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I3 @ N )
% 5.46/5.74 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.46/5.74 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.46/5.74 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.46/5.74 => ? [I3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ I3 @ N )
% 5.46/5.74 & ( ( F @ I3 )
% 5.46/5.74 = K ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % nat_ivt_aux
% 5.46/5.74 thf(fact_5764_bit__sum__mult__2__cases,axiom,
% 5.46/5.74 ! [A: code_integer,B2: code_integer,N: nat] :
% 5.46/5.74 ( ! [J2: nat] :
% 5.46/5.74 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J2 ) )
% 5.46/5.74 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) @ N )
% 5.46/5.74 = ( ( ( N = zero_zero_nat )
% 5.46/5.74 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.74 & ( ( N != zero_zero_nat )
% 5.46/5.74 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) @ N ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_sum_mult_2_cases
% 5.46/5.74 thf(fact_5765_bit__sum__mult__2__cases,axiom,
% 5.46/5.74 ! [A: int,B2: int,N: nat] :
% 5.46/5.74 ( ! [J2: nat] :
% 5.46/5.74 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J2 ) )
% 5.46/5.74 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) @ N )
% 5.46/5.74 = ( ( ( N = zero_zero_nat )
% 5.46/5.74 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.74 & ( ( N != zero_zero_nat )
% 5.46/5.74 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ N ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_sum_mult_2_cases
% 5.46/5.74 thf(fact_5766_bit__sum__mult__2__cases,axiom,
% 5.46/5.74 ! [A: nat,B2: nat,N: nat] :
% 5.46/5.74 ( ! [J2: nat] :
% 5.46/5.74 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J2 ) )
% 5.46/5.74 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) @ N )
% 5.46/5.74 = ( ( ( N = zero_zero_nat )
% 5.46/5.74 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.46/5.74 & ( ( N != zero_zero_nat )
% 5.46/5.74 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) @ N ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_sum_mult_2_cases
% 5.46/5.74 thf(fact_5767_bit__rec,axiom,
% 5.46/5.74 ( bit_se9216721137139052372nteger
% 5.46/5.74 = ( ^ [A4: code_integer,N2: nat] :
% 5.46/5.74 ( ( ( N2 = zero_zero_nat )
% 5.46/5.74 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) )
% 5.46/5.74 & ( ( N2 != zero_zero_nat )
% 5.46/5.74 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_rec
% 5.46/5.74 thf(fact_5768_bit__rec,axiom,
% 5.46/5.74 ( bit_se1146084159140164899it_int
% 5.46/5.74 = ( ^ [A4: int,N2: nat] :
% 5.46/5.74 ( ( ( N2 = zero_zero_nat )
% 5.46/5.74 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) )
% 5.46/5.74 & ( ( N2 != zero_zero_nat )
% 5.46/5.74 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_rec
% 5.46/5.74 thf(fact_5769_bit__rec,axiom,
% 5.46/5.74 ( bit_se1148574629649215175it_nat
% 5.46/5.74 = ( ^ [A4: nat,N2: nat] :
% 5.46/5.74 ( ( ( N2 = zero_zero_nat )
% 5.46/5.74 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) )
% 5.46/5.74 & ( ( N2 != zero_zero_nat )
% 5.46/5.74 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % bit_rec
% 5.46/5.74 thf(fact_5770_nat0__intermed__int__val,axiom,
% 5.46/5.74 ! [N: nat,F: nat > int,K: int] :
% 5.46/5.74 ( ! [I3: nat] :
% 5.46/5.74 ( ( ord_less_nat @ I3 @ N )
% 5.46/5.74 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.46/5.74 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.46/5.74 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.46/5.74 => ? [I3: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ I3 @ N )
% 5.46/5.74 & ( ( F @ I3 )
% 5.46/5.74 = K ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % nat0_intermed_int_val
% 5.46/5.74 thf(fact_5771_set__bit__eq,axiom,
% 5.46/5.74 ( bit_se7879613467334960850it_int
% 5.46/5.74 = ( ^ [N2: nat,K3: int] :
% 5.46/5.74 ( plus_plus_int @ K3
% 5.46/5.74 @ ( times_times_int
% 5.46/5.74 @ ( zero_n2684676970156552555ol_int
% 5.46/5.74 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N2 ) )
% 5.46/5.74 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % set_bit_eq
% 5.46/5.74 thf(fact_5772_unset__bit__eq,axiom,
% 5.46/5.74 ( bit_se4203085406695923979it_int
% 5.46/5.74 = ( ^ [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 ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % unset_bit_eq
% 5.46/5.74 thf(fact_5773_arctan__add,axiom,
% 5.46/5.74 ! [X4: real,Y3: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.74 => ( ( ord_less_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.46/5.74 => ( ( plus_plus_real @ ( arctan @ X4 ) @ ( arctan @ Y3 ) )
% 5.46/5.74 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y3 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X4 @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % arctan_add
% 5.46/5.74 thf(fact_5774_take__bit__Suc__from__most,axiom,
% 5.46/5.74 ! [N: nat,K: int] :
% 5.46/5.74 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.46/5.74 = ( 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 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % take_bit_Suc_from_most
% 5.46/5.74 thf(fact_5775_Bernoulli__inequality__even,axiom,
% 5.46/5.74 ! [N: nat,X4: real] :
% 5.46/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X4 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X4 ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % Bernoulli_inequality_even
% 5.46/5.74 thf(fact_5776_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.46/5.74 ! [N: nat,X4: real] :
% 5.46/5.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X4 )
% 5.46/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.74 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X4 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % exp_ge_one_plus_x_over_n_power_n
% 5.46/5.74 thf(fact_5777_lemma__termdiff3,axiom,
% 5.46/5.74 ! [H2: real,Z: real,K5: real,N: nat] :
% 5.46/5.74 ( ( H2 != zero_zero_real )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.46/5.74 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % lemma_termdiff3
% 5.46/5.74 thf(fact_5778_lemma__termdiff3,axiom,
% 5.46/5.74 ! [H2: complex,Z: complex,K5: real,N: nat] :
% 5.46/5.74 ( ( H2 != zero_zero_complex )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.46/5.74 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.46/5.74 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % lemma_termdiff3
% 5.46/5.74 thf(fact_5779_ceiling__log2__div2,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.74 = ( 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 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_log2_div2
% 5.46/5.74 thf(fact_5780_pochhammer__double,axiom,
% 5.46/5.74 ! [Z: complex,N: nat] :
% 5.46/5.74 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.74 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % pochhammer_double
% 5.46/5.74 thf(fact_5781_pochhammer__double,axiom,
% 5.46/5.74 ! [Z: real,N: nat] :
% 5.46/5.74 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.74 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % pochhammer_double
% 5.46/5.74 thf(fact_5782_pochhammer__double,axiom,
% 5.46/5.74 ! [Z: rat,N: nat] :
% 5.46/5.74 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.74 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % pochhammer_double
% 5.46/5.74 thf(fact_5783_central__binomial__lower__bound,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.74 => ( 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 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % central_binomial_lower_bound
% 5.46/5.74 thf(fact_5784_floor__log2__div2,axiom,
% 5.46/5.74 ! [N: nat] :
% 5.46/5.74 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.74 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.74 = ( 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 ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_log2_div2
% 5.46/5.74 thf(fact_5785_machin,axiom,
% 5.46/5.74 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.74 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % machin
% 5.46/5.74 thf(fact_5786_of__int__floor__cancel,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.74 = X4 )
% 5.46/5.74 = ( ? [N2: int] :
% 5.46/5.74 ( X4
% 5.46/5.74 = ( ring_1_of_int_real @ N2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_floor_cancel
% 5.46/5.74 thf(fact_5787_of__int__floor__cancel,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.74 = X4 )
% 5.46/5.74 = ( ? [N2: int] :
% 5.46/5.74 ( X4
% 5.46/5.74 = ( ring_1_of_int_rat @ N2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_floor_cancel
% 5.46/5.74 thf(fact_5788_of__int__ceiling__cancel,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.74 = X4 )
% 5.46/5.74 = ( ? [N2: int] :
% 5.46/5.74 ( X4
% 5.46/5.74 = ( ring_1_of_int_rat @ N2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_ceiling_cancel
% 5.46/5.74 thf(fact_5789_of__int__ceiling__cancel,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.74 = X4 )
% 5.46/5.74 = ( ? [N2: int] :
% 5.46/5.74 ( X4
% 5.46/5.74 = ( ring_1_of_int_real @ N2 ) ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % of_int_ceiling_cancel
% 5.46/5.74 thf(fact_5790_int__eq__iff__numeral,axiom,
% 5.46/5.74 ! [M: nat,V: num] :
% 5.46/5.74 ( ( ( semiri1314217659103216013at_int @ M )
% 5.46/5.74 = ( numeral_numeral_int @ V ) )
% 5.46/5.74 = ( M
% 5.46/5.74 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % int_eq_iff_numeral
% 5.46/5.74 thf(fact_5791_floor__numeral,axiom,
% 5.46/5.74 ! [V: num] :
% 5.46/5.74 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.46/5.74 = ( numeral_numeral_int @ V ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_numeral
% 5.46/5.74 thf(fact_5792_floor__numeral,axiom,
% 5.46/5.74 ! [V: num] :
% 5.46/5.74 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 5.46/5.74 = ( numeral_numeral_int @ V ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_numeral
% 5.46/5.74 thf(fact_5793_floor__one,axiom,
% 5.46/5.74 ( ( archim6058952711729229775r_real @ one_one_real )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % floor_one
% 5.46/5.74 thf(fact_5794_floor__one,axiom,
% 5.46/5.74 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % floor_one
% 5.46/5.74 thf(fact_5795_ceiling__numeral,axiom,
% 5.46/5.74 ! [V: num] :
% 5.46/5.74 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.46/5.74 = ( numeral_numeral_int @ V ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_numeral
% 5.46/5.74 thf(fact_5796_ceiling__numeral,axiom,
% 5.46/5.74 ! [V: num] :
% 5.46/5.74 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 5.46/5.74 = ( numeral_numeral_int @ V ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_numeral
% 5.46/5.74 thf(fact_5797_pochhammer__0,axiom,
% 5.46/5.74 ! [A: complex] :
% 5.46/5.74 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.46/5.74 = one_one_complex ) ).
% 5.46/5.74
% 5.46/5.74 % pochhammer_0
% 5.46/5.74 thf(fact_5798_pochhammer__0,axiom,
% 5.46/5.74 ! [A: real] :
% 5.46/5.74 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.46/5.74 = one_one_real ) ).
% 5.46/5.74
% 5.46/5.74 % pochhammer_0
% 5.46/5.74 thf(fact_5799_pochhammer__0,axiom,
% 5.46/5.74 ! [A: rat] :
% 5.46/5.74 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.46/5.74 = one_one_rat ) ).
% 5.46/5.74
% 5.46/5.74 % pochhammer_0
% 5.46/5.74 thf(fact_5800_pochhammer__0,axiom,
% 5.46/5.74 ! [A: nat] :
% 5.46/5.74 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.46/5.74 = one_one_nat ) ).
% 5.46/5.74
% 5.46/5.74 % pochhammer_0
% 5.46/5.74 thf(fact_5801_pochhammer__0,axiom,
% 5.46/5.74 ! [A: int] :
% 5.46/5.74 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % pochhammer_0
% 5.46/5.74 thf(fact_5802_ceiling__one,axiom,
% 5.46/5.74 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_one
% 5.46/5.74 thf(fact_5803_ceiling__one,axiom,
% 5.46/5.74 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.46/5.74 = one_one_int ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_one
% 5.46/5.74 thf(fact_5804_negative__zless,axiom,
% 5.46/5.74 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.46/5.74
% 5.46/5.74 % negative_zless
% 5.46/5.74 thf(fact_5805_ceiling__add__of__int,axiom,
% 5.46/5.74 ! [X4: rat,Z: int] :
% 5.46/5.74 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.46/5.74 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_add_of_int
% 5.46/5.74 thf(fact_5806_ceiling__add__of__int,axiom,
% 5.46/5.74 ! [X4: real,Z: int] :
% 5.46/5.74 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ ( ring_1_of_int_real @ Z ) ) )
% 5.46/5.74 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ Z ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_add_of_int
% 5.46/5.74 thf(fact_5807_floor__diff__of__int,axiom,
% 5.46/5.74 ! [X4: real,Z: int] :
% 5.46/5.74 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X4 @ ( ring_1_of_int_real @ Z ) ) )
% 5.46/5.74 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X4 ) @ Z ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_diff_of_int
% 5.46/5.74 thf(fact_5808_floor__diff__of__int,axiom,
% 5.46/5.74 ! [X4: rat,Z: int] :
% 5.46/5.74 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.46/5.74 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_diff_of_int
% 5.46/5.74 thf(fact_5809_ceiling__diff__of__int,axiom,
% 5.46/5.74 ! [X4: rat,Z: int] :
% 5.46/5.74 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.46/5.74 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_diff_of_int
% 5.46/5.74 thf(fact_5810_ceiling__diff__of__int,axiom,
% 5.46/5.74 ! [X4: real,Z: int] :
% 5.46/5.74 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X4 @ ( ring_1_of_int_real @ Z ) ) )
% 5.46/5.74 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ Z ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_diff_of_int
% 5.46/5.74 thf(fact_5811_zero__le__floor,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_le_floor
% 5.46/5.74 thf(fact_5812_zero__le__floor,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_rat @ zero_zero_rat @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_le_floor
% 5.46/5.74 thf(fact_5813_floor__less__zero,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ zero_zero_int )
% 5.46/5.74 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_less_zero
% 5.46/5.74 thf(fact_5814_floor__less__zero,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ zero_zero_int )
% 5.46/5.74 = ( ord_less_rat @ X4 @ zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_less_zero
% 5.46/5.74 thf(fact_5815_numeral__le__floor,axiom,
% 5.46/5.74 ! [V: num,X4: real] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_le_floor
% 5.46/5.74 thf(fact_5816_numeral__le__floor,axiom,
% 5.46/5.74 ! [V: num,X4: rat] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_le_floor
% 5.46/5.74 thf(fact_5817_zero__less__floor,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_real @ one_one_real @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_floor
% 5.46/5.74 thf(fact_5818_zero__less__floor,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_floor
% 5.46/5.74 thf(fact_5819_floor__le__zero,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ zero_zero_int )
% 5.46/5.74 = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_le_zero
% 5.46/5.74 thf(fact_5820_floor__le__zero,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ zero_zero_int )
% 5.46/5.74 = ( ord_less_rat @ X4 @ one_one_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_le_zero
% 5.46/5.74 thf(fact_5821_ceiling__le__zero,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ zero_zero_int )
% 5.46/5.74 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_le_zero
% 5.46/5.74 thf(fact_5822_ceiling__le__zero,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ zero_zero_int )
% 5.46/5.74 = ( ord_less_eq_rat @ X4 @ zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_le_zero
% 5.46/5.74 thf(fact_5823_floor__less__numeral,axiom,
% 5.46/5.74 ! [X4: real,V: num] :
% 5.46/5.74 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.74 = ( ord_less_real @ X4 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_less_numeral
% 5.46/5.74 thf(fact_5824_floor__less__numeral,axiom,
% 5.46/5.74 ! [X4: rat,V: num] :
% 5.46/5.74 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.74 = ( ord_less_rat @ X4 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_less_numeral
% 5.46/5.74 thf(fact_5825_zero__less__ceiling,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_rat @ zero_zero_rat @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_ceiling
% 5.46/5.74 thf(fact_5826_zero__less__ceiling,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.74 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % zero_less_ceiling
% 5.46/5.74 thf(fact_5827_one__le__floor,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_real @ one_one_real @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % one_le_floor
% 5.46/5.74 thf(fact_5828_one__le__floor,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % one_le_floor
% 5.46/5.74 thf(fact_5829_ceiling__le__numeral,axiom,
% 5.46/5.74 ! [X4: real,V: num] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.74 = ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_le_numeral
% 5.46/5.74 thf(fact_5830_ceiling__le__numeral,axiom,
% 5.46/5.74 ! [X4: rat,V: num] :
% 5.46/5.74 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.74 = ( ord_less_eq_rat @ X4 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_le_numeral
% 5.46/5.74 thf(fact_5831_floor__less__one,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 5.46/5.74 = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_less_one
% 5.46/5.74 thf(fact_5832_floor__less__one,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 5.46/5.74 = ( ord_less_rat @ X4 @ one_one_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % floor_less_one
% 5.46/5.74 thf(fact_5833_ceiling__less__one,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int )
% 5.46/5.74 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_less_one
% 5.46/5.74 thf(fact_5834_ceiling__less__one,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int )
% 5.46/5.74 = ( ord_less_eq_rat @ X4 @ zero_zero_rat ) ) ).
% 5.46/5.74
% 5.46/5.74 % ceiling_less_one
% 5.46/5.74 thf(fact_5835_one__le__ceiling,axiom,
% 5.46/5.74 ! [X4: rat] :
% 5.46/5.74 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_rat @ zero_zero_rat @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % one_le_ceiling
% 5.46/5.74 thf(fact_5836_one__le__ceiling,axiom,
% 5.46/5.74 ! [X4: real] :
% 5.46/5.74 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.74 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % one_le_ceiling
% 5.46/5.74 thf(fact_5837_numeral__less__ceiling,axiom,
% 5.46/5.74 ! [V: num,X4: real] :
% 5.46/5.74 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.74 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_less_ceiling
% 5.46/5.74 thf(fact_5838_numeral__less__ceiling,axiom,
% 5.46/5.74 ! [V: num,X4: rat] :
% 5.46/5.74 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.74 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X4 ) ) ).
% 5.46/5.74
% 5.46/5.74 % numeral_less_ceiling
% 5.46/5.74 thf(fact_5839_floor__neg__numeral,axiom,
% 5.46/5.74 ! [V: num] :
% 5.46/5.74 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_neg_numeral
% 5.46/5.75 thf(fact_5840_floor__neg__numeral,axiom,
% 5.46/5.75 ! [V: num] :
% 5.46/5.75 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.75 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_neg_numeral
% 5.46/5.75 thf(fact_5841_ceiling__le__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_le_one
% 5.46/5.75 thf(fact_5842_ceiling__le__one,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int )
% 5.46/5.75 = ( ord_less_eq_rat @ X4 @ one_one_rat ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_le_one
% 5.46/5.75 thf(fact_5843_one__less__ceiling,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_rat @ one_one_rat @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % one_less_ceiling
% 5.46/5.75 thf(fact_5844_one__less__ceiling,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.75 = ( ord_less_real @ one_one_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % one_less_ceiling
% 5.46/5.75 thf(fact_5845_ceiling__add__numeral,axiom,
% 5.46/5.75 ! [X4: real,V: num] :
% 5.46/5.75 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.75 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_add_numeral
% 5.46/5.75 thf(fact_5846_ceiling__add__numeral,axiom,
% 5.46/5.75 ! [X4: rat,V: num] :
% 5.46/5.75 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.75 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_add_numeral
% 5.46/5.75 thf(fact_5847_floor__diff__numeral,axiom,
% 5.46/5.75 ! [X4: real,V: num] :
% 5.46/5.75 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.75 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_diff_numeral
% 5.46/5.75 thf(fact_5848_floor__diff__numeral,axiom,
% 5.46/5.75 ! [X4: rat,V: num] :
% 5.46/5.75 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.75 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_diff_numeral
% 5.46/5.75 thf(fact_5849_ceiling__neg__numeral,axiom,
% 5.46/5.75 ! [V: num] :
% 5.46/5.75 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.75 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_neg_numeral
% 5.46/5.75 thf(fact_5850_ceiling__neg__numeral,axiom,
% 5.46/5.75 ! [V: num] :
% 5.46/5.75 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.75 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_neg_numeral
% 5.46/5.75 thf(fact_5851_ceiling__add__one,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) )
% 5.46/5.75 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_add_one
% 5.46/5.75 thf(fact_5852_ceiling__add__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ one_one_real ) )
% 5.46/5.75 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_add_one
% 5.46/5.75 thf(fact_5853_floor__diff__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X4 @ one_one_real ) )
% 5.46/5.75 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_diff_one
% 5.46/5.75 thf(fact_5854_floor__diff__one,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) )
% 5.46/5.75 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_diff_one
% 5.46/5.75 thf(fact_5855_ceiling__diff__numeral,axiom,
% 5.46/5.75 ! [X4: real,V: num] :
% 5.46/5.75 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 5.46/5.75 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_diff_numeral
% 5.46/5.75 thf(fact_5856_ceiling__diff__numeral,axiom,
% 5.46/5.75 ! [X4: rat,V: num] :
% 5.46/5.75 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 5.46/5.75 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_diff_numeral
% 5.46/5.75 thf(fact_5857_ceiling__diff__one,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) )
% 5.46/5.75 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_diff_one
% 5.46/5.75 thf(fact_5858_ceiling__diff__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X4 @ one_one_real ) )
% 5.46/5.75 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_diff_one
% 5.46/5.75 thf(fact_5859_floor__numeral__power,axiom,
% 5.46/5.75 ! [X4: num,N: nat] :
% 5.46/5.75 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N ) )
% 5.46/5.75 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_numeral_power
% 5.46/5.75 thf(fact_5860_floor__numeral__power,axiom,
% 5.46/5.75 ! [X4: num,N: nat] :
% 5.46/5.75 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N ) )
% 5.46/5.75 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_numeral_power
% 5.46/5.75 thf(fact_5861_ceiling__numeral__power,axiom,
% 5.46/5.75 ! [X4: num,N: nat] :
% 5.46/5.75 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N ) )
% 5.46/5.75 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_numeral_power
% 5.46/5.75 thf(fact_5862_ceiling__numeral__power,axiom,
% 5.46/5.75 ! [X4: num,N: nat] :
% 5.46/5.75 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N ) )
% 5.46/5.75 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_numeral_power
% 5.46/5.75 thf(fact_5863_floor__divide__eq__div__numeral,axiom,
% 5.46/5.75 ! [A: num,B2: num] :
% 5.46/5.75 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B2 ) ) )
% 5.46/5.75 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_divide_eq_div_numeral
% 5.46/5.75 thf(fact_5864_ceiling__less__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ zero_zero_int )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_less_zero
% 5.46/5.75 thf(fact_5865_ceiling__less__zero,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ zero_zero_int )
% 5.46/5.75 = ( ord_less_eq_rat @ X4 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_less_zero
% 5.46/5.75 thf(fact_5866_zero__le__ceiling,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.75 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % zero_le_ceiling
% 5.46/5.75 thf(fact_5867_zero__le__ceiling,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % zero_le_ceiling
% 5.46/5.75 thf(fact_5868_ceiling__divide__eq__div__numeral,axiom,
% 5.46/5.75 ! [A: num,B2: num] :
% 5.46/5.75 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B2 ) ) )
% 5.46/5.75 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_divide_eq_div_numeral
% 5.46/5.75 thf(fact_5869_numeral__less__floor,axiom,
% 5.46/5.75 ! [V: num,X4: real] :
% 5.46/5.75 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % numeral_less_floor
% 5.46/5.75 thf(fact_5870_numeral__less__floor,axiom,
% 5.46/5.75 ! [V: num,X4: rat] :
% 5.46/5.75 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % numeral_less_floor
% 5.46/5.75 thf(fact_5871_floor__le__numeral,axiom,
% 5.46/5.75 ! [X4: real,V: num] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.75 = ( ord_less_real @ X4 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_le_numeral
% 5.46/5.75 thf(fact_5872_floor__le__numeral,axiom,
% 5.46/5.75 ! [X4: rat,V: num] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.75 = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_le_numeral
% 5.46/5.75 thf(fact_5873_one__less__floor,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % one_less_floor
% 5.46/5.75 thf(fact_5874_one__less__floor,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % one_less_floor
% 5.46/5.75 thf(fact_5875_floor__le__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 5.46/5.75 = ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_le_one
% 5.46/5.75 thf(fact_5876_floor__le__one,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 5.46/5.75 = ( ord_less_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_le_one
% 5.46/5.75 thf(fact_5877_ceiling__less__numeral,axiom,
% 5.46/5.75 ! [X4: real,V: num] :
% 5.46/5.75 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_less_numeral
% 5.46/5.75 thf(fact_5878_ceiling__less__numeral,axiom,
% 5.46/5.75 ! [X4: rat,V: num] :
% 5.46/5.75 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.46/5.75 = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_less_numeral
% 5.46/5.75 thf(fact_5879_numeral__le__ceiling,axiom,
% 5.46/5.75 ! [V: num,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.75 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % numeral_le_ceiling
% 5.46/5.75 thf(fact_5880_numeral__le__ceiling,axiom,
% 5.46/5.75 ! [V: num,X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % numeral_le_ceiling
% 5.46/5.75 thf(fact_5881_neg__numeral__le__floor,axiom,
% 5.46/5.75 ! [V: num,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % neg_numeral_le_floor
% 5.46/5.75 thf(fact_5882_neg__numeral__le__floor,axiom,
% 5.46/5.75 ! [V: num,X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % neg_numeral_le_floor
% 5.46/5.75 thf(fact_5883_floor__less__neg__numeral,axiom,
% 5.46/5.75 ! [X4: real,V: num] :
% 5.46/5.75 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.75 = ( ord_less_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_less_neg_numeral
% 5.46/5.75 thf(fact_5884_floor__less__neg__numeral,axiom,
% 5.46/5.75 ! [X4: rat,V: num] :
% 5.46/5.75 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.75 = ( ord_less_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_less_neg_numeral
% 5.46/5.75 thf(fact_5885_ceiling__le__neg__numeral,axiom,
% 5.46/5.75 ! [X4: real,V: num] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_le_neg_numeral
% 5.46/5.75 thf(fact_5886_ceiling__le__neg__numeral,axiom,
% 5.46/5.75 ! [X4: rat,V: num] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.75 = ( ord_less_eq_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_le_neg_numeral
% 5.46/5.75 thf(fact_5887_neg__numeral__less__ceiling,axiom,
% 5.46/5.75 ! [V: num,X4: real] :
% 5.46/5.75 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.75 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % neg_numeral_less_ceiling
% 5.46/5.75 thf(fact_5888_neg__numeral__less__ceiling,axiom,
% 5.46/5.75 ! [V: num,X4: rat] :
% 5.46/5.75 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % neg_numeral_less_ceiling
% 5.46/5.75 thf(fact_5889_floor__one__divide__eq__div__numeral,axiom,
% 5.46/5.75 ! [B2: num] :
% 5.46/5.75 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B2 ) ) )
% 5.46/5.75 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_one_divide_eq_div_numeral
% 5.46/5.75 thf(fact_5890_floor__minus__divide__eq__div__numeral,axiom,
% 5.46/5.75 ! [A: num,B2: num] :
% 5.46/5.75 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B2 ) ) ) )
% 5.46/5.75 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_minus_divide_eq_div_numeral
% 5.46/5.75 thf(fact_5891_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.46/5.75 ! [A: num,B2: num] :
% 5.46/5.75 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B2 ) ) ) )
% 5.46/5.75 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_minus_divide_eq_div_numeral
% 5.46/5.75 thf(fact_5892_neg__numeral__less__floor,axiom,
% 5.46/5.75 ! [V: num,X4: real] :
% 5.46/5.75 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % neg_numeral_less_floor
% 5.46/5.75 thf(fact_5893_neg__numeral__less__floor,axiom,
% 5.46/5.75 ! [V: num,X4: rat] :
% 5.46/5.75 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % neg_numeral_less_floor
% 5.46/5.75 thf(fact_5894_floor__le__neg__numeral,axiom,
% 5.46/5.75 ! [X4: real,V: num] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.75 = ( ord_less_real @ X4 @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_le_neg_numeral
% 5.46/5.75 thf(fact_5895_floor__le__neg__numeral,axiom,
% 5.46/5.75 ! [X4: rat,V: num] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.75 = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_le_neg_numeral
% 5.46/5.75 thf(fact_5896_ceiling__less__neg__numeral,axiom,
% 5.46/5.75 ! [X4: real,V: num] :
% 5.46/5.75 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_less_neg_numeral
% 5.46/5.75 thf(fact_5897_ceiling__less__neg__numeral,axiom,
% 5.46/5.75 ! [X4: rat,V: num] :
% 5.46/5.75 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.46/5.75 = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_less_neg_numeral
% 5.46/5.75 thf(fact_5898_neg__numeral__le__ceiling,axiom,
% 5.46/5.75 ! [V: num,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.75 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % neg_numeral_le_ceiling
% 5.46/5.75 thf(fact_5899_neg__numeral__le__ceiling,axiom,
% 5.46/5.75 ! [V: num,X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % neg_numeral_le_ceiling
% 5.46/5.75 thf(fact_5900_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.46/5.75 ! [B2: num] :
% 5.46/5.75 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B2 ) ) ) )
% 5.46/5.75 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_minus_one_divide_eq_div_numeral
% 5.46/5.75 thf(fact_5901_int__if,axiom,
% 5.46/5.75 ! [P: $o,A: nat,B2: nat] :
% 5.46/5.75 ( ( P
% 5.46/5.75 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B2 ) )
% 5.46/5.75 = ( semiri1314217659103216013at_int @ A ) ) )
% 5.46/5.75 & ( ~ P
% 5.46/5.75 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B2 ) )
% 5.46/5.75 = ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_if
% 5.46/5.75 thf(fact_5902_nat__int__comparison_I1_J,axiom,
% 5.46/5.75 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.46/5.75 = ( ^ [A4: nat,B3: nat] :
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ A4 )
% 5.46/5.75 = ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % nat_int_comparison(1)
% 5.46/5.75 thf(fact_5903_int__diff__cases,axiom,
% 5.46/5.75 ! [Z: int] :
% 5.46/5.75 ~ ! [M4: nat,N4: nat] :
% 5.46/5.75 ( Z
% 5.46/5.75 != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_diff_cases
% 5.46/5.75 thf(fact_5904_ceiling__altdef,axiom,
% 5.46/5.75 ( archim7802044766580827645g_real
% 5.46/5.75 = ( ^ [X: real] :
% 5.46/5.75 ( if_int
% 5.46/5.75 @ ( X
% 5.46/5.75 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 5.46/5.75 @ ( archim6058952711729229775r_real @ X )
% 5.46/5.75 @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_altdef
% 5.46/5.75 thf(fact_5905_ceiling__altdef,axiom,
% 5.46/5.75 ( archim2889992004027027881ng_rat
% 5.46/5.75 = ( ^ [X: rat] :
% 5.46/5.75 ( if_int
% 5.46/5.75 @ ( X
% 5.46/5.75 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 5.46/5.75 @ ( archim3151403230148437115or_rat @ X )
% 5.46/5.75 @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_altdef
% 5.46/5.75 thf(fact_5906_ceiling__diff__floor__le__1,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim6058952711729229775r_real @ X4 ) ) @ one_one_int ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_diff_floor_le_1
% 5.46/5.75 thf(fact_5907_ceiling__diff__floor__le__1,axiom,
% 5.46/5.75 ! [X4: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim3151403230148437115or_rat @ X4 ) ) @ one_one_int ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_diff_floor_le_1
% 5.46/5.75 thf(fact_5908_floor__mono,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.75 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_mono
% 5.46/5.75 thf(fact_5909_floor__mono,axiom,
% 5.46/5.75 ! [X4: rat,Y3: rat] :
% 5.46/5.75 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.75 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_mono
% 5.46/5.75 thf(fact_5910_of__int__floor__le,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) @ X4 ) ).
% 5.46/5.75
% 5.46/5.75 % of_int_floor_le
% 5.46/5.75 thf(fact_5911_of__int__floor__le,axiom,
% 5.46/5.75 ! [X4: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) @ X4 ) ).
% 5.46/5.75
% 5.46/5.75 % of_int_floor_le
% 5.46/5.75 thf(fact_5912_floor__less__cancel,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y3 ) )
% 5.46/5.75 => ( ord_less_real @ X4 @ Y3 ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_less_cancel
% 5.46/5.75 thf(fact_5913_floor__less__cancel,axiom,
% 5.46/5.75 ! [X4: rat,Y3: rat] :
% 5.46/5.75 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y3 ) )
% 5.46/5.75 => ( ord_less_rat @ X4 @ Y3 ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_less_cancel
% 5.46/5.75 thf(fact_5914_not__bit__Suc__0__Suc,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % not_bit_Suc_0_Suc
% 5.46/5.75 thf(fact_5915_bit__Suc__0__iff,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.75 = ( N = zero_zero_nat ) ) ).
% 5.46/5.75
% 5.46/5.75 % bit_Suc_0_iff
% 5.46/5.75 thf(fact_5916_ceiling__mono,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ Y3 @ X4 )
% 5.46/5.75 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y3 ) @ ( archim7802044766580827645g_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_mono
% 5.46/5.75 thf(fact_5917_ceiling__mono,axiom,
% 5.46/5.75 ! [Y3: rat,X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_rat @ Y3 @ X4 )
% 5.46/5.75 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y3 ) @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_mono
% 5.46/5.75 thf(fact_5918_le__of__int__ceiling,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_of_int_ceiling
% 5.46/5.75 thf(fact_5919_le__of__int__ceiling,axiom,
% 5.46/5.75 ! [X4: rat] : ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_of_int_ceiling
% 5.46/5.75 thf(fact_5920_ceiling__less__cancel,axiom,
% 5.46/5.75 ! [X4: rat,Y3: rat] :
% 5.46/5.75 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ Y3 ) )
% 5.46/5.75 => ( ord_less_rat @ X4 @ Y3 ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_less_cancel
% 5.46/5.75 thf(fact_5921_ceiling__less__cancel,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim7802044766580827645g_real @ Y3 ) )
% 5.46/5.75 => ( ord_less_real @ X4 @ Y3 ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_less_cancel
% 5.46/5.75 thf(fact_5922_int__ops_I1_J,axiom,
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.46/5.75 = zero_zero_int ) ).
% 5.46/5.75
% 5.46/5.75 % int_ops(1)
% 5.46/5.75 thf(fact_5923_complex__mod__minus__le__complex__mod,axiom,
% 5.46/5.75 ! [X4: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % complex_mod_minus_le_complex_mod
% 5.46/5.75 thf(fact_5924_int__ops_I3_J,axiom,
% 5.46/5.75 ! [N: num] :
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.46/5.75 = ( numeral_numeral_int @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_ops(3)
% 5.46/5.75 thf(fact_5925_pochhammer__pos,axiom,
% 5.46/5.75 ! [X4: real,N: nat] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X4 @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_pos
% 5.46/5.75 thf(fact_5926_pochhammer__pos,axiom,
% 5.46/5.75 ! [X4: rat,N: nat] :
% 5.46/5.75 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.46/5.75 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X4 @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_pos
% 5.46/5.75 thf(fact_5927_pochhammer__pos,axiom,
% 5.46/5.75 ! [X4: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.46/5.75 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X4 @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_pos
% 5.46/5.75 thf(fact_5928_pochhammer__pos,axiom,
% 5.46/5.75 ! [X4: int,N: nat] :
% 5.46/5.75 ( ( ord_less_int @ zero_zero_int @ X4 )
% 5.46/5.75 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X4 @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_pos
% 5.46/5.75 thf(fact_5929_nat__int__comparison_I2_J,axiom,
% 5.46/5.75 ( ord_less_nat
% 5.46/5.75 = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % nat_int_comparison(2)
% 5.46/5.75 thf(fact_5930_int__of__nat__induct,axiom,
% 5.46/5.75 ! [P: int > $o,Z: int] :
% 5.46/5.75 ( ! [N4: nat] : ( P @ ( semiri1314217659103216013at_int @ N4 ) )
% 5.46/5.75 => ( ! [N4: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) )
% 5.46/5.75 => ( P @ Z ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_of_nat_induct
% 5.46/5.75 thf(fact_5931_int__cases,axiom,
% 5.46/5.75 ! [Z: int] :
% 5.46/5.75 ( ! [N4: nat] :
% 5.46/5.75 ( Z
% 5.46/5.75 != ( semiri1314217659103216013at_int @ N4 ) )
% 5.46/5.75 => ~ ! [N4: nat] :
% 5.46/5.75 ( Z
% 5.46/5.75 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_cases
% 5.46/5.75 thf(fact_5932_pi__not__less__zero,axiom,
% 5.46/5.75 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % pi_not_less_zero
% 5.46/5.75 thf(fact_5933_pi__gt__zero,axiom,
% 5.46/5.75 ord_less_real @ zero_zero_real @ pi ).
% 5.46/5.75
% 5.46/5.75 % pi_gt_zero
% 5.46/5.75 thf(fact_5934_pi__ge__zero,axiom,
% 5.46/5.75 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.46/5.75
% 5.46/5.75 % pi_ge_zero
% 5.46/5.75 thf(fact_5935_nat__int__comparison_I3_J,axiom,
% 5.46/5.75 ( ord_less_eq_nat
% 5.46/5.75 = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % nat_int_comparison(3)
% 5.46/5.75 thf(fact_5936_zle__int,axiom,
% 5.46/5.75 ! [M: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.75 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % zle_int
% 5.46/5.75 thf(fact_5937_complex__mod__triangle__ineq2,axiom,
% 5.46/5.75 ! [B2: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B2 @ A ) ) @ ( real_V1022390504157884413omplex @ B2 ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.46/5.75
% 5.46/5.75 % complex_mod_triangle_ineq2
% 5.46/5.75 thf(fact_5938_pochhammer__eq__0__mono,axiom,
% 5.46/5.75 ! [A: real,N: nat,M: nat] :
% 5.46/5.75 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.75 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.46/5.75 = zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_eq_0_mono
% 5.46/5.75 thf(fact_5939_pochhammer__eq__0__mono,axiom,
% 5.46/5.75 ! [A: rat,N: nat,M: nat] :
% 5.46/5.75 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.46/5.75 = zero_zero_rat )
% 5.46/5.75 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.75 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.46/5.75 = zero_zero_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_eq_0_mono
% 5.46/5.75 thf(fact_5940_pochhammer__neq__0__mono,axiom,
% 5.46/5.75 ! [A: real,M: nat,N: nat] :
% 5.46/5.75 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.75 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.46/5.75 != zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_neq_0_mono
% 5.46/5.75 thf(fact_5941_pochhammer__neq__0__mono,axiom,
% 5.46/5.75 ! [A: rat,M: nat,N: nat] :
% 5.46/5.75 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.46/5.75 != zero_zero_rat )
% 5.46/5.75 => ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.75 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.46/5.75 != zero_zero_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_neq_0_mono
% 5.46/5.75 thf(fact_5942_int__ops_I5_J,axiom,
% 5.46/5.75 ! [A: nat,B2: nat] :
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B2 ) )
% 5.46/5.75 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_ops(5)
% 5.46/5.75 thf(fact_5943_int__plus,axiom,
% 5.46/5.75 ! [N: nat,M: nat] :
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.75 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_plus
% 5.46/5.75 thf(fact_5944_zadd__int__left,axiom,
% 5.46/5.75 ! [M: nat,N: nat,Z: int] :
% 5.46/5.75 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 5.46/5.75 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 5.46/5.75
% 5.46/5.75 % zadd_int_left
% 5.46/5.75 thf(fact_5945_int__ops_I2_J,axiom,
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.46/5.75 = one_one_int ) ).
% 5.46/5.75
% 5.46/5.75 % int_ops(2)
% 5.46/5.75 thf(fact_5946_int__ops_I7_J,axiom,
% 5.46/5.75 ! [A: nat,B2: nat] :
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B2 ) )
% 5.46/5.75 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_ops(7)
% 5.46/5.75 thf(fact_5947_zle__iff__zadd,axiom,
% 5.46/5.75 ( ord_less_eq_int
% 5.46/5.75 = ( ^ [W2: int,Z5: int] :
% 5.46/5.75 ? [N2: nat] :
% 5.46/5.75 ( Z5
% 5.46/5.75 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % zle_iff_zadd
% 5.46/5.75 thf(fact_5948_not__int__zless__negative,axiom,
% 5.46/5.75 ! [N: nat,M: nat] :
% 5.46/5.75 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % not_int_zless_negative
% 5.46/5.75 thf(fact_5949_zdiv__int,axiom,
% 5.46/5.75 ! [A: nat,B2: nat] :
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B2 ) )
% 5.46/5.75 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % zdiv_int
% 5.46/5.75 thf(fact_5950_zmod__int,axiom,
% 5.46/5.75 ! [A: nat,B2: nat] :
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B2 ) )
% 5.46/5.75 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % zmod_int
% 5.46/5.75 thf(fact_5951_not__bit__Suc__0__numeral,axiom,
% 5.46/5.75 ! [N: num] :
% 5.46/5.75 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % not_bit_Suc_0_numeral
% 5.46/5.75 thf(fact_5952_floor__divide__of__nat__eq,axiom,
% 5.46/5.75 ! [M: nat,N: nat] :
% 5.46/5.75 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.75 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_divide_of_nat_eq
% 5.46/5.75 thf(fact_5953_floor__divide__of__nat__eq,axiom,
% 5.46/5.75 ! [M: nat,N: nat] :
% 5.46/5.75 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 5.46/5.75 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_divide_of_nat_eq
% 5.46/5.75 thf(fact_5954_le__floor__iff,axiom,
% 5.46/5.75 ! [Z: int,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_floor_iff
% 5.46/5.75 thf(fact_5955_le__floor__iff,axiom,
% 5.46/5.75 ! [Z: int,X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_floor_iff
% 5.46/5.75 thf(fact_5956_floor__less__iff,axiom,
% 5.46/5.75 ! [X4: real,Z: int] :
% 5.46/5.75 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 5.46/5.75 = ( ord_less_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_less_iff
% 5.46/5.75 thf(fact_5957_floor__less__iff,axiom,
% 5.46/5.75 ! [X4: rat,Z: int] :
% 5.46/5.75 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 5.46/5.75 = ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_less_iff
% 5.46/5.75 thf(fact_5958_le__floor__add,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y3 ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_floor_add
% 5.46/5.75 thf(fact_5959_le__floor__add,axiom,
% 5.46/5.75 ! [X4: rat,Y3: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_floor_add
% 5.46/5.75 thf(fact_5960_int__add__floor,axiom,
% 5.46/5.75 ! [Z: int,X4: real] :
% 5.46/5.75 ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.75 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_add_floor
% 5.46/5.75 thf(fact_5961_int__add__floor,axiom,
% 5.46/5.75 ! [Z: int,X4: rat] :
% 5.46/5.75 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.75 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_add_floor
% 5.46/5.75 thf(fact_5962_floor__add__int,axiom,
% 5.46/5.75 ! [X4: real,Z: int] :
% 5.46/5.75 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 5.46/5.75 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_add_int
% 5.46/5.75 thf(fact_5963_floor__add__int,axiom,
% 5.46/5.75 ! [X4: rat,Z: int] :
% 5.46/5.75 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 5.46/5.75 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_add_int
% 5.46/5.75 thf(fact_5964_floor__divide__of__int__eq,axiom,
% 5.46/5.75 ! [K: int,L2: int] :
% 5.46/5.75 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L2 ) ) )
% 5.46/5.75 = ( divide_divide_int @ K @ L2 ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_divide_of_int_eq
% 5.46/5.75 thf(fact_5965_floor__divide__of__int__eq,axiom,
% 5.46/5.75 ! [K: int,L2: int] :
% 5.46/5.75 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L2 ) ) )
% 5.46/5.75 = ( divide_divide_int @ K @ L2 ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_divide_of_int_eq
% 5.46/5.75 thf(fact_5966_floor__power,axiom,
% 5.46/5.75 ! [X4: real,N: nat] :
% 5.46/5.75 ( ( X4
% 5.46/5.75 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) )
% 5.46/5.75 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X4 @ N ) )
% 5.46/5.75 = ( power_power_int @ ( archim6058952711729229775r_real @ X4 ) @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_power
% 5.46/5.75 thf(fact_5967_floor__power,axiom,
% 5.46/5.75 ! [X4: rat,N: nat] :
% 5.46/5.75 ( ( X4
% 5.46/5.75 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) )
% 5.46/5.75 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X4 @ N ) )
% 5.46/5.75 = ( power_power_int @ ( archim3151403230148437115or_rat @ X4 ) @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_power
% 5.46/5.75 thf(fact_5968_ceiling__le,axiom,
% 5.46/5.75 ! [X4: real,A: int] :
% 5.46/5.75 ( ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ A ) )
% 5.46/5.75 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ A ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_le
% 5.46/5.75 thf(fact_5969_ceiling__le,axiom,
% 5.46/5.75 ! [X4: rat,A: int] :
% 5.46/5.75 ( ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ A ) )
% 5.46/5.75 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ A ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_le
% 5.46/5.75 thf(fact_5970_ceiling__le__iff,axiom,
% 5.46/5.75 ! [X4: real,Z: int] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ Z )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_le_iff
% 5.46/5.75 thf(fact_5971_ceiling__le__iff,axiom,
% 5.46/5.75 ! [X4: rat,Z: int] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z )
% 5.46/5.75 = ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_le_iff
% 5.46/5.75 thf(fact_5972_less__ceiling__iff,axiom,
% 5.46/5.75 ! [Z: int,X4: rat] :
% 5.46/5.75 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % less_ceiling_iff
% 5.46/5.75 thf(fact_5973_less__ceiling__iff,axiom,
% 5.46/5.75 ! [Z: int,X4: real] :
% 5.46/5.75 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.75 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % less_ceiling_iff
% 5.46/5.75 thf(fact_5974_ceiling__add__le,axiom,
% 5.46/5.75 ! [X4: rat,Y3: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ Y3 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_add_le
% 5.46/5.75 thf(fact_5975_ceiling__add__le,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ Y3 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim7802044766580827645g_real @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_add_le
% 5.46/5.75 thf(fact_5976_pochhammer__nonneg,axiom,
% 5.46/5.75 ! [X4: real,N: nat] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X4 @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_nonneg
% 5.46/5.75 thf(fact_5977_pochhammer__nonneg,axiom,
% 5.46/5.75 ! [X4: rat,N: nat] :
% 5.46/5.75 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.46/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X4 @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_nonneg
% 5.46/5.75 thf(fact_5978_pochhammer__nonneg,axiom,
% 5.46/5.75 ! [X4: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.46/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X4 @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_nonneg
% 5.46/5.75 thf(fact_5979_pochhammer__nonneg,axiom,
% 5.46/5.75 ! [X4: int,N: nat] :
% 5.46/5.75 ( ( ord_less_int @ zero_zero_int @ X4 )
% 5.46/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X4 @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_nonneg
% 5.46/5.75 thf(fact_5980_int__cases4,axiom,
% 5.46/5.75 ! [M: int] :
% 5.46/5.75 ( ! [N4: nat] :
% 5.46/5.75 ( M
% 5.46/5.75 != ( semiri1314217659103216013at_int @ N4 ) )
% 5.46/5.75 => ~ ! [N4: nat] :
% 5.46/5.75 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.46/5.75 => ( M
% 5.46/5.75 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_cases4
% 5.46/5.75 thf(fact_5981_pochhammer__0__left,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( ( N = zero_zero_nat )
% 5.46/5.75 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.46/5.75 = one_one_complex ) )
% 5.46/5.75 & ( ( N != zero_zero_nat )
% 5.46/5.75 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.46/5.75 = zero_zero_complex ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_0_left
% 5.46/5.75 thf(fact_5982_pochhammer__0__left,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( ( N = zero_zero_nat )
% 5.46/5.75 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.46/5.75 = one_one_real ) )
% 5.46/5.75 & ( ( N != zero_zero_nat )
% 5.46/5.75 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.46/5.75 = zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_0_left
% 5.46/5.75 thf(fact_5983_pochhammer__0__left,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( ( N = zero_zero_nat )
% 5.46/5.75 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.46/5.75 = one_one_rat ) )
% 5.46/5.75 & ( ( N != zero_zero_nat )
% 5.46/5.75 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.46/5.75 = zero_zero_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_0_left
% 5.46/5.75 thf(fact_5984_pochhammer__0__left,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( ( N = zero_zero_nat )
% 5.46/5.75 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.46/5.75 = one_one_nat ) )
% 5.46/5.75 & ( ( N != zero_zero_nat )
% 5.46/5.75 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.46/5.75 = zero_zero_nat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_0_left
% 5.46/5.75 thf(fact_5985_pochhammer__0__left,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( ( N = zero_zero_nat )
% 5.46/5.75 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.46/5.75 = one_one_int ) )
% 5.46/5.75 & ( ( N != zero_zero_nat )
% 5.46/5.75 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.46/5.75 = zero_zero_int ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_0_left
% 5.46/5.75 thf(fact_5986_int__Suc,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.46/5.75 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_Suc
% 5.46/5.75 thf(fact_5987_int__ops_I4_J,axiom,
% 5.46/5.75 ! [A: nat] :
% 5.46/5.75 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.46/5.75 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_ops(4)
% 5.46/5.75 thf(fact_5988_zless__iff__Suc__zadd,axiom,
% 5.46/5.75 ( ord_less_int
% 5.46/5.75 = ( ^ [W2: int,Z5: int] :
% 5.46/5.75 ? [N2: nat] :
% 5.46/5.75 ( Z5
% 5.46/5.75 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % zless_iff_Suc_zadd
% 5.46/5.75 thf(fact_5989_norm__exp,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X4 ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_exp
% 5.46/5.75 thf(fact_5990_norm__exp,axiom,
% 5.46/5.75 ! [X4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X4 ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_exp
% 5.46/5.75 thf(fact_5991_one__add__floor,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 5.46/5.75 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % one_add_floor
% 5.46/5.75 thf(fact_5992_one__add__floor,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 5.46/5.75 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % one_add_floor
% 5.46/5.75 thf(fact_5993_of__int__ceiling__le__add__one,axiom,
% 5.46/5.75 ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_int_ceiling_le_add_one
% 5.46/5.75 thf(fact_5994_of__int__ceiling__le__add__one,axiom,
% 5.46/5.75 ! [R2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ ( plus_plus_rat @ R2 @ one_one_rat ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_int_ceiling_le_add_one
% 5.46/5.75 thf(fact_5995_of__int__ceiling__diff__one__le,axiom,
% 5.46/5.75 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 5.46/5.75
% 5.46/5.75 % of_int_ceiling_diff_one_le
% 5.46/5.75 thf(fact_5996_of__int__ceiling__diff__one__le,axiom,
% 5.46/5.75 ! [R2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ one_one_rat ) @ R2 ) ).
% 5.46/5.75
% 5.46/5.75 % of_int_ceiling_diff_one_le
% 5.46/5.75 thf(fact_5997_floor__eq,axiom,
% 5.46/5.75 ! [N: int,X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.46/5.75 => ( ( archim6058952711729229775r_real @ X4 )
% 5.46/5.75 = N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_eq
% 5.46/5.75 thf(fact_5998_real__of__int__floor__add__one__gt,axiom,
% 5.46/5.75 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % real_of_int_floor_add_one_gt
% 5.46/5.75 thf(fact_5999_real__of__int__floor__add__one__ge,axiom,
% 5.46/5.75 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % real_of_int_floor_add_one_ge
% 5.46/5.75 thf(fact_6000_real__of__int__floor__gt__diff__one,axiom,
% 5.46/5.75 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % real_of_int_floor_gt_diff_one
% 5.46/5.75 thf(fact_6001_real__of__int__floor__ge__diff__one,axiom,
% 5.46/5.75 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % real_of_int_floor_ge_diff_one
% 5.46/5.75 thf(fact_6002_ceiling__divide__eq__div,axiom,
% 5.46/5.75 ! [A: int,B2: int] :
% 5.46/5.75 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B2 ) ) )
% 5.46/5.75 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_divide_eq_div
% 5.46/5.75 thf(fact_6003_ceiling__divide__eq__div,axiom,
% 5.46/5.75 ! [A: int,B2: int] :
% 5.46/5.75 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B2 ) ) )
% 5.46/5.75 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_divide_eq_div
% 5.46/5.75 thf(fact_6004_zero__less__imp__eq__int,axiom,
% 5.46/5.75 ! [K: int] :
% 5.46/5.75 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.75 => ? [N4: nat] :
% 5.46/5.75 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.46/5.75 & ( K
% 5.46/5.75 = ( semiri1314217659103216013at_int @ N4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % zero_less_imp_eq_int
% 5.46/5.75 thf(fact_6005_pos__int__cases,axiom,
% 5.46/5.75 ! [K: int] :
% 5.46/5.75 ( ( ord_less_int @ zero_zero_int @ K )
% 5.46/5.75 => ~ ! [N4: nat] :
% 5.46/5.75 ( ( K
% 5.46/5.75 = ( semiri1314217659103216013at_int @ N4 ) )
% 5.46/5.75 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pos_int_cases
% 5.46/5.75 thf(fact_6006_int__cases3,axiom,
% 5.46/5.75 ! [K: int] :
% 5.46/5.75 ( ( K != zero_zero_int )
% 5.46/5.75 => ( ! [N4: nat] :
% 5.46/5.75 ( ( K
% 5.46/5.75 = ( semiri1314217659103216013at_int @ N4 ) )
% 5.46/5.75 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) )
% 5.46/5.75 => ~ ! [N4: nat] :
% 5.46/5.75 ( ( K
% 5.46/5.75 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N4 ) ) )
% 5.46/5.75 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_cases3
% 5.46/5.75 thf(fact_6007_pi__less__4,axiom,
% 5.46/5.75 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pi_less_4
% 5.46/5.75 thf(fact_6008_pi__ge__two,axiom,
% 5.46/5.75 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.46/5.75
% 5.46/5.75 % pi_ge_two
% 5.46/5.75 thf(fact_6009_zmult__zless__mono2__lemma,axiom,
% 5.46/5.75 ! [I: int,J: int,K: nat] :
% 5.46/5.75 ( ( ord_less_int @ I @ J )
% 5.46/5.75 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.75 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % zmult_zless_mono2_lemma
% 5.46/5.75 thf(fact_6010_not__zle__0__negative,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % not_zle_0_negative
% 5.46/5.75 thf(fact_6011_negative__zless__0,axiom,
% 5.46/5.75 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.46/5.75
% 5.46/5.75 % negative_zless_0
% 5.46/5.75 thf(fact_6012_negD,axiom,
% 5.46/5.75 ! [X4: int] :
% 5.46/5.75 ( ( ord_less_int @ X4 @ zero_zero_int )
% 5.46/5.75 => ? [N4: nat] :
% 5.46/5.75 ( X4
% 5.46/5.75 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % negD
% 5.46/5.75 thf(fact_6013_pi__half__neq__two,axiom,
% 5.46/5.75 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.75 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pi_half_neq_two
% 5.46/5.75 thf(fact_6014_pochhammer__rec,axiom,
% 5.46/5.75 ! [A: complex,N: nat] :
% 5.46/5.75 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_rec
% 5.46/5.75 thf(fact_6015_pochhammer__rec,axiom,
% 5.46/5.75 ! [A: real,N: nat] :
% 5.46/5.75 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_rec
% 5.46/5.75 thf(fact_6016_pochhammer__rec,axiom,
% 5.46/5.75 ! [A: rat,N: nat] :
% 5.46/5.75 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_rec
% 5.46/5.75 thf(fact_6017_pochhammer__rec,axiom,
% 5.46/5.75 ! [A: nat,N: nat] :
% 5.46/5.75 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_rec
% 5.46/5.75 thf(fact_6018_pochhammer__rec,axiom,
% 5.46/5.75 ! [A: int,N: nat] :
% 5.46/5.75 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_rec
% 5.46/5.75 thf(fact_6019_pochhammer__Suc,axiom,
% 5.46/5.75 ! [A: complex,N: nat] :
% 5.46/5.75 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_Suc
% 5.46/5.75 thf(fact_6020_pochhammer__Suc,axiom,
% 5.46/5.75 ! [A: real,N: nat] :
% 5.46/5.75 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_Suc
% 5.46/5.75 thf(fact_6021_pochhammer__Suc,axiom,
% 5.46/5.75 ! [A: rat,N: nat] :
% 5.46/5.75 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_Suc
% 5.46/5.75 thf(fact_6022_pochhammer__Suc,axiom,
% 5.46/5.75 ! [A: nat,N: nat] :
% 5.46/5.75 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_Suc
% 5.46/5.75 thf(fact_6023_pochhammer__Suc,axiom,
% 5.46/5.75 ! [A: int,N: nat] :
% 5.46/5.75 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_Suc
% 5.46/5.75 thf(fact_6024_pochhammer__rec_H,axiom,
% 5.46/5.75 ! [Z: complex,N: nat] :
% 5.46/5.75 ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_rec'
% 5.46/5.75 thf(fact_6025_pochhammer__rec_H,axiom,
% 5.46/5.75 ! [Z: real,N: nat] :
% 5.46/5.75 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_rec'
% 5.46/5.75 thf(fact_6026_pochhammer__rec_H,axiom,
% 5.46/5.75 ! [Z: rat,N: nat] :
% 5.46/5.75 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_rec'
% 5.46/5.75 thf(fact_6027_pochhammer__rec_H,axiom,
% 5.46/5.75 ! [Z: nat,N: nat] :
% 5.46/5.75 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_rec'
% 5.46/5.75 thf(fact_6028_pochhammer__rec_H,axiom,
% 5.46/5.75 ! [Z: int,N: nat] :
% 5.46/5.75 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 5.46/5.75 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_rec'
% 5.46/5.75 thf(fact_6029_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_nat @ N @ K )
% 5.46/5.75 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.46/5.75 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_lemma
% 5.46/5.75 thf(fact_6030_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_nat @ N @ K )
% 5.46/5.75 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.46/5.75 = zero_zero_complex ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_lemma
% 5.46/5.75 thf(fact_6031_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_nat @ N @ K )
% 5.46/5.75 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.46/5.75 = zero_zero_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_lemma
% 5.46/5.75 thf(fact_6032_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_nat @ N @ K )
% 5.46/5.75 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.46/5.75 = zero_zero_rat ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_lemma
% 5.46/5.75 thf(fact_6033_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_nat @ N @ K )
% 5.46/5.75 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.46/5.75 = zero_zero_int ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_lemma
% 5.46/5.75 thf(fact_6034_pochhammer__of__nat__eq__0__iff,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.46/5.75 = zero_z3403309356797280102nteger )
% 5.46/5.75 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_iff
% 5.46/5.75 thf(fact_6035_pochhammer__of__nat__eq__0__iff,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.46/5.75 = zero_zero_complex )
% 5.46/5.75 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_iff
% 5.46/5.75 thf(fact_6036_pochhammer__of__nat__eq__0__iff,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_iff
% 5.46/5.75 thf(fact_6037_pochhammer__of__nat__eq__0__iff,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.46/5.75 = zero_zero_rat )
% 5.46/5.75 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_iff
% 5.46/5.75 thf(fact_6038_pochhammer__of__nat__eq__0__iff,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.46/5.75 = zero_zero_int )
% 5.46/5.75 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_iff
% 5.46/5.75 thf(fact_6039_pochhammer__eq__0__iff,axiom,
% 5.46/5.75 ! [A: complex,N: nat] :
% 5.46/5.75 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.46/5.75 = zero_zero_complex )
% 5.46/5.75 = ( ? [K3: nat] :
% 5.46/5.75 ( ( ord_less_nat @ K3 @ N )
% 5.46/5.75 & ( A
% 5.46/5.75 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_eq_0_iff
% 5.46/5.75 thf(fact_6040_pochhammer__eq__0__iff,axiom,
% 5.46/5.75 ! [A: real,N: nat] :
% 5.46/5.75 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 = ( ? [K3: nat] :
% 5.46/5.75 ( ( ord_less_nat @ K3 @ N )
% 5.46/5.75 & ( A
% 5.46/5.75 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_eq_0_iff
% 5.46/5.75 thf(fact_6041_pochhammer__eq__0__iff,axiom,
% 5.46/5.75 ! [A: rat,N: nat] :
% 5.46/5.75 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.46/5.75 = zero_zero_rat )
% 5.46/5.75 = ( ? [K3: nat] :
% 5.46/5.75 ( ( ord_less_nat @ K3 @ N )
% 5.46/5.75 & ( A
% 5.46/5.75 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_eq_0_iff
% 5.46/5.75 thf(fact_6042_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.75 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.46/5.75 != zero_z3403309356797280102nteger ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_lemma'
% 5.46/5.75 thf(fact_6043_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.75 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.46/5.75 != zero_zero_complex ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_lemma'
% 5.46/5.75 thf(fact_6044_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.75 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.46/5.75 != zero_zero_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_lemma'
% 5.46/5.75 thf(fact_6045_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.75 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.46/5.75 != zero_zero_rat ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_lemma'
% 5.46/5.75 thf(fact_6046_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.75 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.46/5.75 != zero_zero_int ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_of_nat_eq_0_lemma'
% 5.46/5.75 thf(fact_6047_int__ops_I6_J,axiom,
% 5.46/5.75 ! [A: nat,B2: nat] :
% 5.46/5.75 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) )
% 5.46/5.75 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B2 ) )
% 5.46/5.75 = zero_zero_int ) )
% 5.46/5.75 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) )
% 5.46/5.75 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B2 ) )
% 5.46/5.75 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % int_ops(6)
% 5.46/5.75 thf(fact_6048_pochhammer__product_H,axiom,
% 5.46/5.75 ! [Z: complex,N: nat,M: nat] :
% 5.46/5.75 ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.75 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_product'
% 5.46/5.75 thf(fact_6049_pochhammer__product_H,axiom,
% 5.46/5.75 ! [Z: real,N: nat,M: nat] :
% 5.46/5.75 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.75 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_product'
% 5.46/5.75 thf(fact_6050_pochhammer__product_H,axiom,
% 5.46/5.75 ! [Z: rat,N: nat,M: nat] :
% 5.46/5.75 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.75 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_product'
% 5.46/5.75 thf(fact_6051_pochhammer__product_H,axiom,
% 5.46/5.75 ! [Z: nat,N: nat,M: nat] :
% 5.46/5.75 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.75 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_product'
% 5.46/5.75 thf(fact_6052_pochhammer__product_H,axiom,
% 5.46/5.75 ! [Z: int,N: nat,M: nat] :
% 5.46/5.75 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.46/5.75 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_product'
% 5.46/5.75 thf(fact_6053_floor__split,axiom,
% 5.46/5.75 ! [P: int > $o,T: real] :
% 5.46/5.75 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 5.46/5.75 = ( ! [I2: int] :
% 5.46/5.75 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I2 ) @ T )
% 5.46/5.75 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I2 ) @ one_one_real ) ) )
% 5.46/5.75 => ( P @ I2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_split
% 5.46/5.75 thf(fact_6054_floor__split,axiom,
% 5.46/5.75 ! [P: int > $o,T: rat] :
% 5.46/5.75 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 5.46/5.75 = ( ! [I2: int] :
% 5.46/5.75 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I2 ) @ T )
% 5.46/5.75 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) ) )
% 5.46/5.75 => ( P @ I2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_split
% 5.46/5.75 thf(fact_6055_floor__eq__iff,axiom,
% 5.46/5.75 ! [X4: real,A: int] :
% 5.46/5.75 ( ( ( archim6058952711729229775r_real @ X4 )
% 5.46/5.75 = A )
% 5.46/5.75 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X4 )
% 5.46/5.75 & ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_eq_iff
% 5.46/5.75 thf(fact_6056_floor__eq__iff,axiom,
% 5.46/5.75 ! [X4: rat,A: int] :
% 5.46/5.75 ( ( ( archim3151403230148437115or_rat @ X4 )
% 5.46/5.75 = A )
% 5.46/5.75 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X4 )
% 5.46/5.75 & ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_eq_iff
% 5.46/5.75 thf(fact_6057_floor__unique,axiom,
% 5.46/5.75 ! [Z: int,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 5.46/5.75 => ( ( archim6058952711729229775r_real @ X4 )
% 5.46/5.75 = Z ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_unique
% 5.46/5.75 thf(fact_6058_floor__unique,axiom,
% 5.46/5.75 ! [Z: int,X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X4 )
% 5.46/5.75 => ( ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 5.46/5.75 => ( ( archim3151403230148437115or_rat @ X4 )
% 5.46/5.75 = Z ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_unique
% 5.46/5.75 thf(fact_6059_le__mult__floor,axiom,
% 5.46/5.75 ! [A: real,B2: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.75 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B2 ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B2 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_mult_floor
% 5.46/5.75 thf(fact_6060_le__mult__floor,axiom,
% 5.46/5.75 ! [A: rat,B2: rat] :
% 5.46/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.75 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B2 ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B2 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_mult_floor
% 5.46/5.75 thf(fact_6061_less__floor__iff,axiom,
% 5.46/5.75 ! [Z: int,X4: real] :
% 5.46/5.75 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % less_floor_iff
% 5.46/5.75 thf(fact_6062_less__floor__iff,axiom,
% 5.46/5.75 ! [Z: int,X4: rat] :
% 5.46/5.75 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % less_floor_iff
% 5.46/5.75 thf(fact_6063_floor__le__iff,axiom,
% 5.46/5.75 ! [X4: real,Z: int] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 5.46/5.75 = ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_le_iff
% 5.46/5.75 thf(fact_6064_floor__le__iff,axiom,
% 5.46/5.75 ! [X4: rat,Z: int] :
% 5.46/5.75 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 5.46/5.75 = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_le_iff
% 5.46/5.75 thf(fact_6065_binomial__mono,axiom,
% 5.46/5.75 ! [K: nat,K6: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ K6 )
% 5.46/5.75 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.46/5.75 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_mono
% 5.46/5.75 thf(fact_6066_binomial__maximum_H,axiom,
% 5.46/5.75 ! [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 ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_maximum'
% 5.46/5.75 thf(fact_6067_binomial__maximum,axiom,
% 5.46/5.75 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_maximum
% 5.46/5.75 thf(fact_6068_binomial__antimono,axiom,
% 5.46/5.75 ! [K: nat,K6: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ K6 )
% 5.46/5.75 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.46/5.75 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.46/5.75 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_antimono
% 5.46/5.75 thf(fact_6069_floor__correct,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) @ X4 )
% 5.46/5.75 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_correct
% 5.46/5.75 thf(fact_6070_floor__correct,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) @ X4 )
% 5.46/5.75 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_correct
% 5.46/5.75 thf(fact_6071_ceiling__split,axiom,
% 5.46/5.75 ! [P: int > $o,T: real] :
% 5.46/5.75 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.46/5.75 = ( ! [I2: int] :
% 5.46/5.75 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I2 ) @ one_one_real ) @ T )
% 5.46/5.75 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I2 ) ) )
% 5.46/5.75 => ( P @ I2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_split
% 5.46/5.75 thf(fact_6072_ceiling__split,axiom,
% 5.46/5.75 ! [P: int > $o,T: rat] :
% 5.46/5.75 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 5.46/5.75 = ( ! [I2: int] :
% 5.46/5.75 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) @ T )
% 5.46/5.75 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I2 ) ) )
% 5.46/5.75 => ( P @ I2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_split
% 5.46/5.75 thf(fact_6073_ceiling__eq__iff,axiom,
% 5.46/5.75 ! [X4: real,A: int] :
% 5.46/5.75 ( ( ( archim7802044766580827645g_real @ X4 )
% 5.46/5.75 = A )
% 5.46/5.75 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X4 )
% 5.46/5.75 & ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_eq_iff
% 5.46/5.75 thf(fact_6074_ceiling__eq__iff,axiom,
% 5.46/5.75 ! [X4: rat,A: int] :
% 5.46/5.75 ( ( ( archim2889992004027027881ng_rat @ X4 )
% 5.46/5.75 = A )
% 5.46/5.75 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X4 )
% 5.46/5.75 & ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_eq_iff
% 5.46/5.75 thf(fact_6075_ceiling__unique,axiom,
% 5.46/5.75 ! [Z: int,X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z ) )
% 5.46/5.75 => ( ( archim7802044766580827645g_real @ X4 )
% 5.46/5.75 = Z ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_unique
% 5.46/5.75 thf(fact_6076_ceiling__unique,axiom,
% 5.46/5.75 ! [Z: int,X4: rat] :
% 5.46/5.75 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z ) )
% 5.46/5.75 => ( ( archim2889992004027027881ng_rat @ X4 )
% 5.46/5.75 = Z ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_unique
% 5.46/5.75 thf(fact_6077_ceiling__correct,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) @ one_one_real ) @ X4 )
% 5.46/5.75 & ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_correct
% 5.46/5.75 thf(fact_6078_ceiling__correct,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) @ one_one_rat ) @ X4 )
% 5.46/5.75 & ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_correct
% 5.46/5.75 thf(fact_6079_mult__ceiling__le,axiom,
% 5.46/5.75 ! [A: real,B2: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ B2 )
% 5.46/5.75 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B2 ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B2 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % mult_ceiling_le
% 5.46/5.75 thf(fact_6080_mult__ceiling__le,axiom,
% 5.46/5.75 ! [A: rat,B2: rat] :
% 5.46/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ B2 )
% 5.46/5.75 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B2 ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B2 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % mult_ceiling_le
% 5.46/5.75 thf(fact_6081_floor__log__nat__eq__if,axiom,
% 5.46/5.75 ! [B2: nat,N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ N ) @ K )
% 5.46/5.75 => ( ( ord_less_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.46/5.75 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.46/5.75 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.46/5.75 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_log_nat_eq_if
% 5.46/5.75 thf(fact_6082_ceiling__less__iff,axiom,
% 5.46/5.75 ! [X4: real,Z: int] :
% 5.46/5.75 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ Z )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_less_iff
% 5.46/5.75 thf(fact_6083_ceiling__less__iff,axiom,
% 5.46/5.75 ! [X4: rat,Z: int] :
% 5.46/5.75 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z )
% 5.46/5.75 = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_less_iff
% 5.46/5.75 thf(fact_6084_le__ceiling__iff,axiom,
% 5.46/5.75 ! [Z: int,X4: rat] :
% 5.46/5.75 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.46/5.75 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_ceiling_iff
% 5.46/5.75 thf(fact_6085_le__ceiling__iff,axiom,
% 5.46/5.75 ! [Z: int,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X4 ) )
% 5.46/5.75 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_ceiling_iff
% 5.46/5.75 thf(fact_6086_floor__eq2,axiom,
% 5.46/5.75 ! [N: int,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.46/5.75 => ( ( archim6058952711729229775r_real @ X4 )
% 5.46/5.75 = N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_eq2
% 5.46/5.75 thf(fact_6087_floor__divide__real__eq__div,axiom,
% 5.46/5.75 ! [B2: int,A: real] :
% 5.46/5.75 ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.75 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B2 ) ) )
% 5.46/5.75 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_divide_real_eq_div
% 5.46/5.75 thf(fact_6088_neg__int__cases,axiom,
% 5.46/5.75 ! [K: int] :
% 5.46/5.75 ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.75 => ~ ! [N4: nat] :
% 5.46/5.75 ( ( K
% 5.46/5.75 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N4 ) ) )
% 5.46/5.75 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % neg_int_cases
% 5.46/5.75 thf(fact_6089_pi__half__neq__zero,axiom,
% 5.46/5.75 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.75 != zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % pi_half_neq_zero
% 5.46/5.75 thf(fact_6090_pi__half__less__two,axiom,
% 5.46/5.75 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.46/5.75
% 5.46/5.75 % pi_half_less_two
% 5.46/5.75 thf(fact_6091_pi__half__le__two,axiom,
% 5.46/5.75 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.46/5.75
% 5.46/5.75 % pi_half_le_two
% 5.46/5.75 thf(fact_6092_zdiff__int__split,axiom,
% 5.46/5.75 ! [P: int > $o,X4: nat,Y3: nat] :
% 5.46/5.75 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X4 @ Y3 ) ) )
% 5.46/5.75 = ( ( ( ord_less_eq_nat @ Y3 @ X4 )
% 5.46/5.75 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) )
% 5.46/5.75 & ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.75 => ( P @ zero_zero_int ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % zdiff_int_split
% 5.46/5.75 thf(fact_6093_floor__log__nat__eq__powr__iff,axiom,
% 5.46/5.75 ! [B2: nat,K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.46/5.75 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.75 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.46/5.75 = ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.75 = ( ( ord_less_eq_nat @ ( power_power_nat @ B2 @ N ) @ K )
% 5.46/5.75 & ( ord_less_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_log_nat_eq_powr_iff
% 5.46/5.75 thf(fact_6094_pochhammer__product,axiom,
% 5.46/5.75 ! [M: nat,N: nat,Z: complex] :
% 5.46/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.75 => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 5.46/5.75 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_product
% 5.46/5.75 thf(fact_6095_pochhammer__product,axiom,
% 5.46/5.75 ! [M: nat,N: nat,Z: real] :
% 5.46/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.75 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 5.46/5.75 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_product
% 5.46/5.75 thf(fact_6096_pochhammer__product,axiom,
% 5.46/5.75 ! [M: nat,N: nat,Z: rat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.75 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 5.46/5.75 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_product
% 5.46/5.75 thf(fact_6097_pochhammer__product,axiom,
% 5.46/5.75 ! [M: nat,N: nat,Z: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.75 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 5.46/5.75 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_product
% 5.46/5.75 thf(fact_6098_pochhammer__product,axiom,
% 5.46/5.75 ! [M: nat,N: nat,Z: int] :
% 5.46/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.75 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 5.46/5.75 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_product
% 5.46/5.75 thf(fact_6099_floor__divide__lower,axiom,
% 5.46/5.75 ! [Q2: real,P2: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.46/5.75 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q2 ) ) ) @ Q2 ) @ P2 ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_divide_lower
% 5.46/5.75 thf(fact_6100_floor__divide__lower,axiom,
% 5.46/5.75 ! [Q2: rat,P2: rat] :
% 5.46/5.75 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.46/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q2 ) ) ) @ Q2 ) @ P2 ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_divide_lower
% 5.46/5.75 thf(fact_6101_binomial__less__binomial__Suc,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_less_binomial_Suc
% 5.46/5.75 thf(fact_6102_binomial__strict__mono,axiom,
% 5.46/5.75 ! [K: nat,K6: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_nat @ K @ K6 )
% 5.46/5.75 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.46/5.75 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_strict_mono
% 5.46/5.75 thf(fact_6103_binomial__strict__antimono,axiom,
% 5.46/5.75 ! [K: nat,K6: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_nat @ K @ K6 )
% 5.46/5.75 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.46/5.75 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.46/5.75 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_strict_antimono
% 5.46/5.75 thf(fact_6104_central__binomial__odd,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.75 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.75 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % central_binomial_odd
% 5.46/5.75 thf(fact_6105_ceiling__divide__upper,axiom,
% 5.46/5.75 ! [Q2: real,P2: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.46/5.75 => ( ord_less_eq_real @ P2 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_divide_upper
% 5.46/5.75 thf(fact_6106_ceiling__divide__upper,axiom,
% 5.46/5.75 ! [Q2: rat,P2: rat] :
% 5.46/5.75 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.46/5.75 => ( ord_less_eq_rat @ P2 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_divide_upper
% 5.46/5.75 thf(fact_6107_bit__nat__def,axiom,
% 5.46/5.75 ( bit_se1148574629649215175it_nat
% 5.46/5.75 = ( ^ [M6: nat,N2: nat] :
% 5.46/5.75 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % bit_nat_def
% 5.46/5.75 thf(fact_6108_ceiling__log__nat__eq__if,axiom,
% 5.46/5.75 ! [B2: nat,N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_nat @ ( power_power_nat @ B2 @ N ) @ K )
% 5.46/5.75 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.46/5.75 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.46/5.75 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.46/5.75 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_log_nat_eq_if
% 5.46/5.75 thf(fact_6109_pi__half__gt__zero,axiom,
% 5.46/5.75 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pi_half_gt_zero
% 5.46/5.75 thf(fact_6110_pi__half__ge__zero,axiom,
% 5.46/5.75 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pi_half_ge_zero
% 5.46/5.75 thf(fact_6111_pochhammer__absorb__comp,axiom,
% 5.46/5.75 ! [R2: code_integer,K: nat] :
% 5.46/5.75 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 5.46/5.75 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_absorb_comp
% 5.46/5.75 thf(fact_6112_pochhammer__absorb__comp,axiom,
% 5.46/5.75 ! [R2: complex,K: nat] :
% 5.46/5.75 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 5.46/5.75 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_absorb_comp
% 5.46/5.75 thf(fact_6113_pochhammer__absorb__comp,axiom,
% 5.46/5.75 ! [R2: real,K: nat] :
% 5.46/5.75 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 5.46/5.75 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_absorb_comp
% 5.46/5.75 thf(fact_6114_pochhammer__absorb__comp,axiom,
% 5.46/5.75 ! [R2: rat,K: nat] :
% 5.46/5.75 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 5.46/5.75 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_absorb_comp
% 5.46/5.75 thf(fact_6115_pochhammer__absorb__comp,axiom,
% 5.46/5.75 ! [R2: int,K: nat] :
% 5.46/5.75 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 5.46/5.75 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_absorb_comp
% 5.46/5.75 thf(fact_6116_m2pi__less__pi,axiom,
% 5.46/5.75 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.46/5.75
% 5.46/5.75 % m2pi_less_pi
% 5.46/5.75 thf(fact_6117_ceiling__log__nat__eq__powr__iff,axiom,
% 5.46/5.75 ! [B2: nat,K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 )
% 5.46/5.75 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.75 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B2 ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.46/5.75 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.46/5.75 = ( ( ord_less_nat @ ( power_power_nat @ B2 @ N ) @ K )
% 5.46/5.75 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_log_nat_eq_powr_iff
% 5.46/5.75 thf(fact_6118_floor__divide__upper,axiom,
% 5.46/5.75 ! [Q2: real,P2: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.46/5.75 => ( ord_less_real @ P2 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_divide_upper
% 5.46/5.75 thf(fact_6119_floor__divide__upper,axiom,
% 5.46/5.75 ! [Q2: rat,P2: rat] :
% 5.46/5.75 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.46/5.75 => ( ord_less_rat @ P2 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_divide_upper
% 5.46/5.75 thf(fact_6120_arctan__ubound,axiom,
% 5.46/5.75 ! [Y3: real] : ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arctan_ubound
% 5.46/5.75 thf(fact_6121_arctan__one,axiom,
% 5.46/5.75 ( ( arctan @ one_one_real )
% 5.46/5.75 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arctan_one
% 5.46/5.75 thf(fact_6122_round__def,axiom,
% 5.46/5.75 ( archim8280529875227126926d_real
% 5.46/5.75 = ( ^ [X: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % round_def
% 5.46/5.75 thf(fact_6123_round__def,axiom,
% 5.46/5.75 ( archim7778729529865785530nd_rat
% 5.46/5.75 = ( ^ [X: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % round_def
% 5.46/5.75 thf(fact_6124_ceiling__divide__lower,axiom,
% 5.46/5.75 ! [Q2: real,P2: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.46/5.75 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) @ P2 ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_divide_lower
% 5.46/5.75 thf(fact_6125_ceiling__divide__lower,axiom,
% 5.46/5.75 ! [Q2: rat,P2: rat] :
% 5.46/5.75 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.46/5.75 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) @ P2 ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_divide_lower
% 5.46/5.75 thf(fact_6126_ceiling__eq,axiom,
% 5.46/5.75 ! [N: int,X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.46/5.75 => ( ( archim7802044766580827645g_real @ X4 )
% 5.46/5.75 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_eq
% 5.46/5.75 thf(fact_6127_ceiling__eq,axiom,
% 5.46/5.75 ! [N: int,X4: rat] :
% 5.46/5.75 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 5.46/5.75 => ( ( archim2889992004027027881ng_rat @ X4 )
% 5.46/5.75 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_eq
% 5.46/5.75 thf(fact_6128_exp__bound__half,axiom,
% 5.46/5.75 ! [Z: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % exp_bound_half
% 5.46/5.75 thf(fact_6129_exp__bound__half,axiom,
% 5.46/5.75 ! [Z: complex] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % exp_bound_half
% 5.46/5.75 thf(fact_6130_minus__pi__half__less__zero,axiom,
% 5.46/5.75 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.46/5.75
% 5.46/5.75 % minus_pi_half_less_zero
% 5.46/5.75 thf(fact_6131_pochhammer__minus,axiom,
% 5.46/5.75 ! [B2: code_integer,K: nat] :
% 5.46/5.75 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B2 ) @ K )
% 5.46/5.75 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B2 @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_minus
% 5.46/5.75 thf(fact_6132_pochhammer__minus,axiom,
% 5.46/5.75 ! [B2: complex,K: nat] :
% 5.46/5.75 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B2 ) @ K )
% 5.46/5.75 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B2 @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_minus
% 5.46/5.75 thf(fact_6133_pochhammer__minus,axiom,
% 5.46/5.75 ! [B2: real,K: nat] :
% 5.46/5.75 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B2 ) @ K )
% 5.46/5.75 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B2 @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_minus
% 5.46/5.75 thf(fact_6134_pochhammer__minus,axiom,
% 5.46/5.75 ! [B2: rat,K: nat] :
% 5.46/5.75 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B2 ) @ K )
% 5.46/5.75 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B2 @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_minus
% 5.46/5.75 thf(fact_6135_pochhammer__minus,axiom,
% 5.46/5.75 ! [B2: int,K: nat] :
% 5.46/5.75 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B2 ) @ K )
% 5.46/5.75 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B2 @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_minus
% 5.46/5.75 thf(fact_6136_pochhammer__minus_H,axiom,
% 5.46/5.75 ! [B2: code_integer,K: nat] :
% 5.46/5.75 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B2 @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.46/5.75 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B2 ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_minus'
% 5.46/5.75 thf(fact_6137_pochhammer__minus_H,axiom,
% 5.46/5.75 ! [B2: complex,K: nat] :
% 5.46/5.75 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B2 @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.46/5.75 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B2 ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_minus'
% 5.46/5.75 thf(fact_6138_pochhammer__minus_H,axiom,
% 5.46/5.75 ! [B2: real,K: nat] :
% 5.46/5.75 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B2 @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.46/5.75 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B2 ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_minus'
% 5.46/5.75 thf(fact_6139_pochhammer__minus_H,axiom,
% 5.46/5.75 ! [B2: rat,K: nat] :
% 5.46/5.75 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B2 @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.46/5.75 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B2 ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_minus'
% 5.46/5.75 thf(fact_6140_pochhammer__minus_H,axiom,
% 5.46/5.75 ! [B2: int,K: nat] :
% 5.46/5.75 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B2 @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.46/5.75 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B2 ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % pochhammer_minus'
% 5.46/5.75 thf(fact_6141_arctan__lbound,axiom,
% 5.46/5.75 ! [Y3: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) ) ).
% 5.46/5.75
% 5.46/5.75 % arctan_lbound
% 5.46/5.75 thf(fact_6142_arctan__bounded,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) )
% 5.46/5.75 & ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arctan_bounded
% 5.46/5.75 thf(fact_6143_exp__bound__lemma,axiom,
% 5.46/5.75 ! [Z: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % exp_bound_lemma
% 5.46/5.75 thf(fact_6144_exp__bound__lemma,axiom,
% 5.46/5.75 ! [Z: complex] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % exp_bound_lemma
% 5.46/5.75 thf(fact_6145_machin__Euler,axiom,
% 5.46/5.75 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.75 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % machin_Euler
% 5.46/5.75 thf(fact_6146_norm__divide__numeral,axiom,
% 5.46/5.75 ! [A: real,W: num] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.75 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_divide_numeral
% 5.46/5.75 thf(fact_6147_norm__divide__numeral,axiom,
% 5.46/5.75 ! [A: complex,W: num] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.75 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_divide_numeral
% 5.46/5.75 thf(fact_6148_norm__mult__numeral1,axiom,
% 5.46/5.75 ! [W: num,A: real] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.46/5.75 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_mult_numeral1
% 5.46/5.75 thf(fact_6149_norm__mult__numeral1,axiom,
% 5.46/5.75 ! [W: num,A: complex] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.46/5.75 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_mult_numeral1
% 5.46/5.75 thf(fact_6150_norm__mult__numeral2,axiom,
% 5.46/5.75 ! [A: real,W: num] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.75 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_mult_numeral2
% 5.46/5.75 thf(fact_6151_norm__mult__numeral2,axiom,
% 5.46/5.75 ! [A: complex,W: num] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.75 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_mult_numeral2
% 5.46/5.75 thf(fact_6152_zero__less__binomial__iff,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.46/5.75 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % zero_less_binomial_iff
% 5.46/5.75 thf(fact_6153_norm__neg__numeral,axiom,
% 5.46/5.75 ! [W: num] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.75 = ( numeral_numeral_real @ W ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_neg_numeral
% 5.46/5.75 thf(fact_6154_norm__neg__numeral,axiom,
% 5.46/5.75 ! [W: num] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.75 = ( numeral_numeral_real @ W ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_neg_numeral
% 5.46/5.75 thf(fact_6155_norm__le__zero__iff,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X4 ) @ zero_zero_real )
% 5.46/5.75 = ( X4 = zero_zero_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_le_zero_iff
% 5.46/5.75 thf(fact_6156_norm__le__zero__iff,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ zero_zero_real )
% 5.46/5.75 = ( X4 = zero_zero_complex ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_le_zero_iff
% 5.46/5.75 thf(fact_6157_binomial__Suc__n,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( binomial @ ( suc @ N ) @ N )
% 5.46/5.75 = ( suc @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_Suc_n
% 5.46/5.75 thf(fact_6158_binomial__n__n,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( binomial @ N @ N )
% 5.46/5.75 = one_one_nat ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_n_n
% 5.46/5.75 thf(fact_6159_norm__one,axiom,
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % norm_one
% 5.46/5.75 thf(fact_6160_norm__one,axiom,
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % norm_one
% 5.46/5.75 thf(fact_6161_norm__numeral,axiom,
% 5.46/5.75 ! [W: num] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.75 = ( numeral_numeral_real @ W ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_numeral
% 5.46/5.75 thf(fact_6162_norm__numeral,axiom,
% 5.46/5.75 ! [W: num] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.75 = ( numeral_numeral_real @ W ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_numeral
% 5.46/5.75 thf(fact_6163_binomial__0__Suc,axiom,
% 5.46/5.75 ! [K: nat] :
% 5.46/5.75 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.46/5.75 = zero_zero_nat ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_0_Suc
% 5.46/5.75 thf(fact_6164_binomial__1,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.75 = N ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_1
% 5.46/5.75 thf(fact_6165_binomial__eq__0__iff,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ( binomial @ N @ K )
% 5.46/5.75 = zero_zero_nat )
% 5.46/5.75 = ( ord_less_nat @ N @ K ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_eq_0_iff
% 5.46/5.75 thf(fact_6166_binomial__Suc__Suc,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.46/5.75 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_Suc_Suc
% 5.46/5.75 thf(fact_6167_binomial__n__0,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( binomial @ N @ zero_zero_nat )
% 5.46/5.75 = one_one_nat ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_n_0
% 5.46/5.75 thf(fact_6168_zero__less__norm__iff,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X4 ) )
% 5.46/5.75 = ( X4 != zero_zero_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % zero_less_norm_iff
% 5.46/5.75 thf(fact_6169_zero__less__norm__iff,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X4 ) )
% 5.46/5.75 = ( X4 != zero_zero_complex ) ) ).
% 5.46/5.75
% 5.46/5.75 % zero_less_norm_iff
% 5.46/5.75 thf(fact_6170_norm__minus__commute,axiom,
% 5.46/5.75 ! [A: real,B2: real] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B2 ) )
% 5.46/5.75 = ( real_V7735802525324610683m_real @ ( minus_minus_real @ B2 @ A ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_minus_commute
% 5.46/5.75 thf(fact_6171_norm__minus__commute,axiom,
% 5.46/5.75 ! [A: complex,B2: complex] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B2 ) )
% 5.46/5.75 = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B2 @ A ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_minus_commute
% 5.46/5.75 thf(fact_6172_choose__one,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( binomial @ N @ one_one_nat )
% 5.46/5.75 = N ) ).
% 5.46/5.75
% 5.46/5.75 % choose_one
% 5.46/5.75 thf(fact_6173_norm__not__less__zero,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % norm_not_less_zero
% 5.46/5.75 thf(fact_6174_norm__ge__zero,axiom,
% 5.46/5.75 ! [X4: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_ge_zero
% 5.46/5.75 thf(fact_6175_norm__mult,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( times_times_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_mult
% 5.46/5.75 thf(fact_6176_norm__mult,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X4 @ Y3 ) )
% 5.46/5.75 = ( times_times_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_mult
% 5.46/5.75 thf(fact_6177_norm__divide,axiom,
% 5.46/5.75 ! [A: real,B2: real] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.75 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_divide
% 5.46/5.75 thf(fact_6178_norm__divide,axiom,
% 5.46/5.75 ! [A: complex,B2: complex] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.75 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_divide
% 5.46/5.75 thf(fact_6179_norm__power,axiom,
% 5.46/5.75 ! [X4: real,N: nat] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X4 @ N ) )
% 5.46/5.75 = ( power_power_real @ ( real_V7735802525324610683m_real @ X4 ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_power
% 5.46/5.75 thf(fact_6180_norm__power,axiom,
% 5.46/5.75 ! [X4: complex,N: nat] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X4 @ N ) )
% 5.46/5.75 = ( power_power_real @ ( real_V1022390504157884413omplex @ X4 ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_power
% 5.46/5.75 thf(fact_6181_binomial__eq__0,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_nat @ N @ K )
% 5.46/5.75 => ( ( binomial @ N @ K )
% 5.46/5.75 = zero_zero_nat ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_eq_0
% 5.46/5.75 thf(fact_6182_Suc__times__binomial,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.46/5.75 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % Suc_times_binomial
% 5.46/5.75 thf(fact_6183_Suc__times__binomial__eq,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.46/5.75 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % Suc_times_binomial_eq
% 5.46/5.75 thf(fact_6184_binomial__symmetric,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.75 => ( ( binomial @ N @ K )
% 5.46/5.75 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_symmetric
% 5.46/5.75 thf(fact_6185_choose__mult__lemma,axiom,
% 5.46/5.75 ! [M: nat,R2: nat,K: nat] :
% 5.46/5.75 ( ( 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 ) )
% 5.46/5.75 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % choose_mult_lemma
% 5.46/5.75 thf(fact_6186_binomial__le__pow,axiom,
% 5.46/5.75 ! [R2: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ R2 @ N )
% 5.46/5.75 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_le_pow
% 5.46/5.75 thf(fact_6187_norm__uminus__minus,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ Y3 ) )
% 5.46/5.75 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_uminus_minus
% 5.46/5.75 thf(fact_6188_norm__uminus__minus,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ Y3 ) )
% 5.46/5.75 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_uminus_minus
% 5.46/5.75 thf(fact_6189_nonzero__norm__divide,axiom,
% 5.46/5.75 ! [B2: real,A: real] :
% 5.46/5.75 ( ( B2 != zero_zero_real )
% 5.46/5.75 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.75 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % nonzero_norm_divide
% 5.46/5.75 thf(fact_6190_nonzero__norm__divide,axiom,
% 5.46/5.75 ! [B2: complex,A: complex] :
% 5.46/5.75 ( ( B2 != zero_zero_complex )
% 5.46/5.75 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.75 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % nonzero_norm_divide
% 5.46/5.75 thf(fact_6191_power__eq__imp__eq__norm,axiom,
% 5.46/5.75 ! [W: real,N: nat,Z: real] :
% 5.46/5.75 ( ( ( power_power_real @ W @ N )
% 5.46/5.75 = ( power_power_real @ Z @ N ) )
% 5.46/5.75 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.75 => ( ( real_V7735802525324610683m_real @ W )
% 5.46/5.75 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % power_eq_imp_eq_norm
% 5.46/5.75 thf(fact_6192_power__eq__imp__eq__norm,axiom,
% 5.46/5.75 ! [W: complex,N: nat,Z: complex] :
% 5.46/5.75 ( ( ( power_power_complex @ W @ N )
% 5.46/5.75 = ( power_power_complex @ Z @ N ) )
% 5.46/5.75 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.75 => ( ( real_V1022390504157884413omplex @ W )
% 5.46/5.75 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % power_eq_imp_eq_norm
% 5.46/5.75 thf(fact_6193_norm__mult__less,axiom,
% 5.46/5.75 ! [X4: real,R2: real,Y3: real,S: real] :
% 5.46/5.75 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ R2 )
% 5.46/5.75 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y3 ) @ S )
% 5.46/5.75 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X4 @ Y3 ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_mult_less
% 5.46/5.75 thf(fact_6194_norm__mult__less,axiom,
% 5.46/5.75 ! [X4: complex,R2: real,Y3: complex,S: real] :
% 5.46/5.75 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ R2 )
% 5.46/5.75 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y3 ) @ S )
% 5.46/5.75 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X4 @ Y3 ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_mult_less
% 5.46/5.75 thf(fact_6195_norm__mult__ineq,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X4 @ Y3 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_mult_ineq
% 5.46/5.75 thf(fact_6196_norm__mult__ineq,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X4 @ Y3 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_mult_ineq
% 5.46/5.75 thf(fact_6197_norm__triangle__lt,axiom,
% 5.46/5.75 ! [X4: real,Y3: real,E: real] :
% 5.46/5.75 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E )
% 5.46/5.75 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y3 ) ) @ E ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_lt
% 5.46/5.75 thf(fact_6198_norm__triangle__lt,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex,E: real] :
% 5.46/5.75 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E )
% 5.46/5.75 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y3 ) ) @ E ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_lt
% 5.46/5.75 thf(fact_6199_norm__add__less,axiom,
% 5.46/5.75 ! [X4: real,R2: real,Y3: real,S: real] :
% 5.46/5.75 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ R2 )
% 5.46/5.75 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y3 ) @ S )
% 5.46/5.75 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y3 ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_add_less
% 5.46/5.75 thf(fact_6200_norm__add__less,axiom,
% 5.46/5.75 ! [X4: complex,R2: real,Y3: complex,S: real] :
% 5.46/5.75 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ R2 )
% 5.46/5.75 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y3 ) @ S )
% 5.46/5.75 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y3 ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_add_less
% 5.46/5.75 thf(fact_6201_norm__power__ineq,axiom,
% 5.46/5.75 ! [X4: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X4 @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X4 ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_power_ineq
% 5.46/5.75 thf(fact_6202_norm__power__ineq,axiom,
% 5.46/5.75 ! [X4: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X4 @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X4 ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_power_ineq
% 5.46/5.75 thf(fact_6203_norm__triangle__mono,axiom,
% 5.46/5.75 ! [A: real,R2: real,B2: real,S: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B2 ) @ S )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B2 ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_mono
% 5.46/5.75 thf(fact_6204_norm__triangle__mono,axiom,
% 5.46/5.75 ! [A: complex,R2: real,B2: complex,S: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B2 ) @ S )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B2 ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_mono
% 5.46/5.75 thf(fact_6205_norm__triangle__ineq,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y3 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_ineq
% 5.46/5.75 thf(fact_6206_norm__triangle__ineq,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y3 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_ineq
% 5.46/5.75 thf(fact_6207_norm__triangle__le,axiom,
% 5.46/5.75 ! [X4: real,Y3: real,E: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y3 ) ) @ E ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_le
% 5.46/5.75 thf(fact_6208_norm__triangle__le,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex,E: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y3 ) ) @ E ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_le
% 5.46/5.75 thf(fact_6209_norm__add__leD,axiom,
% 5.46/5.75 ! [A: real,B2: real,C: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B2 ) ) @ C )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B2 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_add_leD
% 5.46/5.75 thf(fact_6210_norm__add__leD,axiom,
% 5.46/5.75 ! [A: complex,B2: complex,C: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B2 ) ) @ C )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_add_leD
% 5.46/5.75 thf(fact_6211_norm__diff__triangle__less,axiom,
% 5.46/5.75 ! [X4: real,Y3: real,E1: real,Z: real,E22: real] :
% 5.46/5.75 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ E1 )
% 5.46/5.75 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y3 @ Z ) ) @ E22 )
% 5.46/5.75 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_diff_triangle_less
% 5.46/5.75 thf(fact_6212_norm__diff__triangle__less,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex,E1: real,Z: complex,E22: real] :
% 5.46/5.75 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y3 ) ) @ E1 )
% 5.46/5.75 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y3 @ Z ) ) @ E22 )
% 5.46/5.75 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_diff_triangle_less
% 5.46/5.75 thf(fact_6213_norm__triangle__sub,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y3 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_sub
% 5.46/5.75 thf(fact_6214_norm__triangle__sub,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y3 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_sub
% 5.46/5.75 thf(fact_6215_norm__triangle__ineq4,axiom,
% 5.46/5.75 ! [A: real,B2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B2 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_ineq4
% 5.46/5.75 thf(fact_6216_norm__triangle__ineq4,axiom,
% 5.46/5.75 ! [A: complex,B2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B2 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_ineq4
% 5.46/5.75 thf(fact_6217_norm__diff__triangle__le,axiom,
% 5.46/5.75 ! [X4: real,Y3: real,E1: real,Z: real,E22: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ E1 )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y3 @ Z ) ) @ E22 )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_diff_triangle_le
% 5.46/5.75 thf(fact_6218_norm__diff__triangle__le,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex,E1: real,Z: complex,E22: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y3 ) ) @ E1 )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y3 @ Z ) ) @ E22 )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_diff_triangle_le
% 5.46/5.75 thf(fact_6219_norm__triangle__le__diff,axiom,
% 5.46/5.75 ! [X4: real,Y3: real,E: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y3 ) ) @ E )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ E ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_le_diff
% 5.46/5.75 thf(fact_6220_norm__triangle__le__diff,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex,E: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y3 ) ) @ E )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y3 ) ) @ E ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_le_diff
% 5.46/5.75 thf(fact_6221_norm__diff__ineq,axiom,
% 5.46/5.75 ! [A: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B2 ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_diff_ineq
% 5.46/5.75 thf(fact_6222_norm__diff__ineq,axiom,
% 5.46/5.75 ! [A: complex,B2: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B2 ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_diff_ineq
% 5.46/5.75 thf(fact_6223_norm__triangle__ineq2,axiom,
% 5.46/5.75 ! [A: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B2 ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_ineq2
% 5.46/5.75 thf(fact_6224_norm__triangle__ineq2,axiom,
% 5.46/5.75 ! [A: complex,B2: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B2 ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_ineq2
% 5.46/5.75 thf(fact_6225_zero__less__binomial,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.75 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % zero_less_binomial
% 5.46/5.75 thf(fact_6226_Suc__times__binomial__add,axiom,
% 5.46/5.75 ! [A: nat,B2: nat] :
% 5.46/5.75 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B2 ) ) @ ( suc @ A ) ) )
% 5.46/5.75 = ( times_times_nat @ ( suc @ B2 ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B2 ) ) @ A ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % Suc_times_binomial_add
% 5.46/5.75 thf(fact_6227_binomial__Suc__Suc__eq__times,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.46/5.75 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_Suc_Suc_eq_times
% 5.46/5.75 thf(fact_6228_choose__mult,axiom,
% 5.46/5.75 ! [K: nat,M: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ M )
% 5.46/5.75 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.75 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.46/5.75 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % choose_mult
% 5.46/5.75 thf(fact_6229_binomial__absorb__comp,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.46/5.75 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_absorb_comp
% 5.46/5.75 thf(fact_6230_power__eq__1__iff,axiom,
% 5.46/5.75 ! [W: real,N: nat] :
% 5.46/5.75 ( ( ( power_power_real @ W @ N )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % power_eq_1_iff
% 5.46/5.75 thf(fact_6231_power__eq__1__iff,axiom,
% 5.46/5.75 ! [W: complex,N: nat] :
% 5.46/5.75 ( ( ( power_power_complex @ W @ N )
% 5.46/5.75 = one_one_complex )
% 5.46/5.75 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 | ( N = zero_zero_nat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % power_eq_1_iff
% 5.46/5.75 thf(fact_6232_norm__diff__triangle__ineq,axiom,
% 5.46/5.75 ! [A: real,B2: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B2 ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B2 @ D ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_diff_triangle_ineq
% 5.46/5.75 thf(fact_6233_norm__diff__triangle__ineq,axiom,
% 5.46/5.75 ! [A: complex,B2: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B2 ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B2 @ D ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_diff_triangle_ineq
% 5.46/5.75 thf(fact_6234_norm__triangle__ineq3,axiom,
% 5.46/5.75 ! [A: real,B2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B2 ) ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_ineq3
% 5.46/5.75 thf(fact_6235_norm__triangle__ineq3,axiom,
% 5.46/5.75 ! [A: complex,B2: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B2 ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_triangle_ineq3
% 5.46/5.75 thf(fact_6236_binomial__absorption,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.46/5.75 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_absorption
% 5.46/5.75 thf(fact_6237_binomial__ge__n__over__k__pow__k,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.75 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_ge_n_over_k_pow_k
% 5.46/5.75 thf(fact_6238_binomial__ge__n__over__k__pow__k,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.75 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_ge_n_over_k_pow_k
% 5.46/5.75 thf(fact_6239_binomial__le__pow2,axiom,
% 5.46/5.75 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_le_pow2
% 5.46/5.75 thf(fact_6240_choose__reduce__nat,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.75 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.75 => ( ( binomial @ N @ K )
% 5.46/5.75 = ( 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 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % choose_reduce_nat
% 5.46/5.75 thf(fact_6241_times__binomial__minus1__eq,axiom,
% 5.46/5.75 ! [K: nat,N: nat] :
% 5.46/5.75 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.75 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.46/5.75 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % times_binomial_minus1_eq
% 5.46/5.75 thf(fact_6242_square__norm__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 => ( ( real_V7735802525324610683m_real @ X4 )
% 5.46/5.75 = one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % square_norm_one
% 5.46/5.75 thf(fact_6243_square__norm__one,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.75 = one_one_complex )
% 5.46/5.75 => ( ( real_V1022390504157884413omplex @ X4 )
% 5.46/5.75 = one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % square_norm_one
% 5.46/5.75 thf(fact_6244_norm__power__diff,axiom,
% 5.46/5.75 ! [Z: real,W: real,M: nat] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_power_diff
% 5.46/5.75 thf(fact_6245_norm__power__diff,axiom,
% 5.46/5.75 ! [Z: complex,W: complex,M: nat] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.46/5.75 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_power_diff
% 5.46/5.75 thf(fact_6246_binomial__addition__formula,axiom,
% 5.46/5.75 ! [N: nat,K: nat] :
% 5.46/5.75 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.75 => ( ( binomial @ N @ ( suc @ K ) )
% 5.46/5.75 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % binomial_addition_formula
% 5.46/5.75 thf(fact_6247_choose__two,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.75 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % choose_two
% 5.46/5.75 thf(fact_6248_sin__cos__npi,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( 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 ) ) ) )
% 5.46/5.75 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_npi
% 5.46/5.75 thf(fact_6249_cos__pi__eq__zero,axiom,
% 5.46/5.75 ! [M: nat] :
% 5.46/5.75 ( ( 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 ) ) ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % cos_pi_eq_zero
% 5.46/5.75 thf(fact_6250_round__altdef,axiom,
% 5.46/5.75 ( archim8280529875227126926d_real
% 5.46/5.75 = ( ^ [X: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X ) ) @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % round_altdef
% 5.46/5.75 thf(fact_6251_round__altdef,axiom,
% 5.46/5.75 ( archim7778729529865785530nd_rat
% 5.46/5.75 = ( ^ [X: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X ) ) @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % round_altdef
% 5.46/5.75 thf(fact_6252_ceiling__log__eq__powr__iff,axiom,
% 5.46/5.75 ! [X4: real,B2: real,K: nat] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.75 => ( ( ( archim7802044766580827645g_real @ ( log @ B2 @ X4 ) )
% 5.46/5.75 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.46/5.75 = ( ( ord_less_real @ ( powr_real @ B2 @ ( semiri5074537144036343181t_real @ K ) ) @ X4 )
% 5.46/5.75 & ( ord_less_eq_real @ X4 @ ( powr_real @ B2 @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ceiling_log_eq_powr_iff
% 5.46/5.75 thf(fact_6253_cos__zero__iff,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( cos_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 = ( ? [N2: nat] :
% 5.46/5.75 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.75 | ? [N2: nat] :
% 5.46/5.75 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_zero_iff
% 5.46/5.75 thf(fact_6254_cot__less__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.46/5.75 => ( ord_less_real @ ( cot_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cot_less_zero
% 5.46/5.75 thf(fact_6255_powr__one__eq__one,axiom,
% 5.46/5.75 ! [A: real] :
% 5.46/5.75 ( ( powr_real @ one_one_real @ A )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % powr_one_eq_one
% 5.46/5.75 thf(fact_6256_cos__zero,axiom,
% 5.46/5.75 ( ( cos_complex @ zero_zero_complex )
% 5.46/5.75 = one_one_complex ) ).
% 5.46/5.75
% 5.46/5.75 % cos_zero
% 5.46/5.75 thf(fact_6257_cos__zero,axiom,
% 5.46/5.75 ( ( cos_real @ zero_zero_real )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % cos_zero
% 5.46/5.75 thf(fact_6258_powr__zero__eq__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( X4 = zero_zero_real )
% 5.46/5.75 => ( ( powr_real @ X4 @ zero_zero_real )
% 5.46/5.75 = zero_zero_real ) )
% 5.46/5.75 & ( ( X4 != zero_zero_real )
% 5.46/5.75 => ( ( powr_real @ X4 @ zero_zero_real )
% 5.46/5.75 = one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_zero_eq_one
% 5.46/5.75 thf(fact_6259_powr__gt__zero,axiom,
% 5.46/5.75 ! [X4: real,A: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X4 @ A ) )
% 5.46/5.75 = ( X4 != zero_zero_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_gt_zero
% 5.46/5.75 thf(fact_6260_powr__nonneg__iff,axiom,
% 5.46/5.75 ! [A: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( powr_real @ A @ X4 ) @ zero_zero_real )
% 5.46/5.75 = ( A = zero_zero_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_nonneg_iff
% 5.46/5.75 thf(fact_6261_powr__less__cancel__iff,axiom,
% 5.46/5.75 ! [X4: real,A: real,B2: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B2 ) )
% 5.46/5.75 = ( ord_less_real @ A @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_less_cancel_iff
% 5.46/5.75 thf(fact_6262_sin__pi__minus,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( sin_real @ ( minus_minus_real @ pi @ X4 ) )
% 5.46/5.75 = ( sin_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_pi_minus
% 5.46/5.75 thf(fact_6263_powr__eq__one__iff,axiom,
% 5.46/5.75 ! [A: real,X4: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ A )
% 5.46/5.75 => ( ( ( powr_real @ A @ X4 )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 = ( X4 = zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_eq_one_iff
% 5.46/5.75 thf(fact_6264_powr__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( powr_real @ X4 @ one_one_real )
% 5.46/5.75 = X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_one
% 5.46/5.75 thf(fact_6265_powr__one__gt__zero__iff,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( powr_real @ X4 @ one_one_real )
% 5.46/5.75 = X4 )
% 5.46/5.75 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_one_gt_zero_iff
% 5.46/5.75 thf(fact_6266_powr__le__cancel__iff,axiom,
% 5.46/5.75 ! [X4: real,A: real,B2: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B2 ) )
% 5.46/5.75 = ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_le_cancel_iff
% 5.46/5.75 thf(fact_6267_numeral__powr__numeral__real,axiom,
% 5.46/5.75 ! [M: num,N: num] :
% 5.46/5.75 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.46/5.75 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % numeral_powr_numeral_real
% 5.46/5.75 thf(fact_6268_cos__pi,axiom,
% 5.46/5.75 ( ( cos_real @ pi )
% 5.46/5.75 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_pi
% 5.46/5.75 thf(fact_6269_cos__periodic__pi2,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( cos_real @ ( plus_plus_real @ pi @ X4 ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( cos_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_periodic_pi2
% 5.46/5.75 thf(fact_6270_cos__periodic__pi,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( cos_real @ ( plus_plus_real @ X4 @ pi ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( cos_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_periodic_pi
% 5.46/5.75 thf(fact_6271_sin__periodic__pi2,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( sin_real @ ( plus_plus_real @ pi @ X4 ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( sin_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_periodic_pi2
% 5.46/5.75 thf(fact_6272_sin__periodic__pi,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( sin_real @ ( plus_plus_real @ X4 @ pi ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( sin_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_periodic_pi
% 5.46/5.75 thf(fact_6273_cos__pi__minus,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( cos_real @ ( minus_minus_real @ pi @ X4 ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( cos_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_pi_minus
% 5.46/5.75 thf(fact_6274_cos__minus__pi,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( cos_real @ ( minus_minus_real @ X4 @ pi ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( cos_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_minus_pi
% 5.46/5.75 thf(fact_6275_sin__minus__pi,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( sin_real @ ( minus_minus_real @ X4 @ pi ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( sin_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_minus_pi
% 5.46/5.75 thf(fact_6276_sin__cos__squared__add3,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ X4 ) ) @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ X4 ) ) )
% 5.46/5.75 = one_one_complex ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_squared_add3
% 5.46/5.75 thf(fact_6277_sin__cos__squared__add3,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ X4 ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ X4 ) ) )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_squared_add3
% 5.46/5.75 thf(fact_6278_log__powr__cancel,axiom,
% 5.46/5.75 ! [A: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ( A != one_one_real )
% 5.46/5.75 => ( ( log @ A @ ( powr_real @ A @ Y3 ) )
% 5.46/5.75 = Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % log_powr_cancel
% 5.46/5.75 thf(fact_6279_powr__log__cancel,axiom,
% 5.46/5.75 ! [A: real,X4: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ( A != one_one_real )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( powr_real @ A @ ( log @ A @ X4 ) )
% 5.46/5.75 = X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_log_cancel
% 5.46/5.75 thf(fact_6280_sin__npi2,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_npi2
% 5.46/5.75 thf(fact_6281_sin__npi,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_npi
% 5.46/5.75 thf(fact_6282_sin__npi__int,axiom,
% 5.46/5.75 ! [N: int] :
% 5.46/5.75 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_npi_int
% 5.46/5.75 thf(fact_6283_cot__npi,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % cot_npi
% 5.46/5.75 thf(fact_6284_powr__numeral,axiom,
% 5.46/5.75 ! [X4: real,N: num] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( powr_real @ X4 @ ( numeral_numeral_real @ N ) )
% 5.46/5.75 = ( power_power_real @ X4 @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_numeral
% 5.46/5.75 thf(fact_6285_cos__pi__half,axiom,
% 5.46/5.75 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % cos_pi_half
% 5.46/5.75 thf(fact_6286_sin__two__pi,axiom,
% 5.46/5.75 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_two_pi
% 5.46/5.75 thf(fact_6287_sin__pi__half,axiom,
% 5.46/5.75 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_pi_half
% 5.46/5.75 thf(fact_6288_cos__two__pi,axiom,
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % cos_two_pi
% 5.46/5.75 thf(fact_6289_cos__periodic,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( cos_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.46/5.75 = ( cos_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_periodic
% 5.46/5.75 thf(fact_6290_sin__periodic,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( sin_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.46/5.75 = ( sin_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_periodic
% 5.46/5.75 thf(fact_6291_cos__2pi__minus,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X4 ) )
% 5.46/5.75 = ( cos_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_2pi_minus
% 5.46/5.75 thf(fact_6292_cos__npi,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.46/5.75 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_npi
% 5.46/5.75 thf(fact_6293_cos__npi2,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.75 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_npi2
% 5.46/5.75 thf(fact_6294_cot__periodic,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( cot_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.46/5.75 = ( cot_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % cot_periodic
% 5.46/5.75 thf(fact_6295_sin__cos__squared__add2,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_squared_add2
% 5.46/5.75 thf(fact_6296_sin__cos__squared__add2,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_complex ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_squared_add2
% 5.46/5.75 thf(fact_6297_sin__cos__squared__add,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_squared_add
% 5.46/5.75 thf(fact_6298_sin__cos__squared__add,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_complex ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_squared_add
% 5.46/5.75 thf(fact_6299_sin__2npi,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_2npi
% 5.46/5.75 thf(fact_6300_cos__2npi,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % cos_2npi
% 5.46/5.75 thf(fact_6301_sin__2pi__minus,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X4 ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( sin_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_2pi_minus
% 5.46/5.75 thf(fact_6302_sin__int__2pin,axiom,
% 5.46/5.75 ! [N: int] :
% 5.46/5.75 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_int_2pin
% 5.46/5.75 thf(fact_6303_cos__int__2pin,axiom,
% 5.46/5.75 ! [N: int] :
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % cos_int_2pin
% 5.46/5.75 thf(fact_6304_cos__3over2__pi,axiom,
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % cos_3over2_pi
% 5.46/5.75 thf(fact_6305_square__powr__half,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( powr_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = ( abs_abs_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % square_powr_half
% 5.46/5.75 thf(fact_6306_sin__3over2__pi,axiom,
% 5.46/5.75 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.46/5.75 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_3over2_pi
% 5.46/5.75 thf(fact_6307_cos__npi__int,axiom,
% 5.46/5.75 ! [N: int] :
% 5.46/5.75 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.75 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.46/5.75 = one_one_real ) )
% 5.46/5.75 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.75 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.46/5.75 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_npi_int
% 5.46/5.75 thf(fact_6308_sin__add,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( sin_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X4 ) @ ( cos_real @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( sin_real @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_add
% 5.46/5.75 thf(fact_6309_sin__diff,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( sin_real @ ( minus_minus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X4 ) @ ( cos_real @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( sin_real @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_diff
% 5.46/5.75 thf(fact_6310_cot__def,axiom,
% 5.46/5.75 ( cot_complex
% 5.46/5.75 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( cos_complex @ X ) @ ( sin_complex @ X ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cot_def
% 5.46/5.75 thf(fact_6311_cot__def,axiom,
% 5.46/5.75 ( cot_real
% 5.46/5.75 = ( ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cot_def
% 5.46/5.75 thf(fact_6312_polar__Ex,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ? [R3: real,A5: real] :
% 5.46/5.75 ( ( X4
% 5.46/5.75 = ( times_times_real @ R3 @ ( cos_real @ A5 ) ) )
% 5.46/5.75 & ( Y3
% 5.46/5.75 = ( times_times_real @ R3 @ ( sin_real @ A5 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % polar_Ex
% 5.46/5.75 thf(fact_6313_cos__one__sin__zero,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( ( cos_complex @ X4 )
% 5.46/5.75 = one_one_complex )
% 5.46/5.75 => ( ( sin_complex @ X4 )
% 5.46/5.75 = zero_zero_complex ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_one_sin_zero
% 5.46/5.75 thf(fact_6314_cos__one__sin__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( cos_real @ X4 )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 => ( ( sin_real @ X4 )
% 5.46/5.75 = zero_zero_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_one_sin_zero
% 5.46/5.75 thf(fact_6315_powr__powr,axiom,
% 5.46/5.75 ! [X4: real,A: real,B2: real] :
% 5.46/5.75 ( ( powr_real @ ( powr_real @ X4 @ A ) @ B2 )
% 5.46/5.75 = ( powr_real @ X4 @ ( times_times_real @ A @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_powr
% 5.46/5.75 thf(fact_6316_cos__add,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( cos_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y3 ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_add
% 5.46/5.75 thf(fact_6317_cos__diff,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( cos_real @ ( minus_minus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y3 ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_diff
% 5.46/5.75 thf(fact_6318_sin__zero__norm__cos__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( sin_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X4 ) )
% 5.46/5.75 = one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_zero_norm_cos_one
% 5.46/5.75 thf(fact_6319_sin__zero__norm__cos__one,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( ( sin_complex @ X4 )
% 5.46/5.75 = zero_zero_complex )
% 5.46/5.75 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X4 ) )
% 5.46/5.75 = one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_zero_norm_cos_one
% 5.46/5.75 thf(fact_6320_sin__zero__abs__cos__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( sin_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 => ( ( abs_abs_real @ ( cos_real @ X4 ) )
% 5.46/5.75 = one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_zero_abs_cos_one
% 5.46/5.75 thf(fact_6321_sin__double,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.75 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X4 ) ) @ ( cos_complex @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_double
% 5.46/5.75 thf(fact_6322_sin__double,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.75 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X4 ) ) @ ( cos_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_double
% 5.46/5.75 thf(fact_6323_sincos__principal__value,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ? [Y4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y4 )
% 5.46/5.75 & ( ord_less_eq_real @ Y4 @ pi )
% 5.46/5.75 & ( ( sin_real @ Y4 )
% 5.46/5.75 = ( sin_real @ X4 ) )
% 5.46/5.75 & ( ( cos_real @ Y4 )
% 5.46/5.75 = ( cos_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sincos_principal_value
% 5.46/5.75 thf(fact_6324_powr__less__mono2__neg,axiom,
% 5.46/5.75 ! [A: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.75 => ( ord_less_real @ ( powr_real @ Y3 @ A ) @ ( powr_real @ X4 @ A ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_less_mono2_neg
% 5.46/5.75 thf(fact_6325_powr__non__neg,axiom,
% 5.46/5.75 ! [A: real,X4: real] :
% 5.46/5.75 ~ ( ord_less_real @ ( powr_real @ A @ X4 ) @ zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % powr_non_neg
% 5.46/5.75 thf(fact_6326_powr__mono2,axiom,
% 5.46/5.75 ! [A: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.75 => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_mono2
% 5.46/5.75 thf(fact_6327_powr__ge__pzero,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X4 @ Y3 ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_ge_pzero
% 5.46/5.75 thf(fact_6328_powr__less__mono,axiom,
% 5.46/5.75 ! [A: real,B2: real,X4: real] :
% 5.46/5.75 ( ( ord_less_real @ A @ B2 )
% 5.46/5.75 => ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.75 => ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_less_mono
% 5.46/5.75 thf(fact_6329_powr__less__cancel,axiom,
% 5.46/5.75 ! [X4: real,A: real,B2: real] :
% 5.46/5.75 ( ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B2 ) )
% 5.46/5.75 => ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.75 => ( ord_less_real @ A @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_less_cancel
% 5.46/5.75 thf(fact_6330_powr__mono,axiom,
% 5.46/5.75 ! [A: real,B2: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.75 => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.46/5.75 => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_mono
% 5.46/5.75 thf(fact_6331_sin__x__le__x,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ord_less_eq_real @ ( sin_real @ X4 ) @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_x_le_x
% 5.46/5.75 thf(fact_6332_sin__le__one,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ ( sin_real @ X4 ) @ one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_le_one
% 5.46/5.75 thf(fact_6333_cos__le__one,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ ( cos_real @ X4 ) @ one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % cos_le_one
% 5.46/5.75 thf(fact_6334_abs__sin__x__le__abs__x,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X4 ) ) @ ( abs_abs_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % abs_sin_x_le_abs_x
% 5.46/5.75 thf(fact_6335_sin__cos__le1,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y3 ) ) ) ) @ one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_le1
% 5.46/5.75 thf(fact_6336_frac__ge__0,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % frac_ge_0
% 5.46/5.75 thf(fact_6337_frac__ge__0,axiom,
% 5.46/5.75 ! [X4: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % frac_ge_0
% 5.46/5.75 thf(fact_6338_sin__squared__eq,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.75 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_squared_eq
% 5.46/5.75 thf(fact_6339_sin__squared__eq,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.75 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_squared_eq
% 5.46/5.75 thf(fact_6340_cos__squared__eq,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.75 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_squared_eq
% 5.46/5.75 thf(fact_6341_cos__squared__eq,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.75 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_squared_eq
% 5.46/5.75 thf(fact_6342_frac__lt__1,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X4 ) @ one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % frac_lt_1
% 5.46/5.75 thf(fact_6343_frac__lt__1,axiom,
% 5.46/5.75 ! [X4: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X4 ) @ one_one_rat ) ).
% 5.46/5.75
% 5.46/5.75 % frac_lt_1
% 5.46/5.75 thf(fact_6344_frac__1__eq,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ one_one_real ) )
% 5.46/5.75 = ( archim2898591450579166408c_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % frac_1_eq
% 5.46/5.75 thf(fact_6345_frac__1__eq,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) )
% 5.46/5.75 = ( archimedean_frac_rat @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % frac_1_eq
% 5.46/5.75 thf(fact_6346_powr__mono2_H,axiom,
% 5.46/5.75 ! [A: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.75 => ( ord_less_eq_real @ ( powr_real @ Y3 @ A ) @ ( powr_real @ X4 @ A ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_mono2'
% 5.46/5.75 thf(fact_6347_powr__less__mono2,axiom,
% 5.46/5.75 ! [A: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.75 => ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_less_mono2
% 5.46/5.75 thf(fact_6348_gr__one__powr,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ( ord_less_real @ one_one_real @ ( powr_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % gr_one_powr
% 5.46/5.75 thf(fact_6349_powr__inj,axiom,
% 5.46/5.75 ! [A: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ( A != one_one_real )
% 5.46/5.75 => ( ( ( powr_real @ A @ X4 )
% 5.46/5.75 = ( powr_real @ A @ Y3 ) )
% 5.46/5.75 = ( X4 = Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_inj
% 5.46/5.75 thf(fact_6350_powr__le1,axiom,
% 5.46/5.75 ! [A: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.75 => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ one_one_real ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_le1
% 5.46/5.75 thf(fact_6351_powr__mono__both,axiom,
% 5.46/5.75 ! [A: real,B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.75 => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.75 => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y3 @ B2 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_mono_both
% 5.46/5.75 thf(fact_6352_ge__one__powr__ge__zero,axiom,
% 5.46/5.75 ! [X4: real,A: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X4 @ A ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ge_one_powr_ge_zero
% 5.46/5.75 thf(fact_6353_powr__divide,axiom,
% 5.46/5.75 ! [X4: real,Y3: real,A: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ( ( powr_real @ ( divide_divide_real @ X4 @ Y3 ) @ A )
% 5.46/5.75 = ( divide_divide_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_divide
% 5.46/5.75 thf(fact_6354_powr__mult,axiom,
% 5.46/5.75 ! [X4: real,Y3: real,A: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ( ( powr_real @ ( times_times_real @ X4 @ Y3 ) @ A )
% 5.46/5.75 = ( times_times_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y3 @ A ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_mult
% 5.46/5.75 thf(fact_6355_divide__powr__uminus,axiom,
% 5.46/5.75 ! [A: real,B2: real,C: real] :
% 5.46/5.75 ( ( divide_divide_real @ A @ ( powr_real @ B2 @ C ) )
% 5.46/5.75 = ( times_times_real @ A @ ( powr_real @ B2 @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % divide_powr_uminus
% 5.46/5.75 thf(fact_6356_sin__gt__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ pi )
% 5.46/5.75 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_gt_zero
% 5.46/5.75 thf(fact_6357_sin__x__ge__neg__x,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ord_less_eq_real @ ( uminus_uminus_real @ X4 ) @ ( sin_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_x_ge_neg_x
% 5.46/5.75 thf(fact_6358_sin__ge__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.46/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_ge_zero
% 5.46/5.75 thf(fact_6359_log__base__powr,axiom,
% 5.46/5.75 ! [A: real,B2: real,X4: real] :
% 5.46/5.75 ( ( A != zero_zero_real )
% 5.46/5.75 => ( ( log @ ( powr_real @ A @ B2 ) @ X4 )
% 5.46/5.75 = ( divide_divide_real @ ( log @ A @ X4 ) @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % log_base_powr
% 5.46/5.75 thf(fact_6360_ln__powr,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( X4 != zero_zero_real )
% 5.46/5.75 => ( ( ln_ln_real @ ( powr_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( times_times_real @ Y3 @ ( ln_ln_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ln_powr
% 5.46/5.75 thf(fact_6361_log__powr,axiom,
% 5.46/5.75 ! [X4: real,B2: real,Y3: real] :
% 5.46/5.75 ( ( X4 != zero_zero_real )
% 5.46/5.75 => ( ( log @ B2 @ ( powr_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( times_times_real @ Y3 @ ( log @ B2 @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % log_powr
% 5.46/5.75 thf(fact_6362_sin__ge__minus__one,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_ge_minus_one
% 5.46/5.75 thf(fact_6363_cos__monotone__0__pi__le,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.46/5.75 => ( ord_less_eq_real @ ( cos_real @ X4 ) @ ( cos_real @ Y3 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_monotone_0_pi_le
% 5.46/5.75 thf(fact_6364_cos__mono__le__eq,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ pi )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( cos_real @ X4 ) @ ( cos_real @ Y3 ) )
% 5.46/5.75 = ( ord_less_eq_real @ Y3 @ X4 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_mono_le_eq
% 5.46/5.75 thf(fact_6365_cos__inj__pi,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ pi )
% 5.46/5.75 => ( ( ( cos_real @ X4 )
% 5.46/5.75 = ( cos_real @ Y3 ) )
% 5.46/5.75 => ( X4 = Y3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_inj_pi
% 5.46/5.75 thf(fact_6366_cos__ge__minus__one,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_ge_minus_one
% 5.46/5.75 thf(fact_6367_abs__sin__le__one,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X4 ) ) @ one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % abs_sin_le_one
% 5.46/5.75 thf(fact_6368_abs__cos__le__one,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X4 ) ) @ one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % abs_cos_le_one
% 5.46/5.75 thf(fact_6369_cos__diff__cos,axiom,
% 5.46/5.75 ! [W: complex,Z: complex] :
% 5.46/5.75 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.46/5.75 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z @ W ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_diff_cos
% 5.46/5.75 thf(fact_6370_cos__diff__cos,axiom,
% 5.46/5.75 ! [W: real,Z: real] :
% 5.46/5.75 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.46/5.75 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z @ W ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_diff_cos
% 5.46/5.75 thf(fact_6371_sin__diff__sin,axiom,
% 5.46/5.75 ! [W: complex,Z: complex] :
% 5.46/5.75 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.46/5.75 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_diff_sin
% 5.46/5.75 thf(fact_6372_sin__diff__sin,axiom,
% 5.46/5.75 ! [W: real,Z: real] :
% 5.46/5.75 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.46/5.75 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_diff_sin
% 5.46/5.75 thf(fact_6373_sin__plus__sin,axiom,
% 5.46/5.75 ! [W: complex,Z: complex] :
% 5.46/5.75 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.46/5.75 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_plus_sin
% 5.46/5.75 thf(fact_6374_sin__plus__sin,axiom,
% 5.46/5.75 ! [W: real,Z: real] :
% 5.46/5.75 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.46/5.75 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_plus_sin
% 5.46/5.75 thf(fact_6375_cos__times__sin,axiom,
% 5.46/5.75 ! [W: complex,Z: complex] :
% 5.46/5.75 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_times_sin
% 5.46/5.75 thf(fact_6376_cos__times__sin,axiom,
% 5.46/5.75 ! [W: real,Z: real] :
% 5.46/5.75 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.46/5.75 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_times_sin
% 5.46/5.75 thf(fact_6377_sin__times__cos,axiom,
% 5.46/5.75 ! [W: complex,Z: complex] :
% 5.46/5.75 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_times_cos
% 5.46/5.75 thf(fact_6378_sin__times__cos,axiom,
% 5.46/5.75 ! [W: real,Z: real] :
% 5.46/5.75 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.46/5.75 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_times_cos
% 5.46/5.75 thf(fact_6379_sin__times__sin,axiom,
% 5.46/5.75 ! [W: complex,Z: complex] :
% 5.46/5.75 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_times_sin
% 5.46/5.75 thf(fact_6380_sin__times__sin,axiom,
% 5.46/5.75 ! [W: real,Z: real] :
% 5.46/5.75 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.46/5.75 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_times_sin
% 5.46/5.75 thf(fact_6381_cos__double,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.75 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_double
% 5.46/5.75 thf(fact_6382_cos__double,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.75 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_double
% 5.46/5.75 thf(fact_6383_powr__add,axiom,
% 5.46/5.75 ! [X4: real,A: real,B2: real] :
% 5.46/5.75 ( ( powr_real @ X4 @ ( plus_plus_real @ A @ B2 ) )
% 5.46/5.75 = ( times_times_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_add
% 5.46/5.75 thf(fact_6384_powr__diff,axiom,
% 5.46/5.75 ! [W: real,Z1: real,Z22: real] :
% 5.46/5.75 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.46/5.75 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_diff
% 5.46/5.75 thf(fact_6385_cos__double__sin,axiom,
% 5.46/5.75 ! [W: complex] :
% 5.46/5.75 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.46/5.75 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_double_sin
% 5.46/5.75 thf(fact_6386_cos__double__sin,axiom,
% 5.46/5.75 ! [W: real] :
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.46/5.75 = ( minus_minus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( sin_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_double_sin
% 5.46/5.75 thf(fact_6387_powr__realpow,axiom,
% 5.46/5.75 ! [X4: real,N: nat] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( powr_real @ X4 @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.75 = ( power_power_real @ X4 @ N ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_realpow
% 5.46/5.75 thf(fact_6388_cos__two__neq__zero,axiom,
% 5.46/5.75 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.75 != zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % cos_two_neq_zero
% 5.46/5.75 thf(fact_6389_less__log__iff,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ ( log @ B2 @ X4 ) )
% 5.46/5.75 = ( ord_less_real @ ( powr_real @ B2 @ Y3 ) @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % less_log_iff
% 5.46/5.75 thf(fact_6390_log__less__iff,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ ( log @ B2 @ X4 ) @ Y3 )
% 5.46/5.75 = ( ord_less_real @ X4 @ ( powr_real @ B2 @ Y3 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % log_less_iff
% 5.46/5.75 thf(fact_6391_less__powr__iff,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( powr_real @ B2 @ Y3 ) )
% 5.46/5.75 = ( ord_less_real @ ( log @ B2 @ X4 ) @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % less_powr_iff
% 5.46/5.75 thf(fact_6392_powr__less__iff,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ ( powr_real @ B2 @ Y3 ) @ X4 )
% 5.46/5.75 = ( ord_less_real @ Y3 @ ( log @ B2 @ X4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_less_iff
% 5.46/5.75 thf(fact_6393_cos__monotone__0__pi,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.46/5.75 => ( ord_less_real @ ( cos_real @ X4 ) @ ( cos_real @ Y3 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_monotone_0_pi
% 5.46/5.75 thf(fact_6394_cos__mono__less__eq,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ pi )
% 5.46/5.75 => ( ( ord_less_real @ ( cos_real @ X4 ) @ ( cos_real @ Y3 ) )
% 5.46/5.75 = ( ord_less_real @ Y3 @ X4 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_mono_less_eq
% 5.46/5.75 thf(fact_6395_sin__eq__0__pi,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ pi )
% 5.46/5.75 => ( ( ( sin_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 => ( X4 = zero_zero_real ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_eq_0_pi
% 5.46/5.75 thf(fact_6396_sin__zero__pi__iff,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ pi )
% 5.46/5.75 => ( ( ( sin_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 = ( X4 = zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_zero_pi_iff
% 5.46/5.75 thf(fact_6397_cos__monotone__minus__pi__0_H,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.75 => ( ord_less_eq_real @ ( cos_real @ Y3 ) @ ( cos_real @ X4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_monotone_minus_pi_0'
% 5.46/5.75 thf(fact_6398_sin__zero__iff__int2,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( sin_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 = ( ? [I2: int] :
% 5.46/5.75 ( X4
% 5.46/5.75 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_zero_iff_int2
% 5.46/5.75 thf(fact_6399_frac__def,axiom,
% 5.46/5.75 ( archim2898591450579166408c_real
% 5.46/5.75 = ( ^ [X: real] : ( minus_minus_real @ X @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % frac_def
% 5.46/5.75 thf(fact_6400_frac__def,axiom,
% 5.46/5.75 ( archimedean_frac_rat
% 5.46/5.75 = ( ^ [X: rat] : ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % frac_def
% 5.46/5.75 thf(fact_6401_sincos__total__pi,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 => ? [T2: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ T2 )
% 5.46/5.75 & ( ord_less_eq_real @ T2 @ pi )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( cos_real @ T2 ) )
% 5.46/5.75 & ( Y3
% 5.46/5.75 = ( sin_real @ T2 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sincos_total_pi
% 5.46/5.75 thf(fact_6402_sin__cos__sqrt,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X4 ) )
% 5.46/5.75 => ( ( sin_real @ X4 )
% 5.46/5.75 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_sqrt
% 5.46/5.75 thf(fact_6403_sin__expansion__lemma,axiom,
% 5.46/5.75 ! [X4: real,M: nat] :
% 5.46/5.75 ( ( sin_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.75 = ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_expansion_lemma
% 5.46/5.75 thf(fact_6404_powr__minus__divide,axiom,
% 5.46/5.75 ! [X4: real,A: real] :
% 5.46/5.75 ( ( powr_real @ X4 @ ( uminus_uminus_real @ A ) )
% 5.46/5.75 = ( divide_divide_real @ one_one_real @ ( powr_real @ X4 @ A ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_minus_divide
% 5.46/5.75 thf(fact_6405_cos__expansion__lemma,axiom,
% 5.46/5.75 ! [X4: real,M: nat] :
% 5.46/5.75 ( ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_expansion_lemma
% 5.46/5.75 thf(fact_6406_powr__neg__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( powr_real @ X4 @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.75 = ( divide_divide_real @ one_one_real @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_neg_one
% 5.46/5.75 thf(fact_6407_sin__gt__zero__02,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.75 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_gt_zero_02
% 5.46/5.75 thf(fact_6408_powr__mult__base,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( times_times_real @ X4 @ ( powr_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( powr_real @ X4 @ ( plus_plus_real @ one_one_real @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_mult_base
% 5.46/5.75 thf(fact_6409_powr__le__iff,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( powr_real @ B2 @ Y3 ) @ X4 )
% 5.46/5.75 = ( ord_less_eq_real @ Y3 @ ( log @ B2 @ X4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_le_iff
% 5.46/5.75 thf(fact_6410_le__powr__iff,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ ( powr_real @ B2 @ Y3 ) )
% 5.46/5.75 = ( ord_less_eq_real @ ( log @ B2 @ X4 ) @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_powr_iff
% 5.46/5.75 thf(fact_6411_log__le__iff,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( log @ B2 @ X4 ) @ Y3 )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ ( powr_real @ B2 @ Y3 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % log_le_iff
% 5.46/5.75 thf(fact_6412_le__log__iff,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ ( log @ B2 @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_real @ ( powr_real @ B2 @ Y3 ) @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_log_iff
% 5.46/5.75 thf(fact_6413_cos__two__less__zero,axiom,
% 5.46/5.75 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.46/5.75
% 5.46/5.75 % cos_two_less_zero
% 5.46/5.75 thf(fact_6414_cos__two__le__zero,axiom,
% 5.46/5.75 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.46/5.75
% 5.46/5.75 % cos_two_le_zero
% 5.46/5.75 thf(fact_6415_cos__is__zero,axiom,
% 5.46/5.75 ? [X3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.46/5.75 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.75 & ( ( cos_real @ X3 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 & ! [Y5: real] :
% 5.46/5.75 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.46/5.75 & ( ord_less_eq_real @ Y5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.75 & ( ( cos_real @ Y5 )
% 5.46/5.75 = zero_zero_real ) )
% 5.46/5.75 => ( Y5 = X3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_is_zero
% 5.46/5.75 thf(fact_6416_cos__monotone__minus__pi__0,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.75 => ( ord_less_real @ ( cos_real @ Y3 ) @ ( cos_real @ X4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_monotone_minus_pi_0
% 5.46/5.75 thf(fact_6417_cos__total,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.75 => ? [X3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.46/5.75 & ( ord_less_eq_real @ X3 @ pi )
% 5.46/5.75 & ( ( cos_real @ X3 )
% 5.46/5.75 = Y3 )
% 5.46/5.75 & ! [Y5: real] :
% 5.46/5.75 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.46/5.75 & ( ord_less_eq_real @ Y5 @ pi )
% 5.46/5.75 & ( ( cos_real @ Y5 )
% 5.46/5.75 = Y3 ) )
% 5.46/5.75 => ( Y5 = X3 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_total
% 5.46/5.75 thf(fact_6418_frac__eq,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( archim2898591450579166408c_real @ X4 )
% 5.46/5.75 = X4 )
% 5.46/5.75 = ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 & ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % frac_eq
% 5.46/5.75 thf(fact_6419_frac__eq,axiom,
% 5.46/5.75 ! [X4: rat] :
% 5.46/5.75 ( ( ( archimedean_frac_rat @ X4 )
% 5.46/5.75 = X4 )
% 5.46/5.75 = ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.46/5.75 & ( ord_less_rat @ X4 @ one_one_rat ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % frac_eq
% 5.46/5.75 thf(fact_6420_frac__add,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 5.46/5.75 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y3 ) ) ) )
% 5.46/5.75 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 5.46/5.75 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % frac_add
% 5.46/5.75 thf(fact_6421_frac__add,axiom,
% 5.46/5.75 ! [X4: rat,Y3: rat] :
% 5.46/5.75 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 5.46/5.75 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ Y3 ) )
% 5.46/5.75 = ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y3 ) ) ) )
% 5.46/5.75 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 5.46/5.75 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ Y3 ) )
% 5.46/5.75 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % frac_add
% 5.46/5.75 thf(fact_6422_sincos__total__pi__half,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 => ? [T2: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ T2 )
% 5.46/5.75 & ( ord_less_eq_real @ T2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( cos_real @ T2 ) )
% 5.46/5.75 & ( Y3
% 5.46/5.75 = ( sin_real @ T2 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sincos_total_pi_half
% 5.46/5.75 thf(fact_6423_sincos__total__2pi__le,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 => ? [T2: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ T2 )
% 5.46/5.75 & ( ord_less_eq_real @ T2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( cos_real @ T2 ) )
% 5.46/5.75 & ( Y3
% 5.46/5.75 = ( sin_real @ T2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sincos_total_2pi_le
% 5.46/5.75 thf(fact_6424_sincos__total__2pi,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 => ~ ! [T2: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ T2 )
% 5.46/5.75 => ( ( ord_less_real @ T2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.75 => ( ( X4
% 5.46/5.75 = ( cos_real @ T2 ) )
% 5.46/5.75 => ( Y3
% 5.46/5.75 != ( sin_real @ T2 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sincos_total_2pi
% 5.46/5.75 thf(fact_6425_ln__powr__bound,axiom,
% 5.46/5.75 ! [X4: real,A: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( divide_divide_real @ ( powr_real @ X4 @ A ) @ A ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ln_powr_bound
% 5.46/5.75 thf(fact_6426_ln__powr__bound2,axiom,
% 5.46/5.75 ! [X4: real,A: real] :
% 5.46/5.75 ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.75 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X4 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % ln_powr_bound2
% 5.46/5.75 thf(fact_6427_log__add__eq__powr,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.75 => ( ( B2 != one_one_real )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( plus_plus_real @ ( log @ B2 @ X4 ) @ Y3 )
% 5.46/5.75 = ( log @ B2 @ ( times_times_real @ X4 @ ( powr_real @ B2 @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % log_add_eq_powr
% 5.46/5.75 thf(fact_6428_add__log__eq__powr,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.75 => ( ( B2 != one_one_real )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( plus_plus_real @ Y3 @ ( log @ B2 @ X4 ) )
% 5.46/5.75 = ( log @ B2 @ ( times_times_real @ ( powr_real @ B2 @ Y3 ) @ X4 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % add_log_eq_powr
% 5.46/5.75 thf(fact_6429_minus__log__eq__powr,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.75 => ( ( B2 != one_one_real )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( minus_minus_real @ Y3 @ ( log @ B2 @ X4 ) )
% 5.46/5.75 = ( log @ B2 @ ( divide_divide_real @ ( powr_real @ B2 @ Y3 ) @ X4 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % minus_log_eq_powr
% 5.46/5.75 thf(fact_6430_sin__pi__divide__n__ge__0,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( N != zero_zero_nat )
% 5.46/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_pi_divide_n_ge_0
% 5.46/5.75 thf(fact_6431_sin__45,axiom,
% 5.46/5.75 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.75 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_45
% 5.46/5.75 thf(fact_6432_cos__45,axiom,
% 5.46/5.75 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.75 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_45
% 5.46/5.75 thf(fact_6433_powr__def,axiom,
% 5.46/5.75 ( powr_real
% 5.46/5.75 = ( ^ [X: real,A4: real] : ( if_real @ ( X = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A4 @ ( ln_ln_real @ X ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_def
% 5.46/5.75 thf(fact_6434_cos__plus__cos,axiom,
% 5.46/5.75 ! [W: complex,Z: complex] :
% 5.46/5.75 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.46/5.75 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_plus_cos
% 5.46/5.75 thf(fact_6435_cos__plus__cos,axiom,
% 5.46/5.75 ! [W: real,Z: real] :
% 5.46/5.75 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.46/5.75 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_plus_cos
% 5.46/5.75 thf(fact_6436_cos__times__cos,axiom,
% 5.46/5.75 ! [W: complex,Z: complex] :
% 5.46/5.75 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_times_cos
% 5.46/5.75 thf(fact_6437_cos__times__cos,axiom,
% 5.46/5.75 ! [W: real,Z: real] :
% 5.46/5.75 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.46/5.75 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_times_cos
% 5.46/5.75 thf(fact_6438_sin__gt__zero2,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_gt_zero2
% 5.46/5.75 thf(fact_6439_sin__lt__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ pi @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.75 => ( ord_less_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_lt_zero
% 5.46/5.75 thf(fact_6440_cos__double__less__one,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.75 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_double_less_one
% 5.46/5.75 thf(fact_6441_sin__30,axiom,
% 5.46/5.75 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.46/5.75 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_30
% 5.46/5.75 thf(fact_6442_cos__gt__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_gt_zero
% 5.46/5.75 thf(fact_6443_sin__monotone__2pi__le,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_eq_real @ ( sin_real @ Y3 ) @ ( sin_real @ X4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_monotone_2pi_le
% 5.46/5.75 thf(fact_6444_sin__mono__le__eq,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( sin_real @ X4 ) @ ( sin_real @ Y3 ) )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ Y3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_mono_le_eq
% 5.46/5.75 thf(fact_6445_sin__inj__pi,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ( sin_real @ X4 )
% 5.46/5.75 = ( sin_real @ Y3 ) )
% 5.46/5.75 => ( X4 = Y3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_inj_pi
% 5.46/5.75 thf(fact_6446_log__minus__eq__powr,axiom,
% 5.46/5.75 ! [B2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.75 => ( ( B2 != one_one_real )
% 5.46/5.75 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( minus_minus_real @ ( log @ B2 @ X4 ) @ Y3 )
% 5.46/5.75 = ( log @ B2 @ ( times_times_real @ X4 @ ( powr_real @ B2 @ ( uminus_uminus_real @ Y3 ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % log_minus_eq_powr
% 5.46/5.75 thf(fact_6447_cos__60,axiom,
% 5.46/5.75 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.46/5.75 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_60
% 5.46/5.75 thf(fact_6448_sin__60,axiom,
% 5.46/5.75 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.46/5.75 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_60
% 5.46/5.75 thf(fact_6449_cos__30,axiom,
% 5.46/5.75 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.46/5.75 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_30
% 5.46/5.75 thf(fact_6450_cos__one__2pi__int,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( cos_real @ X4 )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 = ( ? [X: int] :
% 5.46/5.75 ( X4
% 5.46/5.75 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_one_2pi_int
% 5.46/5.75 thf(fact_6451_cos__double__cos,axiom,
% 5.46/5.75 ! [W: complex] :
% 5.46/5.75 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.46/5.75 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_double_cos
% 5.46/5.75 thf(fact_6452_cos__double__cos,axiom,
% 5.46/5.75 ! [W: real] :
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.46/5.75 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_double_cos
% 5.46/5.75 thf(fact_6453_cos__treble__cos,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X4 ) )
% 5.46/5.75 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_treble_cos
% 5.46/5.75 thf(fact_6454_cos__treble__cos,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X4 ) )
% 5.46/5.75 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_treble_cos
% 5.46/5.75 thf(fact_6455_powr__half__sqrt,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( powr_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = ( sqrt @ X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_half_sqrt
% 5.46/5.75 thf(fact_6456_powr__neg__numeral,axiom,
% 5.46/5.75 ! [X4: real,N: num] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( powr_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.46/5.75 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % powr_neg_numeral
% 5.46/5.75 thf(fact_6457_sin__le__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ pi @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.75 => ( ord_less_eq_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_le_zero
% 5.46/5.75 thf(fact_6458_sin__less__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.46/5.75 => ( ord_less_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_less_zero
% 5.46/5.75 thf(fact_6459_sin__monotone__2pi,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_real @ ( sin_real @ Y3 ) @ ( sin_real @ X4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_monotone_2pi
% 5.46/5.75 thf(fact_6460_sin__mono__less__eq,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_real @ ( sin_real @ X4 ) @ ( sin_real @ Y3 ) )
% 5.46/5.75 = ( ord_less_real @ X4 @ Y3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_mono_less_eq
% 5.46/5.75 thf(fact_6461_sin__total,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.75 => ? [X3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.46/5.75 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 & ( ( sin_real @ X3 )
% 5.46/5.75 = Y3 )
% 5.46/5.75 & ! [Y5: real] :
% 5.46/5.75 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.46/5.75 & ( ord_less_eq_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 & ( ( sin_real @ Y5 )
% 5.46/5.75 = Y3 ) )
% 5.46/5.75 => ( Y5 = X3 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_total
% 5.46/5.75 thf(fact_6462_cos__gt__zero__pi,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_gt_zero_pi
% 5.46/5.75 thf(fact_6463_cos__ge__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_ge_zero
% 5.46/5.75 thf(fact_6464_cos__one__2pi,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( cos_real @ X4 )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 = ( ? [X: nat] :
% 5.46/5.75 ( X4
% 5.46/5.75 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.46/5.75 | ? [X: nat] :
% 5.46/5.75 ( X4
% 5.46/5.75 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_one_2pi
% 5.46/5.75 thf(fact_6465_floor__add,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 5.46/5.75 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y3 ) ) ) )
% 5.46/5.75 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y3 ) ) @ one_one_real )
% 5.46/5.75 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y3 ) ) @ one_one_int ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_add
% 5.46/5.75 thf(fact_6466_floor__add,axiom,
% 5.46/5.75 ! [X4: rat,Y3: rat] :
% 5.46/5.75 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 5.46/5.75 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y3 ) )
% 5.46/5.75 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) ) )
% 5.46/5.75 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y3 ) ) @ one_one_rat )
% 5.46/5.75 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y3 ) )
% 5.46/5.75 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) @ one_one_int ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_add
% 5.46/5.75 thf(fact_6467_sin__pi__divide__n__gt__0,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.75 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_pi_divide_n_gt_0
% 5.46/5.75 thf(fact_6468_sin__arctan,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( sin_real @ ( arctan @ X4 ) )
% 5.46/5.75 = ( divide_divide_real @ X4 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_arctan
% 5.46/5.75 thf(fact_6469_floor__log__eq__powr__iff,axiom,
% 5.46/5.75 ! [X4: real,B2: real,K: int] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.75 => ( ( ( archim6058952711729229775r_real @ ( log @ B2 @ X4 ) )
% 5.46/5.75 = K )
% 5.46/5.75 = ( ( ord_less_eq_real @ ( powr_real @ B2 @ ( ring_1_of_int_real @ K ) ) @ X4 )
% 5.46/5.75 & ( ord_less_real @ X4 @ ( powr_real @ B2 @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % floor_log_eq_powr_iff
% 5.46/5.75 thf(fact_6470_cos__arctan,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( cos_real @ ( arctan @ X4 ) )
% 5.46/5.75 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_arctan
% 5.46/5.75 thf(fact_6471_cot__gt__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cot_gt_zero
% 5.46/5.75 thf(fact_6472_sin__zero__iff__int,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( sin_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 = ( ? [I2: int] :
% 5.46/5.75 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I2 )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_zero_iff_int
% 5.46/5.75 thf(fact_6473_cos__zero__iff__int,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( cos_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 = ( ? [I2: int] :
% 5.46/5.75 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I2 )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_zero_iff_int
% 5.46/5.75 thf(fact_6474_sin__zero__lemma,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ( sin_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 => ? [N4: nat] :
% 5.46/5.75 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_zero_lemma
% 5.46/5.75 thf(fact_6475_sin__zero__iff,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( sin_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 = ( ? [N2: nat] :
% 5.46/5.75 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.75 | ? [N2: nat] :
% 5.46/5.75 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_zero_iff
% 5.46/5.75 thf(fact_6476_cos__zero__lemma,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ( cos_real @ X4 )
% 5.46/5.75 = zero_zero_real )
% 5.46/5.75 => ? [N4: nat] :
% 5.46/5.75 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.46/5.75 & ( X4
% 5.46/5.75 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_zero_lemma
% 5.46/5.75 thf(fact_6477_tan__double,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( ( cos_complex @ X4 )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X4 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_double
% 5.46/5.75 thf(fact_6478_tan__double,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( cos_real @ X4 )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.75 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X4 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_double
% 5.46/5.75 thf(fact_6479_sin__tan,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( sin_real @ X4 )
% 5.46/5.75 = ( divide_divide_real @ ( tan_real @ X4 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_tan
% 5.46/5.75 thf(fact_6480_cos__tan,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( cos_real @ X4 )
% 5.46/5.75 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_tan
% 5.46/5.75 thf(fact_6481_arcosh__def,axiom,
% 5.46/5.75 ( arcosh_real
% 5.46/5.75 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcosh_def
% 5.46/5.75 thf(fact_6482_complex__unimodular__polar,axiom,
% 5.46/5.75 ! [Z: complex] :
% 5.46/5.75 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 => ~ ! [T2: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ T2 )
% 5.46/5.75 => ( ( ord_less_real @ T2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.75 => ( Z
% 5.46/5.75 != ( complex2 @ ( cos_real @ T2 ) @ ( sin_real @ T2 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % complex_unimodular_polar
% 5.46/5.75 thf(fact_6483_cos__arcsin,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.75 => ( ( cos_real @ ( arcsin @ X4 ) )
% 5.46/5.75 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_arcsin
% 5.46/5.75 thf(fact_6484_of__real__1,axiom,
% 5.46/5.75 ( ( real_V1803761363581548252l_real @ one_one_real )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_1
% 5.46/5.75 thf(fact_6485_of__real__1,axiom,
% 5.46/5.75 ( ( real_V4546457046886955230omplex @ one_one_real )
% 5.46/5.75 = one_one_complex ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_1
% 5.46/5.75 thf(fact_6486_of__real__eq__1__iff,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( real_V1803761363581548252l_real @ X4 )
% 5.46/5.75 = one_one_real )
% 5.46/5.75 = ( X4 = one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_eq_1_iff
% 5.46/5.75 thf(fact_6487_of__real__eq__1__iff,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ( real_V4546457046886955230omplex @ X4 )
% 5.46/5.75 = one_one_complex )
% 5.46/5.75 = ( X4 = one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_eq_1_iff
% 5.46/5.75 thf(fact_6488_of__real__mult,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V1803761363581548252l_real @ ( times_times_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( times_times_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_mult
% 5.46/5.75 thf(fact_6489_of__real__mult,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V4546457046886955230omplex @ ( times_times_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( times_times_complex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_mult
% 5.46/5.75 thf(fact_6490_of__real__numeral,axiom,
% 5.46/5.75 ! [W: num] :
% 5.46/5.75 ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.75 = ( numeral_numeral_real @ W ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_numeral
% 5.46/5.75 thf(fact_6491_of__real__numeral,axiom,
% 5.46/5.75 ! [W: num] :
% 5.46/5.75 ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 5.46/5.75 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_numeral
% 5.46/5.75 thf(fact_6492_of__real__divide,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_divide
% 5.46/5.75 thf(fact_6493_of__real__divide,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_divide
% 5.46/5.75 thf(fact_6494_of__real__power,axiom,
% 5.46/5.75 ! [X4: real,N: nat] :
% 5.46/5.75 ( ( real_V1803761363581548252l_real @ ( power_power_real @ X4 @ N ) )
% 5.46/5.75 = ( power_power_real @ ( real_V1803761363581548252l_real @ X4 ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_power
% 5.46/5.75 thf(fact_6495_of__real__power,axiom,
% 5.46/5.75 ! [X4: real,N: nat] :
% 5.46/5.75 ( ( real_V4546457046886955230omplex @ ( power_power_real @ X4 @ N ) )
% 5.46/5.75 = ( power_power_complex @ ( real_V4546457046886955230omplex @ X4 ) @ N ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_power
% 5.46/5.75 thf(fact_6496_of__real__add,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_add
% 5.46/5.75 thf(fact_6497_of__real__add,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_add
% 5.46/5.75 thf(fact_6498_of__real__diff,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V1803761363581548252l_real @ ( minus_minus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( minus_minus_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_diff
% 5.46/5.75 thf(fact_6499_of__real__diff,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V4546457046886955230omplex @ ( minus_minus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( minus_minus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_diff
% 5.46/5.75 thf(fact_6500_tan__periodic__pi,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( tan_real @ ( plus_plus_real @ X4 @ pi ) )
% 5.46/5.75 = ( tan_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_periodic_pi
% 5.46/5.75 thf(fact_6501_of__real__neg__numeral,axiom,
% 5.46/5.75 ! [W: num] :
% 5.46/5.75 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_neg_numeral
% 5.46/5.75 thf(fact_6502_of__real__neg__numeral,axiom,
% 5.46/5.75 ! [W: num] :
% 5.46/5.75 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.75 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % of_real_neg_numeral
% 5.46/5.75 thf(fact_6503_cos__of__real__pi,axiom,
% 5.46/5.75 ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.46/5.75 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_of_real_pi
% 5.46/5.75 thf(fact_6504_cos__of__real__pi,axiom,
% 5.46/5.75 ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.46/5.75 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_of_real_pi
% 5.46/5.75 thf(fact_6505_tan__npi,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % tan_npi
% 5.46/5.75 thf(fact_6506_tan__periodic__n,axiom,
% 5.46/5.75 ! [X4: real,N: num] :
% 5.46/5.75 ( ( tan_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.46/5.75 = ( tan_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_periodic_n
% 5.46/5.75 thf(fact_6507_sin__arcsin,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.75 => ( ( sin_real @ ( arcsin @ Y3 ) )
% 5.46/5.75 = Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_arcsin
% 5.46/5.75 thf(fact_6508_tan__periodic__nat,axiom,
% 5.46/5.75 ! [X4: real,N: nat] :
% 5.46/5.75 ( ( tan_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.46/5.75 = ( tan_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_periodic_nat
% 5.46/5.75 thf(fact_6509_tan__periodic__int,axiom,
% 5.46/5.75 ! [X4: real,I: int] :
% 5.46/5.75 ( ( tan_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 5.46/5.75 = ( tan_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_periodic_int
% 5.46/5.75 thf(fact_6510_norm__cos__sin,axiom,
% 5.46/5.75 ! [T: real] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % norm_cos_sin
% 5.46/5.75 thf(fact_6511_norm__of__real__add1,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ one_one_real ) )
% 5.46/5.75 = ( abs_abs_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_of_real_add1
% 5.46/5.75 thf(fact_6512_norm__of__real__add1,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ one_one_complex ) )
% 5.46/5.75 = ( abs_abs_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_of_real_add1
% 5.46/5.75 thf(fact_6513_norm__of__real__addn,axiom,
% 5.46/5.75 ! [X4: real,B2: num] :
% 5.46/5.75 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( numeral_numeral_real @ B2 ) ) )
% 5.46/5.75 = ( abs_abs_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ B2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_of_real_addn
% 5.46/5.75 thf(fact_6514_norm__of__real__addn,axiom,
% 5.46/5.75 ! [X4: real,B2: num] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ ( numera6690914467698888265omplex @ B2 ) ) )
% 5.46/5.75 = ( abs_abs_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ B2 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_of_real_addn
% 5.46/5.75 thf(fact_6515_arcsin__1,axiom,
% 5.46/5.75 ( ( arcsin @ one_one_real )
% 5.46/5.75 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_1
% 5.46/5.75 thf(fact_6516_tan__periodic,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( tan_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.46/5.75 = ( tan_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_periodic
% 5.46/5.75 thf(fact_6517_cos__of__real__pi__half,axiom,
% 5.46/5.75 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % cos_of_real_pi_half
% 5.46/5.75 thf(fact_6518_cos__of__real__pi__half,axiom,
% 5.46/5.75 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = zero_zero_complex ) ).
% 5.46/5.75
% 5.46/5.75 % cos_of_real_pi_half
% 5.46/5.75 thf(fact_6519_sin__of__real__pi__half,axiom,
% 5.46/5.75 ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % sin_of_real_pi_half
% 5.46/5.75 thf(fact_6520_sin__of__real__pi__half,axiom,
% 5.46/5.75 ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.46/5.75 = one_one_complex ) ).
% 5.46/5.75
% 5.46/5.75 % sin_of_real_pi_half
% 5.46/5.75 thf(fact_6521_arcsin__minus__1,axiom,
% 5.46/5.75 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_minus_1
% 5.46/5.75 thf(fact_6522_complex__of__real__mult__Complex,axiom,
% 5.46/5.75 ! [R2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X4 @ Y3 ) )
% 5.46/5.75 = ( complex2 @ ( times_times_real @ R2 @ X4 ) @ ( times_times_real @ R2 @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % complex_of_real_mult_Complex
% 5.46/5.75 thf(fact_6523_Complex__mult__complex__of__real,axiom,
% 5.46/5.75 ! [X4: real,Y3: real,R2: real] :
% 5.46/5.75 ( ( times_times_complex @ ( complex2 @ X4 @ Y3 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.46/5.75 = ( complex2 @ ( times_times_real @ X4 @ R2 ) @ ( times_times_real @ Y3 @ R2 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % Complex_mult_complex_of_real
% 5.46/5.75 thf(fact_6524_complex__of__real__add__Complex,axiom,
% 5.46/5.75 ! [R2: real,X4: real,Y3: real] :
% 5.46/5.75 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X4 @ Y3 ) )
% 5.46/5.75 = ( complex2 @ ( plus_plus_real @ R2 @ X4 ) @ Y3 ) ) ).
% 5.46/5.75
% 5.46/5.75 % complex_of_real_add_Complex
% 5.46/5.75 thf(fact_6525_Complex__add__complex__of__real,axiom,
% 5.46/5.75 ! [X4: real,Y3: real,R2: real] :
% 5.46/5.75 ( ( plus_plus_complex @ ( complex2 @ X4 @ Y3 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.46/5.75 = ( complex2 @ ( plus_plus_real @ X4 @ R2 ) @ Y3 ) ) ).
% 5.46/5.75
% 5.46/5.75 % Complex_add_complex_of_real
% 5.46/5.75 thf(fact_6526_complex__diff,axiom,
% 5.46/5.75 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.75 ( ( minus_minus_complex @ ( complex2 @ A @ B2 ) @ ( complex2 @ C @ D ) )
% 5.46/5.75 = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B2 @ D ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % complex_diff
% 5.46/5.75 thf(fact_6527_Complex__eq__1,axiom,
% 5.46/5.75 ! [A: real,B2: real] :
% 5.46/5.75 ( ( ( complex2 @ A @ B2 )
% 5.46/5.75 = one_one_complex )
% 5.46/5.75 = ( ( A = one_one_real )
% 5.46/5.75 & ( B2 = zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % Complex_eq_1
% 5.46/5.75 thf(fact_6528_one__complex_Ocode,axiom,
% 5.46/5.75 ( one_one_complex
% 5.46/5.75 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % one_complex.code
% 5.46/5.75 thf(fact_6529_Complex__eq__numeral,axiom,
% 5.46/5.75 ! [A: real,B2: real,W: num] :
% 5.46/5.75 ( ( ( complex2 @ A @ B2 )
% 5.46/5.75 = ( numera6690914467698888265omplex @ W ) )
% 5.46/5.75 = ( ( A
% 5.46/5.75 = ( numeral_numeral_real @ W ) )
% 5.46/5.75 & ( B2 = zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % Complex_eq_numeral
% 5.46/5.75 thf(fact_6530_complex__add,axiom,
% 5.46/5.75 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.75 ( ( plus_plus_complex @ ( complex2 @ A @ B2 ) @ ( complex2 @ C @ D ) )
% 5.46/5.75 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B2 @ D ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % complex_add
% 5.46/5.75 thf(fact_6531_nonzero__of__real__divide,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( Y3 != zero_zero_real )
% 5.46/5.75 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % nonzero_of_real_divide
% 5.46/5.75 thf(fact_6532_nonzero__of__real__divide,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( Y3 != zero_zero_real )
% 5.46/5.75 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % nonzero_of_real_divide
% 5.46/5.75 thf(fact_6533_Complex__eq__neg__1,axiom,
% 5.46/5.75 ! [A: real,B2: real] :
% 5.46/5.75 ( ( ( complex2 @ A @ B2 )
% 5.46/5.75 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.75 = ( ( A
% 5.46/5.75 = ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.75 & ( B2 = zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % Complex_eq_neg_1
% 5.46/5.75 thf(fact_6534_Complex__eq__neg__numeral,axiom,
% 5.46/5.75 ! [A: real,B2: real,W: num] :
% 5.46/5.75 ( ( ( complex2 @ A @ B2 )
% 5.46/5.75 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.75 = ( ( A
% 5.46/5.75 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.75 & ( B2 = zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % Complex_eq_neg_numeral
% 5.46/5.75 thf(fact_6535_complex__mult,axiom,
% 5.46/5.75 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.75 ( ( times_times_complex @ ( complex2 @ A @ B2 ) @ ( complex2 @ C @ D ) )
% 5.46/5.75 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B2 @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B2 @ C ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % complex_mult
% 5.46/5.75 thf(fact_6536_arcsin__le__arcsin,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.75 => ( ord_less_eq_real @ ( arcsin @ X4 ) @ ( arcsin @ Y3 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_le_arcsin
% 5.46/5.75 thf(fact_6537_arcsin__minus,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.75 => ( ( arcsin @ ( uminus_uminus_real @ X4 ) )
% 5.46/5.75 = ( uminus_uminus_real @ ( arcsin @ X4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_minus
% 5.46/5.75 thf(fact_6538_arcsin__le__mono,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( arcsin @ X4 ) @ ( arcsin @ Y3 ) )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_le_mono
% 5.46/5.75 thf(fact_6539_arcsin__eq__iff,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.46/5.75 => ( ( ( arcsin @ X4 )
% 5.46/5.75 = ( arcsin @ Y3 ) )
% 5.46/5.75 = ( X4 = Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_eq_iff
% 5.46/5.75 thf(fact_6540_norm__less__p1,axiom,
% 5.46/5.75 ! [X4: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X4 ) ) @ one_one_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_less_p1
% 5.46/5.75 thf(fact_6541_norm__less__p1,axiom,
% 5.46/5.75 ! [X4: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X4 ) ) @ one_one_complex ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_less_p1
% 5.46/5.75 thf(fact_6542_tan__def,axiom,
% 5.46/5.75 ( tan_complex
% 5.46/5.75 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X ) @ ( cos_complex @ X ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_def
% 5.46/5.75 thf(fact_6543_tan__def,axiom,
% 5.46/5.75 ( tan_real
% 5.46/5.75 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ X ) @ ( cos_real @ X ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_def
% 5.46/5.75 thf(fact_6544_arcsin__less__arcsin,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.75 => ( ord_less_real @ ( arcsin @ X4 ) @ ( arcsin @ Y3 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_less_arcsin
% 5.46/5.75 thf(fact_6545_arcsin__less__mono,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.46/5.75 => ( ( ord_less_real @ ( arcsin @ X4 ) @ ( arcsin @ Y3 ) )
% 5.46/5.75 = ( ord_less_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_less_mono
% 5.46/5.75 thf(fact_6546_norm__of__real__diff,axiom,
% 5.46/5.75 ! [B2: real,A: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( real_V1803761363581548252l_real @ B2 ) @ ( real_V1803761363581548252l_real @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B2 @ A ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_of_real_diff
% 5.46/5.75 thf(fact_6547_norm__of__real__diff,axiom,
% 5.46/5.75 ! [B2: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B2 ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B2 @ A ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % norm_of_real_diff
% 5.46/5.75 thf(fact_6548_tan__45,axiom,
% 5.46/5.75 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % tan_45
% 5.46/5.75 thf(fact_6549_tan__60,axiom,
% 5.46/5.75 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.46/5.75 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_60
% 5.46/5.75 thf(fact_6550_cos__int__times__real,axiom,
% 5.46/5.75 ! [M: int,X4: real] :
% 5.46/5.75 ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X4 ) ) )
% 5.46/5.75 = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_int_times_real
% 5.46/5.75 thf(fact_6551_cos__int__times__real,axiom,
% 5.46/5.75 ! [M: int,X4: real] :
% 5.46/5.75 ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X4 ) ) )
% 5.46/5.75 = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_int_times_real
% 5.46/5.75 thf(fact_6552_sin__int__times__real,axiom,
% 5.46/5.75 ! [M: int,X4: real] :
% 5.46/5.75 ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X4 ) ) )
% 5.46/5.75 = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_int_times_real
% 5.46/5.75 thf(fact_6553_sin__int__times__real,axiom,
% 5.46/5.75 ! [M: int,X4: real] :
% 5.46/5.75 ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X4 ) ) )
% 5.46/5.75 = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_int_times_real
% 5.46/5.75 thf(fact_6554_cos__arcsin__nonzero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.75 => ( ( cos_real @ ( arcsin @ X4 ) )
% 5.46/5.75 != zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_arcsin_nonzero
% 5.46/5.75 thf(fact_6555_lemma__tan__total,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ? [X3: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.46/5.75 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 & ( ord_less_real @ Y3 @ ( tan_real @ X3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % lemma_tan_total
% 5.46/5.75 thf(fact_6556_tan__gt__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_gt_zero
% 5.46/5.75 thf(fact_6557_tan__total,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ? [X3: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.46/5.75 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 & ( ( tan_real @ X3 )
% 5.46/5.75 = Y3 )
% 5.46/5.75 & ! [Y5: real] :
% 5.46/5.75 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.46/5.75 & ( ord_less_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 & ( ( tan_real @ Y5 )
% 5.46/5.75 = Y3 ) )
% 5.46/5.75 => ( Y5 = X3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_total
% 5.46/5.75 thf(fact_6558_tan__monotone,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_real @ ( tan_real @ Y3 ) @ ( tan_real @ X4 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_monotone
% 5.46/5.75 thf(fact_6559_tan__monotone_H,axiom,
% 5.46/5.75 ! [Y3: real,X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ X4 )
% 5.46/5.75 = ( ord_less_real @ ( tan_real @ Y3 ) @ ( tan_real @ X4 ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_monotone'
% 5.46/5.75 thf(fact_6560_tan__mono__lt__eq,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_real @ ( tan_real @ X4 ) @ ( tan_real @ Y3 ) )
% 5.46/5.75 = ( ord_less_real @ X4 @ Y3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_mono_lt_eq
% 5.46/5.75 thf(fact_6561_lemma__tan__total1,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ? [X3: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.46/5.75 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 & ( ( tan_real @ X3 )
% 5.46/5.75 = Y3 ) ) ).
% 5.46/5.75
% 5.46/5.75 % lemma_tan_total1
% 5.46/5.75 thf(fact_6562_tan__minus__45,axiom,
% 5.46/5.75 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.75 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_minus_45
% 5.46/5.75 thf(fact_6563_tan__inverse,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y3 ) )
% 5.46/5.75 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_inverse
% 5.46/5.75 thf(fact_6564_complex__norm,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( real_V1022390504157884413omplex @ ( complex2 @ X4 @ Y3 ) )
% 5.46/5.75 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % complex_norm
% 5.46/5.75 thf(fact_6565_add__tan__eq,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex] :
% 5.46/5.75 ( ( ( cos_complex @ X4 )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( ( cos_complex @ Y3 )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( plus_plus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y3 ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X4 @ Y3 ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % add_tan_eq
% 5.46/5.75 thf(fact_6566_add__tan__eq,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ( cos_real @ X4 )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( ( cos_real @ Y3 )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( plus_plus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y3 ) )
% 5.46/5.75 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X4 @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % add_tan_eq
% 5.46/5.75 thf(fact_6567_tan__cot_H,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) )
% 5.46/5.75 = ( cot_real @ X4 ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_cot'
% 5.46/5.75 thf(fact_6568_sin__cos__eq,axiom,
% 5.46/5.75 ( sin_real
% 5.46/5.75 = ( ^ [X: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_eq
% 5.46/5.75 thf(fact_6569_sin__cos__eq,axiom,
% 5.46/5.75 ( sin_complex
% 5.46/5.75 = ( ^ [X: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_cos_eq
% 5.46/5.75 thf(fact_6570_cos__sin__eq,axiom,
% 5.46/5.75 ( cos_real
% 5.46/5.75 = ( ^ [X: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_sin_eq
% 5.46/5.75 thf(fact_6571_cos__sin__eq,axiom,
% 5.46/5.75 ( cos_complex
% 5.46/5.75 = ( ^ [X: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % cos_sin_eq
% 5.46/5.75 thf(fact_6572_tan__pos__pi2__le,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_pos_pi2_le
% 5.46/5.75 thf(fact_6573_tan__total__pos,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.75 => ? [X3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.46/5.75 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 & ( ( tan_real @ X3 )
% 5.46/5.75 = Y3 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_total_pos
% 5.46/5.75 thf(fact_6574_tan__less__zero,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.46/5.75 => ( ord_less_real @ ( tan_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_less_zero
% 5.46/5.75 thf(fact_6575_tan__mono__le,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ord_less_eq_real @ ( tan_real @ X4 ) @ ( tan_real @ Y3 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_mono_le
% 5.46/5.75 thf(fact_6576_tan__mono__le__eq,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( tan_real @ X4 ) @ ( tan_real @ Y3 ) )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ Y3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_mono_le_eq
% 5.46/5.75 thf(fact_6577_tan__bound__pi2,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.75 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X4 ) ) @ one_one_real ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_bound_pi2
% 5.46/5.75 thf(fact_6578_tan__30,axiom,
% 5.46/5.75 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.46/5.75 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_30
% 5.46/5.75 thf(fact_6579_arctan,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y3 ) )
% 5.46/5.75 & ( ord_less_real @ ( arctan @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 & ( ( tan_real @ ( arctan @ Y3 ) )
% 5.46/5.75 = Y3 ) ) ).
% 5.46/5.75
% 5.46/5.75 % arctan
% 5.46/5.75 thf(fact_6580_arctan__tan,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( arctan @ ( tan_real @ X4 ) )
% 5.46/5.75 = X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arctan_tan
% 5.46/5.75 thf(fact_6581_arctan__unique,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ( tan_real @ X4 )
% 5.46/5.75 = Y3 )
% 5.46/5.75 => ( ( arctan @ Y3 )
% 5.46/5.75 = X4 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arctan_unique
% 5.46/5.75 thf(fact_6582_lemma__tan__add1,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex] :
% 5.46/5.75 ( ( ( cos_complex @ X4 )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( ( cos_complex @ Y3 )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y3 ) ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X4 @ Y3 ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % lemma_tan_add1
% 5.46/5.75 thf(fact_6583_lemma__tan__add1,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ( cos_real @ X4 )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( ( cos_real @ Y3 )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y3 ) ) )
% 5.46/5.75 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X4 @ Y3 ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y3 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % lemma_tan_add1
% 5.46/5.75 thf(fact_6584_tan__diff,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex] :
% 5.46/5.75 ( ( ( cos_complex @ X4 )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( ( cos_complex @ Y3 )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( ( cos_complex @ ( minus_minus_complex @ X4 @ Y3 ) )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( tan_complex @ ( minus_minus_complex @ X4 @ Y3 ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y3 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y3 ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_diff
% 5.46/5.75 thf(fact_6585_tan__diff,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ( cos_real @ X4 )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( ( cos_real @ Y3 )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( ( cos_real @ ( minus_minus_real @ X4 @ Y3 ) )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( tan_real @ ( minus_minus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y3 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y3 ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_diff
% 5.46/5.75 thf(fact_6586_tan__add,axiom,
% 5.46/5.75 ! [X4: complex,Y3: complex] :
% 5.46/5.75 ( ( ( cos_complex @ X4 )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( ( cos_complex @ Y3 )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( ( cos_complex @ ( plus_plus_complex @ X4 @ Y3 ) )
% 5.46/5.75 != zero_zero_complex )
% 5.46/5.75 => ( ( tan_complex @ ( plus_plus_complex @ X4 @ Y3 ) )
% 5.46/5.75 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y3 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y3 ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_add
% 5.46/5.75 thf(fact_6587_tan__add,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ( cos_real @ X4 )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( ( cos_real @ Y3 )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( ( cos_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.75 != zero_zero_real )
% 5.46/5.75 => ( ( tan_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.75 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y3 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y3 ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_add
% 5.46/5.75 thf(fact_6588_minus__sin__cos__eq,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( uminus_uminus_real @ ( sin_real @ X4 ) )
% 5.46/5.75 = ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % minus_sin_cos_eq
% 5.46/5.75 thf(fact_6589_minus__sin__cos__eq,axiom,
% 5.46/5.75 ! [X4: complex] :
% 5.46/5.75 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X4 ) )
% 5.46/5.75 = ( cos_complex @ ( plus_plus_complex @ X4 @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % minus_sin_cos_eq
% 5.46/5.75 thf(fact_6590_tan__total__pi4,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.75 => ? [Z2: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z2 )
% 5.46/5.75 & ( ord_less_real @ Z2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.46/5.75 & ( ( tan_real @ Z2 )
% 5.46/5.75 = X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_total_pi4
% 5.46/5.75 thf(fact_6591_arcsin__lt__bounded,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_real @ Y3 @ one_one_real )
% 5.46/5.75 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.46/5.75 & ( ord_less_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_lt_bounded
% 5.46/5.75 thf(fact_6592_arcsin__lbound,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.75 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_lbound
% 5.46/5.75 thf(fact_6593_arcsin__ubound,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.75 => ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_ubound
% 5.46/5.75 thf(fact_6594_arcsin__bounded,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.46/5.75 & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_bounded
% 5.46/5.75 thf(fact_6595_arcsin__sin,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( arcsin @ ( sin_real @ X4 ) )
% 5.46/5.75 = X4 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_sin
% 5.46/5.75 thf(fact_6596_tan__half,axiom,
% 5.46/5.75 ( tan_complex
% 5.46/5.75 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ one_one_complex ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_half
% 5.46/5.75 thf(fact_6597_tan__half,axiom,
% 5.46/5.75 ( tan_real
% 5.46/5.75 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % tan_half
% 5.46/5.75 thf(fact_6598_le__arcsin__iff,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ ( arcsin @ X4 ) )
% 5.46/5.75 = ( ord_less_eq_real @ ( sin_real @ Y3 ) @ X4 ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % le_arcsin_iff
% 5.46/5.75 thf(fact_6599_arcsin__le__iff,axiom,
% 5.46/5.75 ! [X4: real,Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( arcsin @ X4 ) @ Y3 )
% 5.46/5.75 = ( ord_less_eq_real @ X4 @ ( sin_real @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_le_iff
% 5.46/5.75 thf(fact_6600_arcsin__pi,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.46/5.75 & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ pi )
% 5.46/5.75 & ( ( sin_real @ ( arcsin @ Y3 ) )
% 5.46/5.75 = Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin_pi
% 5.46/5.75 thf(fact_6601_arcsin,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.75 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.75 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y3 ) )
% 5.46/5.75 & ( ord_less_eq_real @ ( arcsin @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.75 & ( ( sin_real @ ( arcsin @ Y3 ) )
% 5.46/5.75 = Y3 ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arcsin
% 5.46/5.75 thf(fact_6602_arsinh__def,axiom,
% 5.46/5.75 ( arsinh_real
% 5.46/5.75 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arsinh_def
% 5.46/5.75 thf(fact_6603_sin__arccos__abs,axiom,
% 5.46/5.75 ! [Y3: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.46/5.75 => ( ( sin_real @ ( arccos @ Y3 ) )
% 5.46/5.75 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_arccos_abs
% 5.46/5.75 thf(fact_6604_sin__arccos,axiom,
% 5.46/5.75 ! [X4: real] :
% 5.46/5.75 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.75 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.75 => ( ( sin_real @ ( arccos @ X4 ) )
% 5.46/5.75 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % sin_arccos
% 5.46/5.75 thf(fact_6605_arccos__cos__eq__abs__2pi,axiom,
% 5.46/5.75 ! [Theta: real] :
% 5.46/5.75 ~ ! [K2: int] :
% 5.46/5.75 ( ( arccos @ ( cos_real @ Theta ) )
% 5.46/5.75 != ( 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 ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % arccos_cos_eq_abs_2pi
% 5.46/5.75 thf(fact_6606_fact__double,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.75 = ( 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 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % fact_double
% 5.46/5.75 thf(fact_6607_fact__double,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.75 = ( 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 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % fact_double
% 5.46/5.75 thf(fact_6608_fact__double,axiom,
% 5.46/5.75 ! [N: nat] :
% 5.46/5.75 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.75 = ( 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 ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % fact_double
% 5.46/5.75 thf(fact_6609_modulo__int__unfold,axiom,
% 5.46/5.75 ! [L2: int,K: int,N: nat,M: nat] :
% 5.46/5.75 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.46/5.75 = zero_zero_int )
% 5.46/5.75 | ( ( sgn_sgn_int @ K )
% 5.46/5.75 = zero_zero_int )
% 5.46/5.75 | ( N = zero_zero_nat ) )
% 5.46/5.75 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.75 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.46/5.75 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.46/5.75 = zero_zero_int )
% 5.46/5.75 | ( ( sgn_sgn_int @ K )
% 5.46/5.75 = zero_zero_int )
% 5.46/5.75 | ( N = zero_zero_nat ) )
% 5.46/5.75 => ( ( ( ( sgn_sgn_int @ K )
% 5.46/5.75 = ( sgn_sgn_int @ L2 ) )
% 5.46/5.75 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.75 = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.46/5.75 & ( ( ( sgn_sgn_int @ K )
% 5.46/5.75 != ( sgn_sgn_int @ L2 ) )
% 5.46/5.75 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.75 = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.46/5.75 @ ( minus_minus_int
% 5.46/5.75 @ ( semiri1314217659103216013at_int
% 5.46/5.75 @ ( times_times_nat @ N
% 5.46/5.75 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.75 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.46/5.75 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.46/5.75
% 5.46/5.75 % modulo_int_unfold
% 5.46/5.75 thf(fact_6610_sgn__sgn,axiom,
% 5.46/5.75 ! [A: int] :
% 5.46/5.75 ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 5.46/5.75 = ( sgn_sgn_int @ A ) ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_sgn
% 5.46/5.75 thf(fact_6611_sgn__sgn,axiom,
% 5.46/5.75 ! [A: real] :
% 5.46/5.75 ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 5.46/5.75 = ( sgn_sgn_real @ A ) ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_sgn
% 5.46/5.75 thf(fact_6612_sgn__sgn,axiom,
% 5.46/5.75 ! [A: complex] :
% 5.46/5.75 ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 5.46/5.75 = ( sgn_sgn_complex @ A ) ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_sgn
% 5.46/5.75 thf(fact_6613_sgn__sgn,axiom,
% 5.46/5.75 ! [A: code_integer] :
% 5.46/5.75 ( ( sgn_sgn_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.75 = ( sgn_sgn_Code_integer @ A ) ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_sgn
% 5.46/5.75 thf(fact_6614_sgn__sgn,axiom,
% 5.46/5.75 ! [A: rat] :
% 5.46/5.75 ( ( sgn_sgn_rat @ ( sgn_sgn_rat @ A ) )
% 5.46/5.75 = ( sgn_sgn_rat @ A ) ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_sgn
% 5.46/5.75 thf(fact_6615_sgn__0,axiom,
% 5.46/5.75 ( ( sgn_sgn_complex @ zero_zero_complex )
% 5.46/5.75 = zero_zero_complex ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_0
% 5.46/5.75 thf(fact_6616_sgn__0,axiom,
% 5.46/5.75 ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 5.46/5.75 = zero_z3403309356797280102nteger ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_0
% 5.46/5.75 thf(fact_6617_sgn__0,axiom,
% 5.46/5.75 ( ( sgn_sgn_real @ zero_zero_real )
% 5.46/5.75 = zero_zero_real ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_0
% 5.46/5.75 thf(fact_6618_sgn__0,axiom,
% 5.46/5.75 ( ( sgn_sgn_rat @ zero_zero_rat )
% 5.46/5.75 = zero_zero_rat ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_0
% 5.46/5.75 thf(fact_6619_sgn__0,axiom,
% 5.46/5.75 ( ( sgn_sgn_int @ zero_zero_int )
% 5.46/5.75 = zero_zero_int ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_0
% 5.46/5.75 thf(fact_6620_sgn__1,axiom,
% 5.46/5.75 ( ( sgn_sgn_int @ one_one_int )
% 5.46/5.75 = one_one_int ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_1
% 5.46/5.75 thf(fact_6621_sgn__1,axiom,
% 5.46/5.75 ( ( sgn_sgn_real @ one_one_real )
% 5.46/5.75 = one_one_real ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_1
% 5.46/5.75 thf(fact_6622_sgn__1,axiom,
% 5.46/5.75 ( ( sgn_sgn_complex @ one_one_complex )
% 5.46/5.75 = one_one_complex ) ).
% 5.46/5.75
% 5.46/5.75 % sgn_1
% 5.46/5.76 thf(fact_6623_sgn__1,axiom,
% 5.46/5.76 ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 5.46/5.76 = one_one_Code_integer ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_1
% 5.46/5.76 thf(fact_6624_sgn__1,axiom,
% 5.46/5.76 ( ( sgn_sgn_rat @ one_one_rat )
% 5.46/5.76 = one_one_rat ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_1
% 5.46/5.76 thf(fact_6625_sgn__one,axiom,
% 5.46/5.76 ( ( sgn_sgn_real @ one_one_real )
% 5.46/5.76 = one_one_real ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_one
% 5.46/5.76 thf(fact_6626_sgn__one,axiom,
% 5.46/5.76 ( ( sgn_sgn_complex @ one_one_complex )
% 5.46/5.76 = one_one_complex ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_one
% 5.46/5.76 thf(fact_6627_sgn__divide,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( sgn_sgn_complex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.76 = ( divide1717551699836669952omplex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_divide
% 5.46/5.76 thf(fact_6628_sgn__divide,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.76 = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_divide
% 5.46/5.76 thf(fact_6629_sgn__divide,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( sgn_sgn_rat @ ( divide_divide_rat @ A @ B2 ) )
% 5.46/5.76 = ( divide_divide_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_divide
% 5.46/5.76 thf(fact_6630_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.76 = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % idom_abs_sgn_class.sgn_minus
% 5.46/5.76 thf(fact_6631_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 5.46/5.76 = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % idom_abs_sgn_class.sgn_minus
% 5.46/5.76 thf(fact_6632_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % idom_abs_sgn_class.sgn_minus
% 5.46/5.76 thf(fact_6633_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.76 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % idom_abs_sgn_class.sgn_minus
% 5.46/5.76 thf(fact_6634_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.76 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % idom_abs_sgn_class.sgn_minus
% 5.46/5.76 thf(fact_6635_power__sgn,axiom,
% 5.46/5.76 ! [A: code_integer,N: nat] :
% 5.46/5.76 ( ( sgn_sgn_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.46/5.76 = ( power_8256067586552552935nteger @ ( sgn_sgn_Code_integer @ A ) @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_sgn
% 5.46/5.76 thf(fact_6636_power__sgn,axiom,
% 5.46/5.76 ! [A: rat,N: nat] :
% 5.46/5.76 ( ( sgn_sgn_rat @ ( power_power_rat @ A @ N ) )
% 5.46/5.76 = ( power_power_rat @ ( sgn_sgn_rat @ A ) @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_sgn
% 5.46/5.76 thf(fact_6637_power__sgn,axiom,
% 5.46/5.76 ! [A: real,N: nat] :
% 5.46/5.76 ( ( sgn_sgn_real @ ( power_power_real @ A @ N ) )
% 5.46/5.76 = ( power_power_real @ ( sgn_sgn_real @ A ) @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_sgn
% 5.46/5.76 thf(fact_6638_power__sgn,axiom,
% 5.46/5.76 ! [A: int,N: nat] :
% 5.46/5.76 ( ( sgn_sgn_int @ ( power_power_int @ A @ N ) )
% 5.46/5.76 = ( power_power_int @ ( sgn_sgn_int @ A ) @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_sgn
% 5.46/5.76 thf(fact_6639_sgn__greater,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.76 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_greater
% 5.46/5.76 thf(fact_6640_sgn__greater,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 5.46/5.76 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_greater
% 5.46/5.76 thf(fact_6641_sgn__greater,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 5.46/5.76 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_greater
% 5.46/5.76 thf(fact_6642_sgn__greater,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 5.46/5.76 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_greater
% 5.46/5.76 thf(fact_6643_sgn__less,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.46/5.76 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_less
% 5.46/5.76 thf(fact_6644_sgn__less,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 5.46/5.76 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_less
% 5.46/5.76 thf(fact_6645_sgn__less,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 5.46/5.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_less
% 5.46/5.76 thf(fact_6646_sgn__less,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 5.46/5.76 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_less
% 5.46/5.76 thf(fact_6647_divide__sgn,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B2 ) )
% 5.46/5.76 = ( times_times_real @ A @ ( sgn_sgn_real @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_sgn
% 5.46/5.76 thf(fact_6648_divide__sgn,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B2 ) )
% 5.46/5.76 = ( times_times_rat @ A @ ( sgn_sgn_rat @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_sgn
% 5.46/5.76 thf(fact_6649_fact__0,axiom,
% 5.46/5.76 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.46/5.76 = one_one_complex ) ).
% 5.46/5.76
% 5.46/5.76 % fact_0
% 5.46/5.76 thf(fact_6650_fact__0,axiom,
% 5.46/5.76 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.46/5.76 = one_one_rat ) ).
% 5.46/5.76
% 5.46/5.76 % fact_0
% 5.46/5.76 thf(fact_6651_fact__0,axiom,
% 5.46/5.76 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.46/5.76 = one_one_int ) ).
% 5.46/5.76
% 5.46/5.76 % fact_0
% 5.46/5.76 thf(fact_6652_fact__0,axiom,
% 5.46/5.76 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.46/5.76 = one_one_nat ) ).
% 5.46/5.76
% 5.46/5.76 % fact_0
% 5.46/5.76 thf(fact_6653_fact__0,axiom,
% 5.46/5.76 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.46/5.76 = one_one_real ) ).
% 5.46/5.76
% 5.46/5.76 % fact_0
% 5.46/5.76 thf(fact_6654_fact__1,axiom,
% 5.46/5.76 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.46/5.76 = one_one_complex ) ).
% 5.46/5.76
% 5.46/5.76 % fact_1
% 5.46/5.76 thf(fact_6655_fact__1,axiom,
% 5.46/5.76 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.46/5.76 = one_one_rat ) ).
% 5.46/5.76
% 5.46/5.76 % fact_1
% 5.46/5.76 thf(fact_6656_fact__1,axiom,
% 5.46/5.76 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.46/5.76 = one_one_int ) ).
% 5.46/5.76
% 5.46/5.76 % fact_1
% 5.46/5.76 thf(fact_6657_fact__1,axiom,
% 5.46/5.76 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.46/5.76 = one_one_nat ) ).
% 5.46/5.76
% 5.46/5.76 % fact_1
% 5.46/5.76 thf(fact_6658_fact__1,axiom,
% 5.46/5.76 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.46/5.76 = one_one_real ) ).
% 5.46/5.76
% 5.46/5.76 % fact_1
% 5.46/5.76 thf(fact_6659_arccos__1,axiom,
% 5.46/5.76 ( ( arccos @ one_one_real )
% 5.46/5.76 = zero_zero_real ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_1
% 5.46/5.76 thf(fact_6660_sgn__pos,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.46/5.76 => ( ( sgn_sgn_Code_integer @ A )
% 5.46/5.76 = one_one_Code_integer ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_pos
% 5.46/5.76 thf(fact_6661_sgn__pos,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( sgn_sgn_real @ A )
% 5.46/5.76 = one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_pos
% 5.46/5.76 thf(fact_6662_sgn__pos,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( sgn_sgn_rat @ A )
% 5.46/5.76 = one_one_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_pos
% 5.46/5.76 thf(fact_6663_sgn__pos,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.76 => ( ( sgn_sgn_int @ A )
% 5.46/5.76 = one_one_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_pos
% 5.46/5.76 thf(fact_6664_abs__sgn__eq__1,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.76 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.76 = one_one_Code_integer ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_sgn_eq_1
% 5.46/5.76 thf(fact_6665_abs__sgn__eq__1,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.46/5.76 = one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_sgn_eq_1
% 5.46/5.76 thf(fact_6666_abs__sgn__eq__1,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.46/5.76 = one_one_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_sgn_eq_1
% 5.46/5.76 thf(fact_6667_abs__sgn__eq__1,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( A != zero_zero_int )
% 5.46/5.76 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.46/5.76 = one_one_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_sgn_eq_1
% 5.46/5.76 thf(fact_6668_fact__Suc__0,axiom,
% 5.46/5.76 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.46/5.76 = one_one_complex ) ).
% 5.46/5.76
% 5.46/5.76 % fact_Suc_0
% 5.46/5.76 thf(fact_6669_fact__Suc__0,axiom,
% 5.46/5.76 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.46/5.76 = one_one_rat ) ).
% 5.46/5.76
% 5.46/5.76 % fact_Suc_0
% 5.46/5.76 thf(fact_6670_fact__Suc__0,axiom,
% 5.46/5.76 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.46/5.76 = one_one_int ) ).
% 5.46/5.76
% 5.46/5.76 % fact_Suc_0
% 5.46/5.76 thf(fact_6671_fact__Suc__0,axiom,
% 5.46/5.76 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.46/5.76 = one_one_nat ) ).
% 5.46/5.76
% 5.46/5.76 % fact_Suc_0
% 5.46/5.76 thf(fact_6672_fact__Suc__0,axiom,
% 5.46/5.76 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.46/5.76 = one_one_real ) ).
% 5.46/5.76
% 5.46/5.76 % fact_Suc_0
% 5.46/5.76 thf(fact_6673_fact__Suc,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( semiri5044797733671781792omplex @ ( suc @ N ) )
% 5.46/5.76 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_Suc
% 5.46/5.76 thf(fact_6674_fact__Suc,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.46/5.76 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_Suc
% 5.46/5.76 thf(fact_6675_fact__Suc,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.46/5.76 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_Suc
% 5.46/5.76 thf(fact_6676_fact__Suc,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.46/5.76 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_Suc
% 5.46/5.76 thf(fact_6677_fact__Suc,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.46/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_Suc
% 5.46/5.76 thf(fact_6678_sgn__mult__self__eq,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 5.46/5.76 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult_self_eq
% 5.46/5.76 thf(fact_6679_sgn__mult__self__eq,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.46/5.76 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult_self_eq
% 5.46/5.76 thf(fact_6680_sgn__mult__self__eq,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.46/5.76 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult_self_eq
% 5.46/5.76 thf(fact_6681_sgn__mult__self__eq,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.76 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult_self_eq
% 5.46/5.76 thf(fact_6682_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 5.46/5.76 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % idom_abs_sgn_class.abs_sgn
% 5.46/5.76 thf(fact_6683_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 5.46/5.76 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % idom_abs_sgn_class.abs_sgn
% 5.46/5.76 thf(fact_6684_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( sgn_sgn_rat @ ( abs_abs_rat @ A ) )
% 5.46/5.76 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % idom_abs_sgn_class.abs_sgn
% 5.46/5.76 thf(fact_6685_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 5.46/5.76 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % idom_abs_sgn_class.abs_sgn
% 5.46/5.76 thf(fact_6686_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( sgn_sgn_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.46/5.76 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % idom_abs_sgn_class.abs_sgn
% 5.46/5.76 thf(fact_6687_sgn__abs,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 5.46/5.76 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_abs
% 5.46/5.76 thf(fact_6688_sgn__abs,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.46/5.76 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_abs
% 5.46/5.76 thf(fact_6689_sgn__abs,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.46/5.76 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_abs
% 5.46/5.76 thf(fact_6690_sgn__abs,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.46/5.76 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_abs
% 5.46/5.76 thf(fact_6691_sgn__abs,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.76 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_abs
% 5.46/5.76 thf(fact_6692_arccos__minus__1,axiom,
% 5.46/5.76 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.76 = pi ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_minus_1
% 5.46/5.76 thf(fact_6693_sgn__mult__dvd__iff,axiom,
% 5.46/5.76 ! [R2: int,L2: int,K: int] :
% 5.46/5.76 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L2 ) @ K )
% 5.46/5.76 = ( ( dvd_dvd_int @ L2 @ K )
% 5.46/5.76 & ( ( R2 = zero_zero_int )
% 5.46/5.76 => ( K = zero_zero_int ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult_dvd_iff
% 5.46/5.76 thf(fact_6694_mult__sgn__dvd__iff,axiom,
% 5.46/5.76 ! [L2: int,R2: int,K: int] :
% 5.46/5.76 ( ( dvd_dvd_int @ ( times_times_int @ L2 @ ( sgn_sgn_int @ R2 ) ) @ K )
% 5.46/5.76 = ( ( dvd_dvd_int @ L2 @ K )
% 5.46/5.76 & ( ( R2 = zero_zero_int )
% 5.46/5.76 => ( K = zero_zero_int ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_sgn_dvd_iff
% 5.46/5.76 thf(fact_6695_dvd__sgn__mult__iff,axiom,
% 5.46/5.76 ! [L2: int,R2: int,K: int] :
% 5.46/5.76 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 5.46/5.76 = ( ( dvd_dvd_int @ L2 @ K )
% 5.46/5.76 | ( R2 = zero_zero_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % dvd_sgn_mult_iff
% 5.46/5.76 thf(fact_6696_dvd__mult__sgn__iff,axiom,
% 5.46/5.76 ! [L2: int,K: int,R2: int] :
% 5.46/5.76 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 5.46/5.76 = ( ( dvd_dvd_int @ L2 @ K )
% 5.46/5.76 | ( R2 = zero_zero_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % dvd_mult_sgn_iff
% 5.46/5.76 thf(fact_6697_sgn__neg,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.76 => ( ( sgn_sgn_real @ A )
% 5.46/5.76 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_neg
% 5.46/5.76 thf(fact_6698_sgn__neg,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( ord_less_int @ A @ zero_zero_int )
% 5.46/5.76 => ( ( sgn_sgn_int @ A )
% 5.46/5.76 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_neg
% 5.46/5.76 thf(fact_6699_sgn__neg,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.46/5.76 => ( ( sgn_sgn_Code_integer @ A )
% 5.46/5.76 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_neg
% 5.46/5.76 thf(fact_6700_sgn__neg,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.76 => ( ( sgn_sgn_rat @ A )
% 5.46/5.76 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_neg
% 5.46/5.76 thf(fact_6701_fact__2,axiom,
% 5.46/5.76 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.76 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_2
% 5.46/5.76 thf(fact_6702_fact__2,axiom,
% 5.46/5.76 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.76 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_2
% 5.46/5.76 thf(fact_6703_fact__2,axiom,
% 5.46/5.76 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.76 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_2
% 5.46/5.76 thf(fact_6704_fact__2,axiom,
% 5.46/5.76 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.76 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_2
% 5.46/5.76 thf(fact_6705_fact__2,axiom,
% 5.46/5.76 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.76 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_2
% 5.46/5.76 thf(fact_6706_sgn__of__nat,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.46/5.76 = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_of_nat
% 5.46/5.76 thf(fact_6707_sgn__of__nat,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.46/5.76 = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_of_nat
% 5.46/5.76 thf(fact_6708_sgn__of__nat,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.76 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_of_nat
% 5.46/5.76 thf(fact_6709_sgn__of__nat,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.46/5.76 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_of_nat
% 5.46/5.76 thf(fact_6710_cos__arccos,axiom,
% 5.46/5.76 ! [Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.76 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.76 => ( ( cos_real @ ( arccos @ Y3 ) )
% 5.46/5.76 = Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % cos_arccos
% 5.46/5.76 thf(fact_6711_arccos__0,axiom,
% 5.46/5.76 ( ( arccos @ zero_zero_real )
% 5.46/5.76 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_0
% 5.46/5.76 thf(fact_6712_complex__exp__exists,axiom,
% 5.46/5.76 ! [Z: complex] :
% 5.46/5.76 ? [A5: complex,R3: real] :
% 5.46/5.76 ( Z
% 5.46/5.76 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( exp_complex @ A5 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % complex_exp_exists
% 5.46/5.76 thf(fact_6713_fact__mono__nat,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_mono_nat
% 5.46/5.76 thf(fact_6714_fact__ge__self,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_ge_self
% 5.46/5.76 thf(fact_6715_sgn__eq__0__iff,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( ( sgn_sgn_complex @ A )
% 5.46/5.76 = zero_zero_complex )
% 5.46/5.76 = ( A = zero_zero_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_eq_0_iff
% 5.46/5.76 thf(fact_6716_sgn__eq__0__iff,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( ( sgn_sgn_Code_integer @ A )
% 5.46/5.76 = zero_z3403309356797280102nteger )
% 5.46/5.76 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_eq_0_iff
% 5.46/5.76 thf(fact_6717_sgn__eq__0__iff,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ( sgn_sgn_real @ A )
% 5.46/5.76 = zero_zero_real )
% 5.46/5.76 = ( A = zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_eq_0_iff
% 5.46/5.76 thf(fact_6718_sgn__eq__0__iff,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ( sgn_sgn_rat @ A )
% 5.46/5.76 = zero_zero_rat )
% 5.46/5.76 = ( A = zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_eq_0_iff
% 5.46/5.76 thf(fact_6719_sgn__eq__0__iff,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( ( sgn_sgn_int @ A )
% 5.46/5.76 = zero_zero_int )
% 5.46/5.76 = ( A = zero_zero_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_eq_0_iff
% 5.46/5.76 thf(fact_6720_sgn__0__0,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( ( sgn_sgn_Code_integer @ A )
% 5.46/5.76 = zero_z3403309356797280102nteger )
% 5.46/5.76 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_0_0
% 5.46/5.76 thf(fact_6721_sgn__0__0,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ( sgn_sgn_real @ A )
% 5.46/5.76 = zero_zero_real )
% 5.46/5.76 = ( A = zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_0_0
% 5.46/5.76 thf(fact_6722_sgn__0__0,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ( sgn_sgn_rat @ A )
% 5.46/5.76 = zero_zero_rat )
% 5.46/5.76 = ( A = zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_0_0
% 5.46/5.76 thf(fact_6723_sgn__0__0,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( ( sgn_sgn_int @ A )
% 5.46/5.76 = zero_zero_int )
% 5.46/5.76 = ( A = zero_zero_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_0_0
% 5.46/5.76 thf(fact_6724_Real__Vector__Spaces_Osgn__mult,axiom,
% 5.46/5.76 ! [X4: complex,Y3: complex] :
% 5.46/5.76 ( ( sgn_sgn_complex @ ( times_times_complex @ X4 @ Y3 ) )
% 5.46/5.76 = ( times_times_complex @ ( sgn_sgn_complex @ X4 ) @ ( sgn_sgn_complex @ Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Real_Vector_Spaces.sgn_mult
% 5.46/5.76 thf(fact_6725_Real__Vector__Spaces_Osgn__mult,axiom,
% 5.46/5.76 ! [X4: real,Y3: real] :
% 5.46/5.76 ( ( sgn_sgn_real @ ( times_times_real @ X4 @ Y3 ) )
% 5.46/5.76 = ( times_times_real @ ( sgn_sgn_real @ X4 ) @ ( sgn_sgn_real @ Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Real_Vector_Spaces.sgn_mult
% 5.46/5.76 thf(fact_6726_sgn__mult,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B2 ) )
% 5.46/5.76 = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult
% 5.46/5.76 thf(fact_6727_sgn__mult,axiom,
% 5.46/5.76 ! [A: code_integer,B2: code_integer] :
% 5.46/5.76 ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B2 ) )
% 5.46/5.76 = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult
% 5.46/5.76 thf(fact_6728_sgn__mult,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( sgn_sgn_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.76 = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult
% 5.46/5.76 thf(fact_6729_sgn__mult,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.76 = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult
% 5.46/5.76 thf(fact_6730_sgn__mult,axiom,
% 5.46/5.76 ! [A: int,B2: int] :
% 5.46/5.76 ( ( sgn_sgn_int @ ( times_times_int @ A @ B2 ) )
% 5.46/5.76 = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult
% 5.46/5.76 thf(fact_6731_same__sgn__sgn__add,axiom,
% 5.46/5.76 ! [B2: code_integer,A: code_integer] :
% 5.46/5.76 ( ( ( sgn_sgn_Code_integer @ B2 )
% 5.46/5.76 = ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.76 => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B2 ) )
% 5.46/5.76 = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % same_sgn_sgn_add
% 5.46/5.76 thf(fact_6732_same__sgn__sgn__add,axiom,
% 5.46/5.76 ! [B2: real,A: real] :
% 5.46/5.76 ( ( ( sgn_sgn_real @ B2 )
% 5.46/5.76 = ( sgn_sgn_real @ A ) )
% 5.46/5.76 => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B2 ) )
% 5.46/5.76 = ( sgn_sgn_real @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % same_sgn_sgn_add
% 5.46/5.76 thf(fact_6733_same__sgn__sgn__add,axiom,
% 5.46/5.76 ! [B2: rat,A: rat] :
% 5.46/5.76 ( ( ( sgn_sgn_rat @ B2 )
% 5.46/5.76 = ( sgn_sgn_rat @ A ) )
% 5.46/5.76 => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B2 ) )
% 5.46/5.76 = ( sgn_sgn_rat @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % same_sgn_sgn_add
% 5.46/5.76 thf(fact_6734_same__sgn__sgn__add,axiom,
% 5.46/5.76 ! [B2: int,A: int] :
% 5.46/5.76 ( ( ( sgn_sgn_int @ B2 )
% 5.46/5.76 = ( sgn_sgn_int @ A ) )
% 5.46/5.76 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B2 ) )
% 5.46/5.76 = ( sgn_sgn_int @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % same_sgn_sgn_add
% 5.46/5.76 thf(fact_6735_fact__less__mono__nat,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.76 => ( ( ord_less_nat @ M @ N )
% 5.46/5.76 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_less_mono_nat
% 5.46/5.76 thf(fact_6736_sgn__not__eq__imp,axiom,
% 5.46/5.76 ! [B2: real,A: real] :
% 5.46/5.76 ( ( ( sgn_sgn_real @ B2 )
% 5.46/5.76 != ( sgn_sgn_real @ A ) )
% 5.46/5.76 => ( ( ( sgn_sgn_real @ A )
% 5.46/5.76 != zero_zero_real )
% 5.46/5.76 => ( ( ( sgn_sgn_real @ B2 )
% 5.46/5.76 != zero_zero_real )
% 5.46/5.76 => ( ( sgn_sgn_real @ A )
% 5.46/5.76 = ( uminus_uminus_real @ ( sgn_sgn_real @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_not_eq_imp
% 5.46/5.76 thf(fact_6737_sgn__not__eq__imp,axiom,
% 5.46/5.76 ! [B2: int,A: int] :
% 5.46/5.76 ( ( ( sgn_sgn_int @ B2 )
% 5.46/5.76 != ( sgn_sgn_int @ A ) )
% 5.46/5.76 => ( ( ( sgn_sgn_int @ A )
% 5.46/5.76 != zero_zero_int )
% 5.46/5.76 => ( ( ( sgn_sgn_int @ B2 )
% 5.46/5.76 != zero_zero_int )
% 5.46/5.76 => ( ( sgn_sgn_int @ A )
% 5.46/5.76 = ( uminus_uminus_int @ ( sgn_sgn_int @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_not_eq_imp
% 5.46/5.76 thf(fact_6738_sgn__not__eq__imp,axiom,
% 5.46/5.76 ! [B2: code_integer,A: code_integer] :
% 5.46/5.76 ( ( ( sgn_sgn_Code_integer @ B2 )
% 5.46/5.76 != ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.76 => ( ( ( sgn_sgn_Code_integer @ A )
% 5.46/5.76 != zero_z3403309356797280102nteger )
% 5.46/5.76 => ( ( ( sgn_sgn_Code_integer @ B2 )
% 5.46/5.76 != zero_z3403309356797280102nteger )
% 5.46/5.76 => ( ( sgn_sgn_Code_integer @ A )
% 5.46/5.76 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_not_eq_imp
% 5.46/5.76 thf(fact_6739_sgn__not__eq__imp,axiom,
% 5.46/5.76 ! [B2: rat,A: rat] :
% 5.46/5.76 ( ( ( sgn_sgn_rat @ B2 )
% 5.46/5.76 != ( sgn_sgn_rat @ A ) )
% 5.46/5.76 => ( ( ( sgn_sgn_rat @ A )
% 5.46/5.76 != zero_zero_rat )
% 5.46/5.76 => ( ( ( sgn_sgn_rat @ B2 )
% 5.46/5.76 != zero_zero_rat )
% 5.46/5.76 => ( ( sgn_sgn_rat @ A )
% 5.46/5.76 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_not_eq_imp
% 5.46/5.76 thf(fact_6740_sgn__minus__1,axiom,
% 5.46/5.76 ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.76 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_minus_1
% 5.46/5.76 thf(fact_6741_sgn__minus__1,axiom,
% 5.46/5.76 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.76 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_minus_1
% 5.46/5.76 thf(fact_6742_sgn__minus__1,axiom,
% 5.46/5.76 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_minus_1
% 5.46/5.76 thf(fact_6743_sgn__minus__1,axiom,
% 5.46/5.76 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.76 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_minus_1
% 5.46/5.76 thf(fact_6744_sgn__minus__1,axiom,
% 5.46/5.76 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.76 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_minus_1
% 5.46/5.76 thf(fact_6745_fact__ge__zero,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_ge_zero
% 5.46/5.76 thf(fact_6746_fact__ge__zero,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_ge_zero
% 5.46/5.76 thf(fact_6747_fact__ge__zero,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_ge_zero
% 5.46/5.76 thf(fact_6748_fact__ge__zero,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_ge_zero
% 5.46/5.76 thf(fact_6749_linordered__idom__class_Oabs__sgn,axiom,
% 5.46/5.76 ( abs_abs_Code_integer
% 5.46/5.76 = ( ^ [K3: code_integer] : ( times_3573771949741848930nteger @ K3 @ ( sgn_sgn_Code_integer @ K3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % linordered_idom_class.abs_sgn
% 5.46/5.76 thf(fact_6750_linordered__idom__class_Oabs__sgn,axiom,
% 5.46/5.76 ( abs_abs_real
% 5.46/5.76 = ( ^ [K3: real] : ( times_times_real @ K3 @ ( sgn_sgn_real @ K3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % linordered_idom_class.abs_sgn
% 5.46/5.76 thf(fact_6751_linordered__idom__class_Oabs__sgn,axiom,
% 5.46/5.76 ( abs_abs_rat
% 5.46/5.76 = ( ^ [K3: rat] : ( times_times_rat @ K3 @ ( sgn_sgn_rat @ K3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % linordered_idom_class.abs_sgn
% 5.46/5.76 thf(fact_6752_linordered__idom__class_Oabs__sgn,axiom,
% 5.46/5.76 ( abs_abs_int
% 5.46/5.76 = ( ^ [K3: int] : ( times_times_int @ K3 @ ( sgn_sgn_int @ K3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % linordered_idom_class.abs_sgn
% 5.46/5.76 thf(fact_6753_abs__mult__sgn,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % abs_mult_sgn
% 5.46/5.76 thf(fact_6754_abs__mult__sgn,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % abs_mult_sgn
% 5.46/5.76 thf(fact_6755_abs__mult__sgn,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % abs_mult_sgn
% 5.46/5.76 thf(fact_6756_abs__mult__sgn,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % abs_mult_sgn
% 5.46/5.76 thf(fact_6757_abs__mult__sgn,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % abs_mult_sgn
% 5.46/5.76 thf(fact_6758_sgn__mult__abs,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult_abs
% 5.46/5.76 thf(fact_6759_sgn__mult__abs,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult_abs
% 5.46/5.76 thf(fact_6760_sgn__mult__abs,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult_abs
% 5.46/5.76 thf(fact_6761_sgn__mult__abs,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult_abs
% 5.46/5.76 thf(fact_6762_sgn__mult__abs,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mult_abs
% 5.46/5.76 thf(fact_6763_mult__sgn__abs,axiom,
% 5.46/5.76 ! [X4: code_integer] :
% 5.46/5.76 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X4 ) @ ( abs_abs_Code_integer @ X4 ) )
% 5.46/5.76 = X4 ) ).
% 5.46/5.76
% 5.46/5.76 % mult_sgn_abs
% 5.46/5.76 thf(fact_6764_mult__sgn__abs,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( times_times_real @ ( sgn_sgn_real @ X4 ) @ ( abs_abs_real @ X4 ) )
% 5.46/5.76 = X4 ) ).
% 5.46/5.76
% 5.46/5.76 % mult_sgn_abs
% 5.46/5.76 thf(fact_6765_mult__sgn__abs,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( times_times_rat @ ( sgn_sgn_rat @ X4 ) @ ( abs_abs_rat @ X4 ) )
% 5.46/5.76 = X4 ) ).
% 5.46/5.76
% 5.46/5.76 % mult_sgn_abs
% 5.46/5.76 thf(fact_6766_mult__sgn__abs,axiom,
% 5.46/5.76 ! [X4: int] :
% 5.46/5.76 ( ( times_times_int @ ( sgn_sgn_int @ X4 ) @ ( abs_abs_int @ X4 ) )
% 5.46/5.76 = X4 ) ).
% 5.46/5.76
% 5.46/5.76 % mult_sgn_abs
% 5.46/5.76 thf(fact_6767_fact__not__neg,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.46/5.76
% 5.46/5.76 % fact_not_neg
% 5.46/5.76 thf(fact_6768_fact__not__neg,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.46/5.76
% 5.46/5.76 % fact_not_neg
% 5.46/5.76 thf(fact_6769_fact__not__neg,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.46/5.76
% 5.46/5.76 % fact_not_neg
% 5.46/5.76 thf(fact_6770_fact__not__neg,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.46/5.76
% 5.46/5.76 % fact_not_neg
% 5.46/5.76 thf(fact_6771_fact__gt__zero,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_gt_zero
% 5.46/5.76 thf(fact_6772_fact__gt__zero,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_gt_zero
% 5.46/5.76 thf(fact_6773_fact__gt__zero,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_gt_zero
% 5.46/5.76 thf(fact_6774_fact__gt__zero,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_gt_zero
% 5.46/5.76 thf(fact_6775_int__sgnE,axiom,
% 5.46/5.76 ! [K: int] :
% 5.46/5.76 ~ ! [N4: nat,L3: int] :
% 5.46/5.76 ( K
% 5.46/5.76 != ( times_times_int @ ( sgn_sgn_int @ L3 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % int_sgnE
% 5.46/5.76 thf(fact_6776_same__sgn__abs__add,axiom,
% 5.46/5.76 ! [B2: code_integer,A: code_integer] :
% 5.46/5.76 ( ( ( sgn_sgn_Code_integer @ B2 )
% 5.46/5.76 = ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.76 => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B2 ) )
% 5.46/5.76 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % same_sgn_abs_add
% 5.46/5.76 thf(fact_6777_same__sgn__abs__add,axiom,
% 5.46/5.76 ! [B2: real,A: real] :
% 5.46/5.76 ( ( ( sgn_sgn_real @ B2 )
% 5.46/5.76 = ( sgn_sgn_real @ A ) )
% 5.46/5.76 => ( ( abs_abs_real @ ( plus_plus_real @ A @ B2 ) )
% 5.46/5.76 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % same_sgn_abs_add
% 5.46/5.76 thf(fact_6778_same__sgn__abs__add,axiom,
% 5.46/5.76 ! [B2: rat,A: rat] :
% 5.46/5.76 ( ( ( sgn_sgn_rat @ B2 )
% 5.46/5.76 = ( sgn_sgn_rat @ A ) )
% 5.46/5.76 => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B2 ) )
% 5.46/5.76 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % same_sgn_abs_add
% 5.46/5.76 thf(fact_6779_same__sgn__abs__add,axiom,
% 5.46/5.76 ! [B2: int,A: int] :
% 5.46/5.76 ( ( ( sgn_sgn_int @ B2 )
% 5.46/5.76 = ( sgn_sgn_int @ A ) )
% 5.46/5.76 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B2 ) )
% 5.46/5.76 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % same_sgn_abs_add
% 5.46/5.76 thf(fact_6780_fact__ge__1,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_ge_1
% 5.46/5.76 thf(fact_6781_fact__ge__1,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_ge_1
% 5.46/5.76 thf(fact_6782_fact__ge__1,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_ge_1
% 5.46/5.76 thf(fact_6783_fact__ge__1,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_ge_1
% 5.46/5.76 thf(fact_6784_fact__mono,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_mono
% 5.46/5.76 thf(fact_6785_fact__mono,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_mono
% 5.46/5.76 thf(fact_6786_fact__mono,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_mono
% 5.46/5.76 thf(fact_6787_fact__mono,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_mono
% 5.46/5.76 thf(fact_6788_div__eq__sgn__abs,axiom,
% 5.46/5.76 ! [K: int,L2: int] :
% 5.46/5.76 ( ( ( sgn_sgn_int @ K )
% 5.46/5.76 = ( sgn_sgn_int @ L2 ) )
% 5.46/5.76 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.76 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % div_eq_sgn_abs
% 5.46/5.76 thf(fact_6789_fact__dvd,axiom,
% 5.46/5.76 ! [N: nat,M: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.76 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_dvd
% 5.46/5.76 thf(fact_6790_fact__dvd,axiom,
% 5.46/5.76 ! [N: nat,M: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.76 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_dvd
% 5.46/5.76 thf(fact_6791_fact__dvd,axiom,
% 5.46/5.76 ! [N: nat,M: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.76 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_dvd
% 5.46/5.76 thf(fact_6792_fact__dvd,axiom,
% 5.46/5.76 ! [N: nat,M: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.76 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_dvd
% 5.46/5.76 thf(fact_6793_pochhammer__fact,axiom,
% 5.46/5.76 ( semiri5044797733671781792omplex
% 5.46/5.76 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % pochhammer_fact
% 5.46/5.76 thf(fact_6794_pochhammer__fact,axiom,
% 5.46/5.76 ( semiri773545260158071498ct_rat
% 5.46/5.76 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % pochhammer_fact
% 5.46/5.76 thf(fact_6795_pochhammer__fact,axiom,
% 5.46/5.76 ( semiri1406184849735516958ct_int
% 5.46/5.76 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % pochhammer_fact
% 5.46/5.76 thf(fact_6796_pochhammer__fact,axiom,
% 5.46/5.76 ( semiri1408675320244567234ct_nat
% 5.46/5.76 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.46/5.76
% 5.46/5.76 % pochhammer_fact
% 5.46/5.76 thf(fact_6797_pochhammer__fact,axiom,
% 5.46/5.76 ( semiri2265585572941072030t_real
% 5.46/5.76 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % pochhammer_fact
% 5.46/5.76 thf(fact_6798_fact__ge__Suc__0__nat,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_ge_Suc_0_nat
% 5.46/5.76 thf(fact_6799_sgn__1__pos,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( ( sgn_sgn_Code_integer @ A )
% 5.46/5.76 = one_one_Code_integer )
% 5.46/5.76 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_1_pos
% 5.46/5.76 thf(fact_6800_sgn__1__pos,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ( sgn_sgn_real @ A )
% 5.46/5.76 = one_one_real )
% 5.46/5.76 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_1_pos
% 5.46/5.76 thf(fact_6801_sgn__1__pos,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ( sgn_sgn_rat @ A )
% 5.46/5.76 = one_one_rat )
% 5.46/5.76 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_1_pos
% 5.46/5.76 thf(fact_6802_sgn__1__pos,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( ( sgn_sgn_int @ A )
% 5.46/5.76 = one_one_int )
% 5.46/5.76 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_1_pos
% 5.46/5.76 thf(fact_6803_abs__sgn__eq,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( ( A = zero_z3403309356797280102nteger )
% 5.46/5.76 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.76 = zero_z3403309356797280102nteger ) )
% 5.46/5.76 & ( ( A != zero_z3403309356797280102nteger )
% 5.46/5.76 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.46/5.76 = one_one_Code_integer ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_sgn_eq
% 5.46/5.76 thf(fact_6804_abs__sgn__eq,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ( A = zero_zero_real )
% 5.46/5.76 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.46/5.76 = zero_zero_real ) )
% 5.46/5.76 & ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.46/5.76 = one_one_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_sgn_eq
% 5.46/5.76 thf(fact_6805_abs__sgn__eq,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ( A = zero_zero_rat )
% 5.46/5.76 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.46/5.76 = zero_zero_rat ) )
% 5.46/5.76 & ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.46/5.76 = one_one_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_sgn_eq
% 5.46/5.76 thf(fact_6806_abs__sgn__eq,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( ( A = zero_zero_int )
% 5.46/5.76 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.46/5.76 = zero_zero_int ) )
% 5.46/5.76 & ( ( A != zero_zero_int )
% 5.46/5.76 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.46/5.76 = one_one_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_sgn_eq
% 5.46/5.76 thf(fact_6807_dvd__fact,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.46/5.76 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % dvd_fact
% 5.46/5.76 thf(fact_6808_fact__less__mono,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.76 => ( ( ord_less_nat @ M @ N )
% 5.46/5.76 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_less_mono
% 5.46/5.76 thf(fact_6809_fact__less__mono,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.76 => ( ( ord_less_nat @ M @ N )
% 5.46/5.76 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_less_mono
% 5.46/5.76 thf(fact_6810_fact__less__mono,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.76 => ( ( ord_less_nat @ M @ N )
% 5.46/5.76 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_less_mono
% 5.46/5.76 thf(fact_6811_fact__less__mono,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.76 => ( ( ord_less_nat @ M @ N )
% 5.46/5.76 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_less_mono
% 5.46/5.76 thf(fact_6812_sgn__mod,axiom,
% 5.46/5.76 ! [L2: int,K: int] :
% 5.46/5.76 ( ( L2 != zero_zero_int )
% 5.46/5.76 => ( ~ ( dvd_dvd_int @ L2 @ K )
% 5.46/5.76 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.46/5.76 = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_mod
% 5.46/5.76 thf(fact_6813_fact__mod,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.46/5.76 = zero_zero_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_mod
% 5.46/5.76 thf(fact_6814_fact__mod,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.46/5.76 = zero_z3403309356797280102nteger ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_mod
% 5.46/5.76 thf(fact_6815_fact__mod,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.46/5.76 = zero_zero_nat ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_mod
% 5.46/5.76 thf(fact_6816_fact__fact__dvd__fact,axiom,
% 5.46/5.76 ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_fact_dvd_fact
% 5.46/5.76 thf(fact_6817_fact__fact__dvd__fact,axiom,
% 5.46/5.76 ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_fact_dvd_fact
% 5.46/5.76 thf(fact_6818_fact__fact__dvd__fact,axiom,
% 5.46/5.76 ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_fact_dvd_fact
% 5.46/5.76 thf(fact_6819_fact__fact__dvd__fact,axiom,
% 5.46/5.76 ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_fact_dvd_fact
% 5.46/5.76 thf(fact_6820_fact__fact__dvd__fact,axiom,
% 5.46/5.76 ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_fact_dvd_fact
% 5.46/5.76 thf(fact_6821_fact__le__power,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_le_power
% 5.46/5.76 thf(fact_6822_fact__le__power,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_le_power
% 5.46/5.76 thf(fact_6823_fact__le__power,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_le_power
% 5.46/5.76 thf(fact_6824_fact__le__power,axiom,
% 5.46/5.76 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_le_power
% 5.46/5.76 thf(fact_6825_arccos__le__arccos,axiom,
% 5.46/5.76 ! [X4: real,Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.76 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.76 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.76 => ( ord_less_eq_real @ ( arccos @ Y3 ) @ ( arccos @ X4 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_le_arccos
% 5.46/5.76 thf(fact_6826_arccos__eq__iff,axiom,
% 5.46/5.76 ! [X4: real,Y3: real] :
% 5.46/5.76 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.76 & ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real ) )
% 5.46/5.76 => ( ( ( arccos @ X4 )
% 5.46/5.76 = ( arccos @ Y3 ) )
% 5.46/5.76 = ( X4 = Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_eq_iff
% 5.46/5.76 thf(fact_6827_arccos__le__mono,axiom,
% 5.46/5.76 ! [X4: real,Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.76 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.46/5.76 => ( ( ord_less_eq_real @ ( arccos @ X4 ) @ ( arccos @ Y3 ) )
% 5.46/5.76 = ( ord_less_eq_real @ Y3 @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_le_mono
% 5.46/5.76 thf(fact_6828_fact__diff__Suc,axiom,
% 5.46/5.76 ! [N: nat,M: nat] :
% 5.46/5.76 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.46/5.76 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.46/5.76 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_diff_Suc
% 5.46/5.76 thf(fact_6829_sgn__if,axiom,
% 5.46/5.76 ( sgn_sgn_real
% 5.46/5.76 = ( ^ [X: real] : ( if_real @ ( X = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ X ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_if
% 5.46/5.76 thf(fact_6830_sgn__if,axiom,
% 5.46/5.76 ( sgn_sgn_int
% 5.46/5.76 = ( ^ [X: int] : ( if_int @ ( X = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_if
% 5.46/5.76 thf(fact_6831_sgn__if,axiom,
% 5.46/5.76 ( sgn_sgn_Code_integer
% 5.46/5.76 = ( ^ [X: code_integer] : ( if_Code_integer @ ( X = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_if
% 5.46/5.76 thf(fact_6832_sgn__if,axiom,
% 5.46/5.76 ( sgn_sgn_rat
% 5.46/5.76 = ( ^ [X: rat] : ( if_rat @ ( X = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_if
% 5.46/5.76 thf(fact_6833_sgn__1__neg,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ( sgn_sgn_real @ A )
% 5.46/5.76 = ( uminus_uminus_real @ one_one_real ) )
% 5.46/5.76 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_1_neg
% 5.46/5.76 thf(fact_6834_sgn__1__neg,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( ( sgn_sgn_int @ A )
% 5.46/5.76 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.76 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_1_neg
% 5.46/5.76 thf(fact_6835_sgn__1__neg,axiom,
% 5.46/5.76 ! [A: code_integer] :
% 5.46/5.76 ( ( ( sgn_sgn_Code_integer @ A )
% 5.46/5.76 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.76 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_1_neg
% 5.46/5.76 thf(fact_6836_sgn__1__neg,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ( sgn_sgn_rat @ A )
% 5.46/5.76 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.46/5.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_1_neg
% 5.46/5.76 thf(fact_6837_zsgn__def,axiom,
% 5.46/5.76 ( sgn_sgn_int
% 5.46/5.76 = ( ^ [I2: int] : ( if_int @ ( I2 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % zsgn_def
% 5.46/5.76 thf(fact_6838_fact__div__fact__le__pow,axiom,
% 5.46/5.76 ! [R2: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ R2 @ N )
% 5.46/5.76 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_div_fact_le_pow
% 5.46/5.76 thf(fact_6839_binomial__fact__lemma,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.46/5.76 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % binomial_fact_lemma
% 5.46/5.76 thf(fact_6840_norm__sgn,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ( X4 = zero_zero_real )
% 5.46/5.76 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X4 ) )
% 5.46/5.76 = zero_zero_real ) )
% 5.46/5.76 & ( ( X4 != zero_zero_real )
% 5.46/5.76 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X4 ) )
% 5.46/5.76 = one_one_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % norm_sgn
% 5.46/5.76 thf(fact_6841_norm__sgn,axiom,
% 5.46/5.76 ! [X4: complex] :
% 5.46/5.76 ( ( ( X4 = zero_zero_complex )
% 5.46/5.76 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X4 ) )
% 5.46/5.76 = zero_zero_real ) )
% 5.46/5.76 & ( ( X4 != zero_zero_complex )
% 5.46/5.76 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X4 ) )
% 5.46/5.76 = one_one_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % norm_sgn
% 5.46/5.76 thf(fact_6842_div__sgn__abs__cancel,axiom,
% 5.46/5.76 ! [V: int,K: int,L2: int] :
% 5.46/5.76 ( ( V != zero_zero_int )
% 5.46/5.76 => ( ( 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 ) ) )
% 5.46/5.76 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % div_sgn_abs_cancel
% 5.46/5.76 thf(fact_6843_div__dvd__sgn__abs,axiom,
% 5.46/5.76 ! [L2: int,K: int] :
% 5.46/5.76 ( ( dvd_dvd_int @ L2 @ K )
% 5.46/5.76 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.76 = ( 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 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % div_dvd_sgn_abs
% 5.46/5.76 thf(fact_6844_choose__dvd,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % choose_dvd
% 5.46/5.76 thf(fact_6845_choose__dvd,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % choose_dvd
% 5.46/5.76 thf(fact_6846_choose__dvd,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % choose_dvd
% 5.46/5.76 thf(fact_6847_choose__dvd,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % choose_dvd
% 5.46/5.76 thf(fact_6848_choose__dvd,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % choose_dvd
% 5.46/5.76 thf(fact_6849_fact__numeral,axiom,
% 5.46/5.76 ! [K: num] :
% 5.46/5.76 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.46/5.76 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_numeral
% 5.46/5.76 thf(fact_6850_fact__numeral,axiom,
% 5.46/5.76 ! [K: num] :
% 5.46/5.76 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.46/5.76 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_numeral
% 5.46/5.76 thf(fact_6851_fact__numeral,axiom,
% 5.46/5.76 ! [K: num] :
% 5.46/5.76 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.46/5.76 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_numeral
% 5.46/5.76 thf(fact_6852_fact__numeral,axiom,
% 5.46/5.76 ! [K: num] :
% 5.46/5.76 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.46/5.76 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_numeral
% 5.46/5.76 thf(fact_6853_fact__numeral,axiom,
% 5.46/5.76 ! [K: num] :
% 5.46/5.76 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.46/5.76 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_numeral
% 5.46/5.76 thf(fact_6854_arccos__lbound,axiom,
% 5.46/5.76 ! [Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.76 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_lbound
% 5.46/5.76 thf(fact_6855_arccos__less__arccos,axiom,
% 5.46/5.76 ! [X4: real,Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.76 => ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.76 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.76 => ( ord_less_real @ ( arccos @ Y3 ) @ ( arccos @ X4 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_less_arccos
% 5.46/5.76 thf(fact_6856_arccos__less__mono,axiom,
% 5.46/5.76 ! [X4: real,Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.76 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.46/5.76 => ( ( ord_less_real @ ( arccos @ X4 ) @ ( arccos @ Y3 ) )
% 5.46/5.76 = ( ord_less_real @ Y3 @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_less_mono
% 5.46/5.76 thf(fact_6857_arccos__ubound,axiom,
% 5.46/5.76 ! [Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.76 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.76 => ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_ubound
% 5.46/5.76 thf(fact_6858_arccos__cos,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.46/5.76 => ( ( arccos @ ( cos_real @ X4 ) )
% 5.46/5.76 = X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_cos
% 5.46/5.76 thf(fact_6859_cos__arccos__abs,axiom,
% 5.46/5.76 ! [Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ Y3 ) @ one_one_real )
% 5.46/5.76 => ( ( cos_real @ ( arccos @ Y3 ) )
% 5.46/5.76 = Y3 ) ) ).
% 5.46/5.76
% 5.46/5.76 % cos_arccos_abs
% 5.46/5.76 thf(fact_6860_arccos__cos__eq__abs,axiom,
% 5.46/5.76 ! [Theta: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.46/5.76 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.46/5.76 = ( abs_abs_real @ Theta ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_cos_eq_abs
% 5.46/5.76 thf(fact_6861_binomial__altdef__nat,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( binomial @ N @ K )
% 5.46/5.76 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % binomial_altdef_nat
% 5.46/5.76 thf(fact_6862_square__fact__le__2__fact,axiom,
% 5.46/5.76 ! [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 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % square_fact_le_2_fact
% 5.46/5.76 thf(fact_6863_arccos__lt__bounded,axiom,
% 5.46/5.76 ! [Y3: real] :
% 5.46/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.76 => ( ( ord_less_real @ Y3 @ one_one_real )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 5.46/5.76 & ( ord_less_real @ ( arccos @ Y3 ) @ pi ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_lt_bounded
% 5.46/5.76 thf(fact_6864_arccos__bounded,axiom,
% 5.46/5.76 ! [Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.76 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 5.46/5.76 & ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_bounded
% 5.46/5.76 thf(fact_6865_sin__arccos__nonzero,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.76 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.76 => ( ( sin_real @ ( arccos @ X4 ) )
% 5.46/5.76 != zero_zero_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sin_arccos_nonzero
% 5.46/5.76 thf(fact_6866_arccos__cos2,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.76 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 5.46/5.76 => ( ( arccos @ ( cos_real @ X4 ) )
% 5.46/5.76 = ( uminus_uminus_real @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_cos2
% 5.46/5.76 thf(fact_6867_arccos__minus,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.76 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.76 => ( ( arccos @ ( uminus_uminus_real @ X4 ) )
% 5.46/5.76 = ( minus_minus_real @ pi @ ( arccos @ X4 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_minus
% 5.46/5.76 thf(fact_6868_fact__num__eq__if,axiom,
% 5.46/5.76 ( semiri5044797733671781792omplex
% 5.46/5.76 = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_num_eq_if
% 5.46/5.76 thf(fact_6869_fact__num__eq__if,axiom,
% 5.46/5.76 ( semiri773545260158071498ct_rat
% 5.46/5.76 = ( ^ [M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M6 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_num_eq_if
% 5.46/5.76 thf(fact_6870_fact__num__eq__if,axiom,
% 5.46/5.76 ( semiri1406184849735516958ct_int
% 5.46/5.76 = ( ^ [M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_num_eq_if
% 5.46/5.76 thf(fact_6871_fact__num__eq__if,axiom,
% 5.46/5.76 ( semiri1408675320244567234ct_nat
% 5.46/5.76 = ( ^ [M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M6 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_num_eq_if
% 5.46/5.76 thf(fact_6872_fact__num__eq__if,axiom,
% 5.46/5.76 ( semiri2265585572941072030t_real
% 5.46/5.76 = ( ^ [M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M6 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_num_eq_if
% 5.46/5.76 thf(fact_6873_fact__reduce,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.76 => ( ( semiri5044797733671781792omplex @ N )
% 5.46/5.76 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_reduce
% 5.46/5.76 thf(fact_6874_fact__reduce,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.76 => ( ( semiri773545260158071498ct_rat @ N )
% 5.46/5.76 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_reduce
% 5.46/5.76 thf(fact_6875_fact__reduce,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.76 => ( ( semiri1406184849735516958ct_int @ N )
% 5.46/5.76 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_reduce
% 5.46/5.76 thf(fact_6876_fact__reduce,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.76 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.46/5.76 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_reduce
% 5.46/5.76 thf(fact_6877_fact__reduce,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.76 => ( ( semiri2265585572941072030t_real @ N )
% 5.46/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_reduce
% 5.46/5.76 thf(fact_6878_pochhammer__same,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.46/5.76 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % pochhammer_same
% 5.46/5.76 thf(fact_6879_pochhammer__same,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.46/5.76 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % pochhammer_same
% 5.46/5.76 thf(fact_6880_pochhammer__same,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.46/5.76 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % pochhammer_same
% 5.46/5.76 thf(fact_6881_pochhammer__same,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.46/5.76 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % pochhammer_same
% 5.46/5.76 thf(fact_6882_pochhammer__same,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.46/5.76 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % pochhammer_same
% 5.46/5.76 thf(fact_6883_binomial__fact,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.46/5.76 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % binomial_fact
% 5.46/5.76 thf(fact_6884_binomial__fact,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.46/5.76 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % binomial_fact
% 5.46/5.76 thf(fact_6885_binomial__fact,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.46/5.76 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % binomial_fact
% 5.46/5.76 thf(fact_6886_fact__binomial,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) ) )
% 5.46/5.76 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_binomial
% 5.46/5.76 thf(fact_6887_fact__binomial,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 5.46/5.76 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_binomial
% 5.46/5.76 thf(fact_6888_fact__binomial,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) )
% 5.46/5.76 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_binomial
% 5.46/5.76 thf(fact_6889_arccos,axiom,
% 5.46/5.76 ! [Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y3 )
% 5.46/5.76 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y3 ) )
% 5.46/5.76 & ( ord_less_eq_real @ ( arccos @ Y3 ) @ pi )
% 5.46/5.76 & ( ( cos_real @ ( arccos @ Y3 ) )
% 5.46/5.76 = Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos
% 5.46/5.76 thf(fact_6890_arccos__minus__abs,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.76 => ( ( arccos @ ( uminus_uminus_real @ X4 ) )
% 5.46/5.76 = ( minus_minus_real @ pi @ ( arccos @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_minus_abs
% 5.46/5.76 thf(fact_6891_div__noneq__sgn__abs,axiom,
% 5.46/5.76 ! [L2: int,K: int] :
% 5.46/5.76 ( ( L2 != zero_zero_int )
% 5.46/5.76 => ( ( ( sgn_sgn_int @ K )
% 5.46/5.76 != ( sgn_sgn_int @ L2 ) )
% 5.46/5.76 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.76 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) )
% 5.46/5.76 @ ( zero_n2684676970156552555ol_int
% 5.46/5.76 @ ~ ( dvd_dvd_int @ L2 @ K ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % div_noneq_sgn_abs
% 5.46/5.76 thf(fact_6892_arccos__le__pi2,axiom,
% 5.46/5.76 ! [Y3: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.76 => ( ( ord_less_eq_real @ Y3 @ one_one_real )
% 5.46/5.76 => ( ord_less_eq_real @ ( arccos @ Y3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arccos_le_pi2
% 5.46/5.76 thf(fact_6893_divide__int__unfold,axiom,
% 5.46/5.76 ! [L2: int,K: int,N: nat,M: nat] :
% 5.46/5.76 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.46/5.76 = zero_zero_int )
% 5.46/5.76 | ( ( sgn_sgn_int @ K )
% 5.46/5.76 = zero_zero_int )
% 5.46/5.76 | ( N = zero_zero_nat ) )
% 5.46/5.76 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.76 = zero_zero_int ) )
% 5.46/5.76 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.46/5.76 = zero_zero_int )
% 5.46/5.76 | ( ( sgn_sgn_int @ K )
% 5.46/5.76 = zero_zero_int )
% 5.46/5.76 | ( N = zero_zero_nat ) )
% 5.46/5.76 => ( ( ( ( sgn_sgn_int @ K )
% 5.46/5.76 = ( sgn_sgn_int @ L2 ) )
% 5.46/5.76 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.76 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.46/5.76 & ( ( ( sgn_sgn_int @ K )
% 5.46/5.76 != ( sgn_sgn_int @ L2 ) )
% 5.46/5.76 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.46/5.76 = ( uminus_uminus_int
% 5.46/5.76 @ ( semiri1314217659103216013at_int
% 5.46/5.76 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.46/5.76 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.76 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_int_unfold
% 5.46/5.76 thf(fact_6894_sin__coeff__def,axiom,
% 5.46/5.76 ( sin_coeff
% 5.46/5.76 = ( ^ [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 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sin_coeff_def
% 5.46/5.76 thf(fact_6895_binomial__code,axiom,
% 5.46/5.76 ( binomial
% 5.46/5.76 = ( ^ [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 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % binomial_code
% 5.46/5.76 thf(fact_6896_cos__coeff__def,axiom,
% 5.46/5.76 ( cos_coeff
% 5.46/5.76 = ( ^ [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 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % cos_coeff_def
% 5.46/5.76 thf(fact_6897_exp__two__pi__i,axiom,
% 5.46/5.76 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.46/5.76 = one_one_complex ) ).
% 5.46/5.76
% 5.46/5.76 % exp_two_pi_i
% 5.46/5.76 thf(fact_6898_exp__two__pi__i_H,axiom,
% 5.46/5.76 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.46/5.76 = one_one_complex ) ).
% 5.46/5.76
% 5.46/5.76 % exp_two_pi_i'
% 5.46/5.76 thf(fact_6899_zero__le__sgn__iff,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X4 ) )
% 5.46/5.76 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.76
% 5.46/5.76 % zero_le_sgn_iff
% 5.46/5.76 thf(fact_6900_sgn__le__0__iff,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X4 ) @ zero_zero_real )
% 5.46/5.76 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_le_0_iff
% 5.46/5.76 thf(fact_6901_norm__ii,axiom,
% 5.46/5.76 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.46/5.76 = one_one_real ) ).
% 5.46/5.76
% 5.46/5.76 % norm_ii
% 5.46/5.76 thf(fact_6902_cos__coeff__0,axiom,
% 5.46/5.76 ( ( cos_coeff @ zero_zero_nat )
% 5.46/5.76 = one_one_real ) ).
% 5.46/5.76
% 5.46/5.76 % cos_coeff_0
% 5.46/5.76 thf(fact_6903_divide__i,axiom,
% 5.46/5.76 ! [X4: complex] :
% 5.46/5.76 ( ( divide1717551699836669952omplex @ X4 @ imaginary_unit )
% 5.46/5.76 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X4 ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_i
% 5.46/5.76 thf(fact_6904_complex__i__mult__minus,axiom,
% 5.46/5.76 ! [X4: complex] :
% 5.46/5.76 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X4 ) )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ X4 ) ) ).
% 5.46/5.76
% 5.46/5.76 % complex_i_mult_minus
% 5.46/5.76 thf(fact_6905_i__squared,axiom,
% 5.46/5.76 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % i_squared
% 5.46/5.76 thf(fact_6906_divide__numeral__i,axiom,
% 5.46/5.76 ! [Z: complex,N: num] :
% 5.46/5.76 ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 5.46/5.76 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_numeral_i
% 5.46/5.76 thf(fact_6907_power2__i,axiom,
% 5.46/5.76 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % power2_i
% 5.46/5.76 thf(fact_6908_i__even__power,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.76 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % i_even_power
% 5.46/5.76 thf(fact_6909_exp__pi__i_H,axiom,
% 5.46/5.76 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % exp_pi_i'
% 5.46/5.76 thf(fact_6910_exp__pi__i,axiom,
% 5.46/5.76 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % exp_pi_i
% 5.46/5.76 thf(fact_6911_real__sgn__eq,axiom,
% 5.46/5.76 ( sgn_sgn_real
% 5.46/5.76 = ( ^ [X: real] : ( divide_divide_real @ X @ ( abs_abs_real @ X ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % real_sgn_eq
% 5.46/5.76 thf(fact_6912_sgn__eq,axiom,
% 5.46/5.76 ( sgn_sgn_complex
% 5.46/5.76 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ Z5 @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ Z5 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_eq
% 5.46/5.76 thf(fact_6913_sin__coeff__Suc,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( sin_coeff @ ( suc @ N ) )
% 5.46/5.76 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sin_coeff_Suc
% 5.46/5.76 thf(fact_6914_i__times__eq__iff,axiom,
% 5.46/5.76 ! [W: complex,Z: complex] :
% 5.46/5.76 ( ( ( times_times_complex @ imaginary_unit @ W )
% 5.46/5.76 = Z )
% 5.46/5.76 = ( W
% 5.46/5.76 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % i_times_eq_iff
% 5.46/5.76 thf(fact_6915_cos__coeff__Suc,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( cos_coeff @ ( suc @ N ) )
% 5.46/5.76 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % cos_coeff_Suc
% 5.46/5.76 thf(fact_6916_imaginary__unit_Ocode,axiom,
% 5.46/5.76 ( imaginary_unit
% 5.46/5.76 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % imaginary_unit.code
% 5.46/5.76 thf(fact_6917_Complex__eq__i,axiom,
% 5.46/5.76 ! [X4: real,Y3: real] :
% 5.46/5.76 ( ( ( complex2 @ X4 @ Y3 )
% 5.46/5.76 = imaginary_unit )
% 5.46/5.76 = ( ( X4 = zero_zero_real )
% 5.46/5.76 & ( Y3 = one_one_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Complex_eq_i
% 5.46/5.76 thf(fact_6918_i__mult__Complex,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B2 ) )
% 5.46/5.76 = ( complex2 @ ( uminus_uminus_real @ B2 ) @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % i_mult_Complex
% 5.46/5.76 thf(fact_6919_Complex__mult__i,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( times_times_complex @ ( complex2 @ A @ B2 ) @ imaginary_unit )
% 5.46/5.76 = ( complex2 @ ( uminus_uminus_real @ B2 ) @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % Complex_mult_i
% 5.46/5.76 thf(fact_6920_sgn__real__def,axiom,
% 5.46/5.76 ( sgn_sgn_real
% 5.46/5.76 = ( ^ [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 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_real_def
% 5.46/5.76 thf(fact_6921_sgn__power__injE,axiom,
% 5.46/5.76 ! [A: real,N: nat,X4: real,B2: real] :
% 5.46/5.76 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.46/5.76 = X4 )
% 5.46/5.76 => ( ( X4
% 5.46/5.76 = ( times_times_real @ ( sgn_sgn_real @ B2 ) @ ( power_power_real @ ( abs_abs_real @ B2 ) @ N ) ) )
% 5.46/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.76 => ( A = B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_power_injE
% 5.46/5.76 thf(fact_6922_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.46/5.76 ( set_fo2584398358068434914at_nat
% 5.46/5.76 = ( ^ [F2: nat > nat > nat,A4: nat,B3: nat,Acc: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A4 ) @ Acc @ ( set_fo2584398358068434914at_nat @ F2 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B3 @ ( F2 @ A4 @ Acc ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fold_atLeastAtMost_nat.simps
% 5.46/5.76 thf(fact_6923_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.46/5.76 ! [X4: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y3: nat] :
% 5.46/5.76 ( ( ( set_fo2584398358068434914at_nat @ X4 @ Xa @ Xb @ Xc )
% 5.46/5.76 = Y3 )
% 5.46/5.76 => ( ( ( ord_less_nat @ Xb @ Xa )
% 5.46/5.76 => ( Y3 = Xc ) )
% 5.46/5.76 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 5.46/5.76 => ( Y3
% 5.46/5.76 = ( set_fo2584398358068434914at_nat @ X4 @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X4 @ Xa @ Xc ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fold_atLeastAtMost_nat.elims
% 5.46/5.76 thf(fact_6924_complex__of__real__i,axiom,
% 5.46/5.76 ! [R2: real] :
% 5.46/5.76 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 5.46/5.76 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % complex_of_real_i
% 5.46/5.76 thf(fact_6925_i__complex__of__real,axiom,
% 5.46/5.76 ! [R2: real] :
% 5.46/5.76 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.46/5.76 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % i_complex_of_real
% 5.46/5.76 thf(fact_6926_Complex__eq,axiom,
% 5.46/5.76 ( complex2
% 5.46/5.76 = ( ^ [A4: real,B3: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A4 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Complex_eq
% 5.46/5.76 thf(fact_6927_complex__split__polar,axiom,
% 5.46/5.76 ! [Z: complex] :
% 5.46/5.76 ? [R3: real,A5: real] :
% 5.46/5.76 ( Z
% 5.46/5.76 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A5 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A5 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % complex_split_polar
% 5.46/5.76 thf(fact_6928_cmod__unit__one,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.46/5.76 = one_one_real ) ).
% 5.46/5.76
% 5.46/5.76 % cmod_unit_one
% 5.46/5.76 thf(fact_6929_cmod__complex__polar,axiom,
% 5.46/5.76 ! [R2: real,A: real] :
% 5.46/5.76 ( ( 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 ) ) ) ) ) )
% 5.46/5.76 = ( abs_abs_real @ R2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % cmod_complex_polar
% 5.46/5.76 thf(fact_6930_arctan__inverse,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( X4 != zero_zero_real )
% 5.46/5.76 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X4 ) )
% 5.46/5.76 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X4 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % arctan_inverse
% 5.46/5.76 thf(fact_6931_fact__code,axiom,
% 5.46/5.76 ( semiri5044797733671781792omplex
% 5.46/5.76 = ( ^ [N2: nat] : ( semiri8010041392384452111omplex @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_code
% 5.46/5.76 thf(fact_6932_fact__code,axiom,
% 5.46/5.76 ( semiri773545260158071498ct_rat
% 5.46/5.76 = ( ^ [N2: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_code
% 5.46/5.76 thf(fact_6933_fact__code,axiom,
% 5.46/5.76 ( semiri1406184849735516958ct_int
% 5.46/5.76 = ( ^ [N2: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_code
% 5.46/5.76 thf(fact_6934_fact__code,axiom,
% 5.46/5.76 ( semiri1408675320244567234ct_nat
% 5.46/5.76 = ( ^ [N2: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_code
% 5.46/5.76 thf(fact_6935_fact__code,axiom,
% 5.46/5.76 ( semiri2265585572941072030t_real
% 5.46/5.76 = ( ^ [N2: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % fact_code
% 5.46/5.76 thf(fact_6936_Arg__minus__ii,axiom,
% 5.46/5.76 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.46/5.76 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Arg_minus_ii
% 5.46/5.76 thf(fact_6937_csqrt__ii,axiom,
% 5.46/5.76 ( ( csqrt @ imaginary_unit )
% 5.46/5.76 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % csqrt_ii
% 5.46/5.76 thf(fact_6938_Arg__ii,axiom,
% 5.46/5.76 ( ( arg @ imaginary_unit )
% 5.46/5.76 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Arg_ii
% 5.46/5.76 thf(fact_6939_cis__minus__pi__half,axiom,
% 5.46/5.76 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.46/5.76
% 5.46/5.76 % cis_minus_pi_half
% 5.46/5.76 thf(fact_6940_modulo__int__def,axiom,
% 5.46/5.76 ( modulo_modulo_int
% 5.46/5.76 = ( ^ [K3: int,L: int] :
% 5.46/5.76 ( if_int @ ( L = zero_zero_int ) @ K3
% 5.46/5.76 @ ( if_int
% 5.46/5.76 @ ( ( sgn_sgn_int @ K3 )
% 5.46/5.76 = ( sgn_sgn_int @ L ) )
% 5.46/5.76 @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 5.46/5.76 @ ( times_times_int @ ( sgn_sgn_int @ L )
% 5.46/5.76 @ ( minus_minus_int
% 5.46/5.76 @ ( times_times_int @ ( abs_abs_int @ L )
% 5.46/5.76 @ ( zero_n2684676970156552555ol_int
% 5.46/5.76 @ ~ ( dvd_dvd_int @ L @ K3 ) ) )
% 5.46/5.76 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % modulo_int_def
% 5.46/5.76 thf(fact_6941_nat__numeral,axiom,
% 5.46/5.76 ! [K: num] :
% 5.46/5.76 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.46/5.76 = ( numeral_numeral_nat @ K ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_numeral
% 5.46/5.76 thf(fact_6942_norm__cis,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.46/5.76 = one_one_real ) ).
% 5.46/5.76
% 5.46/5.76 % norm_cis
% 5.46/5.76 thf(fact_6943_nat__1,axiom,
% 5.46/5.76 ( ( nat2 @ one_one_int )
% 5.46/5.76 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_1
% 5.46/5.76 thf(fact_6944_zless__nat__conj,axiom,
% 5.46/5.76 ! [W: int,Z: int] :
% 5.46/5.76 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.46/5.76 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.76 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % zless_nat_conj
% 5.46/5.76 thf(fact_6945_of__nat__nat__take__bit__eq,axiom,
% 5.46/5.76 ! [N: nat,K: int] :
% 5.46/5.76 ( ( semiri8010041392384452111omplex @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.46/5.76 = ( ring_17405671764205052669omplex @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_nat_nat_take_bit_eq
% 5.46/5.76 thf(fact_6946_of__nat__nat__take__bit__eq,axiom,
% 5.46/5.76 ! [N: nat,K: int] :
% 5.46/5.76 ( ( semiri5074537144036343181t_real @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.46/5.76 = ( ring_1_of_int_real @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_nat_nat_take_bit_eq
% 5.46/5.76 thf(fact_6947_of__nat__nat__take__bit__eq,axiom,
% 5.46/5.76 ! [N: nat,K: int] :
% 5.46/5.76 ( ( semiri681578069525770553at_rat @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.46/5.76 = ( ring_1_of_int_rat @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_nat_nat_take_bit_eq
% 5.46/5.76 thf(fact_6948_of__nat__nat__take__bit__eq,axiom,
% 5.46/5.76 ! [N: nat,K: int] :
% 5.46/5.76 ( ( semiri1314217659103216013at_int @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.46/5.76 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_nat_nat_take_bit_eq
% 5.46/5.76 thf(fact_6949_zero__less__nat__eq,axiom,
% 5.46/5.76 ! [Z: int] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.46/5.76 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.46/5.76
% 5.46/5.76 % zero_less_nat_eq
% 5.46/5.76 thf(fact_6950_diff__nat__numeral,axiom,
% 5.46/5.76 ! [V: num,V2: num] :
% 5.46/5.76 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V2 ) )
% 5.46/5.76 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % diff_nat_numeral
% 5.46/5.76 thf(fact_6951_numeral__power__eq__nat__cancel__iff,axiom,
% 5.46/5.76 ! [X4: num,N: nat,Y3: int] :
% 5.46/5.76 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N )
% 5.46/5.76 = ( nat2 @ Y3 ) )
% 5.46/5.76 = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N )
% 5.46/5.76 = Y3 ) ) ).
% 5.46/5.76
% 5.46/5.76 % numeral_power_eq_nat_cancel_iff
% 5.46/5.76 thf(fact_6952_nat__eq__numeral__power__cancel__iff,axiom,
% 5.46/5.76 ! [Y3: int,X4: num,N: nat] :
% 5.46/5.76 ( ( ( nat2 @ Y3 )
% 5.46/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) )
% 5.46/5.76 = ( Y3
% 5.46/5.76 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_eq_numeral_power_cancel_iff
% 5.46/5.76 thf(fact_6953_power2__csqrt,axiom,
% 5.46/5.76 ! [Z: complex] :
% 5.46/5.76 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.76 = Z ) ).
% 5.46/5.76
% 5.46/5.76 % power2_csqrt
% 5.46/5.76 thf(fact_6954_nat__ceiling__le__eq,axiom,
% 5.46/5.76 ! [X4: real,A: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X4 ) ) @ A )
% 5.46/5.76 = ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_ceiling_le_eq
% 5.46/5.76 thf(fact_6955_one__less__nat__eq,axiom,
% 5.46/5.76 ! [Z: int] :
% 5.46/5.76 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.46/5.76 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.46/5.76
% 5.46/5.76 % one_less_nat_eq
% 5.46/5.76 thf(fact_6956_nat__numeral__diff__1,axiom,
% 5.46/5.76 ! [V: num] :
% 5.46/5.76 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.46/5.76 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_numeral_diff_1
% 5.46/5.76 thf(fact_6957_numeral__power__less__nat__cancel__iff,axiom,
% 5.46/5.76 ! [X4: num,N: nat,A: int] :
% 5.46/5.76 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) @ ( nat2 @ A ) )
% 5.46/5.76 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % numeral_power_less_nat_cancel_iff
% 5.46/5.76 thf(fact_6958_nat__less__numeral__power__cancel__iff,axiom,
% 5.46/5.76 ! [A: int,X4: num,N: nat] :
% 5.46/5.76 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) )
% 5.46/5.76 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_less_numeral_power_cancel_iff
% 5.46/5.76 thf(fact_6959_numeral__power__le__nat__cancel__iff,axiom,
% 5.46/5.76 ! [X4: num,N: nat,A: int] :
% 5.46/5.76 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) @ ( nat2 @ A ) )
% 5.46/5.76 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % numeral_power_le_nat_cancel_iff
% 5.46/5.76 thf(fact_6960_nat__le__numeral__power__cancel__iff,axiom,
% 5.46/5.76 ! [A: int,X4: num,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N ) )
% 5.46/5.76 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_le_numeral_power_cancel_iff
% 5.46/5.76 thf(fact_6961_cis__pi__half,axiom,
% 5.46/5.76 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.76 = imaginary_unit ) ).
% 5.46/5.76
% 5.46/5.76 % cis_pi_half
% 5.46/5.76 thf(fact_6962_cis__2pi,axiom,
% 5.46/5.76 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.46/5.76 = one_one_complex ) ).
% 5.46/5.76
% 5.46/5.76 % cis_2pi
% 5.46/5.76 thf(fact_6963_cis__divide,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B2 ) )
% 5.46/5.76 = ( cis @ ( minus_minus_real @ A @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % cis_divide
% 5.46/5.76 thf(fact_6964_nat__zero__as__int,axiom,
% 5.46/5.76 ( zero_zero_nat
% 5.46/5.76 = ( nat2 @ zero_zero_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_zero_as_int
% 5.46/5.76 thf(fact_6965_nat__numeral__as__int,axiom,
% 5.46/5.76 ( numeral_numeral_nat
% 5.46/5.76 = ( ^ [I2: num] : ( nat2 @ ( numeral_numeral_int @ I2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_numeral_as_int
% 5.46/5.76 thf(fact_6966_nat__mono,axiom,
% 5.46/5.76 ! [X4: int,Y3: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.76 => ( ord_less_eq_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_mono
% 5.46/5.76 thf(fact_6967_nat__one__as__int,axiom,
% 5.46/5.76 ( one_one_nat
% 5.46/5.76 = ( nat2 @ one_one_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_one_as_int
% 5.46/5.76 thf(fact_6968_unset__bit__nat__def,axiom,
% 5.46/5.76 ( bit_se4205575877204974255it_nat
% 5.46/5.76 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % unset_bit_nat_def
% 5.46/5.76 thf(fact_6969_DeMoivre,axiom,
% 5.46/5.76 ! [A: real,N: nat] :
% 5.46/5.76 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.46/5.76 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % DeMoivre
% 5.46/5.76 thf(fact_6970_nat__mask__eq,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.76 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_mask_eq
% 5.46/5.76 thf(fact_6971_Arg__correct,axiom,
% 5.46/5.76 ! [Z: complex] :
% 5.46/5.76 ( ( Z != zero_zero_complex )
% 5.46/5.76 => ( ( ( sgn_sgn_complex @ Z )
% 5.46/5.76 = ( cis @ ( arg @ Z ) ) )
% 5.46/5.76 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.46/5.76 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Arg_correct
% 5.46/5.76 thf(fact_6972_cis__Arg__unique,axiom,
% 5.46/5.76 ! [Z: complex,X4: real] :
% 5.46/5.76 ( ( ( sgn_sgn_complex @ Z )
% 5.46/5.76 = ( cis @ X4 ) )
% 5.46/5.76 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 5.46/5.76 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.46/5.76 => ( ( arg @ Z )
% 5.46/5.76 = X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % cis_Arg_unique
% 5.46/5.76 thf(fact_6973_cis__mult,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B2 ) )
% 5.46/5.76 = ( cis @ ( plus_plus_real @ A @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % cis_mult
% 5.46/5.76 thf(fact_6974_nat__mono__iff,axiom,
% 5.46/5.76 ! [Z: int,W: int] :
% 5.46/5.76 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.46/5.76 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.46/5.76 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_mono_iff
% 5.46/5.76 thf(fact_6975_of__nat__ceiling,axiom,
% 5.46/5.76 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_nat_ceiling
% 5.46/5.76 thf(fact_6976_of__nat__ceiling,axiom,
% 5.46/5.76 ! [R2: rat] : ( ord_less_eq_rat @ R2 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_nat_ceiling
% 5.46/5.76 thf(fact_6977_zless__nat__eq__int__zless,axiom,
% 5.46/5.76 ! [M: nat,Z: int] :
% 5.46/5.76 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.46/5.76 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.46/5.76
% 5.46/5.76 % zless_nat_eq_int_zless
% 5.46/5.76 thf(fact_6978_nat__le__iff,axiom,
% 5.46/5.76 ! [X4: int,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ ( nat2 @ X4 ) @ N )
% 5.46/5.76 = ( ord_less_eq_int @ X4 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_le_iff
% 5.46/5.76 thf(fact_6979_nat__int__add,axiom,
% 5.46/5.76 ! [A: nat,B2: nat] :
% 5.46/5.76 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) )
% 5.46/5.76 = ( plus_plus_nat @ A @ B2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_int_add
% 5.46/5.76 thf(fact_6980_int__minus,axiom,
% 5.46/5.76 ! [N: nat,M: nat] :
% 5.46/5.76 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.76 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % int_minus
% 5.46/5.76 thf(fact_6981_nat__abs__mult__distrib,axiom,
% 5.46/5.76 ! [W: int,Z: int] :
% 5.46/5.76 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.46/5.76 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_abs_mult_distrib
% 5.46/5.76 thf(fact_6982_and__nat__def,axiom,
% 5.46/5.76 ( bit_se727722235901077358nd_nat
% 5.46/5.76 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % and_nat_def
% 5.46/5.76 thf(fact_6983_real__nat__ceiling__ge,axiom,
% 5.46/5.76 ! [X4: real] : ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % real_nat_ceiling_ge
% 5.46/5.76 thf(fact_6984_of__nat__floor,axiom,
% 5.46/5.76 ! [R2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.46/5.76 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R2 ) ) ) @ R2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_nat_floor
% 5.46/5.76 thf(fact_6985_of__nat__floor,axiom,
% 5.46/5.76 ! [R2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.46/5.76 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R2 ) ) ) @ R2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_nat_floor
% 5.46/5.76 thf(fact_6986_nat__less__eq__zless,axiom,
% 5.46/5.76 ! [W: int,Z: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.46/5.76 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.46/5.76 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_less_eq_zless
% 5.46/5.76 thf(fact_6987_nat__le__eq__zle,axiom,
% 5.46/5.76 ! [W: int,Z: int] :
% 5.46/5.76 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.46/5.76 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.46/5.76 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.46/5.76 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_le_eq_zle
% 5.46/5.76 thf(fact_6988_split__nat,axiom,
% 5.46/5.76 ! [P: nat > $o,I: int] :
% 5.46/5.76 ( ( P @ ( nat2 @ I ) )
% 5.46/5.76 = ( ! [N2: nat] :
% 5.46/5.76 ( ( I
% 5.46/5.76 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.46/5.76 => ( P @ N2 ) )
% 5.46/5.76 & ( ( ord_less_int @ I @ zero_zero_int )
% 5.46/5.76 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % split_nat
% 5.46/5.76 thf(fact_6989_le__mult__nat__floor,axiom,
% 5.46/5.76 ! [A: real,B2: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B2 ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_mult_nat_floor
% 5.46/5.76 thf(fact_6990_le__mult__nat__floor,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim3151403230148437115or_rat @ A ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ B2 ) ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_mult_nat_floor
% 5.46/5.76 thf(fact_6991_le__nat__iff,axiom,
% 5.46/5.76 ! [K: int,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.76 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.46/5.76 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_nat_iff
% 5.46/5.76 thf(fact_6992_nat__add__distrib,axiom,
% 5.46/5.76 ! [Z: int,Z6: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.46/5.76 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 5.46/5.76 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_add_distrib
% 5.46/5.76 thf(fact_6993_nat__mult__distrib,axiom,
% 5.46/5.76 ! [Z: int,Z6: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.76 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.46/5.76 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_mult_distrib
% 5.46/5.76 thf(fact_6994_Suc__as__int,axiom,
% 5.46/5.76 ( suc
% 5.46/5.76 = ( ^ [A4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ one_one_int ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Suc_as_int
% 5.46/5.76 thf(fact_6995_nat__diff__distrib,axiom,
% 5.46/5.76 ! [Z6: int,Z: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.46/5.76 => ( ( ord_less_eq_int @ Z6 @ Z )
% 5.46/5.76 => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 5.46/5.76 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_diff_distrib
% 5.46/5.76 thf(fact_6996_nat__diff__distrib_H,axiom,
% 5.46/5.76 ! [X4: int,Y3: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.76 => ( ( nat2 @ ( minus_minus_int @ X4 @ Y3 ) )
% 5.46/5.76 = ( minus_minus_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_diff_distrib'
% 5.46/5.76 thf(fact_6997_nat__abs__triangle__ineq,axiom,
% 5.46/5.76 ! [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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_abs_triangle_ineq
% 5.46/5.76 thf(fact_6998_nat__div__distrib,axiom,
% 5.46/5.76 ! [X4: int,Y3: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.76 => ( ( nat2 @ ( divide_divide_int @ X4 @ Y3 ) )
% 5.46/5.76 = ( divide_divide_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_div_distrib
% 5.46/5.76 thf(fact_6999_nat__div__distrib_H,axiom,
% 5.46/5.76 ! [Y3: int,X4: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.76 => ( ( nat2 @ ( divide_divide_int @ X4 @ Y3 ) )
% 5.46/5.76 = ( divide_divide_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_div_distrib'
% 5.46/5.76 thf(fact_7000_nat__power__eq,axiom,
% 5.46/5.76 ! [Z: int,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.76 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.46/5.76 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_power_eq
% 5.46/5.76 thf(fact_7001_nat__floor__neg,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.76 => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.76 = zero_zero_nat ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_floor_neg
% 5.46/5.76 thf(fact_7002_nat__mod__distrib,axiom,
% 5.46/5.76 ! [X4: int,Y3: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.76 => ( ( nat2 @ ( modulo_modulo_int @ X4 @ Y3 ) )
% 5.46/5.76 = ( modulo_modulo_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_mod_distrib
% 5.46/5.76 thf(fact_7003_div__abs__eq__div__nat,axiom,
% 5.46/5.76 ! [K: int,L2: int] :
% 5.46/5.76 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.46/5.76 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % div_abs_eq_div_nat
% 5.46/5.76 thf(fact_7004_floor__eq3,axiom,
% 5.46/5.76 ! [N: nat,X4: real] :
% 5.46/5.76 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X4 )
% 5.46/5.76 => ( ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.46/5.76 => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.76 = N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % floor_eq3
% 5.46/5.76 thf(fact_7005_le__nat__floor,axiom,
% 5.46/5.76 ! [X4: nat,A: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ A )
% 5.46/5.76 => ( ord_less_eq_nat @ X4 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_nat_floor
% 5.46/5.76 thf(fact_7006_mod__abs__eq__div__nat,axiom,
% 5.46/5.76 ! [K: int,L2: int] :
% 5.46/5.76 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.46/5.76 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mod_abs_eq_div_nat
% 5.46/5.76 thf(fact_7007_nat__take__bit__eq,axiom,
% 5.46/5.76 ! [K: int,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.76 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.46/5.76 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_take_bit_eq
% 5.46/5.76 thf(fact_7008_take__bit__nat__eq,axiom,
% 5.46/5.76 ! [K: int,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.76 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.46/5.76 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % take_bit_nat_eq
% 5.46/5.76 thf(fact_7009_bit__nat__iff,axiom,
% 5.46/5.76 ! [K: int,N: nat] :
% 5.46/5.76 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.46/5.76 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.76 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % bit_nat_iff
% 5.46/5.76 thf(fact_7010_nat__2,axiom,
% 5.46/5.76 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.76 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_2
% 5.46/5.76 thf(fact_7011_Suc__nat__eq__nat__zadd1,axiom,
% 5.46/5.76 ! [Z: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.46/5.76 => ( ( suc @ ( nat2 @ Z ) )
% 5.46/5.76 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Suc_nat_eq_nat_zadd1
% 5.46/5.76 thf(fact_7012_nat__less__iff,axiom,
% 5.46/5.76 ! [W: int,M: nat] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.46/5.76 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.46/5.76 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_less_iff
% 5.46/5.76 thf(fact_7013_nat__mult__distrib__neg,axiom,
% 5.46/5.76 ! [Z: int,Z6: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.46/5.76 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.46/5.76 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_mult_distrib_neg
% 5.46/5.76 thf(fact_7014_nat__abs__int__diff,axiom,
% 5.46/5.76 ! [A: nat,B2: nat] :
% 5.46/5.76 ( ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.76 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) )
% 5.46/5.76 = ( minus_minus_nat @ B2 @ A ) ) )
% 5.46/5.76 & ( ~ ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.76 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) )
% 5.46/5.76 = ( minus_minus_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nat_abs_int_diff
% 5.46/5.76 thf(fact_7015_floor__eq4,axiom,
% 5.46/5.76 ! [N: nat,X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X4 )
% 5.46/5.76 => ( ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.46/5.76 => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 5.46/5.76 = N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % floor_eq4
% 5.46/5.76 thf(fact_7016_cis__conv__exp,axiom,
% 5.46/5.76 ( cis
% 5.46/5.76 = ( ^ [B3: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % cis_conv_exp
% 5.46/5.76 thf(fact_7017_of__int__of__nat,axiom,
% 5.46/5.76 ( ring_18347121197199848620nteger
% 5.46/5.76 = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_int_of_nat
% 5.46/5.76 thf(fact_7018_of__int__of__nat,axiom,
% 5.46/5.76 ( ring_17405671764205052669omplex
% 5.46/5.76 = ( ^ [K3: int] : ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri8010041392384452111omplex @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_int_of_nat
% 5.46/5.76 thf(fact_7019_of__int__of__nat,axiom,
% 5.46/5.76 ( ring_1_of_int_real
% 5.46/5.76 = ( ^ [K3: int] : ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri5074537144036343181t_real @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_int_of_nat
% 5.46/5.76 thf(fact_7020_of__int__of__nat,axiom,
% 5.46/5.76 ( ring_1_of_int_rat
% 5.46/5.76 = ( ^ [K3: int] : ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_int_of_nat
% 5.46/5.76 thf(fact_7021_of__int__of__nat,axiom,
% 5.46/5.76 ( ring_1_of_int_int
% 5.46/5.76 = ( ^ [K3: int] : ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_int_of_nat
% 5.46/5.76 thf(fact_7022_of__real__sqrt,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X4 ) )
% 5.46/5.76 = ( csqrt @ ( real_V4546457046886955230omplex @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_real_sqrt
% 5.46/5.76 thf(fact_7023_Arg__bounded,axiom,
% 5.46/5.76 ! [Z: complex] :
% 5.46/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.46/5.76 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.46/5.76
% 5.46/5.76 % Arg_bounded
% 5.46/5.76 thf(fact_7024_even__nat__iff,axiom,
% 5.46/5.76 ! [K: int] :
% 5.46/5.76 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.76 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.46/5.76 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % even_nat_iff
% 5.46/5.76 thf(fact_7025_powr__int,axiom,
% 5.46/5.76 ! [X4: real,I: int] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.46/5.76 => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ I ) )
% 5.46/5.76 = ( power_power_real @ X4 @ ( nat2 @ I ) ) ) )
% 5.46/5.76 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.46/5.76 => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ I ) )
% 5.46/5.76 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X4 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % powr_int
% 5.46/5.76 thf(fact_7026_divide__int__def,axiom,
% 5.46/5.76 ( divide_divide_int
% 5.46/5.76 = ( ^ [K3: int,L: int] :
% 5.46/5.76 ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 5.46/5.76 @ ( if_int
% 5.46/5.76 @ ( ( sgn_sgn_int @ K3 )
% 5.46/5.76 = ( sgn_sgn_int @ L ) )
% 5.46/5.76 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 5.46/5.76 @ ( uminus_uminus_int
% 5.46/5.76 @ ( semiri1314217659103216013at_int
% 5.46/5.76 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 5.46/5.76 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.76 @ ~ ( dvd_dvd_int @ L @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_int_def
% 5.46/5.76 thf(fact_7027_cis__multiple__2pi,axiom,
% 5.46/5.76 ! [N: real] :
% 5.46/5.76 ( ( member_real @ N @ ring_1_Ints_real )
% 5.46/5.76 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.46/5.76 = one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % cis_multiple_2pi
% 5.46/5.76 thf(fact_7028_powr__real__of__int,axiom,
% 5.46/5.76 ! [X4: real,N: int] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.46/5.76 => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ N ) )
% 5.46/5.76 = ( power_power_real @ X4 @ ( nat2 @ N ) ) ) )
% 5.46/5.76 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.46/5.76 => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ N ) )
% 5.46/5.76 = ( inverse_inverse_real @ ( power_power_real @ X4 @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % powr_real_of_int
% 5.46/5.76 thf(fact_7029_Suc__0__xor__eq,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.76 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.76 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.76 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Suc_0_xor_eq
% 5.46/5.76 thf(fact_7030_xor__Suc__0__eq,axiom,
% 5.46/5.76 ! [N: nat] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.76 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.76 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.76 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_Suc_0_eq
% 5.46/5.76 thf(fact_7031_gbinomial__absorption_H,axiom,
% 5.46/5.76 ! [K: nat,A: complex] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.76 => ( ( gbinomial_complex @ A @ K )
% 5.46/5.76 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_absorption'
% 5.46/5.76 thf(fact_7032_gbinomial__absorption_H,axiom,
% 5.46/5.76 ! [K: nat,A: real] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.76 => ( ( gbinomial_real @ A @ K )
% 5.46/5.76 = ( 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 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_absorption'
% 5.46/5.76 thf(fact_7033_gbinomial__absorption_H,axiom,
% 5.46/5.76 ! [K: nat,A: rat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.76 => ( ( gbinomial_rat @ A @ K )
% 5.46/5.76 = ( 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 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_absorption'
% 5.46/5.76 thf(fact_7034_inverse__inverse__eq,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_inverse_eq
% 5.46/5.76 thf(fact_7035_inverse__inverse__eq,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_inverse_eq
% 5.46/5.76 thf(fact_7036_inverse__inverse__eq,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_inverse_eq
% 5.46/5.76 thf(fact_7037_inverse__eq__iff__eq,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ( inverse_inverse_real @ A )
% 5.46/5.76 = ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( A = B2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_iff_eq
% 5.46/5.76 thf(fact_7038_inverse__eq__iff__eq,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( ( invers8013647133539491842omplex @ A )
% 5.46/5.76 = ( invers8013647133539491842omplex @ B2 ) )
% 5.46/5.76 = ( A = B2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_iff_eq
% 5.46/5.76 thf(fact_7039_inverse__eq__iff__eq,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ( inverse_inverse_rat @ A )
% 5.46/5.76 = ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( A = B2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_iff_eq
% 5.46/5.76 thf(fact_7040_bit_Oxor__left__self,axiom,
% 5.46/5.76 ! [X4: int,Y3: int] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_se6526347334894502574or_int @ X4 @ Y3 ) )
% 5.46/5.76 = Y3 ) ).
% 5.46/5.76
% 5.46/5.76 % bit.xor_left_self
% 5.46/5.76 thf(fact_7041_inverse__nonzero__iff__nonzero,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ( inverse_inverse_real @ A )
% 5.46/5.76 = zero_zero_real )
% 5.46/5.76 = ( A = zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_nonzero_iff_nonzero
% 5.46/5.76 thf(fact_7042_inverse__nonzero__iff__nonzero,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( ( invers8013647133539491842omplex @ A )
% 5.46/5.76 = zero_zero_complex )
% 5.46/5.76 = ( A = zero_zero_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_nonzero_iff_nonzero
% 5.46/5.76 thf(fact_7043_inverse__nonzero__iff__nonzero,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ( inverse_inverse_rat @ A )
% 5.46/5.76 = zero_zero_rat )
% 5.46/5.76 = ( A = zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_nonzero_iff_nonzero
% 5.46/5.76 thf(fact_7044_inverse__zero,axiom,
% 5.46/5.76 ( ( inverse_inverse_real @ zero_zero_real )
% 5.46/5.76 = zero_zero_real ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_zero
% 5.46/5.76 thf(fact_7045_inverse__zero,axiom,
% 5.46/5.76 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.46/5.76 = zero_zero_complex ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_zero
% 5.46/5.76 thf(fact_7046_inverse__zero,axiom,
% 5.46/5.76 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.46/5.76 = zero_zero_rat ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_zero
% 5.46/5.76 thf(fact_7047_inverse__mult__distrib,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( inverse_inverse_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.76 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_mult_distrib
% 5.46/5.76 thf(fact_7048_inverse__mult__distrib,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B2 ) )
% 5.46/5.76 = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_mult_distrib
% 5.46/5.76 thf(fact_7049_inverse__mult__distrib,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.76 = ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_mult_distrib
% 5.46/5.76 thf(fact_7050_inverse__eq__1__iff,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ( inverse_inverse_real @ X4 )
% 5.46/5.76 = one_one_real )
% 5.46/5.76 = ( X4 = one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_1_iff
% 5.46/5.76 thf(fact_7051_inverse__eq__1__iff,axiom,
% 5.46/5.76 ! [X4: complex] :
% 5.46/5.76 ( ( ( invers8013647133539491842omplex @ X4 )
% 5.46/5.76 = one_one_complex )
% 5.46/5.76 = ( X4 = one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_1_iff
% 5.46/5.76 thf(fact_7052_inverse__eq__1__iff,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( ( inverse_inverse_rat @ X4 )
% 5.46/5.76 = one_one_rat )
% 5.46/5.76 = ( X4 = one_one_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_1_iff
% 5.46/5.76 thf(fact_7053_inverse__1,axiom,
% 5.46/5.76 ( ( inverse_inverse_real @ one_one_real )
% 5.46/5.76 = one_one_real ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_1
% 5.46/5.76 thf(fact_7054_inverse__1,axiom,
% 5.46/5.76 ( ( invers8013647133539491842omplex @ one_one_complex )
% 5.46/5.76 = one_one_complex ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_1
% 5.46/5.76 thf(fact_7055_inverse__1,axiom,
% 5.46/5.76 ( ( inverse_inverse_rat @ one_one_rat )
% 5.46/5.76 = one_one_rat ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_1
% 5.46/5.76 thf(fact_7056_inverse__divide,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B2 ) )
% 5.46/5.76 = ( divide_divide_real @ B2 @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_divide
% 5.46/5.76 thf(fact_7057_inverse__divide,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.76 = ( divide1717551699836669952omplex @ B2 @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_divide
% 5.46/5.76 thf(fact_7058_inverse__divide,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( inverse_inverse_rat @ ( divide_divide_rat @ A @ B2 ) )
% 5.46/5.76 = ( divide_divide_rat @ B2 @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_divide
% 5.46/5.76 thf(fact_7059_inverse__minus__eq,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.76 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_minus_eq
% 5.46/5.76 thf(fact_7060_inverse__minus__eq,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_minus_eq
% 5.46/5.76 thf(fact_7061_inverse__minus__eq,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.76 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_minus_eq
% 5.46/5.76 thf(fact_7062_xor_Oright__neutral,axiom,
% 5.46/5.76 ! [A: nat] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ A @ zero_zero_nat )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % xor.right_neutral
% 5.46/5.76 thf(fact_7063_xor_Oright__neutral,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ A @ zero_zero_int )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % xor.right_neutral
% 5.46/5.76 thf(fact_7064_xor_Oleft__neutral,axiom,
% 5.46/5.76 ! [A: nat] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ zero_zero_nat @ A )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % xor.left_neutral
% 5.46/5.76 thf(fact_7065_xor_Oleft__neutral,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ zero_zero_int @ A )
% 5.46/5.76 = A ) ).
% 5.46/5.76
% 5.46/5.76 % xor.left_neutral
% 5.46/5.76 thf(fact_7066_xor__self__eq,axiom,
% 5.46/5.76 ! [A: nat] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ A @ A )
% 5.46/5.76 = zero_zero_nat ) ).
% 5.46/5.76
% 5.46/5.76 % xor_self_eq
% 5.46/5.76 thf(fact_7067_xor__self__eq,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ A @ A )
% 5.46/5.76 = zero_zero_int ) ).
% 5.46/5.76
% 5.46/5.76 % xor_self_eq
% 5.46/5.76 thf(fact_7068_bit_Oxor__self,axiom,
% 5.46/5.76 ! [X4: int] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ X4 @ X4 )
% 5.46/5.76 = zero_zero_int ) ).
% 5.46/5.76
% 5.46/5.76 % bit.xor_self
% 5.46/5.76 thf(fact_7069_abs__inverse,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.46/5.76 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_inverse
% 5.46/5.76 thf(fact_7070_abs__inverse,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( abs_abs_complex @ ( invers8013647133539491842omplex @ A ) )
% 5.46/5.76 = ( invers8013647133539491842omplex @ ( abs_abs_complex @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_inverse
% 5.46/5.76 thf(fact_7071_abs__inverse,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.46/5.76 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % abs_inverse
% 5.46/5.76 thf(fact_7072_inverse__sgn,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( inverse_inverse_real @ ( sgn_sgn_real @ A ) )
% 5.46/5.76 = ( sgn_sgn_real @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_sgn
% 5.46/5.76 thf(fact_7073_inverse__sgn,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) )
% 5.46/5.76 = ( sgn_sgn_rat @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_sgn
% 5.46/5.76 thf(fact_7074_sgn__inverse,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( sgn_sgn_real @ ( inverse_inverse_real @ A ) )
% 5.46/5.76 = ( inverse_inverse_real @ ( sgn_sgn_real @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_inverse
% 5.46/5.76 thf(fact_7075_sgn__inverse,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( sgn_sgn_complex @ ( invers8013647133539491842omplex @ A ) )
% 5.46/5.76 = ( invers8013647133539491842omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_inverse
% 5.46/5.76 thf(fact_7076_sgn__inverse,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( sgn_sgn_rat @ ( inverse_inverse_rat @ A ) )
% 5.46/5.76 = ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sgn_inverse
% 5.46/5.76 thf(fact_7077_take__bit__xor,axiom,
% 5.46/5.76 ! [N: nat,A: int,B2: int] :
% 5.46/5.76 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se6526347334894502574or_int @ A @ B2 ) )
% 5.46/5.76 = ( bit_se6526347334894502574or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % take_bit_xor
% 5.46/5.76 thf(fact_7078_take__bit__xor,axiom,
% 5.46/5.76 ! [N: nat,A: nat,B2: nat] :
% 5.46/5.76 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se6528837805403552850or_nat @ A @ B2 ) )
% 5.46/5.76 = ( bit_se6528837805403552850or_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % take_bit_xor
% 5.46/5.76 thf(fact_7079_inverse__nonpositive__iff__nonpositive,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.46/5.76 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_nonpositive_iff_nonpositive
% 5.46/5.76 thf(fact_7080_inverse__nonpositive__iff__nonpositive,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.46/5.76 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_nonpositive_iff_nonpositive
% 5.46/5.76 thf(fact_7081_inverse__nonnegative__iff__nonnegative,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.46/5.76 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_nonnegative_iff_nonnegative
% 5.46/5.76 thf(fact_7082_inverse__nonnegative__iff__nonnegative,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.46/5.76 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_nonnegative_iff_nonnegative
% 5.46/5.76 thf(fact_7083_inverse__positive__iff__positive,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.46/5.76 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_positive_iff_positive
% 5.46/5.76 thf(fact_7084_inverse__positive__iff__positive,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.46/5.76 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_positive_iff_positive
% 5.46/5.76 thf(fact_7085_inverse__negative__iff__negative,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.46/5.76 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_negative_iff_negative
% 5.46/5.76 thf(fact_7086_inverse__negative__iff__negative,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.46/5.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_negative_iff_negative
% 5.46/5.76 thf(fact_7087_inverse__less__iff__less__neg,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.76 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.76 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( ord_less_real @ B2 @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_iff_less_neg
% 5.46/5.76 thf(fact_7088_inverse__less__iff__less__neg,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.76 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.76 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( ord_less_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_iff_less_neg
% 5.46/5.76 thf(fact_7089_inverse__less__iff__less,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.76 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( ord_less_real @ B2 @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_iff_less
% 5.46/5.76 thf(fact_7090_inverse__less__iff__less,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.46/5.76 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( ord_less_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_iff_less
% 5.46/5.76 thf(fact_7091_gbinomial__0_I2_J,axiom,
% 5.46/5.76 ! [K: nat] :
% 5.46/5.76 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.46/5.76 = zero_zero_real ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_0(2)
% 5.46/5.76 thf(fact_7092_gbinomial__0_I2_J,axiom,
% 5.46/5.76 ! [K: nat] :
% 5.46/5.76 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.46/5.76 = zero_zero_rat ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_0(2)
% 5.46/5.76 thf(fact_7093_gbinomial__0_I2_J,axiom,
% 5.46/5.76 ! [K: nat] :
% 5.46/5.76 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.46/5.76 = zero_zero_nat ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_0(2)
% 5.46/5.76 thf(fact_7094_gbinomial__0_I2_J,axiom,
% 5.46/5.76 ! [K: nat] :
% 5.46/5.76 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.46/5.76 = zero_zero_int ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_0(2)
% 5.46/5.76 thf(fact_7095_gbinomial__0_I1_J,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.46/5.76 = one_one_complex ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_0(1)
% 5.46/5.76 thf(fact_7096_gbinomial__0_I1_J,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.46/5.76 = one_one_real ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_0(1)
% 5.46/5.76 thf(fact_7097_gbinomial__0_I1_J,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.46/5.76 = one_one_rat ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_0(1)
% 5.46/5.76 thf(fact_7098_gbinomial__0_I1_J,axiom,
% 5.46/5.76 ! [A: nat] :
% 5.46/5.76 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.46/5.76 = one_one_nat ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_0(1)
% 5.46/5.76 thf(fact_7099_gbinomial__0_I1_J,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.46/5.76 = one_one_int ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_0(1)
% 5.46/5.76 thf(fact_7100_inverse__le__iff__le,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.76 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_iff_le
% 5.46/5.76 thf(fact_7101_inverse__le__iff__le,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( ord_less_rat @ zero_zero_rat @ B2 )
% 5.46/5.76 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( ord_less_eq_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_iff_le
% 5.46/5.76 thf(fact_7102_inverse__le__iff__le__neg,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.76 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.76 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( ord_less_eq_real @ B2 @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_iff_le_neg
% 5.46/5.76 thf(fact_7103_inverse__le__iff__le__neg,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.76 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.76 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( ord_less_eq_rat @ B2 @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_iff_le_neg
% 5.46/5.76 thf(fact_7104_right__inverse,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 5.46/5.76 = one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % right_inverse
% 5.46/5.76 thf(fact_7105_right__inverse,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 5.46/5.76 = one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % right_inverse
% 5.46/5.76 thf(fact_7106_right__inverse,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 5.46/5.76 = one_one_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % right_inverse
% 5.46/5.76 thf(fact_7107_left__inverse,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.46/5.76 = one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % left_inverse
% 5.46/5.76 thf(fact_7108_left__inverse,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.46/5.76 = one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % left_inverse
% 5.46/5.76 thf(fact_7109_left__inverse,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.46/5.76 = one_one_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % left_inverse
% 5.46/5.76 thf(fact_7110_inverse__eq__divide__numeral,axiom,
% 5.46/5.76 ! [W: num] :
% 5.46/5.76 ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 5.46/5.76 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_divide_numeral
% 5.46/5.76 thf(fact_7111_inverse__eq__divide__numeral,axiom,
% 5.46/5.76 ! [W: num] :
% 5.46/5.76 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.46/5.76 = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_divide_numeral
% 5.46/5.76 thf(fact_7112_inverse__eq__divide__numeral,axiom,
% 5.46/5.76 ! [W: num] :
% 5.46/5.76 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 5.46/5.76 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_divide_numeral
% 5.46/5.76 thf(fact_7113_floor__add2,axiom,
% 5.46/5.76 ! [X4: real,Y3: real] :
% 5.46/5.76 ( ( ( member_real @ X4 @ ring_1_Ints_real )
% 5.46/5.76 | ( member_real @ Y3 @ ring_1_Ints_real ) )
% 5.46/5.76 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.76 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % floor_add2
% 5.46/5.76 thf(fact_7114_floor__add2,axiom,
% 5.46/5.76 ! [X4: rat,Y3: rat] :
% 5.46/5.76 ( ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.46/5.76 | ( member_rat @ Y3 @ ring_1_Ints_rat ) )
% 5.46/5.76 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y3 ) )
% 5.46/5.76 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % floor_add2
% 5.46/5.76 thf(fact_7115_frac__gt__0__iff,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X4 ) )
% 5.46/5.76 = ( ~ ( member_real @ X4 @ ring_1_Ints_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % frac_gt_0_iff
% 5.46/5.76 thf(fact_7116_frac__gt__0__iff,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X4 ) )
% 5.46/5.76 = ( ~ ( member_rat @ X4 @ ring_1_Ints_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % frac_gt_0_iff
% 5.46/5.76 thf(fact_7117_inverse__eq__divide__neg__numeral,axiom,
% 5.46/5.76 ! [W: num] :
% 5.46/5.76 ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.46/5.76 = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_divide_neg_numeral
% 5.46/5.76 thf(fact_7118_inverse__eq__divide__neg__numeral,axiom,
% 5.46/5.76 ! [W: num] :
% 5.46/5.76 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.76 = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_divide_neg_numeral
% 5.46/5.76 thf(fact_7119_inverse__eq__divide__neg__numeral,axiom,
% 5.46/5.76 ! [W: num] :
% 5.46/5.76 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.46/5.76 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_divide_neg_numeral
% 5.46/5.76 thf(fact_7120_xor__numerals_I3_J,axiom,
% 5.46/5.76 ! [X4: num,Y3: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.46/5.76 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(3)
% 5.46/5.76 thf(fact_7121_xor__numerals_I3_J,axiom,
% 5.46/5.76 ! [X4: num,Y3: num] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 5.46/5.76 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(3)
% 5.46/5.76 thf(fact_7122_xor__numerals_I1_J,axiom,
% 5.46/5.76 ! [Y3: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.46/5.76 = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(1)
% 5.46/5.76 thf(fact_7123_xor__numerals_I1_J,axiom,
% 5.46/5.76 ! [Y3: num] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 5.46/5.76 = ( numeral_numeral_int @ ( bit1 @ Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(1)
% 5.46/5.76 thf(fact_7124_xor__numerals_I2_J,axiom,
% 5.46/5.76 ! [Y3: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.46/5.76 = ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(2)
% 5.46/5.76 thf(fact_7125_xor__numerals_I2_J,axiom,
% 5.46/5.76 ! [Y3: num] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 5.46/5.76 = ( numeral_numeral_int @ ( bit0 @ Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(2)
% 5.46/5.76 thf(fact_7126_xor__numerals_I5_J,axiom,
% 5.46/5.76 ! [X4: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ one_one_nat )
% 5.46/5.76 = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(5)
% 5.46/5.76 thf(fact_7127_xor__numerals_I5_J,axiom,
% 5.46/5.76 ! [X4: num] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ one_one_int )
% 5.46/5.76 = ( numeral_numeral_int @ ( bit1 @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(5)
% 5.46/5.76 thf(fact_7128_xor__numerals_I8_J,axiom,
% 5.46/5.76 ! [X4: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ one_one_nat )
% 5.46/5.76 = ( numeral_numeral_nat @ ( bit0 @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(8)
% 5.46/5.76 thf(fact_7129_xor__numerals_I8_J,axiom,
% 5.46/5.76 ! [X4: num] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ one_one_int )
% 5.46/5.76 = ( numeral_numeral_int @ ( bit0 @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(8)
% 5.46/5.76 thf(fact_7130_xor__numerals_I7_J,axiom,
% 5.46/5.76 ! [X4: num,Y3: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.46/5.76 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(7)
% 5.46/5.76 thf(fact_7131_xor__numerals_I7_J,axiom,
% 5.46/5.76 ! [X4: num,Y3: num] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 5.46/5.76 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(7)
% 5.46/5.76 thf(fact_7132_xor__nat__numerals_I1_J,axiom,
% 5.46/5.76 ! [Y3: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.46/5.76 = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_nat_numerals(1)
% 5.46/5.76 thf(fact_7133_xor__nat__numerals_I2_J,axiom,
% 5.46/5.76 ! [Y3: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.46/5.76 = ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_nat_numerals(2)
% 5.46/5.76 thf(fact_7134_xor__nat__numerals_I3_J,axiom,
% 5.46/5.76 ! [X4: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.76 = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_nat_numerals(3)
% 5.46/5.76 thf(fact_7135_xor__nat__numerals_I4_J,axiom,
% 5.46/5.76 ! [X4: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.76 = ( numeral_numeral_nat @ ( bit0 @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_nat_numerals(4)
% 5.46/5.76 thf(fact_7136_xor__numerals_I4_J,axiom,
% 5.46/5.76 ! [X4: num,Y3: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.46/5.76 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(4)
% 5.46/5.76 thf(fact_7137_xor__numerals_I4_J,axiom,
% 5.46/5.76 ! [X4: num,Y3: num] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y3 ) ) )
% 5.46/5.76 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(4)
% 5.46/5.76 thf(fact_7138_xor__numerals_I6_J,axiom,
% 5.46/5.76 ! [X4: num,Y3: num] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.46/5.76 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(6)
% 5.46/5.76 thf(fact_7139_xor__numerals_I6_J,axiom,
% 5.46/5.76 ! [X4: num,Y3: num] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y3 ) ) )
% 5.46/5.76 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y3 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor_numerals(6)
% 5.46/5.76 thf(fact_7140_power__inverse,axiom,
% 5.46/5.76 ! [A: real,N: nat] :
% 5.46/5.76 ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N )
% 5.46/5.76 = ( inverse_inverse_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_inverse
% 5.46/5.76 thf(fact_7141_power__inverse,axiom,
% 5.46/5.76 ! [A: complex,N: nat] :
% 5.46/5.76 ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N )
% 5.46/5.76 = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_inverse
% 5.46/5.76 thf(fact_7142_power__inverse,axiom,
% 5.46/5.76 ! [A: rat,N: nat] :
% 5.46/5.76 ( ( power_power_rat @ ( inverse_inverse_rat @ A ) @ N )
% 5.46/5.76 = ( inverse_inverse_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_inverse
% 5.46/5.76 thf(fact_7143_mult__commute__imp__mult__inverse__commute,axiom,
% 5.46/5.76 ! [Y3: real,X4: real] :
% 5.46/5.76 ( ( ( times_times_real @ Y3 @ X4 )
% 5.46/5.76 = ( times_times_real @ X4 @ Y3 ) )
% 5.46/5.76 => ( ( times_times_real @ ( inverse_inverse_real @ Y3 ) @ X4 )
% 5.46/5.76 = ( times_times_real @ X4 @ ( inverse_inverse_real @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_commute_imp_mult_inverse_commute
% 5.46/5.76 thf(fact_7144_mult__commute__imp__mult__inverse__commute,axiom,
% 5.46/5.76 ! [Y3: complex,X4: complex] :
% 5.46/5.76 ( ( ( times_times_complex @ Y3 @ X4 )
% 5.46/5.76 = ( times_times_complex @ X4 @ Y3 ) )
% 5.46/5.76 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y3 ) @ X4 )
% 5.46/5.76 = ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_commute_imp_mult_inverse_commute
% 5.46/5.76 thf(fact_7145_mult__commute__imp__mult__inverse__commute,axiom,
% 5.46/5.76 ! [Y3: rat,X4: rat] :
% 5.46/5.76 ( ( ( times_times_rat @ Y3 @ X4 )
% 5.46/5.76 = ( times_times_rat @ X4 @ Y3 ) )
% 5.46/5.76 => ( ( times_times_rat @ ( inverse_inverse_rat @ Y3 ) @ X4 )
% 5.46/5.76 = ( times_times_rat @ X4 @ ( inverse_inverse_rat @ Y3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_commute_imp_mult_inverse_commute
% 5.46/5.76 thf(fact_7146_of__nat__xor__eq,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( semiri1316708129612266289at_nat @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 5.46/5.76 = ( bit_se6528837805403552850or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_nat_xor_eq
% 5.46/5.76 thf(fact_7147_of__nat__xor__eq,axiom,
% 5.46/5.76 ! [M: nat,N: nat] :
% 5.46/5.76 ( ( semiri1314217659103216013at_int @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 5.46/5.76 = ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_nat_xor_eq
% 5.46/5.76 thf(fact_7148_of__int__xor__eq,axiom,
% 5.46/5.76 ! [K: int,L2: int] :
% 5.46/5.76 ( ( ring_1_of_int_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 5.46/5.76 = ( bit_se6526347334894502574or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_int_xor_eq
% 5.46/5.76 thf(fact_7149_xor_Oleft__commute,axiom,
% 5.46/5.76 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ B2 @ ( bit_se6528837805403552850or_nat @ A @ C ) )
% 5.46/5.76 = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B2 @ C ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor.left_commute
% 5.46/5.76 thf(fact_7150_xor_Oleft__commute,axiom,
% 5.46/5.76 ! [B2: int,A: int,C: int] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ B2 @ ( bit_se6526347334894502574or_int @ A @ C ) )
% 5.46/5.76 = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B2 @ C ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor.left_commute
% 5.46/5.76 thf(fact_7151_xor_Ocommute,axiom,
% 5.46/5.76 ( bit_se6528837805403552850or_nat
% 5.46/5.76 = ( ^ [A4: nat,B3: nat] : ( bit_se6528837805403552850or_nat @ B3 @ A4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor.commute
% 5.46/5.76 thf(fact_7152_xor_Ocommute,axiom,
% 5.46/5.76 ( bit_se6526347334894502574or_int
% 5.46/5.76 = ( ^ [A4: int,B3: int] : ( bit_se6526347334894502574or_int @ B3 @ A4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor.commute
% 5.46/5.76 thf(fact_7153_xor_Oassoc,axiom,
% 5.46/5.76 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.76 ( ( bit_se6528837805403552850or_nat @ ( bit_se6528837805403552850or_nat @ A @ B2 ) @ C )
% 5.46/5.76 = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B2 @ C ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor.assoc
% 5.46/5.76 thf(fact_7154_xor_Oassoc,axiom,
% 5.46/5.76 ! [A: int,B2: int,C: int] :
% 5.46/5.76 ( ( bit_se6526347334894502574or_int @ ( bit_se6526347334894502574or_int @ A @ B2 ) @ C )
% 5.46/5.76 = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B2 @ C ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % xor.assoc
% 5.46/5.76 thf(fact_7155_inverse__eq__imp__eq,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ( inverse_inverse_real @ A )
% 5.46/5.76 = ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 => ( A = B2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_imp_eq
% 5.46/5.76 thf(fact_7156_inverse__eq__imp__eq,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( ( invers8013647133539491842omplex @ A )
% 5.46/5.76 = ( invers8013647133539491842omplex @ B2 ) )
% 5.46/5.76 => ( A = B2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_imp_eq
% 5.46/5.76 thf(fact_7157_inverse__eq__imp__eq,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ( inverse_inverse_rat @ A )
% 5.46/5.76 = ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 => ( A = B2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_imp_eq
% 5.46/5.76 thf(fact_7158_field__class_Ofield__inverse__zero,axiom,
% 5.46/5.76 ( ( inverse_inverse_real @ zero_zero_real )
% 5.46/5.76 = zero_zero_real ) ).
% 5.46/5.76
% 5.46/5.76 % field_class.field_inverse_zero
% 5.46/5.76 thf(fact_7159_field__class_Ofield__inverse__zero,axiom,
% 5.46/5.76 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.46/5.76 = zero_zero_complex ) ).
% 5.46/5.76
% 5.46/5.76 % field_class.field_inverse_zero
% 5.46/5.76 thf(fact_7160_field__class_Ofield__inverse__zero,axiom,
% 5.46/5.76 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.46/5.76 = zero_zero_rat ) ).
% 5.46/5.76
% 5.46/5.76 % field_class.field_inverse_zero
% 5.46/5.76 thf(fact_7161_inverse__zero__imp__zero,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ( inverse_inverse_real @ A )
% 5.46/5.76 = zero_zero_real )
% 5.46/5.76 => ( A = zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_zero_imp_zero
% 5.46/5.76 thf(fact_7162_inverse__zero__imp__zero,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( ( invers8013647133539491842omplex @ A )
% 5.46/5.76 = zero_zero_complex )
% 5.46/5.76 => ( A = zero_zero_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_zero_imp_zero
% 5.46/5.76 thf(fact_7163_inverse__zero__imp__zero,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ( inverse_inverse_rat @ A )
% 5.46/5.76 = zero_zero_rat )
% 5.46/5.76 => ( A = zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_zero_imp_zero
% 5.46/5.76 thf(fact_7164_nonzero__inverse__eq__imp__eq,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ( inverse_inverse_real @ A )
% 5.46/5.76 = ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 => ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( B2 != zero_zero_real )
% 5.46/5.76 => ( A = B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_eq_imp_eq
% 5.46/5.76 thf(fact_7165_nonzero__inverse__eq__imp__eq,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( ( invers8013647133539491842omplex @ A )
% 5.46/5.76 = ( invers8013647133539491842omplex @ B2 ) )
% 5.46/5.76 => ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( B2 != zero_zero_complex )
% 5.46/5.76 => ( A = B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_eq_imp_eq
% 5.46/5.76 thf(fact_7166_nonzero__inverse__eq__imp__eq,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ( inverse_inverse_rat @ A )
% 5.46/5.76 = ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 => ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( B2 != zero_zero_rat )
% 5.46/5.76 => ( A = B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_eq_imp_eq
% 5.46/5.76 thf(fact_7167_nonzero__inverse__inverse__eq,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.46/5.76 = A ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_inverse_eq
% 5.46/5.76 thf(fact_7168_nonzero__inverse__inverse__eq,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.46/5.76 = A ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_inverse_eq
% 5.46/5.76 thf(fact_7169_nonzero__inverse__inverse__eq,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.46/5.76 = A ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_inverse_eq
% 5.46/5.76 thf(fact_7170_nonzero__imp__inverse__nonzero,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( inverse_inverse_real @ A )
% 5.46/5.76 != zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_imp_inverse_nonzero
% 5.46/5.76 thf(fact_7171_nonzero__imp__inverse__nonzero,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( invers8013647133539491842omplex @ A )
% 5.46/5.76 != zero_zero_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_imp_inverse_nonzero
% 5.46/5.76 thf(fact_7172_nonzero__imp__inverse__nonzero,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( inverse_inverse_rat @ A )
% 5.46/5.76 != zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_imp_inverse_nonzero
% 5.46/5.76 thf(fact_7173_Ints__numeral,axiom,
% 5.46/5.76 ! [N: num] : ( member_complex @ ( numera6690914467698888265omplex @ N ) @ ring_1_Ints_complex ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_numeral
% 5.46/5.76 thf(fact_7174_Ints__numeral,axiom,
% 5.46/5.76 ! [N: num] : ( member_real @ ( numeral_numeral_real @ N ) @ ring_1_Ints_real ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_numeral
% 5.46/5.76 thf(fact_7175_Ints__numeral,axiom,
% 5.46/5.76 ! [N: num] : ( member_rat @ ( numeral_numeral_rat @ N ) @ ring_1_Ints_rat ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_numeral
% 5.46/5.76 thf(fact_7176_Ints__numeral,axiom,
% 5.46/5.76 ! [N: num] : ( member_int @ ( numeral_numeral_int @ N ) @ ring_1_Ints_int ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_numeral
% 5.46/5.76 thf(fact_7177_Ints__mult,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.46/5.76 => ( ( member_complex @ B2 @ ring_1_Ints_complex )
% 5.46/5.76 => ( member_complex @ ( times_times_complex @ A @ B2 ) @ ring_1_Ints_complex ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_mult
% 5.46/5.76 thf(fact_7178_Ints__mult,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ( member_real @ B2 @ ring_1_Ints_real )
% 5.46/5.76 => ( member_real @ ( times_times_real @ A @ B2 ) @ ring_1_Ints_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_mult
% 5.46/5.76 thf(fact_7179_Ints__mult,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( member_rat @ B2 @ ring_1_Ints_rat )
% 5.46/5.76 => ( member_rat @ ( times_times_rat @ A @ B2 ) @ ring_1_Ints_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_mult
% 5.46/5.76 thf(fact_7180_Ints__mult,axiom,
% 5.46/5.76 ! [A: int,B2: int] :
% 5.46/5.76 ( ( member_int @ A @ ring_1_Ints_int )
% 5.46/5.76 => ( ( member_int @ B2 @ ring_1_Ints_int )
% 5.46/5.76 => ( member_int @ ( times_times_int @ A @ B2 ) @ ring_1_Ints_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_mult
% 5.46/5.76 thf(fact_7181_Ints__1,axiom,
% 5.46/5.76 member_complex @ one_one_complex @ ring_1_Ints_complex ).
% 5.46/5.76
% 5.46/5.76 % Ints_1
% 5.46/5.76 thf(fact_7182_Ints__1,axiom,
% 5.46/5.76 member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 5.46/5.76
% 5.46/5.76 % Ints_1
% 5.46/5.76 thf(fact_7183_Ints__1,axiom,
% 5.46/5.76 member_int @ one_one_int @ ring_1_Ints_int ).
% 5.46/5.76
% 5.46/5.76 % Ints_1
% 5.46/5.76 thf(fact_7184_Ints__1,axiom,
% 5.46/5.76 member_real @ one_one_real @ ring_1_Ints_real ).
% 5.46/5.76
% 5.46/5.76 % Ints_1
% 5.46/5.76 thf(fact_7185_Ints__add,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.46/5.76 => ( ( member_complex @ B2 @ ring_1_Ints_complex )
% 5.46/5.76 => ( member_complex @ ( plus_plus_complex @ A @ B2 ) @ ring_1_Ints_complex ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_add
% 5.46/5.76 thf(fact_7186_Ints__add,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ( member_real @ B2 @ ring_1_Ints_real )
% 5.46/5.76 => ( member_real @ ( plus_plus_real @ A @ B2 ) @ ring_1_Ints_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_add
% 5.46/5.76 thf(fact_7187_Ints__add,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( member_rat @ B2 @ ring_1_Ints_rat )
% 5.46/5.76 => ( member_rat @ ( plus_plus_rat @ A @ B2 ) @ ring_1_Ints_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_add
% 5.46/5.76 thf(fact_7188_Ints__add,axiom,
% 5.46/5.76 ! [A: int,B2: int] :
% 5.46/5.76 ( ( member_int @ A @ ring_1_Ints_int )
% 5.46/5.76 => ( ( member_int @ B2 @ ring_1_Ints_int )
% 5.46/5.76 => ( member_int @ ( plus_plus_int @ A @ B2 ) @ ring_1_Ints_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_add
% 5.46/5.76 thf(fact_7189_real__sqrt__inverse,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( sqrt @ ( inverse_inverse_real @ X4 ) )
% 5.46/5.76 = ( inverse_inverse_real @ ( sqrt @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % real_sqrt_inverse
% 5.46/5.76 thf(fact_7190_Ints__diff,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.46/5.76 => ( ( member_complex @ B2 @ ring_1_Ints_complex )
% 5.46/5.76 => ( member_complex @ ( minus_minus_complex @ A @ B2 ) @ ring_1_Ints_complex ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_diff
% 5.46/5.76 thf(fact_7191_Ints__diff,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ( member_real @ B2 @ ring_1_Ints_real )
% 5.46/5.76 => ( member_real @ ( minus_minus_real @ A @ B2 ) @ ring_1_Ints_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_diff
% 5.46/5.76 thf(fact_7192_Ints__diff,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( member_rat @ B2 @ ring_1_Ints_rat )
% 5.46/5.76 => ( member_rat @ ( minus_minus_rat @ A @ B2 ) @ ring_1_Ints_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_diff
% 5.46/5.76 thf(fact_7193_Ints__diff,axiom,
% 5.46/5.76 ! [A: int,B2: int] :
% 5.46/5.76 ( ( member_int @ A @ ring_1_Ints_int )
% 5.46/5.76 => ( ( member_int @ B2 @ ring_1_Ints_int )
% 5.46/5.76 => ( member_int @ ( minus_minus_int @ A @ B2 ) @ ring_1_Ints_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_diff
% 5.46/5.76 thf(fact_7194_Ints__power,axiom,
% 5.46/5.76 ! [A: real,N: nat] :
% 5.46/5.76 ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( member_real @ ( power_power_real @ A @ N ) @ ring_1_Ints_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_power
% 5.46/5.76 thf(fact_7195_Ints__power,axiom,
% 5.46/5.76 ! [A: int,N: nat] :
% 5.46/5.76 ( ( member_int @ A @ ring_1_Ints_int )
% 5.46/5.76 => ( member_int @ ( power_power_int @ A @ N ) @ ring_1_Ints_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_power
% 5.46/5.76 thf(fact_7196_Ints__power,axiom,
% 5.46/5.76 ! [A: complex,N: nat] :
% 5.46/5.76 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.46/5.76 => ( member_complex @ ( power_power_complex @ A @ N ) @ ring_1_Ints_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_power
% 5.46/5.76 thf(fact_7197_bit_Oconj__xor__distrib2,axiom,
% 5.46/5.76 ! [Y3: int,Z: int,X4: int] :
% 5.46/5.76 ( ( bit_se725231765392027082nd_int @ ( bit_se6526347334894502574or_int @ Y3 @ Z ) @ X4 )
% 5.46/5.76 = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ Y3 @ X4 ) @ ( bit_se725231765392027082nd_int @ Z @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % bit.conj_xor_distrib2
% 5.46/5.76 thf(fact_7198_bit_Oconj__xor__distrib,axiom,
% 5.46/5.76 ! [X4: int,Y3: int,Z: int] :
% 5.46/5.76 ( ( bit_se725231765392027082nd_int @ X4 @ ( bit_se6526347334894502574or_int @ Y3 @ Z ) )
% 5.46/5.76 = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ X4 @ Y3 ) @ ( bit_se725231765392027082nd_int @ X4 @ Z ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % bit.conj_xor_distrib
% 5.46/5.76 thf(fact_7199_bit__xor__iff,axiom,
% 5.46/5.76 ! [A: nat,B2: nat,N: nat] :
% 5.46/5.76 ( ( bit_se1148574629649215175it_nat @ ( bit_se6528837805403552850or_nat @ A @ B2 ) @ N )
% 5.46/5.76 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.46/5.76 != ( bit_se1148574629649215175it_nat @ B2 @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % bit_xor_iff
% 5.46/5.76 thf(fact_7200_bit__xor__iff,axiom,
% 5.46/5.76 ! [A: int,B2: int,N: nat] :
% 5.46/5.76 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ A @ B2 ) @ N )
% 5.46/5.76 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.46/5.76 != ( bit_se1146084159140164899it_int @ B2 @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % bit_xor_iff
% 5.46/5.76 thf(fact_7201_norm__inverse__le__norm,axiom,
% 5.46/5.76 ! [R2: real,X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ R2 @ ( real_V7735802525324610683m_real @ X4 ) )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.46/5.76 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X4 ) ) @ ( inverse_inverse_real @ R2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % norm_inverse_le_norm
% 5.46/5.76 thf(fact_7202_norm__inverse__le__norm,axiom,
% 5.46/5.76 ! [R2: real,X4: complex] :
% 5.46/5.76 ( ( ord_less_eq_real @ R2 @ ( real_V1022390504157884413omplex @ X4 ) )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.46/5.76 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X4 ) ) @ ( inverse_inverse_real @ R2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % norm_inverse_le_norm
% 5.46/5.76 thf(fact_7203_positive__imp__inverse__positive,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % positive_imp_inverse_positive
% 5.46/5.76 thf(fact_7204_positive__imp__inverse__positive,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % positive_imp_inverse_positive
% 5.46/5.76 thf(fact_7205_negative__imp__inverse__negative,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ A @ zero_zero_real )
% 5.46/5.76 => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % negative_imp_inverse_negative
% 5.46/5.76 thf(fact_7206_negative__imp__inverse__negative,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.46/5.76 => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % negative_imp_inverse_negative
% 5.46/5.76 thf(fact_7207_inverse__positive__imp__positive,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.46/5.76 => ( ( A != zero_zero_real )
% 5.46/5.76 => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_positive_imp_positive
% 5.46/5.76 thf(fact_7208_inverse__positive__imp__positive,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.46/5.76 => ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_positive_imp_positive
% 5.46/5.76 thf(fact_7209_inverse__negative__imp__negative,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.46/5.76 => ( ( A != zero_zero_real )
% 5.46/5.76 => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_negative_imp_negative
% 5.46/5.76 thf(fact_7210_inverse__negative__imp__negative,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.46/5.76 => ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_negative_imp_negative
% 5.46/5.76 thf(fact_7211_less__imp__inverse__less__neg,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_real @ A @ B2 )
% 5.46/5.76 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.76 => ( ord_less_real @ ( inverse_inverse_real @ B2 ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % less_imp_inverse_less_neg
% 5.46/5.76 thf(fact_7212_less__imp__inverse__less__neg,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.76 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.76 => ( ord_less_rat @ ( inverse_inverse_rat @ B2 ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % less_imp_inverse_less_neg
% 5.46/5.76 thf(fact_7213_inverse__less__imp__less__neg,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.76 => ( ord_less_real @ B2 @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_imp_less_neg
% 5.46/5.76 thf(fact_7214_inverse__less__imp__less__neg,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.76 => ( ord_less_rat @ B2 @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_imp_less_neg
% 5.46/5.76 thf(fact_7215_less__imp__inverse__less,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_real @ A @ B2 )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ord_less_real @ ( inverse_inverse_real @ B2 ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % less_imp_inverse_less
% 5.46/5.76 thf(fact_7216_less__imp__inverse__less,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.76 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ord_less_rat @ ( inverse_inverse_rat @ B2 ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % less_imp_inverse_less
% 5.46/5.76 thf(fact_7217_inverse__less__imp__less,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ord_less_real @ B2 @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_imp_less
% 5.46/5.76 thf(fact_7218_inverse__less__imp__less,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ord_less_rat @ B2 @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_imp_less
% 5.46/5.76 thf(fact_7219_nonzero__inverse__mult__distrib,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( B2 != zero_zero_real )
% 5.46/5.76 => ( ( inverse_inverse_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.76 = ( times_times_real @ ( inverse_inverse_real @ B2 ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_mult_distrib
% 5.46/5.76 thf(fact_7220_nonzero__inverse__mult__distrib,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( B2 != zero_zero_complex )
% 5.46/5.76 => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B2 ) )
% 5.46/5.76 = ( times_times_complex @ ( invers8013647133539491842omplex @ B2 ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_mult_distrib
% 5.46/5.76 thf(fact_7221_nonzero__inverse__mult__distrib,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( B2 != zero_zero_rat )
% 5.46/5.76 => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.76 = ( times_times_rat @ ( inverse_inverse_rat @ B2 ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_mult_distrib
% 5.46/5.76 thf(fact_7222_nonzero__inverse__minus__eq,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.46/5.76 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_minus_eq
% 5.46/5.76 thf(fact_7223_nonzero__inverse__minus__eq,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_minus_eq
% 5.46/5.76 thf(fact_7224_nonzero__inverse__minus__eq,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.46/5.76 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_minus_eq
% 5.46/5.76 thf(fact_7225_inverse__numeral__1,axiom,
% 5.46/5.76 ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 5.46/5.76 = ( numeral_numeral_real @ one ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_numeral_1
% 5.46/5.76 thf(fact_7226_inverse__numeral__1,axiom,
% 5.46/5.76 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.46/5.76 = ( numera6690914467698888265omplex @ one ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_numeral_1
% 5.46/5.76 thf(fact_7227_inverse__numeral__1,axiom,
% 5.46/5.76 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ one ) )
% 5.46/5.76 = ( numeral_numeral_rat @ one ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_numeral_1
% 5.46/5.76 thf(fact_7228_inverse__unique,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ( times_times_real @ A @ B2 )
% 5.46/5.76 = one_one_real )
% 5.46/5.76 => ( ( inverse_inverse_real @ A )
% 5.46/5.76 = B2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_unique
% 5.46/5.76 thf(fact_7229_inverse__unique,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( ( times_times_complex @ A @ B2 )
% 5.46/5.76 = one_one_complex )
% 5.46/5.76 => ( ( invers8013647133539491842omplex @ A )
% 5.46/5.76 = B2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_unique
% 5.46/5.76 thf(fact_7230_inverse__unique,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ( times_times_rat @ A @ B2 )
% 5.46/5.76 = one_one_rat )
% 5.46/5.76 => ( ( inverse_inverse_rat @ A )
% 5.46/5.76 = B2 ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_unique
% 5.46/5.76 thf(fact_7231_divide__inverse__commute,axiom,
% 5.46/5.76 ( divide_divide_real
% 5.46/5.76 = ( ^ [A4: real,B3: real] : ( times_times_real @ ( inverse_inverse_real @ B3 ) @ A4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_inverse_commute
% 5.46/5.76 thf(fact_7232_divide__inverse__commute,axiom,
% 5.46/5.76 ( divide1717551699836669952omplex
% 5.46/5.76 = ( ^ [A4: complex,B3: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B3 ) @ A4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_inverse_commute
% 5.46/5.76 thf(fact_7233_divide__inverse__commute,axiom,
% 5.46/5.76 ( divide_divide_rat
% 5.46/5.76 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ ( inverse_inverse_rat @ B3 ) @ A4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_inverse_commute
% 5.46/5.76 thf(fact_7234_divide__inverse,axiom,
% 5.46/5.76 ( divide_divide_real
% 5.46/5.76 = ( ^ [A4: real,B3: real] : ( times_times_real @ A4 @ ( inverse_inverse_real @ B3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_inverse
% 5.46/5.76 thf(fact_7235_divide__inverse,axiom,
% 5.46/5.76 ( divide1717551699836669952omplex
% 5.46/5.76 = ( ^ [A4: complex,B3: complex] : ( times_times_complex @ A4 @ ( invers8013647133539491842omplex @ B3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_inverse
% 5.46/5.76 thf(fact_7236_divide__inverse,axiom,
% 5.46/5.76 ( divide_divide_rat
% 5.46/5.76 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ A4 @ ( inverse_inverse_rat @ B3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_inverse
% 5.46/5.76 thf(fact_7237_field__class_Ofield__divide__inverse,axiom,
% 5.46/5.76 ( divide_divide_real
% 5.46/5.76 = ( ^ [A4: real,B3: real] : ( times_times_real @ A4 @ ( inverse_inverse_real @ B3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % field_class.field_divide_inverse
% 5.46/5.76 thf(fact_7238_field__class_Ofield__divide__inverse,axiom,
% 5.46/5.76 ( divide1717551699836669952omplex
% 5.46/5.76 = ( ^ [A4: complex,B3: complex] : ( times_times_complex @ A4 @ ( invers8013647133539491842omplex @ B3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % field_class.field_divide_inverse
% 5.46/5.76 thf(fact_7239_field__class_Ofield__divide__inverse,axiom,
% 5.46/5.76 ( divide_divide_rat
% 5.46/5.76 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ A4 @ ( inverse_inverse_rat @ B3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % field_class.field_divide_inverse
% 5.46/5.76 thf(fact_7240_inverse__eq__divide,axiom,
% 5.46/5.76 ( inverse_inverse_real
% 5.46/5.76 = ( divide_divide_real @ one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_divide
% 5.46/5.76 thf(fact_7241_inverse__eq__divide,axiom,
% 5.46/5.76 ( invers8013647133539491842omplex
% 5.46/5.76 = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_divide
% 5.46/5.76 thf(fact_7242_inverse__eq__divide,axiom,
% 5.46/5.76 ( inverse_inverse_rat
% 5.46/5.76 = ( divide_divide_rat @ one_one_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_eq_divide
% 5.46/5.76 thf(fact_7243_power__mult__power__inverse__commute,axiom,
% 5.46/5.76 ! [X4: real,M: nat,N: nat] :
% 5.46/5.76 ( ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ N ) )
% 5.46/5.76 = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ N ) @ ( power_power_real @ X4 @ M ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_mult_power_inverse_commute
% 5.46/5.76 thf(fact_7244_power__mult__power__inverse__commute,axiom,
% 5.46/5.76 ! [X4: complex,M: nat,N: nat] :
% 5.46/5.76 ( ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ N ) )
% 5.46/5.76 = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ N ) @ ( power_power_complex @ X4 @ M ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_mult_power_inverse_commute
% 5.46/5.76 thf(fact_7245_power__mult__power__inverse__commute,axiom,
% 5.46/5.76 ! [X4: rat,M: nat,N: nat] :
% 5.46/5.76 ( ( times_times_rat @ ( power_power_rat @ X4 @ M ) @ ( power_power_rat @ ( inverse_inverse_rat @ X4 ) @ N ) )
% 5.46/5.76 = ( times_times_rat @ ( power_power_rat @ ( inverse_inverse_rat @ X4 ) @ N ) @ ( power_power_rat @ X4 @ M ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_mult_power_inverse_commute
% 5.46/5.76 thf(fact_7246_power__mult__inverse__distrib,axiom,
% 5.46/5.76 ! [X4: real,M: nat] :
% 5.46/5.76 ( ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( inverse_inverse_real @ X4 ) )
% 5.46/5.76 = ( times_times_real @ ( inverse_inverse_real @ X4 ) @ ( power_power_real @ X4 @ M ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_mult_inverse_distrib
% 5.46/5.76 thf(fact_7247_power__mult__inverse__distrib,axiom,
% 5.46/5.76 ! [X4: complex,M: nat] :
% 5.46/5.76 ( ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( invers8013647133539491842omplex @ X4 ) )
% 5.46/5.76 = ( times_times_complex @ ( invers8013647133539491842omplex @ X4 ) @ ( power_power_complex @ X4 @ M ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_mult_inverse_distrib
% 5.46/5.76 thf(fact_7248_power__mult__inverse__distrib,axiom,
% 5.46/5.76 ! [X4: rat,M: nat] :
% 5.46/5.76 ( ( times_times_rat @ ( power_power_rat @ X4 @ M ) @ ( inverse_inverse_rat @ X4 ) )
% 5.46/5.76 = ( times_times_rat @ ( inverse_inverse_rat @ X4 ) @ ( power_power_rat @ X4 @ M ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_mult_inverse_distrib
% 5.46/5.76 thf(fact_7249_mult__inverse__of__nat__commute,axiom,
% 5.46/5.76 ! [Xa: nat,X4: real] :
% 5.46/5.76 ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) @ X4 )
% 5.46/5.76 = ( times_times_real @ X4 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_inverse_of_nat_commute
% 5.46/5.76 thf(fact_7250_mult__inverse__of__nat__commute,axiom,
% 5.46/5.76 ! [Xa: nat,X4: complex] :
% 5.46/5.76 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) @ X4 )
% 5.46/5.76 = ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_inverse_of_nat_commute
% 5.46/5.76 thf(fact_7251_mult__inverse__of__nat__commute,axiom,
% 5.46/5.76 ! [Xa: nat,X4: rat] :
% 5.46/5.76 ( ( times_times_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa ) ) @ X4 )
% 5.46/5.76 = ( times_times_rat @ X4 @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_inverse_of_nat_commute
% 5.46/5.76 thf(fact_7252_nonzero__abs__inverse,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.46/5.76 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_abs_inverse
% 5.46/5.76 thf(fact_7253_nonzero__abs__inverse,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.46/5.76 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_abs_inverse
% 5.46/5.76 thf(fact_7254_mult__inverse__of__int__commute,axiom,
% 5.46/5.76 ! [Xa: int,X4: real] :
% 5.46/5.76 ( ( times_times_real @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa ) ) @ X4 )
% 5.46/5.76 = ( times_times_real @ X4 @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_inverse_of_int_commute
% 5.46/5.76 thf(fact_7255_mult__inverse__of__int__commute,axiom,
% 5.46/5.76 ! [Xa: int,X4: complex] :
% 5.46/5.76 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa ) ) @ X4 )
% 5.46/5.76 = ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_inverse_of_int_commute
% 5.46/5.76 thf(fact_7256_mult__inverse__of__int__commute,axiom,
% 5.46/5.76 ! [Xa: int,X4: rat] :
% 5.46/5.76 ( ( times_times_rat @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa ) ) @ X4 )
% 5.46/5.76 = ( times_times_rat @ X4 @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_inverse_of_int_commute
% 5.46/5.76 thf(fact_7257_divide__real__def,axiom,
% 5.46/5.76 ( divide_divide_real
% 5.46/5.76 = ( ^ [X: real,Y: real] : ( times_times_real @ X @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % divide_real_def
% 5.46/5.76 thf(fact_7258_Ints__double__eq__0__iff,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.46/5.76 => ( ( ( plus_plus_complex @ A @ A )
% 5.46/5.76 = zero_zero_complex )
% 5.46/5.76 = ( A = zero_zero_complex ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_double_eq_0_iff
% 5.46/5.76 thf(fact_7259_Ints__double__eq__0__iff,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ( ( plus_plus_real @ A @ A )
% 5.46/5.76 = zero_zero_real )
% 5.46/5.76 = ( A = zero_zero_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_double_eq_0_iff
% 5.46/5.76 thf(fact_7260_Ints__double__eq__0__iff,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( ( plus_plus_rat @ A @ A )
% 5.46/5.76 = zero_zero_rat )
% 5.46/5.76 = ( A = zero_zero_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_double_eq_0_iff
% 5.46/5.76 thf(fact_7261_Ints__double__eq__0__iff,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( member_int @ A @ ring_1_Ints_int )
% 5.46/5.76 => ( ( ( plus_plus_int @ A @ A )
% 5.46/5.76 = zero_zero_int )
% 5.46/5.76 = ( A = zero_zero_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_double_eq_0_iff
% 5.46/5.76 thf(fact_7262_inverse__le__imp__le,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ord_less_eq_real @ B2 @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_imp_le
% 5.46/5.76 thf(fact_7263_inverse__le__imp__le,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ord_less_eq_rat @ B2 @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_imp_le
% 5.46/5.76 thf(fact_7264_le__imp__inverse__le,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ord_less_eq_real @ ( inverse_inverse_real @ B2 ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_imp_inverse_le
% 5.46/5.76 thf(fact_7265_le__imp__inverse__le,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.76 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B2 ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_imp_inverse_le
% 5.46/5.76 thf(fact_7266_inverse__le__imp__le__neg,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.76 => ( ord_less_eq_real @ B2 @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_imp_le_neg
% 5.46/5.76 thf(fact_7267_inverse__le__imp__le__neg,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.76 => ( ord_less_eq_rat @ B2 @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_imp_le_neg
% 5.46/5.76 thf(fact_7268_le__imp__inverse__le__neg,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.76 => ( ( ord_less_real @ B2 @ zero_zero_real )
% 5.46/5.76 => ( ord_less_eq_real @ ( inverse_inverse_real @ B2 ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_imp_inverse_le_neg
% 5.46/5.76 thf(fact_7269_le__imp__inverse__le__neg,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.76 => ( ( ord_less_rat @ B2 @ zero_zero_rat )
% 5.46/5.76 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B2 ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_imp_inverse_le_neg
% 5.46/5.76 thf(fact_7270_inverse__le__1__iff,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( inverse_inverse_real @ X4 ) @ one_one_real )
% 5.46/5.76 = ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.76 | ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_1_iff
% 5.46/5.76 thf(fact_7271_inverse__le__1__iff,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X4 ) @ one_one_rat )
% 5.46/5.76 = ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 5.46/5.76 | ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_1_iff
% 5.46/5.76 thf(fact_7272_one__less__inverse__iff,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X4 ) )
% 5.46/5.76 = ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.76 & ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % one_less_inverse_iff
% 5.46/5.76 thf(fact_7273_one__less__inverse__iff,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X4 ) )
% 5.46/5.76 = ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.46/5.76 & ( ord_less_rat @ X4 @ one_one_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % one_less_inverse_iff
% 5.46/5.76 thf(fact_7274_one__less__inverse,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( ord_less_real @ A @ one_one_real )
% 5.46/5.76 => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % one_less_inverse
% 5.46/5.76 thf(fact_7275_one__less__inverse,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.46/5.76 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % one_less_inverse
% 5.46/5.76 thf(fact_7276_field__class_Ofield__inverse,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.46/5.76 = one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % field_class.field_inverse
% 5.46/5.76 thf(fact_7277_field__class_Ofield__inverse,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.46/5.76 = one_one_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % field_class.field_inverse
% 5.46/5.76 thf(fact_7278_field__class_Ofield__inverse,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.46/5.76 = one_one_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % field_class.field_inverse
% 5.46/5.76 thf(fact_7279_division__ring__inverse__add,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( B2 != zero_zero_real )
% 5.46/5.76 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B2 ) ) @ ( inverse_inverse_real @ B2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % division_ring_inverse_add
% 5.46/5.76 thf(fact_7280_division__ring__inverse__add,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( B2 != zero_zero_complex )
% 5.46/5.76 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B2 ) )
% 5.46/5.76 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B2 ) ) @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % division_ring_inverse_add
% 5.46/5.76 thf(fact_7281_division__ring__inverse__add,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( B2 != zero_zero_rat )
% 5.46/5.76 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B2 ) ) @ ( inverse_inverse_rat @ B2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % division_ring_inverse_add
% 5.46/5.76 thf(fact_7282_inverse__add,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( B2 != zero_zero_real )
% 5.46/5.76 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B2 ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_add
% 5.46/5.76 thf(fact_7283_inverse__add,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( B2 != zero_zero_complex )
% 5.46/5.76 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B2 ) )
% 5.46/5.76 = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B2 ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_add
% 5.46/5.76 thf(fact_7284_inverse__add,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( B2 != zero_zero_rat )
% 5.46/5.76 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B2 ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_add
% 5.46/5.76 thf(fact_7285_division__ring__inverse__diff,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( B2 != zero_zero_real )
% 5.46/5.76 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B2 @ A ) ) @ ( inverse_inverse_real @ B2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % division_ring_inverse_diff
% 5.46/5.76 thf(fact_7286_division__ring__inverse__diff,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( B2 != zero_zero_complex )
% 5.46/5.76 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B2 ) )
% 5.46/5.76 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B2 @ A ) ) @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % division_ring_inverse_diff
% 5.46/5.76 thf(fact_7287_division__ring__inverse__diff,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( B2 != zero_zero_rat )
% 5.46/5.76 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B2 @ A ) ) @ ( inverse_inverse_rat @ B2 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % division_ring_inverse_diff
% 5.46/5.76 thf(fact_7288_nonzero__inverse__eq__divide,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( inverse_inverse_real @ A )
% 5.46/5.76 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_eq_divide
% 5.46/5.76 thf(fact_7289_nonzero__inverse__eq__divide,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( invers8013647133539491842omplex @ A )
% 5.46/5.76 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_eq_divide
% 5.46/5.76 thf(fact_7290_nonzero__inverse__eq__divide,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( inverse_inverse_rat @ A )
% 5.46/5.76 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % nonzero_inverse_eq_divide
% 5.46/5.76 thf(fact_7291_gbinomial__Suc__Suc,axiom,
% 5.46/5.76 ! [A: complex,K: nat] :
% 5.46/5.76 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.46/5.76 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_Suc_Suc
% 5.46/5.76 thf(fact_7292_gbinomial__Suc__Suc,axiom,
% 5.46/5.76 ! [A: real,K: nat] :
% 5.46/5.76 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.46/5.76 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_Suc_Suc
% 5.46/5.76 thf(fact_7293_gbinomial__Suc__Suc,axiom,
% 5.46/5.76 ! [A: rat,K: nat] :
% 5.46/5.76 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.46/5.76 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_Suc_Suc
% 5.46/5.76 thf(fact_7294_gbinomial__of__nat__symmetric,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K )
% 5.46/5.76 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_of_nat_symmetric
% 5.46/5.76 thf(fact_7295_gbinomial__of__nat__symmetric,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.46/5.76 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_of_nat_symmetric
% 5.46/5.76 thf(fact_7296_gbinomial__of__nat__symmetric,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ N )
% 5.46/5.76 => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 5.46/5.76 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_of_nat_symmetric
% 5.46/5.76 thf(fact_7297_inverse__powr,axiom,
% 5.46/5.76 ! [Y3: real,A: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.76 => ( ( powr_real @ ( inverse_inverse_real @ Y3 ) @ A )
% 5.46/5.76 = ( inverse_inverse_real @ ( powr_real @ Y3 @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_powr
% 5.46/5.76 thf(fact_7298_Ints__odd__nonzero,axiom,
% 5.46/5.76 ! [A: complex] :
% 5.46/5.76 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.46/5.76 => ( ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ A ) @ A )
% 5.46/5.76 != zero_zero_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_odd_nonzero
% 5.46/5.76 thf(fact_7299_Ints__odd__nonzero,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A )
% 5.46/5.76 != zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_odd_nonzero
% 5.46/5.76 thf(fact_7300_Ints__odd__nonzero,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 5.46/5.76 != zero_zero_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_odd_nonzero
% 5.46/5.76 thf(fact_7301_Ints__odd__nonzero,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( member_int @ A @ ring_1_Ints_int )
% 5.46/5.76 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 5.46/5.76 != zero_zero_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_odd_nonzero
% 5.46/5.76 thf(fact_7302_of__int__divide__in__Ints,axiom,
% 5.46/5.76 ! [B2: int,A: int] :
% 5.46/5.76 ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.76 => ( member_complex @ ( divide1717551699836669952omplex @ ( ring_17405671764205052669omplex @ A ) @ ( ring_17405671764205052669omplex @ B2 ) ) @ ring_1_Ints_complex ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_int_divide_in_Ints
% 5.46/5.76 thf(fact_7303_of__int__divide__in__Ints,axiom,
% 5.46/5.76 ! [B2: int,A: int] :
% 5.46/5.76 ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.76 => ( member_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B2 ) ) @ ring_1_Ints_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_int_divide_in_Ints
% 5.46/5.76 thf(fact_7304_of__int__divide__in__Ints,axiom,
% 5.46/5.76 ! [B2: int,A: int] :
% 5.46/5.76 ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.76 => ( member_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B2 ) ) @ ring_1_Ints_rat ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_int_divide_in_Ints
% 5.46/5.76 thf(fact_7305_of__int__divide__in__Ints,axiom,
% 5.46/5.76 ! [B2: int,A: int] :
% 5.46/5.76 ( ( dvd_dvd_int @ B2 @ A )
% 5.46/5.76 => ( member_int @ ( divide_divide_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B2 ) ) @ ring_1_Ints_int ) ) ).
% 5.46/5.76
% 5.46/5.76 % of_int_divide_in_Ints
% 5.46/5.76 thf(fact_7306_inverse__le__iff,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.76 => ( ord_less_eq_real @ B2 @ A ) )
% 5.46/5.76 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real )
% 5.46/5.76 => ( ord_less_eq_real @ A @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_iff
% 5.46/5.76 thf(fact_7307_inverse__le__iff,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.76 => ( ord_less_eq_rat @ B2 @ A ) )
% 5.46/5.76 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B2 ) @ zero_zero_rat )
% 5.46/5.76 => ( ord_less_eq_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_le_iff
% 5.46/5.76 thf(fact_7308_inverse__less__iff,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B2 ) )
% 5.46/5.76 => ( ord_less_real @ B2 @ A ) )
% 5.46/5.76 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B2 ) @ zero_zero_real )
% 5.46/5.76 => ( ord_less_real @ A @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_iff
% 5.46/5.76 thf(fact_7309_inverse__less__iff,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B2 ) )
% 5.46/5.76 => ( ord_less_rat @ B2 @ A ) )
% 5.46/5.76 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B2 ) @ zero_zero_rat )
% 5.46/5.76 => ( ord_less_rat @ A @ B2 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_iff
% 5.46/5.76 thf(fact_7310_one__le__inverse,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.46/5.76 => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % one_le_inverse
% 5.46/5.76 thf(fact_7311_one__le__inverse,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.46/5.76 => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % one_le_inverse
% 5.46/5.76 thf(fact_7312_inverse__less__1__iff,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_real @ ( inverse_inverse_real @ X4 ) @ one_one_real )
% 5.46/5.76 = ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.76 | ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_1_iff
% 5.46/5.76 thf(fact_7313_inverse__less__1__iff,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( ord_less_rat @ ( inverse_inverse_rat @ X4 ) @ one_one_rat )
% 5.46/5.76 = ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 5.46/5.76 | ( ord_less_rat @ one_one_rat @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_less_1_iff
% 5.46/5.76 thf(fact_7314_one__le__inverse__iff,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X4 ) )
% 5.46/5.76 = ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.76 & ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % one_le_inverse_iff
% 5.46/5.76 thf(fact_7315_one__le__inverse__iff,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X4 ) )
% 5.46/5.76 = ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.46/5.76 & ( ord_less_eq_rat @ X4 @ one_one_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % one_le_inverse_iff
% 5.46/5.76 thf(fact_7316_inverse__diff__inverse,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( A != zero_zero_real )
% 5.46/5.76 => ( ( B2 != zero_zero_real )
% 5.46/5.76 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B2 ) )
% 5.46/5.76 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B2 ) ) @ ( inverse_inverse_real @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_diff_inverse
% 5.46/5.76 thf(fact_7317_inverse__diff__inverse,axiom,
% 5.46/5.76 ! [A: complex,B2: complex] :
% 5.46/5.76 ( ( A != zero_zero_complex )
% 5.46/5.76 => ( ( B2 != zero_zero_complex )
% 5.46/5.76 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B2 ) )
% 5.46/5.76 = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B2 ) ) @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_diff_inverse
% 5.46/5.76 thf(fact_7318_inverse__diff__inverse,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( A != zero_zero_rat )
% 5.46/5.76 => ( ( B2 != zero_zero_rat )
% 5.46/5.76 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B2 ) )
% 5.46/5.76 = ( uminus_uminus_rat @ ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ A @ B2 ) ) @ ( inverse_inverse_rat @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % inverse_diff_inverse
% 5.46/5.76 thf(fact_7319_reals__Archimedean,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ? [N4: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ X4 ) ) ).
% 5.46/5.76
% 5.46/5.76 % reals_Archimedean
% 5.46/5.76 thf(fact_7320_reals__Archimedean,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.46/5.76 => ? [N4: nat] : ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ ( suc @ N4 ) ) ) @ X4 ) ) ).
% 5.46/5.76
% 5.46/5.76 % reals_Archimedean
% 5.46/5.76 thf(fact_7321_gbinomial__addition__formula,axiom,
% 5.46/5.76 ! [A: complex,K: nat] :
% 5.46/5.76 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.46/5.76 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_addition_formula
% 5.46/5.76 thf(fact_7322_gbinomial__addition__formula,axiom,
% 5.46/5.76 ! [A: real,K: nat] :
% 5.46/5.76 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.46/5.76 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_addition_formula
% 5.46/5.76 thf(fact_7323_gbinomial__addition__formula,axiom,
% 5.46/5.76 ! [A: rat,K: nat] :
% 5.46/5.76 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.46/5.76 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_addition_formula
% 5.46/5.76 thf(fact_7324_gbinomial__absorb__comp,axiom,
% 5.46/5.76 ! [A: complex,K: nat] :
% 5.46/5.76 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.46/5.76 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_absorb_comp
% 5.46/5.76 thf(fact_7325_gbinomial__absorb__comp,axiom,
% 5.46/5.76 ! [A: real,K: nat] :
% 5.46/5.76 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.46/5.76 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_absorb_comp
% 5.46/5.76 thf(fact_7326_gbinomial__absorb__comp,axiom,
% 5.46/5.76 ! [A: rat,K: nat] :
% 5.46/5.76 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.46/5.76 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_absorb_comp
% 5.46/5.76 thf(fact_7327_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.46/5.76 ! [K: nat,A: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.46/5.76 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_ge_n_over_k_pow_k
% 5.46/5.76 thf(fact_7328_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.46/5.76 ! [K: nat,A: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.46/5.76 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_ge_n_over_k_pow_k
% 5.46/5.76 thf(fact_7329_gbinomial__mult__1_H,axiom,
% 5.46/5.76 ! [A: complex,K: nat] :
% 5.46/5.76 ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 5.46/5.76 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_mult_1'
% 5.46/5.76 thf(fact_7330_gbinomial__mult__1_H,axiom,
% 5.46/5.76 ! [A: real,K: nat] :
% 5.46/5.76 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.46/5.76 = ( 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 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_mult_1'
% 5.46/5.76 thf(fact_7331_gbinomial__mult__1_H,axiom,
% 5.46/5.76 ! [A: rat,K: nat] :
% 5.46/5.76 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.46/5.76 = ( 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 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_mult_1'
% 5.46/5.76 thf(fact_7332_gbinomial__mult__1,axiom,
% 5.46/5.76 ! [A: complex,K: nat] :
% 5.46/5.76 ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 5.46/5.76 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_mult_1
% 5.46/5.76 thf(fact_7333_gbinomial__mult__1,axiom,
% 5.46/5.76 ! [A: real,K: nat] :
% 5.46/5.76 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.46/5.76 = ( 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 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_mult_1
% 5.46/5.76 thf(fact_7334_gbinomial__mult__1,axiom,
% 5.46/5.76 ! [A: rat,K: nat] :
% 5.46/5.76 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.46/5.76 = ( 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 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_mult_1
% 5.46/5.76 thf(fact_7335_forall__pos__mono__1,axiom,
% 5.46/5.76 ! [P: real > $o,E: real] :
% 5.46/5.76 ( ! [D3: real,E2: real] :
% 5.46/5.76 ( ( ord_less_real @ D3 @ E2 )
% 5.46/5.76 => ( ( P @ D3 )
% 5.46/5.76 => ( P @ E2 ) ) )
% 5.46/5.76 => ( ! [N4: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.76 => ( P @ E ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % forall_pos_mono_1
% 5.46/5.76 thf(fact_7336_forall__pos__mono,axiom,
% 5.46/5.76 ! [P: real > $o,E: real] :
% 5.46/5.76 ( ! [D3: real,E2: real] :
% 5.46/5.76 ( ( ord_less_real @ D3 @ E2 )
% 5.46/5.76 => ( ( P @ D3 )
% 5.46/5.76 => ( P @ E2 ) ) )
% 5.46/5.76 => ( ! [N4: nat] :
% 5.46/5.76 ( ( N4 != zero_zero_nat )
% 5.46/5.76 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) ) )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.76 => ( P @ E ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % forall_pos_mono
% 5.46/5.76 thf(fact_7337_real__arch__inverse,axiom,
% 5.46/5.76 ! [E: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.76 = ( ? [N2: nat] :
% 5.46/5.76 ( ( N2 != zero_zero_nat )
% 5.46/5.76 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.46/5.76 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % real_arch_inverse
% 5.46/5.76 thf(fact_7338_even__xor__iff,axiom,
% 5.46/5.76 ! [A: code_integer,B2: code_integer] :
% 5.46/5.76 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ A @ B2 ) )
% 5.46/5.76 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.46/5.76 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % even_xor_iff
% 5.46/5.76 thf(fact_7339_even__xor__iff,axiom,
% 5.46/5.76 ! [A: nat,B2: nat] :
% 5.46/5.76 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ A @ B2 ) )
% 5.46/5.76 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.46/5.76 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % even_xor_iff
% 5.46/5.76 thf(fact_7340_even__xor__iff,axiom,
% 5.46/5.76 ! [A: int,B2: int] :
% 5.46/5.76 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ A @ B2 ) )
% 5.46/5.76 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.46/5.76 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % even_xor_iff
% 5.46/5.76 thf(fact_7341_sqrt__divide__self__eq,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ( ( divide_divide_real @ ( sqrt @ X4 ) @ X4 )
% 5.46/5.76 = ( inverse_inverse_real @ ( sqrt @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % sqrt_divide_self_eq
% 5.46/5.76 thf(fact_7342_ln__inverse,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ( ( ln_ln_real @ ( inverse_inverse_real @ X4 ) )
% 5.46/5.76 = ( uminus_uminus_real @ ( ln_ln_real @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % ln_inverse
% 5.46/5.76 thf(fact_7343_Ints__odd__less__0,axiom,
% 5.46/5.76 ! [A: real] :
% 5.46/5.76 ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A ) @ zero_zero_real )
% 5.46/5.76 = ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_odd_less_0
% 5.46/5.76 thf(fact_7344_Ints__odd__less__0,axiom,
% 5.46/5.76 ! [A: rat] :
% 5.46/5.76 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 5.46/5.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_odd_less_0
% 5.46/5.76 thf(fact_7345_Ints__odd__less__0,axiom,
% 5.46/5.76 ! [A: int] :
% 5.46/5.76 ( ( member_int @ A @ ring_1_Ints_int )
% 5.46/5.76 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 5.46/5.76 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_odd_less_0
% 5.46/5.76 thf(fact_7346_Ints__nonzero__abs__ge1,axiom,
% 5.46/5.76 ! [X4: code_integer] :
% 5.46/5.76 ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 5.46/5.76 => ( ( X4 != zero_z3403309356797280102nteger )
% 5.46/5.76 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_nonzero_abs_ge1
% 5.46/5.76 thf(fact_7347_Ints__nonzero__abs__ge1,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( member_real @ X4 @ ring_1_Ints_real )
% 5.46/5.76 => ( ( X4 != zero_zero_real )
% 5.46/5.76 => ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_nonzero_abs_ge1
% 5.46/5.76 thf(fact_7348_Ints__nonzero__abs__ge1,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( X4 != zero_zero_rat )
% 5.46/5.76 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_nonzero_abs_ge1
% 5.46/5.76 thf(fact_7349_Ints__nonzero__abs__ge1,axiom,
% 5.46/5.76 ! [X4: int] :
% 5.46/5.76 ( ( member_int @ X4 @ ring_1_Ints_int )
% 5.46/5.76 => ( ( X4 != zero_zero_int )
% 5.46/5.76 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_nonzero_abs_ge1
% 5.46/5.76 thf(fact_7350_Ints__nonzero__abs__less1,axiom,
% 5.46/5.76 ! [X4: code_integer] :
% 5.46/5.76 ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 5.46/5.76 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer )
% 5.46/5.76 => ( X4 = zero_z3403309356797280102nteger ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_nonzero_abs_less1
% 5.46/5.76 thf(fact_7351_Ints__nonzero__abs__less1,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( member_real @ X4 @ ring_1_Ints_real )
% 5.46/5.76 => ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.76 => ( X4 = zero_zero_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_nonzero_abs_less1
% 5.46/5.76 thf(fact_7352_Ints__nonzero__abs__less1,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( ord_less_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat )
% 5.46/5.76 => ( X4 = zero_zero_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_nonzero_abs_less1
% 5.46/5.76 thf(fact_7353_Ints__nonzero__abs__less1,axiom,
% 5.46/5.76 ! [X4: int] :
% 5.46/5.76 ( ( member_int @ X4 @ ring_1_Ints_int )
% 5.46/5.76 => ( ( ord_less_int @ ( abs_abs_int @ X4 ) @ one_one_int )
% 5.46/5.76 => ( X4 = zero_zero_int ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_nonzero_abs_less1
% 5.46/5.76 thf(fact_7354_Ints__eq__abs__less1,axiom,
% 5.46/5.76 ! [X4: code_integer,Y3: code_integer] :
% 5.46/5.76 ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 5.46/5.76 => ( ( member_Code_integer @ Y3 @ ring_11222124179247155820nteger )
% 5.46/5.76 => ( ( X4 = Y3 )
% 5.46/5.76 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ Y3 ) ) @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_eq_abs_less1
% 5.46/5.76 thf(fact_7355_Ints__eq__abs__less1,axiom,
% 5.46/5.76 ! [X4: real,Y3: real] :
% 5.46/5.76 ( ( member_real @ X4 @ ring_1_Ints_real )
% 5.46/5.76 => ( ( member_real @ Y3 @ ring_1_Ints_real )
% 5.46/5.76 => ( ( X4 = Y3 )
% 5.46/5.76 = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ one_one_real ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_eq_abs_less1
% 5.46/5.76 thf(fact_7356_Ints__eq__abs__less1,axiom,
% 5.46/5.76 ! [X4: rat,Y3: rat] :
% 5.46/5.76 ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( member_rat @ Y3 @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( X4 = Y3 )
% 5.46/5.76 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ Y3 ) ) @ one_one_rat ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_eq_abs_less1
% 5.46/5.76 thf(fact_7357_Ints__eq__abs__less1,axiom,
% 5.46/5.76 ! [X4: int,Y3: int] :
% 5.46/5.76 ( ( member_int @ X4 @ ring_1_Ints_int )
% 5.46/5.76 => ( ( member_int @ Y3 @ ring_1_Ints_int )
% 5.46/5.76 => ( ( X4 = Y3 )
% 5.46/5.76 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Y3 ) ) @ one_one_int ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Ints_eq_abs_less1
% 5.46/5.76 thf(fact_7358_sin__times__pi__eq__0,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ( sin_real @ ( times_times_real @ X4 @ pi ) )
% 5.46/5.76 = zero_zero_real )
% 5.46/5.76 = ( member_real @ X4 @ ring_1_Ints_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % sin_times_pi_eq_0
% 5.46/5.76 thf(fact_7359_ex__inverse__of__nat__less,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ? [N4: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.46/5.76 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % ex_inverse_of_nat_less
% 5.46/5.76 thf(fact_7360_ex__inverse__of__nat__less,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.46/5.76 => ? [N4: nat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 5.46/5.76 & ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ N4 ) ) @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % ex_inverse_of_nat_less
% 5.46/5.76 thf(fact_7361_power__diff__conv__inverse,axiom,
% 5.46/5.76 ! [X4: real,M: nat,N: nat] :
% 5.46/5.76 ( ( X4 != zero_zero_real )
% 5.46/5.76 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ( power_power_real @ X4 @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.76 = ( times_times_real @ ( power_power_real @ X4 @ N ) @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ M ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_diff_conv_inverse
% 5.46/5.76 thf(fact_7362_power__diff__conv__inverse,axiom,
% 5.46/5.76 ! [X4: complex,M: nat,N: nat] :
% 5.46/5.76 ( ( X4 != zero_zero_complex )
% 5.46/5.76 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ( power_power_complex @ X4 @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.76 = ( times_times_complex @ ( power_power_complex @ X4 @ N ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ M ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_diff_conv_inverse
% 5.46/5.76 thf(fact_7363_power__diff__conv__inverse,axiom,
% 5.46/5.76 ! [X4: rat,M: nat,N: nat] :
% 5.46/5.76 ( ( X4 != zero_zero_rat )
% 5.46/5.76 => ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.76 => ( ( power_power_rat @ X4 @ ( minus_minus_nat @ N @ M ) )
% 5.46/5.76 = ( times_times_rat @ ( power_power_rat @ X4 @ N ) @ ( power_power_rat @ ( inverse_inverse_rat @ X4 ) @ M ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % power_diff_conv_inverse
% 5.46/5.76 thf(fact_7364_Suc__times__gbinomial,axiom,
% 5.46/5.76 ! [K: nat,A: complex] :
% 5.46/5.76 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.46/5.76 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Suc_times_gbinomial
% 5.46/5.76 thf(fact_7365_Suc__times__gbinomial,axiom,
% 5.46/5.76 ! [K: nat,A: real] :
% 5.46/5.76 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.46/5.76 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Suc_times_gbinomial
% 5.46/5.76 thf(fact_7366_Suc__times__gbinomial,axiom,
% 5.46/5.76 ! [K: nat,A: rat] :
% 5.46/5.76 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.46/5.76 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % Suc_times_gbinomial
% 5.46/5.76 thf(fact_7367_gbinomial__absorption,axiom,
% 5.46/5.76 ! [K: nat,A: complex] :
% 5.46/5.76 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.46/5.76 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_absorption
% 5.46/5.76 thf(fact_7368_gbinomial__absorption,axiom,
% 5.46/5.76 ! [K: nat,A: real] :
% 5.46/5.76 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.46/5.76 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_absorption
% 5.46/5.76 thf(fact_7369_gbinomial__absorption,axiom,
% 5.46/5.76 ! [K: nat,A: rat] :
% 5.46/5.76 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.46/5.76 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_absorption
% 5.46/5.76 thf(fact_7370_gbinomial__trinomial__revision,axiom,
% 5.46/5.76 ! [K: nat,M: nat,A: complex] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ M )
% 5.46/5.76 => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 5.46/5.76 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_trinomial_revision
% 5.46/5.76 thf(fact_7371_gbinomial__trinomial__revision,axiom,
% 5.46/5.76 ! [K: nat,M: nat,A: real] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ M )
% 5.46/5.76 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.46/5.76 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_trinomial_revision
% 5.46/5.76 thf(fact_7372_gbinomial__trinomial__revision,axiom,
% 5.46/5.76 ! [K: nat,M: nat,A: rat] :
% 5.46/5.76 ( ( ord_less_eq_nat @ K @ M )
% 5.46/5.76 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.46/5.76 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_trinomial_revision
% 5.46/5.76 thf(fact_7373_log__inverse,axiom,
% 5.46/5.76 ! [A: real,X4: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( A != one_one_real )
% 5.46/5.76 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ( ( log @ A @ ( inverse_inverse_real @ X4 ) )
% 5.46/5.76 = ( uminus_uminus_real @ ( log @ A @ X4 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % log_inverse
% 5.46/5.76 thf(fact_7374_frac__neg,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ( member_real @ X4 @ ring_1_Ints_real )
% 5.46/5.76 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X4 ) )
% 5.46/5.76 = zero_zero_real ) )
% 5.46/5.76 & ( ~ ( member_real @ X4 @ ring_1_Ints_real )
% 5.46/5.76 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X4 ) )
% 5.46/5.76 = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X4 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % frac_neg
% 5.46/5.76 thf(fact_7375_frac__neg,axiom,
% 5.46/5.76 ! [X4: rat] :
% 5.46/5.76 ( ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X4 ) )
% 5.46/5.76 = zero_zero_rat ) )
% 5.46/5.76 & ( ~ ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.46/5.76 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X4 ) )
% 5.46/5.76 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X4 ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % frac_neg
% 5.46/5.76 thf(fact_7376_gbinomial__factors,axiom,
% 5.46/5.76 ! [A: complex,K: nat] :
% 5.46/5.76 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.46/5.76 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_factors
% 5.46/5.76 thf(fact_7377_gbinomial__factors,axiom,
% 5.46/5.76 ! [A: real,K: nat] :
% 5.46/5.76 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.46/5.76 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_factors
% 5.46/5.76 thf(fact_7378_gbinomial__factors,axiom,
% 5.46/5.76 ! [A: rat,K: nat] :
% 5.46/5.76 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.46/5.76 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_factors
% 5.46/5.76 thf(fact_7379_gbinomial__rec,axiom,
% 5.46/5.76 ! [A: complex,K: nat] :
% 5.46/5.76 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.46/5.76 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_rec
% 5.46/5.76 thf(fact_7380_gbinomial__rec,axiom,
% 5.46/5.76 ! [A: real,K: nat] :
% 5.46/5.76 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.46/5.76 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_rec
% 5.46/5.76 thf(fact_7381_gbinomial__rec,axiom,
% 5.46/5.76 ! [A: rat,K: nat] :
% 5.46/5.76 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.46/5.76 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_rec
% 5.46/5.76 thf(fact_7382_gbinomial__negated__upper,axiom,
% 5.46/5.76 ( gbinomial_complex
% 5.46/5.76 = ( ^ [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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_negated_upper
% 5.46/5.76 thf(fact_7383_gbinomial__negated__upper,axiom,
% 5.46/5.76 ( gbinomial_real
% 5.46/5.76 = ( ^ [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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_negated_upper
% 5.46/5.76 thf(fact_7384_gbinomial__negated__upper,axiom,
% 5.46/5.76 ( gbinomial_rat
% 5.46/5.76 = ( ^ [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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_negated_upper
% 5.46/5.76 thf(fact_7385_gbinomial__index__swap,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 5.46/5.76 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_index_swap
% 5.46/5.76 thf(fact_7386_gbinomial__index__swap,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( 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 ) )
% 5.46/5.76 = ( 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 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_index_swap
% 5.46/5.76 thf(fact_7387_gbinomial__index__swap,axiom,
% 5.46/5.76 ! [K: nat,N: nat] :
% 5.46/5.76 ( ( 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 ) )
% 5.46/5.76 = ( 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 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_index_swap
% 5.46/5.76 thf(fact_7388_exp__plus__inverse__exp,axiom,
% 5.46/5.76 ! [X4: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % exp_plus_inverse_exp
% 5.46/5.76 thf(fact_7389_le__mult__floor__Ints,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B2 ) ) ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_mult_floor_Ints
% 5.46/5.76 thf(fact_7390_le__mult__floor__Ints,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B2 ) ) ) @ ( ring_1_of_int_rat @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_mult_floor_Ints
% 5.46/5.76 thf(fact_7391_le__mult__floor__Ints,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B2 ) ) ) @ ( ring_1_of_int_int @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_mult_floor_Ints
% 5.46/5.76 thf(fact_7392_le__mult__floor__Ints,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B2 ) ) ) @ ( ring_1_of_int_real @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_mult_floor_Ints
% 5.46/5.76 thf(fact_7393_le__mult__floor__Ints,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B2 ) ) ) @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_mult_floor_Ints
% 5.46/5.76 thf(fact_7394_le__mult__floor__Ints,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B2 ) ) ) @ ( ring_1_of_int_int @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % le_mult_floor_Ints
% 5.46/5.76 thf(fact_7395_frac__unique__iff,axiom,
% 5.46/5.76 ! [X4: real,A: real] :
% 5.46/5.76 ( ( ( archim2898591450579166408c_real @ X4 )
% 5.46/5.76 = A )
% 5.46/5.76 = ( ( member_real @ ( minus_minus_real @ X4 @ A ) @ ring_1_Ints_real )
% 5.46/5.76 & ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.76 & ( ord_less_real @ A @ one_one_real ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % frac_unique_iff
% 5.46/5.76 thf(fact_7396_frac__unique__iff,axiom,
% 5.46/5.76 ! [X4: rat,A: rat] :
% 5.46/5.76 ( ( ( archimedean_frac_rat @ X4 )
% 5.46/5.76 = A )
% 5.46/5.76 = ( ( member_rat @ ( minus_minus_rat @ X4 @ A ) @ ring_1_Ints_rat )
% 5.46/5.76 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.76 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % frac_unique_iff
% 5.46/5.76 thf(fact_7397_mult__ceiling__le__Ints,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B2 ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_ceiling_le_Ints
% 5.46/5.76 thf(fact_7398_mult__ceiling__le__Ints,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B2 ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_ceiling_le_Ints
% 5.46/5.76 thf(fact_7399_mult__ceiling__le__Ints,axiom,
% 5.46/5.76 ! [A: real,B2: real] :
% 5.46/5.76 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.46/5.76 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.46/5.76 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B2 ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_ceiling_le_Ints
% 5.46/5.76 thf(fact_7400_mult__ceiling__le__Ints,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B2 ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_ceiling_le_Ints
% 5.46/5.76 thf(fact_7401_mult__ceiling__le__Ints,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B2 ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_ceiling_le_Ints
% 5.46/5.76 thf(fact_7402_mult__ceiling__le__Ints,axiom,
% 5.46/5.76 ! [A: rat,B2: rat] :
% 5.46/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.46/5.76 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.46/5.76 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B2 ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B2 ) ) ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % mult_ceiling_le_Ints
% 5.46/5.76 thf(fact_7403_gbinomial__minus,axiom,
% 5.46/5.76 ! [A: complex,K: nat] :
% 5.46/5.76 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.46/5.76 = ( 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 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_minus
% 5.46/5.76 thf(fact_7404_gbinomial__minus,axiom,
% 5.46/5.76 ! [A: real,K: nat] :
% 5.46/5.76 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.46/5.76 = ( 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 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_minus
% 5.46/5.76 thf(fact_7405_gbinomial__minus,axiom,
% 5.46/5.76 ! [A: rat,K: nat] :
% 5.46/5.76 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.46/5.76 = ( 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 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_minus
% 5.46/5.76 thf(fact_7406_plus__inverse__ge__2,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % plus_inverse_ge_2
% 5.46/5.76 thf(fact_7407_real__inv__sqrt__pow2,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.76 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.76 = ( inverse_inverse_real @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % real_inv_sqrt_pow2
% 5.46/5.76 thf(fact_7408_gbinomial__reduce__nat,axiom,
% 5.46/5.76 ! [K: nat,A: complex] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.76 => ( ( gbinomial_complex @ A @ K )
% 5.46/5.76 = ( 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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_reduce_nat
% 5.46/5.76 thf(fact_7409_gbinomial__reduce__nat,axiom,
% 5.46/5.76 ! [K: nat,A: real] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.76 => ( ( gbinomial_real @ A @ K )
% 5.46/5.76 = ( 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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_reduce_nat
% 5.46/5.76 thf(fact_7410_gbinomial__reduce__nat,axiom,
% 5.46/5.76 ! [K: nat,A: rat] :
% 5.46/5.76 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.46/5.76 => ( ( gbinomial_rat @ A @ K )
% 5.46/5.76 = ( 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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_reduce_nat
% 5.46/5.76 thf(fact_7411_gbinomial__pochhammer,axiom,
% 5.46/5.76 ( gbinomial_complex
% 5.46/5.76 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A4 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_pochhammer
% 5.46/5.76 thf(fact_7412_gbinomial__pochhammer,axiom,
% 5.46/5.76 ( gbinomial_rat
% 5.46/5.76 = ( ^ [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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_pochhammer
% 5.46/5.76 thf(fact_7413_gbinomial__pochhammer,axiom,
% 5.46/5.76 ( gbinomial_real
% 5.46/5.76 = ( ^ [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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_pochhammer
% 5.46/5.76 thf(fact_7414_gbinomial__pochhammer_H,axiom,
% 5.46/5.76 ( gbinomial_complex
% 5.46/5.76 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_pochhammer'
% 5.46/5.76 thf(fact_7415_gbinomial__pochhammer_H,axiom,
% 5.46/5.76 ( gbinomial_rat
% 5.46/5.76 = ( ^ [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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_pochhammer'
% 5.46/5.76 thf(fact_7416_gbinomial__pochhammer_H,axiom,
% 5.46/5.76 ( gbinomial_real
% 5.46/5.76 = ( ^ [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 ) ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % gbinomial_pochhammer'
% 5.46/5.76 thf(fact_7417_tan__cot,axiom,
% 5.46/5.76 ! [X4: real] :
% 5.46/5.76 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) )
% 5.46/5.76 = ( inverse_inverse_real @ ( tan_real @ X4 ) ) ) ).
% 5.46/5.76
% 5.46/5.76 % tan_cot
% 5.46/5.76 thf(fact_7418_sin__integer__2pi,axiom,
% 5.46/5.76 ! [N: real] :
% 5.46/5.76 ( ( member_real @ N @ ring_1_Ints_real )
% 5.46/5.76 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.46/5.76 = zero_zero_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % sin_integer_2pi
% 5.46/5.76 thf(fact_7419_cos__integer__2pi,axiom,
% 5.46/5.76 ! [N: real] :
% 5.46/5.76 ( ( member_real @ N @ ring_1_Ints_real )
% 5.46/5.76 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.46/5.76 = one_one_real ) ) ).
% 5.46/5.76
% 5.46/5.76 % cos_integer_2pi
% 5.46/5.76 thf(fact_7420_xor__nat__unfold,axiom,
% 5.46/5.76 ( bit_se6528837805403552850or_nat
% 5.46/5.76 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % xor_nat_unfold
% 5.46/5.77 thf(fact_7421_xor__nat__rec,axiom,
% 5.46/5.77 ( bit_se6528837805403552850or_nat
% 5.46/5.77 = ( ^ [M6: nat,N2: nat] :
% 5.46/5.77 ( plus_plus_nat
% 5.46/5.77 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.77 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 5.46/5.77 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.46/5.77 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % xor_nat_rec
% 5.46/5.77 thf(fact_7422_real__le__x__sinh,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.77 => ( ord_less_eq_real @ X4 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % real_le_x_sinh
% 5.46/5.77 thf(fact_7423_xor__one__eq,axiom,
% 5.46/5.77 ! [A: code_integer] :
% 5.46/5.77 ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 5.46/5.77 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.46/5.77 @ ( zero_n356916108424825756nteger
% 5.46/5.77 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % xor_one_eq
% 5.46/5.77 thf(fact_7424_xor__one__eq,axiom,
% 5.46/5.77 ! [A: nat] :
% 5.46/5.77 ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 5.46/5.77 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.46/5.77 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.77 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % xor_one_eq
% 5.46/5.77 thf(fact_7425_xor__one__eq,axiom,
% 5.46/5.77 ! [A: int] :
% 5.46/5.77 ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 5.46/5.77 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.46/5.77 @ ( zero_n2684676970156552555ol_int
% 5.46/5.77 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % xor_one_eq
% 5.46/5.77 thf(fact_7426_one__xor__eq,axiom,
% 5.46/5.77 ! [A: code_integer] :
% 5.46/5.77 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 5.46/5.77 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.46/5.77 @ ( zero_n356916108424825756nteger
% 5.46/5.77 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % one_xor_eq
% 5.46/5.77 thf(fact_7427_one__xor__eq,axiom,
% 5.46/5.77 ! [A: nat] :
% 5.46/5.77 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 5.46/5.77 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.46/5.77 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.77 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % one_xor_eq
% 5.46/5.77 thf(fact_7428_one__xor__eq,axiom,
% 5.46/5.77 ! [A: int] :
% 5.46/5.77 ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 5.46/5.77 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.46/5.77 @ ( zero_n2684676970156552555ol_int
% 5.46/5.77 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % one_xor_eq
% 5.46/5.77 thf(fact_7429_real__le__abs__sinh,axiom,
% 5.46/5.77 ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % real_le_abs_sinh
% 5.46/5.77 thf(fact_7430_tan__sec,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( ( cos_real @ X4 )
% 5.46/5.77 != zero_zero_real )
% 5.46/5.77 => ( ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.77 = ( power_power_real @ ( inverse_inverse_real @ ( cos_real @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % tan_sec
% 5.46/5.77 thf(fact_7431_tan__sec,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( ( cos_complex @ X4 )
% 5.46/5.77 != zero_zero_complex )
% 5.46/5.77 => ( ( plus_plus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.77 = ( power_power_complex @ ( invers8013647133539491842omplex @ ( cos_complex @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % tan_sec
% 5.46/5.77 thf(fact_7432_sinh__ln__real,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.77 => ( ( sinh_real @ ( ln_ln_real @ X4 ) )
% 5.46/5.77 = ( divide_divide_real @ ( minus_minus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_ln_real
% 5.46/5.77 thf(fact_7433_cosh__ln__real,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.77 => ( ( cosh_real @ ( ln_ln_real @ X4 ) )
% 5.46/5.77 = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_ln_real
% 5.46/5.77 thf(fact_7434_cosh__zero__iff,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( ( cosh_real @ X4 )
% 5.46/5.77 = zero_zero_real )
% 5.46/5.77 = ( ( power_power_real @ ( exp_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.77 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_zero_iff
% 5.46/5.77 thf(fact_7435_cosh__zero__iff,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( ( cosh_complex @ X4 )
% 5.46/5.77 = zero_zero_complex )
% 5.46/5.77 = ( ( power_power_complex @ ( exp_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.77 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_zero_iff
% 5.46/5.77 thf(fact_7436_psubsetI,axiom,
% 5.46/5.77 ! [A3: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.46/5.77 => ( ( A3 != B4 )
% 5.46/5.77 => ( ord_less_set_nat @ A3 @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubsetI
% 5.46/5.77 thf(fact_7437_push__bit__numeral__minus__1,axiom,
% 5.46/5.77 ! [N: num] :
% 5.46/5.77 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.77 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_numeral_minus_1
% 5.46/5.77 thf(fact_7438_push__bit__numeral__minus__1,axiom,
% 5.46/5.77 ! [N: num] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.77 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_numeral_minus_1
% 5.46/5.77 thf(fact_7439_push__bit__nonnegative__int__iff,axiom,
% 5.46/5.77 ! [N: nat,K: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.46/5.77 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_nonnegative_int_iff
% 5.46/5.77 thf(fact_7440_push__bit__negative__int__iff,axiom,
% 5.46/5.77 ! [N: nat,K: int] :
% 5.46/5.77 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.77 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_negative_int_iff
% 5.46/5.77 thf(fact_7441_push__bit__of__0,axiom,
% 5.46/5.77 ! [N: nat] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ zero_zero_int )
% 5.46/5.77 = zero_zero_int ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_of_0
% 5.46/5.77 thf(fact_7442_push__bit__of__0,axiom,
% 5.46/5.77 ! [N: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ N @ zero_zero_nat )
% 5.46/5.77 = zero_zero_nat ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_of_0
% 5.46/5.77 thf(fact_7443_push__bit__eq__0__iff,axiom,
% 5.46/5.77 ! [N: nat,A: int] :
% 5.46/5.77 ( ( ( bit_se545348938243370406it_int @ N @ A )
% 5.46/5.77 = zero_zero_int )
% 5.46/5.77 = ( A = zero_zero_int ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_eq_0_iff
% 5.46/5.77 thf(fact_7444_push__bit__eq__0__iff,axiom,
% 5.46/5.77 ! [N: nat,A: nat] :
% 5.46/5.77 ( ( ( bit_se547839408752420682it_nat @ N @ A )
% 5.46/5.77 = zero_zero_nat )
% 5.46/5.77 = ( A = zero_zero_nat ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_eq_0_iff
% 5.46/5.77 thf(fact_7445_push__bit__push__bit,axiom,
% 5.46/5.77 ! [M: nat,N: nat,A: int] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ M @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.46/5.77 = ( bit_se545348938243370406it_int @ ( plus_plus_nat @ M @ N ) @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_push_bit
% 5.46/5.77 thf(fact_7446_push__bit__push__bit,axiom,
% 5.46/5.77 ! [M: nat,N: nat,A: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ M @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.46/5.77 = ( bit_se547839408752420682it_nat @ ( plus_plus_nat @ M @ N ) @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_push_bit
% 5.46/5.77 thf(fact_7447_push__bit__and,axiom,
% 5.46/5.77 ! [N: nat,A: int,B2: int] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B2 ) )
% 5.46/5.77 = ( bit_se725231765392027082nd_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( bit_se545348938243370406it_int @ N @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_and
% 5.46/5.77 thf(fact_7448_push__bit__and,axiom,
% 5.46/5.77 ! [N: nat,A: nat,B2: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B2 ) )
% 5.46/5.77 = ( bit_se727722235901077358nd_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( bit_se547839408752420682it_nat @ N @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_and
% 5.46/5.77 thf(fact_7449_push__bit__xor,axiom,
% 5.46/5.77 ! [N: nat,A: int,B2: int] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ ( bit_se6526347334894502574or_int @ A @ B2 ) )
% 5.46/5.77 = ( bit_se6526347334894502574or_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( bit_se545348938243370406it_int @ N @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_xor
% 5.46/5.77 thf(fact_7450_push__bit__xor,axiom,
% 5.46/5.77 ! [N: nat,A: nat,B2: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ N @ ( bit_se6528837805403552850or_nat @ A @ B2 ) )
% 5.46/5.77 = ( bit_se6528837805403552850or_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( bit_se547839408752420682it_nat @ N @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_xor
% 5.46/5.77 thf(fact_7451_concat__bit__of__zero__1,axiom,
% 5.46/5.77 ! [N: nat,L2: int] :
% 5.46/5.77 ( ( bit_concat_bit @ N @ zero_zero_int @ L2 )
% 5.46/5.77 = ( bit_se545348938243370406it_int @ N @ L2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % concat_bit_of_zero_1
% 5.46/5.77 thf(fact_7452_sinh__real__less__iff,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y3 ) )
% 5.46/5.77 = ( ord_less_real @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_real_less_iff
% 5.46/5.77 thf(fact_7453_sinh__real__le__iff,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y3 ) )
% 5.46/5.77 = ( ord_less_eq_real @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_real_le_iff
% 5.46/5.77 thf(fact_7454_cosh__0,axiom,
% 5.46/5.77 ( ( cosh_complex @ zero_zero_complex )
% 5.46/5.77 = one_one_complex ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_0
% 5.46/5.77 thf(fact_7455_cosh__0,axiom,
% 5.46/5.77 ( ( cosh_real @ zero_zero_real )
% 5.46/5.77 = one_one_real ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_0
% 5.46/5.77 thf(fact_7456_sinh__real__pos__iff,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X4 ) )
% 5.46/5.77 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_real_pos_iff
% 5.46/5.77 thf(fact_7457_sinh__real__neg__iff,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( ord_less_real @ ( sinh_real @ X4 ) @ zero_zero_real )
% 5.46/5.77 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_real_neg_iff
% 5.46/5.77 thf(fact_7458_sinh__real__nonneg__iff,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X4 ) )
% 5.46/5.77 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_real_nonneg_iff
% 5.46/5.77 thf(fact_7459_sinh__real__nonpos__iff,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ ( sinh_real @ X4 ) @ zero_zero_real )
% 5.46/5.77 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_real_nonpos_iff
% 5.46/5.77 thf(fact_7460_xor__nonnegative__int__iff,axiom,
% 5.46/5.77 ! [K: int,L2: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 5.46/5.77 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.77 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % xor_nonnegative_int_iff
% 5.46/5.77 thf(fact_7461_xor__negative__int__iff,axiom,
% 5.46/5.77 ! [K: int,L2: int] :
% 5.46/5.77 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 5.46/5.77 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.77 != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % xor_negative_int_iff
% 5.46/5.77 thf(fact_7462_push__bit__Suc__numeral,axiom,
% 5.46/5.77 ! [N: nat,K: num] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( numeral_numeral_int @ K ) )
% 5.46/5.77 = ( bit_se545348938243370406it_int @ N @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_Suc_numeral
% 5.46/5.77 thf(fact_7463_push__bit__Suc__numeral,axiom,
% 5.46/5.77 ! [N: nat,K: num] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.77 = ( bit_se547839408752420682it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_Suc_numeral
% 5.46/5.77 thf(fact_7464_push__bit__Suc__minus__numeral,axiom,
% 5.46/5.77 ! [N: nat,K: num] :
% 5.46/5.77 ( ( bit_se7788150548672797655nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.46/5.77 = ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_Suc_minus_numeral
% 5.46/5.77 thf(fact_7465_push__bit__Suc__minus__numeral,axiom,
% 5.46/5.77 ! [N: nat,K: num] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.77 = ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_Suc_minus_numeral
% 5.46/5.77 thf(fact_7466_push__bit__numeral,axiom,
% 5.46/5.77 ! [L2: num,K: num] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ K ) )
% 5.46/5.77 = ( bit_se545348938243370406it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_numeral
% 5.46/5.77 thf(fact_7467_push__bit__numeral,axiom,
% 5.46/5.77 ! [L2: num,K: num] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.77 = ( bit_se547839408752420682it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_numeral
% 5.46/5.77 thf(fact_7468_push__bit__of__Suc__0,axiom,
% 5.46/5.77 ! [N: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_of_Suc_0
% 5.46/5.77 thf(fact_7469_push__bit__Suc,axiom,
% 5.46/5.77 ! [N: nat,A: int] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ A )
% 5.46/5.77 = ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_Suc
% 5.46/5.77 thf(fact_7470_push__bit__Suc,axiom,
% 5.46/5.77 ! [N: nat,A: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ A )
% 5.46/5.77 = ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_Suc
% 5.46/5.77 thf(fact_7471_push__bit__of__1,axiom,
% 5.46/5.77 ! [N: nat] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ one_one_int )
% 5.46/5.77 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_of_1
% 5.46/5.77 thf(fact_7472_push__bit__of__1,axiom,
% 5.46/5.77 ! [N: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ N @ one_one_nat )
% 5.46/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_of_1
% 5.46/5.77 thf(fact_7473_even__push__bit__iff,axiom,
% 5.46/5.77 ! [N: nat,A: code_integer] :
% 5.46/5.77 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se7788150548672797655nteger @ N @ A ) )
% 5.46/5.77 = ( ( N != zero_zero_nat )
% 5.46/5.77 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % even_push_bit_iff
% 5.46/5.77 thf(fact_7474_even__push__bit__iff,axiom,
% 5.46/5.77 ! [N: nat,A: int] :
% 5.46/5.77 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.46/5.77 = ( ( N != zero_zero_nat )
% 5.46/5.77 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % even_push_bit_iff
% 5.46/5.77 thf(fact_7475_even__push__bit__iff,axiom,
% 5.46/5.77 ! [N: nat,A: nat] :
% 5.46/5.77 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.46/5.77 = ( ( N != zero_zero_nat )
% 5.46/5.77 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % even_push_bit_iff
% 5.46/5.77 thf(fact_7476_push__bit__minus__numeral,axiom,
% 5.46/5.77 ! [L2: num,K: num] :
% 5.46/5.77 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ L2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.46/5.77 = ( bit_se7788150548672797655nteger @ ( pred_numeral @ L2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_minus_numeral
% 5.46/5.77 thf(fact_7477_push__bit__minus__numeral,axiom,
% 5.46/5.77 ! [L2: num,K: num] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.77 = ( bit_se545348938243370406it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_minus_numeral
% 5.46/5.77 thf(fact_7478_flip__bit__int__def,axiom,
% 5.46/5.77 ( bit_se2159334234014336723it_int
% 5.46/5.77 = ( ^ [N2: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % flip_bit_int_def
% 5.46/5.77 thf(fact_7479_push__bit__add,axiom,
% 5.46/5.77 ! [N: nat,A: int,B2: int] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ ( plus_plus_int @ A @ B2 ) )
% 5.46/5.77 = ( plus_plus_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( bit_se545348938243370406it_int @ N @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_add
% 5.46/5.77 thf(fact_7480_push__bit__add,axiom,
% 5.46/5.77 ! [N: nat,A: nat,B2: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ N @ ( plus_plus_nat @ A @ B2 ) )
% 5.46/5.77 = ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( bit_se547839408752420682it_nat @ N @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_add
% 5.46/5.77 thf(fact_7481_cosh__plus__sinh,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( plus_plus_complex @ ( cosh_complex @ X4 ) @ ( sinh_complex @ X4 ) )
% 5.46/5.77 = ( exp_complex @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_plus_sinh
% 5.46/5.77 thf(fact_7482_cosh__plus__sinh,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( plus_plus_real @ ( cosh_real @ X4 ) @ ( sinh_real @ X4 ) )
% 5.46/5.77 = ( exp_real @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_plus_sinh
% 5.46/5.77 thf(fact_7483_sinh__plus__cosh,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( plus_plus_complex @ ( sinh_complex @ X4 ) @ ( cosh_complex @ X4 ) )
% 5.46/5.77 = ( exp_complex @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_plus_cosh
% 5.46/5.77 thf(fact_7484_sinh__plus__cosh,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( plus_plus_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) )
% 5.46/5.77 = ( exp_real @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_plus_cosh
% 5.46/5.77 thf(fact_7485_psubsetD,axiom,
% 5.46/5.77 ! [A3: set_Extended_enat,B4: set_Extended_enat,C: extended_enat] :
% 5.46/5.77 ( ( ord_le2529575680413868914d_enat @ A3 @ B4 )
% 5.46/5.77 => ( ( member_Extended_enat @ C @ A3 )
% 5.46/5.77 => ( member_Extended_enat @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubsetD
% 5.46/5.77 thf(fact_7486_psubsetD,axiom,
% 5.46/5.77 ! [A3: set_complex,B4: set_complex,C: complex] :
% 5.46/5.77 ( ( ord_less_set_complex @ A3 @ B4 )
% 5.46/5.77 => ( ( member_complex @ C @ A3 )
% 5.46/5.77 => ( member_complex @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubsetD
% 5.46/5.77 thf(fact_7487_psubsetD,axiom,
% 5.46/5.77 ! [A3: set_real,B4: set_real,C: real] :
% 5.46/5.77 ( ( ord_less_set_real @ A3 @ B4 )
% 5.46/5.77 => ( ( member_real @ C @ A3 )
% 5.46/5.77 => ( member_real @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubsetD
% 5.46/5.77 thf(fact_7488_psubsetD,axiom,
% 5.46/5.77 ! [A3: set_nat,B4: set_nat,C: nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ A3 @ B4 )
% 5.46/5.77 => ( ( member_nat @ C @ A3 )
% 5.46/5.77 => ( member_nat @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubsetD
% 5.46/5.77 thf(fact_7489_psubsetD,axiom,
% 5.46/5.77 ! [A3: set_int,B4: set_int,C: int] :
% 5.46/5.77 ( ( ord_less_set_int @ A3 @ B4 )
% 5.46/5.77 => ( ( member_int @ C @ A3 )
% 5.46/5.77 => ( member_int @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubsetD
% 5.46/5.77 thf(fact_7490_sinh__le__cosh__real,axiom,
% 5.46/5.77 ! [X4: real] : ( ord_less_eq_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_le_cosh_real
% 5.46/5.77 thf(fact_7491_sinh__less__cosh__real,axiom,
% 5.46/5.77 ! [X4: real] : ( ord_less_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_less_cosh_real
% 5.46/5.77 thf(fact_7492_push__bit__of__int,axiom,
% 5.46/5.77 ! [N: nat,K: int] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ ( ring_1_of_int_int @ K ) )
% 5.46/5.77 = ( ring_1_of_int_int @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_of_int
% 5.46/5.77 thf(fact_7493_of__nat__push__bit,axiom,
% 5.46/5.77 ! [M: nat,N: nat] :
% 5.46/5.77 ( ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ M @ N ) )
% 5.46/5.77 = ( bit_se545348938243370406it_int @ M @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % of_nat_push_bit
% 5.46/5.77 thf(fact_7494_of__nat__push__bit,axiom,
% 5.46/5.77 ! [M: nat,N: nat] :
% 5.46/5.77 ( ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ M @ N ) )
% 5.46/5.77 = ( bit_se547839408752420682it_nat @ M @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % of_nat_push_bit
% 5.46/5.77 thf(fact_7495_push__bit__of__nat,axiom,
% 5.46/5.77 ! [N: nat,M: nat] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.46/5.77 = ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ N @ M ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_of_nat
% 5.46/5.77 thf(fact_7496_push__bit__of__nat,axiom,
% 5.46/5.77 ! [N: nat,M: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.46/5.77 = ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ N @ M ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_of_nat
% 5.46/5.77 thf(fact_7497_psubset__imp__ex__mem,axiom,
% 5.46/5.77 ! [A3: set_Extended_enat,B4: set_Extended_enat] :
% 5.46/5.77 ( ( ord_le2529575680413868914d_enat @ A3 @ B4 )
% 5.46/5.77 => ? [B5: extended_enat] : ( member_Extended_enat @ B5 @ ( minus_925952699566721837d_enat @ B4 @ A3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubset_imp_ex_mem
% 5.46/5.77 thf(fact_7498_psubset__imp__ex__mem,axiom,
% 5.46/5.77 ! [A3: set_complex,B4: set_complex] :
% 5.46/5.77 ( ( ord_less_set_complex @ A3 @ B4 )
% 5.46/5.77 => ? [B5: complex] : ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B4 @ A3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubset_imp_ex_mem
% 5.46/5.77 thf(fact_7499_psubset__imp__ex__mem,axiom,
% 5.46/5.77 ! [A3: set_real,B4: set_real] :
% 5.46/5.77 ( ( ord_less_set_real @ A3 @ B4 )
% 5.46/5.77 => ? [B5: real] : ( member_real @ B5 @ ( minus_minus_set_real @ B4 @ A3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubset_imp_ex_mem
% 5.46/5.77 thf(fact_7500_psubset__imp__ex__mem,axiom,
% 5.46/5.77 ! [A3: set_int,B4: set_int] :
% 5.46/5.77 ( ( ord_less_set_int @ A3 @ B4 )
% 5.46/5.77 => ? [B5: int] : ( member_int @ B5 @ ( minus_minus_set_int @ B4 @ A3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubset_imp_ex_mem
% 5.46/5.77 thf(fact_7501_psubset__imp__ex__mem,axiom,
% 5.46/5.77 ! [A3: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ A3 @ B4 )
% 5.46/5.77 => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B4 @ A3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubset_imp_ex_mem
% 5.46/5.77 thf(fact_7502_sinh__diff,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( sinh_real @ ( minus_minus_real @ X4 @ Y3 ) )
% 5.46/5.77 = ( minus_minus_real @ ( times_times_real @ ( sinh_real @ X4 ) @ ( cosh_real @ Y3 ) ) @ ( times_times_real @ ( cosh_real @ X4 ) @ ( sinh_real @ Y3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_diff
% 5.46/5.77 thf(fact_7503_cosh__diff,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( cosh_real @ ( minus_minus_real @ X4 @ Y3 ) )
% 5.46/5.77 = ( minus_minus_real @ ( times_times_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y3 ) ) @ ( times_times_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_diff
% 5.46/5.77 thf(fact_7504_sinh__add,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( sinh_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.77 = ( plus_plus_real @ ( times_times_real @ ( sinh_real @ X4 ) @ ( cosh_real @ Y3 ) ) @ ( times_times_real @ ( cosh_real @ X4 ) @ ( sinh_real @ Y3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_add
% 5.46/5.77 thf(fact_7505_cosh__add,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( cosh_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.77 = ( plus_plus_real @ ( times_times_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y3 ) ) @ ( times_times_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_add
% 5.46/5.77 thf(fact_7506_push__bit__nat__eq,axiom,
% 5.46/5.77 ! [N: nat,K: int] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 5.46/5.77 = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_nat_eq
% 5.46/5.77 thf(fact_7507_push__bit__minus,axiom,
% 5.46/5.77 ! [N: nat,A: code_integer] :
% 5.46/5.77 ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ A ) )
% 5.46/5.77 = ( uminus1351360451143612070nteger @ ( bit_se7788150548672797655nteger @ N @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_minus
% 5.46/5.77 thf(fact_7508_push__bit__minus,axiom,
% 5.46/5.77 ! [N: nat,A: int] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ A ) )
% 5.46/5.77 = ( uminus_uminus_int @ ( bit_se545348938243370406it_int @ N @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_minus
% 5.46/5.77 thf(fact_7509_tanh__def,axiom,
% 5.46/5.77 ( tanh_complex
% 5.46/5.77 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sinh_complex @ X ) @ ( cosh_complex @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % tanh_def
% 5.46/5.77 thf(fact_7510_tanh__def,axiom,
% 5.46/5.77 ( tanh_real
% 5.46/5.77 = ( ^ [X: real] : ( divide_divide_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % tanh_def
% 5.46/5.77 thf(fact_7511_bit__xor__int__iff,axiom,
% 5.46/5.77 ! [K: int,L2: int,N: nat] :
% 5.46/5.77 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N )
% 5.46/5.77 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.46/5.77 != ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit_xor_int_iff
% 5.46/5.77 thf(fact_7512_sinh__minus__cosh,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( minus_minus_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) )
% 5.46/5.77 = ( uminus_uminus_real @ ( exp_real @ ( uminus_uminus_real @ X4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_minus_cosh
% 5.46/5.77 thf(fact_7513_sinh__minus__cosh,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( minus_minus_complex @ ( sinh_complex @ X4 ) @ ( cosh_complex @ X4 ) )
% 5.46/5.77 = ( uminus1482373934393186551omplex @ ( exp_complex @ ( uminus1482373934393186551omplex @ X4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_minus_cosh
% 5.46/5.77 thf(fact_7514_cosh__minus__sinh,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( minus_minus_real @ ( cosh_real @ X4 ) @ ( sinh_real @ X4 ) )
% 5.46/5.77 = ( exp_real @ ( uminus_uminus_real @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_minus_sinh
% 5.46/5.77 thf(fact_7515_cosh__minus__sinh,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( minus_minus_complex @ ( cosh_complex @ X4 ) @ ( sinh_complex @ X4 ) )
% 5.46/5.77 = ( exp_complex @ ( uminus1482373934393186551omplex @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_minus_sinh
% 5.46/5.77 thf(fact_7516_XOR__lower,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % XOR_lower
% 5.46/5.77 thf(fact_7517_cosh__real__pos,axiom,
% 5.46/5.77 ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_real_pos
% 5.46/5.77 thf(fact_7518_cosh__real__nonneg,axiom,
% 5.46/5.77 ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_real_nonneg
% 5.46/5.77 thf(fact_7519_cosh__real__nonneg__le__iff,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y3 ) )
% 5.46/5.77 = ( ord_less_eq_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_real_nonneg_le_iff
% 5.46/5.77 thf(fact_7520_cosh__real__nonpos__le__iff,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.77 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.46/5.77 => ( ( ord_less_eq_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y3 ) )
% 5.46/5.77 = ( ord_less_eq_real @ Y3 @ X4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_real_nonpos_le_iff
% 5.46/5.77 thf(fact_7521_cosh__real__ge__1,axiom,
% 5.46/5.77 ! [X4: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_real_ge_1
% 5.46/5.77 thf(fact_7522_sinh__double,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( sinh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.77 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sinh_complex @ X4 ) ) @ ( cosh_complex @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_double
% 5.46/5.77 thf(fact_7523_sinh__double,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( sinh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.77 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sinh_real @ X4 ) ) @ ( cosh_real @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_double
% 5.46/5.77 thf(fact_7524_push__bit__take__bit,axiom,
% 5.46/5.77 ! [M: nat,N: nat,A: int] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.46/5.77 = ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ M @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_take_bit
% 5.46/5.77 thf(fact_7525_push__bit__take__bit,axiom,
% 5.46/5.77 ! [M: nat,N: nat,A: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.46/5.77 = ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M @ N ) @ ( bit_se547839408752420682it_nat @ M @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_take_bit
% 5.46/5.77 thf(fact_7526_take__bit__push__bit,axiom,
% 5.46/5.77 ! [M: nat,N: nat,A: int] :
% 5.46/5.77 ( ( bit_se2923211474154528505it_int @ M @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.46/5.77 = ( bit_se545348938243370406it_int @ N @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % take_bit_push_bit
% 5.46/5.77 thf(fact_7527_take__bit__push__bit,axiom,
% 5.46/5.77 ! [M: nat,N: nat,A: nat] :
% 5.46/5.77 ( ( bit_se2925701944663578781it_nat @ M @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.46/5.77 = ( bit_se547839408752420682it_nat @ N @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ M @ N ) @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % take_bit_push_bit
% 5.46/5.77 thf(fact_7528_divide__complex__def,axiom,
% 5.46/5.77 ( divide1717551699836669952omplex
% 5.46/5.77 = ( ^ [X: complex,Y: complex] : ( times_times_complex @ X @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % divide_complex_def
% 5.46/5.77 thf(fact_7529_flip__bit__nat__def,axiom,
% 5.46/5.77 ( bit_se2161824704523386999it_nat
% 5.46/5.77 = ( ^ [M6: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % flip_bit_nat_def
% 5.46/5.77 thf(fact_7530_cosh__real__strict__mono,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.77 => ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_real_strict_mono
% 5.46/5.77 thf(fact_7531_cosh__real__nonneg__less__iff,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.77 => ( ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y3 ) )
% 5.46/5.77 = ( ord_less_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_real_nonneg_less_iff
% 5.46/5.77 thf(fact_7532_cosh__real__nonpos__less__iff,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.77 => ( ( ord_less_eq_real @ Y3 @ zero_zero_real )
% 5.46/5.77 => ( ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y3 ) )
% 5.46/5.77 = ( ord_less_real @ Y3 @ X4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_real_nonpos_less_iff
% 5.46/5.77 thf(fact_7533_bit__push__bit__iff__int,axiom,
% 5.46/5.77 ! [M: nat,K: int,N: nat] :
% 5.46/5.77 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.46/5.77 = ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.77 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit_push_bit_iff_int
% 5.46/5.77 thf(fact_7534_cosh__square__eq,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.77 = ( plus_plus_real @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_square_eq
% 5.46/5.77 thf(fact_7535_cosh__square__eq,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.77 = ( plus_plus_complex @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_square_eq
% 5.46/5.77 thf(fact_7536_sinh__square__eq,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.77 = ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_square_eq
% 5.46/5.77 thf(fact_7537_sinh__square__eq,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.77 = ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_square_eq
% 5.46/5.77 thf(fact_7538_hyperbolic__pythagoras,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.77 = one_one_complex ) ).
% 5.46/5.77
% 5.46/5.77 % hyperbolic_pythagoras
% 5.46/5.77 thf(fact_7539_hyperbolic__pythagoras,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.77 = one_one_real ) ).
% 5.46/5.77
% 5.46/5.77 % hyperbolic_pythagoras
% 5.46/5.77 thf(fact_7540_xor__nat__def,axiom,
% 5.46/5.77 ( bit_se6528837805403552850or_nat
% 5.46/5.77 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % xor_nat_def
% 5.46/5.77 thf(fact_7541_psubsetE,axiom,
% 5.46/5.77 ! [A3: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ A3 @ B4 )
% 5.46/5.77 => ~ ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.46/5.77 => ( ord_less_eq_set_nat @ B4 @ A3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubsetE
% 5.46/5.77 thf(fact_7542_psubset__eq,axiom,
% 5.46/5.77 ( ord_less_set_nat
% 5.46/5.77 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A6 @ B7 )
% 5.46/5.77 & ( A6 != B7 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubset_eq
% 5.46/5.77 thf(fact_7543_psubset__imp__subset,axiom,
% 5.46/5.77 ! [A3: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ A3 @ B4 )
% 5.46/5.77 => ( ord_less_eq_set_nat @ A3 @ B4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubset_imp_subset
% 5.46/5.77 thf(fact_7544_psubset__subset__trans,axiom,
% 5.46/5.77 ! [A3: set_nat,B4: set_nat,C5: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ A3 @ B4 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ B4 @ C5 )
% 5.46/5.77 => ( ord_less_set_nat @ A3 @ C5 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % psubset_subset_trans
% 5.46/5.77 thf(fact_7545_subset__not__subset__eq,axiom,
% 5.46/5.77 ( ord_less_set_nat
% 5.46/5.77 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A6 @ B7 )
% 5.46/5.77 & ~ ( ord_less_eq_set_nat @ B7 @ A6 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % subset_not_subset_eq
% 5.46/5.77 thf(fact_7546_subset__psubset__trans,axiom,
% 5.46/5.77 ! [A3: set_nat,B4: set_nat,C5: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.46/5.77 => ( ( ord_less_set_nat @ B4 @ C5 )
% 5.46/5.77 => ( ord_less_set_nat @ A3 @ C5 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % subset_psubset_trans
% 5.46/5.77 thf(fact_7547_subset__iff__psubset__eq,axiom,
% 5.46/5.77 ( ord_less_eq_set_nat
% 5.46/5.77 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ A6 @ B7 )
% 5.46/5.77 | ( A6 = B7 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % subset_iff_psubset_eq
% 5.46/5.77 thf(fact_7548_double__diff,axiom,
% 5.46/5.77 ! [A3: set_nat,B4: set_nat,C5: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ B4 @ C5 )
% 5.46/5.77 => ( ( minus_minus_set_nat @ B4 @ ( minus_minus_set_nat @ C5 @ A3 ) )
% 5.46/5.77 = A3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % double_diff
% 5.46/5.77 thf(fact_7549_Diff__subset,axiom,
% 5.46/5.77 ! [A3: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ B4 ) @ A3 ) ).
% 5.46/5.77
% 5.46/5.77 % Diff_subset
% 5.46/5.77 thf(fact_7550_Diff__mono,axiom,
% 5.46/5.77 ! [A3: set_nat,C5: set_nat,D4: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A3 @ C5 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ D4 @ B4 )
% 5.46/5.77 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ B4 ) @ ( minus_minus_set_nat @ C5 @ D4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Diff_mono
% 5.46/5.77 thf(fact_7551_bit__push__bit__iff__nat,axiom,
% 5.46/5.77 ! [M: nat,Q2: nat,N: nat] :
% 5.46/5.77 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 5.46/5.77 = ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.77 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit_push_bit_iff_nat
% 5.46/5.77 thf(fact_7552_concat__bit__eq,axiom,
% 5.46/5.77 ( bit_concat_bit
% 5.46/5.77 = ( ^ [N2: nat,K3: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % concat_bit_eq
% 5.46/5.77 thf(fact_7553_arcosh__cosh__real,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.77 => ( ( arcosh_real @ ( cosh_real @ X4 ) )
% 5.46/5.77 = X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % arcosh_cosh_real
% 5.46/5.77 thf(fact_7554_flip__bit__eq__xor,axiom,
% 5.46/5.77 ( bit_se2159334234014336723it_int
% 5.46/5.77 = ( ^ [N2: nat,A4: int] : ( bit_se6526347334894502574or_int @ A4 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % flip_bit_eq_xor
% 5.46/5.77 thf(fact_7555_flip__bit__eq__xor,axiom,
% 5.46/5.77 ( bit_se2161824704523386999it_nat
% 5.46/5.77 = ( ^ [N2: nat,A4: nat] : ( bit_se6528837805403552850or_nat @ A4 @ ( bit_se547839408752420682it_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % flip_bit_eq_xor
% 5.46/5.77 thf(fact_7556_cosh__double,axiom,
% 5.46/5.77 ! [X4: complex] :
% 5.46/5.77 ( ( cosh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.77 = ( plus_plus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_double
% 5.46/5.77 thf(fact_7557_cosh__double,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ( ( cosh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.46/5.77 = ( plus_plus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_double
% 5.46/5.77 thf(fact_7558_push__bit__double,axiom,
% 5.46/5.77 ! [N: nat,A: int] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.46/5.77 = ( times_times_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_double
% 5.46/5.77 thf(fact_7559_push__bit__double,axiom,
% 5.46/5.77 ! [N: nat,A: nat] :
% 5.46/5.77 ( ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.77 = ( times_times_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_double
% 5.46/5.77 thf(fact_7560_bit__iff__and__push__bit__not__eq__0,axiom,
% 5.46/5.77 ( bit_se1146084159140164899it_int
% 5.46/5.77 = ( ^ [A4: int,N2: nat] :
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ A4 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) )
% 5.46/5.77 != zero_zero_int ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit_iff_and_push_bit_not_eq_0
% 5.46/5.77 thf(fact_7561_bit__iff__and__push__bit__not__eq__0,axiom,
% 5.46/5.77 ( bit_se1148574629649215175it_nat
% 5.46/5.77 = ( ^ [A4: nat,N2: nat] :
% 5.46/5.77 ( ( bit_se727722235901077358nd_nat @ A4 @ ( bit_se547839408752420682it_nat @ N2 @ one_one_nat ) )
% 5.46/5.77 != zero_zero_nat ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit_iff_and_push_bit_not_eq_0
% 5.46/5.77 thf(fact_7562_push__bit__int__def,axiom,
% 5.46/5.77 ( bit_se545348938243370406it_int
% 5.46/5.77 = ( ^ [N2: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_int_def
% 5.46/5.77 thf(fact_7563_push__bit__nat__def,axiom,
% 5.46/5.77 ( bit_se547839408752420682it_nat
% 5.46/5.77 = ( ^ [N2: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_nat_def
% 5.46/5.77 thf(fact_7564_push__bit__eq__mult,axiom,
% 5.46/5.77 ( bit_se545348938243370406it_int
% 5.46/5.77 = ( ^ [N2: nat,A4: int] : ( times_times_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_eq_mult
% 5.46/5.77 thf(fact_7565_push__bit__eq__mult,axiom,
% 5.46/5.77 ( bit_se547839408752420682it_nat
% 5.46/5.77 = ( ^ [N2: nat,A4: nat] : ( times_times_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_eq_mult
% 5.46/5.77 thf(fact_7566_exp__dvdE,axiom,
% 5.46/5.77 ! [N: nat,A: code_integer] :
% 5.46/5.77 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A )
% 5.46/5.77 => ~ ! [B5: code_integer] :
% 5.46/5.77 ( A
% 5.46/5.77 != ( bit_se7788150548672797655nteger @ N @ B5 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % exp_dvdE
% 5.46/5.77 thf(fact_7567_exp__dvdE,axiom,
% 5.46/5.77 ! [N: nat,A: int] :
% 5.46/5.77 ( ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A )
% 5.46/5.77 => ~ ! [B5: int] :
% 5.46/5.77 ( A
% 5.46/5.77 != ( bit_se545348938243370406it_int @ N @ B5 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % exp_dvdE
% 5.46/5.77 thf(fact_7568_exp__dvdE,axiom,
% 5.46/5.77 ! [N: nat,A: nat] :
% 5.46/5.77 ( ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A )
% 5.46/5.77 => ~ ! [B5: nat] :
% 5.46/5.77 ( A
% 5.46/5.77 != ( bit_se547839408752420682it_nat @ N @ B5 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % exp_dvdE
% 5.46/5.77 thf(fact_7569_push__bit__minus__one,axiom,
% 5.46/5.77 ! [N: nat] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.77 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_minus_one
% 5.46/5.77 thf(fact_7570_tanh__add,axiom,
% 5.46/5.77 ! [X4: complex,Y3: complex] :
% 5.46/5.77 ( ( ( cosh_complex @ X4 )
% 5.46/5.77 != zero_zero_complex )
% 5.46/5.77 => ( ( ( cosh_complex @ Y3 )
% 5.46/5.77 != zero_zero_complex )
% 5.46/5.77 => ( ( tanh_complex @ ( plus_plus_complex @ X4 @ Y3 ) )
% 5.46/5.77 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tanh_complex @ X4 ) @ ( tanh_complex @ Y3 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tanh_complex @ X4 ) @ ( tanh_complex @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % tanh_add
% 5.46/5.77 thf(fact_7571_tanh__add,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ( cosh_real @ X4 )
% 5.46/5.77 != zero_zero_real )
% 5.46/5.77 => ( ( ( cosh_real @ Y3 )
% 5.46/5.77 != zero_zero_real )
% 5.46/5.77 => ( ( tanh_real @ ( plus_plus_real @ X4 @ Y3 ) )
% 5.46/5.77 = ( divide_divide_real @ ( plus_plus_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y3 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % tanh_add
% 5.46/5.77 thf(fact_7572_XOR__upper,axiom,
% 5.46/5.77 ! [X4: int,N: nat,Y3: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.77 => ( ( ord_less_int @ X4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.77 => ( ( ord_less_int @ Y3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.77 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X4 @ Y3 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % XOR_upper
% 5.46/5.77 thf(fact_7573_cosh__field__def,axiom,
% 5.46/5.77 ( cosh_real
% 5.46/5.77 = ( ^ [Z5: real] : ( divide_divide_real @ ( plus_plus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_field_def
% 5.46/5.77 thf(fact_7574_cosh__field__def,axiom,
% 5.46/5.77 ( cosh_complex
% 5.46/5.77 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % cosh_field_def
% 5.46/5.77 thf(fact_7575_complex__inverse,axiom,
% 5.46/5.77 ! [A: real,B2: real] :
% 5.46/5.77 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B2 ) )
% 5.46/5.77 = ( complex2 @ ( divide_divide_real @ A @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ B2 ) @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % complex_inverse
% 5.46/5.77 thf(fact_7576_xor__int__rec,axiom,
% 5.46/5.77 ( bit_se6526347334894502574or_int
% 5.46/5.77 = ( ^ [K3: int,L: int] :
% 5.46/5.77 ( plus_plus_int
% 5.46/5.77 @ ( zero_n2684676970156552555ol_int
% 5.46/5.77 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.46/5.77 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.46/5.77 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % xor_int_rec
% 5.46/5.77 thf(fact_7577_sinh__field__def,axiom,
% 5.46/5.77 ( sinh_real
% 5.46/5.77 = ( ^ [Z5: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_field_def
% 5.46/5.77 thf(fact_7578_sinh__field__def,axiom,
% 5.46/5.77 ( sinh_complex
% 5.46/5.77 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % sinh_field_def
% 5.46/5.77 thf(fact_7579_xor__int__unfold,axiom,
% 5.46/5.77 ( bit_se6526347334894502574or_int
% 5.46/5.77 = ( ^ [K3: int,L: int] :
% 5.46/5.77 ( if_int
% 5.46/5.77 @ ( K3
% 5.46/5.77 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.77 @ ( bit_ri7919022796975470100ot_int @ L )
% 5.46/5.77 @ ( if_int
% 5.46/5.77 @ ( L
% 5.46/5.77 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.77 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.46/5.77 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % xor_int_unfold
% 5.46/5.77 thf(fact_7580_True,axiom,
% 5.46/5.77 ord_less_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ).
% 5.46/5.77
% 5.46/5.77 % True
% 5.46/5.77 thf(fact_7581_Cauchy__iff2,axiom,
% 5.46/5.77 ( topolo4055970368930404560y_real
% 5.46/5.77 = ( ^ [X6: nat > real] :
% 5.46/5.77 ! [J3: nat] :
% 5.46/5.77 ? [M8: nat] :
% 5.46/5.77 ! [M6: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M8 @ M6 )
% 5.46/5.77 => ! [N2: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M8 @ N2 )
% 5.46/5.77 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Cauchy_iff2
% 5.46/5.77 thf(fact_7582_dual__order_Orefl,axiom,
% 5.46/5.77 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.refl
% 5.46/5.77 thf(fact_7583_dual__order_Orefl,axiom,
% 5.46/5.77 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.refl
% 5.46/5.77 thf(fact_7584_dual__order_Orefl,axiom,
% 5.46/5.77 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.refl
% 5.46/5.77 thf(fact_7585_dual__order_Orefl,axiom,
% 5.46/5.77 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.refl
% 5.46/5.77 thf(fact_7586_dual__order_Orefl,axiom,
% 5.46/5.77 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.refl
% 5.46/5.77 thf(fact_7587_order__refl,axiom,
% 5.46/5.77 ! [X4: set_nat] : ( ord_less_eq_set_nat @ X4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % order_refl
% 5.46/5.77 thf(fact_7588_order__refl,axiom,
% 5.46/5.77 ! [X4: rat] : ( ord_less_eq_rat @ X4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % order_refl
% 5.46/5.77 thf(fact_7589_order__refl,axiom,
% 5.46/5.77 ! [X4: num] : ( ord_less_eq_num @ X4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % order_refl
% 5.46/5.77 thf(fact_7590_order__refl,axiom,
% 5.46/5.77 ! [X4: nat] : ( ord_less_eq_nat @ X4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % order_refl
% 5.46/5.77 thf(fact_7591_order__refl,axiom,
% 5.46/5.77 ! [X4: int] : ( ord_less_eq_int @ X4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % order_refl
% 5.46/5.77 thf(fact_7592__C5_Ohyps_C_I4_J,axiom,
% 5.46/5.77 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.46/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.46/5.77
% 5.46/5.77 % "5.hyps"(4)
% 5.46/5.77 thf(fact_7593_DiffI,axiom,
% 5.46/5.77 ! [C: extended_enat,A3: set_Extended_enat,B4: set_Extended_enat] :
% 5.46/5.77 ( ( member_Extended_enat @ C @ A3 )
% 5.46/5.77 => ( ~ ( member_Extended_enat @ C @ B4 )
% 5.46/5.77 => ( member_Extended_enat @ C @ ( minus_925952699566721837d_enat @ A3 @ B4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffI
% 5.46/5.77 thf(fact_7594_DiffI,axiom,
% 5.46/5.77 ! [C: complex,A3: set_complex,B4: set_complex] :
% 5.46/5.77 ( ( member_complex @ C @ A3 )
% 5.46/5.77 => ( ~ ( member_complex @ C @ B4 )
% 5.46/5.77 => ( member_complex @ C @ ( minus_811609699411566653omplex @ A3 @ B4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffI
% 5.46/5.77 thf(fact_7595_DiffI,axiom,
% 5.46/5.77 ! [C: real,A3: set_real,B4: set_real] :
% 5.46/5.77 ( ( member_real @ C @ A3 )
% 5.46/5.77 => ( ~ ( member_real @ C @ B4 )
% 5.46/5.77 => ( member_real @ C @ ( minus_minus_set_real @ A3 @ B4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffI
% 5.46/5.77 thf(fact_7596_DiffI,axiom,
% 5.46/5.77 ! [C: int,A3: set_int,B4: set_int] :
% 5.46/5.77 ( ( member_int @ C @ A3 )
% 5.46/5.77 => ( ~ ( member_int @ C @ B4 )
% 5.46/5.77 => ( member_int @ C @ ( minus_minus_set_int @ A3 @ B4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffI
% 5.46/5.77 thf(fact_7597_DiffI,axiom,
% 5.46/5.77 ! [C: nat,A3: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( member_nat @ C @ A3 )
% 5.46/5.77 => ( ~ ( member_nat @ C @ B4 )
% 5.46/5.77 => ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffI
% 5.46/5.77 thf(fact_7598_Diff__iff,axiom,
% 5.46/5.77 ! [C: extended_enat,A3: set_Extended_enat,B4: set_Extended_enat] :
% 5.46/5.77 ( ( member_Extended_enat @ C @ ( minus_925952699566721837d_enat @ A3 @ B4 ) )
% 5.46/5.77 = ( ( member_Extended_enat @ C @ A3 )
% 5.46/5.77 & ~ ( member_Extended_enat @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Diff_iff
% 5.46/5.77 thf(fact_7599_Diff__iff,axiom,
% 5.46/5.77 ! [C: complex,A3: set_complex,B4: set_complex] :
% 5.46/5.77 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A3 @ B4 ) )
% 5.46/5.77 = ( ( member_complex @ C @ A3 )
% 5.46/5.77 & ~ ( member_complex @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Diff_iff
% 5.46/5.77 thf(fact_7600_Diff__iff,axiom,
% 5.46/5.77 ! [C: real,A3: set_real,B4: set_real] :
% 5.46/5.77 ( ( member_real @ C @ ( minus_minus_set_real @ A3 @ B4 ) )
% 5.46/5.77 = ( ( member_real @ C @ A3 )
% 5.46/5.77 & ~ ( member_real @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Diff_iff
% 5.46/5.77 thf(fact_7601_Diff__iff,axiom,
% 5.46/5.77 ! [C: int,A3: set_int,B4: set_int] :
% 5.46/5.77 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B4 ) )
% 5.46/5.77 = ( ( member_int @ C @ A3 )
% 5.46/5.77 & ~ ( member_int @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Diff_iff
% 5.46/5.77 thf(fact_7602_Diff__iff,axiom,
% 5.46/5.77 ! [C: nat,A3: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B4 ) )
% 5.46/5.77 = ( ( member_nat @ C @ A3 )
% 5.46/5.77 & ~ ( member_nat @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Diff_iff
% 5.46/5.77 thf(fact_7603_Diff__idemp,axiom,
% 5.46/5.77 ! [A3: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A3 @ B4 ) @ B4 )
% 5.46/5.77 = ( minus_minus_set_nat @ A3 @ B4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % Diff_idemp
% 5.46/5.77 thf(fact_7604_bit_Ocompl__eq__compl__iff,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ( bit_ri7919022796975470100ot_int @ X4 )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.compl_eq_compl_iff
% 5.46/5.77 thf(fact_7605_bit_Odouble__compl,axiom,
% 5.46/5.77 ! [X4: int] :
% 5.46/5.77 ( ( bit_ri7919022796975470100ot_int @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 5.46/5.77 = X4 ) ).
% 5.46/5.77
% 5.46/5.77 % bit.double_compl
% 5.46/5.77 thf(fact_7606_bit_Oxor__compl__right,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_ri7919022796975470100ot_int @ Y3 ) )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X4 @ Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.xor_compl_right
% 5.46/5.77 thf(fact_7607_bit_Oxor__compl__left,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ Y3 )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X4 @ Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.xor_compl_left
% 5.46/5.77 thf(fact_7608_bit_Oconj__cancel__right,axiom,
% 5.46/5.77 ! [X4: int] :
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ X4 @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 5.46/5.77 = zero_zero_int ) ).
% 5.46/5.77
% 5.46/5.77 % bit.conj_cancel_right
% 5.46/5.77 thf(fact_7609_bit_Oconj__cancel__left,axiom,
% 5.46/5.77 ! [X4: int] :
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ X4 )
% 5.46/5.77 = zero_zero_int ) ).
% 5.46/5.77
% 5.46/5.77 % bit.conj_cancel_left
% 5.46/5.77 thf(fact_7610_bit_Ocompl__zero,axiom,
% 5.46/5.77 ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 5.46/5.77 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.compl_zero
% 5.46/5.77 thf(fact_7611_bit_Ocompl__zero,axiom,
% 5.46/5.77 ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 5.46/5.77 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.compl_zero
% 5.46/5.77 thf(fact_7612_bit_Ocompl__one,axiom,
% 5.46/5.77 ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.77 = zero_z3403309356797280102nteger ) ).
% 5.46/5.77
% 5.46/5.77 % bit.compl_one
% 5.46/5.77 thf(fact_7613_bit_Ocompl__one,axiom,
% 5.46/5.77 ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.77 = zero_zero_int ) ).
% 5.46/5.77
% 5.46/5.77 % bit.compl_one
% 5.46/5.77 thf(fact_7614_bit_Oxor__one__left,axiom,
% 5.46/5.77 ! [X4: code_integer] :
% 5.46/5.77 ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X4 )
% 5.46/5.77 = ( bit_ri7632146776885996613nteger @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.xor_one_left
% 5.46/5.77 thf(fact_7615_bit_Oxor__one__left,axiom,
% 5.46/5.77 ! [X4: int] :
% 5.46/5.77 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X4 )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.xor_one_left
% 5.46/5.77 thf(fact_7616_bit_Oxor__one__right,axiom,
% 5.46/5.77 ! [X4: code_integer] :
% 5.46/5.77 ( ( bit_se3222712562003087583nteger @ X4 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.77 = ( bit_ri7632146776885996613nteger @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.xor_one_right
% 5.46/5.77 thf(fact_7617_bit_Oxor__one__right,axiom,
% 5.46/5.77 ! [X4: int] :
% 5.46/5.77 ( ( bit_se6526347334894502574or_int @ X4 @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.xor_one_right
% 5.46/5.77 thf(fact_7618_bit_Oxor__cancel__left,axiom,
% 5.46/5.77 ! [X4: code_integer] :
% 5.46/5.77 ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X4 ) @ X4 )
% 5.46/5.77 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.xor_cancel_left
% 5.46/5.77 thf(fact_7619_bit_Oxor__cancel__left,axiom,
% 5.46/5.77 ! [X4: int] :
% 5.46/5.77 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ X4 )
% 5.46/5.77 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.xor_cancel_left
% 5.46/5.77 thf(fact_7620_bit_Oxor__cancel__right,axiom,
% 5.46/5.77 ! [X4: code_integer] :
% 5.46/5.77 ( ( bit_se3222712562003087583nteger @ X4 @ ( bit_ri7632146776885996613nteger @ X4 ) )
% 5.46/5.77 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.xor_cancel_right
% 5.46/5.77 thf(fact_7621_bit_Oxor__cancel__right,axiom,
% 5.46/5.77 ! [X4: int] :
% 5.46/5.77 ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 5.46/5.77 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit.xor_cancel_right
% 5.46/5.77 thf(fact_7622_not__negative__int__iff,axiom,
% 5.46/5.77 ! [K: int] :
% 5.46/5.77 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.46/5.77 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_negative_int_iff
% 5.46/5.77 thf(fact_7623_not__nonnegative__int__iff,axiom,
% 5.46/5.77 ! [K: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.46/5.77 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_nonnegative_int_iff
% 5.46/5.77 thf(fact_7624_minus__not__numeral__eq,axiom,
% 5.46/5.77 ! [N: num] :
% 5.46/5.77 ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.46/5.77 = ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % minus_not_numeral_eq
% 5.46/5.77 thf(fact_7625_minus__not__numeral__eq,axiom,
% 5.46/5.77 ! [N: num] :
% 5.46/5.77 ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.77 = ( numeral_numeral_int @ ( inc @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % minus_not_numeral_eq
% 5.46/5.77 thf(fact_7626_even__not__iff,axiom,
% 5.46/5.77 ! [A: code_integer] :
% 5.46/5.77 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri7632146776885996613nteger @ A ) )
% 5.46/5.77 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % even_not_iff
% 5.46/5.77 thf(fact_7627_even__not__iff,axiom,
% 5.46/5.77 ! [A: int] :
% 5.46/5.77 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.46/5.77 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % even_not_iff
% 5.46/5.77 thf(fact_7628_push__bit__minus__one__eq__not__mask,axiom,
% 5.46/5.77 ! [N: nat] :
% 5.46/5.77 ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.46/5.77 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_minus_one_eq_not_mask
% 5.46/5.77 thf(fact_7629_push__bit__minus__one__eq__not__mask,axiom,
% 5.46/5.77 ! [N: nat] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_minus_one_eq_not_mask
% 5.46/5.77 thf(fact_7630_not__one__eq,axiom,
% 5.46/5.77 ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 5.46/5.77 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_one_eq
% 5.46/5.77 thf(fact_7631_not__one__eq,axiom,
% 5.46/5.77 ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 5.46/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_one_eq
% 5.46/5.77 thf(fact_7632_length__induct,axiom,
% 5.46/5.77 ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.46/5.77 ( ! [Xs3: list_VEBT_VEBT] :
% 5.46/5.77 ( ! [Ys: list_VEBT_VEBT] :
% 5.46/5.77 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.46/5.77 => ( P @ Ys ) )
% 5.46/5.77 => ( P @ Xs3 ) )
% 5.46/5.77 => ( P @ Xs2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % length_induct
% 5.46/5.77 thf(fact_7633_length__induct,axiom,
% 5.46/5.77 ! [P: list_o > $o,Xs2: list_o] :
% 5.46/5.77 ( ! [Xs3: list_o] :
% 5.46/5.77 ( ! [Ys: list_o] :
% 5.46/5.77 ( ( ord_less_nat @ ( size_size_list_o @ Ys ) @ ( size_size_list_o @ Xs3 ) )
% 5.46/5.77 => ( P @ Ys ) )
% 5.46/5.77 => ( P @ Xs3 ) )
% 5.46/5.77 => ( P @ Xs2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % length_induct
% 5.46/5.77 thf(fact_7634_length__induct,axiom,
% 5.46/5.77 ! [P: list_nat > $o,Xs2: list_nat] :
% 5.46/5.77 ( ! [Xs3: list_nat] :
% 5.46/5.77 ( ! [Ys: list_nat] :
% 5.46/5.77 ( ( ord_less_nat @ ( size_size_list_nat @ Ys ) @ ( size_size_list_nat @ Xs3 ) )
% 5.46/5.77 => ( P @ Ys ) )
% 5.46/5.77 => ( P @ Xs3 ) )
% 5.46/5.77 => ( P @ Xs2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % length_induct
% 5.46/5.77 thf(fact_7635_length__induct,axiom,
% 5.46/5.77 ! [P: list_int > $o,Xs2: list_int] :
% 5.46/5.77 ( ! [Xs3: list_int] :
% 5.46/5.77 ( ! [Ys: list_int] :
% 5.46/5.77 ( ( ord_less_nat @ ( size_size_list_int @ Ys ) @ ( size_size_list_int @ Xs3 ) )
% 5.46/5.77 => ( P @ Ys ) )
% 5.46/5.77 => ( P @ Xs3 ) )
% 5.46/5.77 => ( P @ Xs2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % length_induct
% 5.46/5.77 thf(fact_7636_DiffE,axiom,
% 5.46/5.77 ! [C: extended_enat,A3: set_Extended_enat,B4: set_Extended_enat] :
% 5.46/5.77 ( ( member_Extended_enat @ C @ ( minus_925952699566721837d_enat @ A3 @ B4 ) )
% 5.46/5.77 => ~ ( ( member_Extended_enat @ C @ A3 )
% 5.46/5.77 => ( member_Extended_enat @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffE
% 5.46/5.77 thf(fact_7637_DiffE,axiom,
% 5.46/5.77 ! [C: complex,A3: set_complex,B4: set_complex] :
% 5.46/5.77 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A3 @ B4 ) )
% 5.46/5.77 => ~ ( ( member_complex @ C @ A3 )
% 5.46/5.77 => ( member_complex @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffE
% 5.46/5.77 thf(fact_7638_DiffE,axiom,
% 5.46/5.77 ! [C: real,A3: set_real,B4: set_real] :
% 5.46/5.77 ( ( member_real @ C @ ( minus_minus_set_real @ A3 @ B4 ) )
% 5.46/5.77 => ~ ( ( member_real @ C @ A3 )
% 5.46/5.77 => ( member_real @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffE
% 5.46/5.77 thf(fact_7639_DiffE,axiom,
% 5.46/5.77 ! [C: int,A3: set_int,B4: set_int] :
% 5.46/5.77 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B4 ) )
% 5.46/5.77 => ~ ( ( member_int @ C @ A3 )
% 5.46/5.77 => ( member_int @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffE
% 5.46/5.77 thf(fact_7640_DiffE,axiom,
% 5.46/5.77 ! [C: nat,A3: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B4 ) )
% 5.46/5.77 => ~ ( ( member_nat @ C @ A3 )
% 5.46/5.77 => ( member_nat @ C @ B4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffE
% 5.46/5.77 thf(fact_7641_DiffD1,axiom,
% 5.46/5.77 ! [C: extended_enat,A3: set_Extended_enat,B4: set_Extended_enat] :
% 5.46/5.77 ( ( member_Extended_enat @ C @ ( minus_925952699566721837d_enat @ A3 @ B4 ) )
% 5.46/5.77 => ( member_Extended_enat @ C @ A3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffD1
% 5.46/5.77 thf(fact_7642_DiffD1,axiom,
% 5.46/5.77 ! [C: complex,A3: set_complex,B4: set_complex] :
% 5.46/5.77 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A3 @ B4 ) )
% 5.46/5.77 => ( member_complex @ C @ A3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffD1
% 5.46/5.77 thf(fact_7643_DiffD1,axiom,
% 5.46/5.77 ! [C: real,A3: set_real,B4: set_real] :
% 5.46/5.77 ( ( member_real @ C @ ( minus_minus_set_real @ A3 @ B4 ) )
% 5.46/5.77 => ( member_real @ C @ A3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffD1
% 5.46/5.77 thf(fact_7644_DiffD1,axiom,
% 5.46/5.77 ! [C: int,A3: set_int,B4: set_int] :
% 5.46/5.77 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B4 ) )
% 5.46/5.77 => ( member_int @ C @ A3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffD1
% 5.46/5.77 thf(fact_7645_DiffD1,axiom,
% 5.46/5.77 ! [C: nat,A3: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B4 ) )
% 5.46/5.77 => ( member_nat @ C @ A3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffD1
% 5.46/5.77 thf(fact_7646_DiffD2,axiom,
% 5.46/5.77 ! [C: extended_enat,A3: set_Extended_enat,B4: set_Extended_enat] :
% 5.46/5.77 ( ( member_Extended_enat @ C @ ( minus_925952699566721837d_enat @ A3 @ B4 ) )
% 5.46/5.77 => ~ ( member_Extended_enat @ C @ B4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffD2
% 5.46/5.77 thf(fact_7647_DiffD2,axiom,
% 5.46/5.77 ! [C: complex,A3: set_complex,B4: set_complex] :
% 5.46/5.77 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A3 @ B4 ) )
% 5.46/5.77 => ~ ( member_complex @ C @ B4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffD2
% 5.46/5.77 thf(fact_7648_DiffD2,axiom,
% 5.46/5.77 ! [C: real,A3: set_real,B4: set_real] :
% 5.46/5.77 ( ( member_real @ C @ ( minus_minus_set_real @ A3 @ B4 ) )
% 5.46/5.77 => ~ ( member_real @ C @ B4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffD2
% 5.46/5.77 thf(fact_7649_DiffD2,axiom,
% 5.46/5.77 ! [C: int,A3: set_int,B4: set_int] :
% 5.46/5.77 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B4 ) )
% 5.46/5.77 => ~ ( member_int @ C @ B4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffD2
% 5.46/5.77 thf(fact_7650_DiffD2,axiom,
% 5.46/5.77 ! [C: nat,A3: set_nat,B4: set_nat] :
% 5.46/5.77 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B4 ) )
% 5.46/5.77 => ~ ( member_nat @ C @ B4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % DiffD2
% 5.46/5.77 thf(fact_7651_take__bit__not__iff,axiom,
% 5.46/5.77 ! [N: nat,A: int,B2: int] :
% 5.46/5.77 ( ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.46/5.77 = ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ B2 ) ) )
% 5.46/5.77 = ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.46/5.77 = ( bit_se2923211474154528505it_int @ N @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % take_bit_not_iff
% 5.46/5.77 thf(fact_7652_take__bit__not__take__bit,axiom,
% 5.46/5.77 ! [N: nat,A: int] :
% 5.46/5.77 ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.46/5.77 = ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % take_bit_not_take_bit
% 5.46/5.77 thf(fact_7653_bit__not__int__iff,axiom,
% 5.46/5.77 ! [K: int,N: nat] :
% 5.46/5.77 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 5.46/5.77 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit_not_int_iff
% 5.46/5.77 thf(fact_7654_of__int__not__eq,axiom,
% 5.46/5.77 ! [K: int] :
% 5.46/5.77 ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ ( ring_1_of_int_int @ K ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % of_int_not_eq
% 5.46/5.77 thf(fact_7655_size__neq__size__imp__neq,axiom,
% 5.46/5.77 ! [X4: list_VEBT_VEBT,Y3: list_VEBT_VEBT] :
% 5.46/5.77 ( ( ( size_s6755466524823107622T_VEBT @ X4 )
% 5.46/5.77 != ( size_s6755466524823107622T_VEBT @ Y3 ) )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % size_neq_size_imp_neq
% 5.46/5.77 thf(fact_7656_size__neq__size__imp__neq,axiom,
% 5.46/5.77 ! [X4: list_o,Y3: list_o] :
% 5.46/5.77 ( ( ( size_size_list_o @ X4 )
% 5.46/5.77 != ( size_size_list_o @ Y3 ) )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % size_neq_size_imp_neq
% 5.46/5.77 thf(fact_7657_size__neq__size__imp__neq,axiom,
% 5.46/5.77 ! [X4: list_nat,Y3: list_nat] :
% 5.46/5.77 ( ( ( size_size_list_nat @ X4 )
% 5.46/5.77 != ( size_size_list_nat @ Y3 ) )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % size_neq_size_imp_neq
% 5.46/5.77 thf(fact_7658_size__neq__size__imp__neq,axiom,
% 5.46/5.77 ! [X4: list_int,Y3: list_int] :
% 5.46/5.77 ( ( ( size_size_list_int @ X4 )
% 5.46/5.77 != ( size_size_list_int @ Y3 ) )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % size_neq_size_imp_neq
% 5.46/5.77 thf(fact_7659_size__neq__size__imp__neq,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ( size_size_num @ X4 )
% 5.46/5.77 != ( size_size_num @ Y3 ) )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % size_neq_size_imp_neq
% 5.46/5.77 thf(fact_7660_of__int__not__numeral,axiom,
% 5.46/5.77 ! [K: num] :
% 5.46/5.77 ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % of_int_not_numeral
% 5.46/5.77 thf(fact_7661_not__add__distrib,axiom,
% 5.46/5.77 ! [A: int,B2: int] :
% 5.46/5.77 ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B2 ) )
% 5.46/5.77 = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_add_distrib
% 5.46/5.77 thf(fact_7662_not__diff__distrib,axiom,
% 5.46/5.77 ! [A: int,B2: int] :
% 5.46/5.77 ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B2 ) )
% 5.46/5.77 = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_diff_distrib
% 5.46/5.77 thf(fact_7663_minus__eq__not__plus__1,axiom,
% 5.46/5.77 ( uminus1351360451143612070nteger
% 5.46/5.77 = ( ^ [A4: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A4 ) @ one_one_Code_integer ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % minus_eq_not_plus_1
% 5.46/5.77 thf(fact_7664_minus__eq__not__plus__1,axiom,
% 5.46/5.77 ( uminus_uminus_int
% 5.46/5.77 = ( ^ [A4: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A4 ) @ one_one_int ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % minus_eq_not_plus_1
% 5.46/5.77 thf(fact_7665_not__eq__complement,axiom,
% 5.46/5.77 ( bit_ri7632146776885996613nteger
% 5.46/5.77 = ( ^ [A4: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A4 ) @ one_one_Code_integer ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_eq_complement
% 5.46/5.77 thf(fact_7666_not__eq__complement,axiom,
% 5.46/5.77 ( bit_ri7919022796975470100ot_int
% 5.46/5.77 = ( ^ [A4: int] : ( minus_minus_int @ ( uminus_uminus_int @ A4 ) @ one_one_int ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_eq_complement
% 5.46/5.77 thf(fact_7667_minus__eq__not__minus__1,axiom,
% 5.46/5.77 ( uminus1351360451143612070nteger
% 5.46/5.77 = ( ^ [A4: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A4 @ one_one_Code_integer ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % minus_eq_not_minus_1
% 5.46/5.77 thf(fact_7668_minus__eq__not__minus__1,axiom,
% 5.46/5.77 ( uminus_uminus_int
% 5.46/5.77 = ( ^ [A4: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A4 @ one_one_int ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % minus_eq_not_minus_1
% 5.46/5.77 thf(fact_7669_not__int__def,axiom,
% 5.46/5.77 ( bit_ri7919022796975470100ot_int
% 5.46/5.77 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_int_def
% 5.46/5.77 thf(fact_7670_and__not__numerals_I1_J,axiom,
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.77 = zero_zero_int ) ).
% 5.46/5.77
% 5.46/5.77 % and_not_numerals(1)
% 5.46/5.77 thf(fact_7671_disjunctive__diff,axiom,
% 5.46/5.77 ! [B2: int,A: int] :
% 5.46/5.77 ( ! [N4: nat] :
% 5.46/5.77 ( ( bit_se1146084159140164899it_int @ B2 @ N4 )
% 5.46/5.77 => ( bit_se1146084159140164899it_int @ A @ N4 ) )
% 5.46/5.77 => ( ( minus_minus_int @ A @ B2 )
% 5.46/5.77 = ( bit_se725231765392027082nd_int @ A @ ( bit_ri7919022796975470100ot_int @ B2 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % disjunctive_diff
% 5.46/5.77 thf(fact_7672_nle__le,axiom,
% 5.46/5.77 ! [A: rat,B2: rat] :
% 5.46/5.77 ( ( ~ ( ord_less_eq_rat @ A @ B2 ) )
% 5.46/5.77 = ( ( ord_less_eq_rat @ B2 @ A )
% 5.46/5.77 & ( B2 != A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % nle_le
% 5.46/5.77 thf(fact_7673_nle__le,axiom,
% 5.46/5.77 ! [A: num,B2: num] :
% 5.46/5.77 ( ( ~ ( ord_less_eq_num @ A @ B2 ) )
% 5.46/5.77 = ( ( ord_less_eq_num @ B2 @ A )
% 5.46/5.77 & ( B2 != A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % nle_le
% 5.46/5.77 thf(fact_7674_nle__le,axiom,
% 5.46/5.77 ! [A: nat,B2: nat] :
% 5.46/5.77 ( ( ~ ( ord_less_eq_nat @ A @ B2 ) )
% 5.46/5.77 = ( ( ord_less_eq_nat @ B2 @ A )
% 5.46/5.77 & ( B2 != A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % nle_le
% 5.46/5.77 thf(fact_7675_nle__le,axiom,
% 5.46/5.77 ! [A: int,B2: int] :
% 5.46/5.77 ( ( ~ ( ord_less_eq_int @ A @ B2 ) )
% 5.46/5.77 = ( ( ord_less_eq_int @ B2 @ A )
% 5.46/5.77 & ( B2 != A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % nle_le
% 5.46/5.77 thf(fact_7676_le__cases3,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat,Z: rat] :
% 5.46/5.77 ( ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_eq_rat @ Y3 @ Z ) )
% 5.46/5.77 => ( ( ( ord_less_eq_rat @ Y3 @ X4 )
% 5.46/5.77 => ~ ( ord_less_eq_rat @ X4 @ Z ) )
% 5.46/5.77 => ( ( ( ord_less_eq_rat @ X4 @ Z )
% 5.46/5.77 => ~ ( ord_less_eq_rat @ Z @ Y3 ) )
% 5.46/5.77 => ( ( ( ord_less_eq_rat @ Z @ Y3 )
% 5.46/5.77 => ~ ( ord_less_eq_rat @ Y3 @ X4 ) )
% 5.46/5.77 => ( ( ( ord_less_eq_rat @ Y3 @ Z )
% 5.46/5.77 => ~ ( ord_less_eq_rat @ Z @ X4 ) )
% 5.46/5.77 => ~ ( ( ord_less_eq_rat @ Z @ X4 )
% 5.46/5.77 => ~ ( ord_less_eq_rat @ X4 @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % le_cases3
% 5.46/5.77 thf(fact_7677_le__cases3,axiom,
% 5.46/5.77 ! [X4: num,Y3: num,Z: num] :
% 5.46/5.77 ( ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_eq_num @ Y3 @ Z ) )
% 5.46/5.77 => ( ( ( ord_less_eq_num @ Y3 @ X4 )
% 5.46/5.77 => ~ ( ord_less_eq_num @ X4 @ Z ) )
% 5.46/5.77 => ( ( ( ord_less_eq_num @ X4 @ Z )
% 5.46/5.77 => ~ ( ord_less_eq_num @ Z @ Y3 ) )
% 5.46/5.77 => ( ( ( ord_less_eq_num @ Z @ Y3 )
% 5.46/5.77 => ~ ( ord_less_eq_num @ Y3 @ X4 ) )
% 5.46/5.77 => ( ( ( ord_less_eq_num @ Y3 @ Z )
% 5.46/5.77 => ~ ( ord_less_eq_num @ Z @ X4 ) )
% 5.46/5.77 => ~ ( ( ord_less_eq_num @ Z @ X4 )
% 5.46/5.77 => ~ ( ord_less_eq_num @ X4 @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % le_cases3
% 5.46/5.77 thf(fact_7678_le__cases3,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat,Z: nat] :
% 5.46/5.77 ( ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_eq_nat @ Y3 @ Z ) )
% 5.46/5.77 => ( ( ( ord_less_eq_nat @ Y3 @ X4 )
% 5.46/5.77 => ~ ( ord_less_eq_nat @ X4 @ Z ) )
% 5.46/5.77 => ( ( ( ord_less_eq_nat @ X4 @ Z )
% 5.46/5.77 => ~ ( ord_less_eq_nat @ Z @ Y3 ) )
% 5.46/5.77 => ( ( ( ord_less_eq_nat @ Z @ Y3 )
% 5.46/5.77 => ~ ( ord_less_eq_nat @ Y3 @ X4 ) )
% 5.46/5.77 => ( ( ( ord_less_eq_nat @ Y3 @ Z )
% 5.46/5.77 => ~ ( ord_less_eq_nat @ Z @ X4 ) )
% 5.46/5.77 => ~ ( ( ord_less_eq_nat @ Z @ X4 )
% 5.46/5.77 => ~ ( ord_less_eq_nat @ X4 @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % le_cases3
% 5.46/5.77 thf(fact_7679_le__cases3,axiom,
% 5.46/5.77 ! [X4: int,Y3: int,Z: int] :
% 5.46/5.77 ( ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_eq_int @ Y3 @ Z ) )
% 5.46/5.77 => ( ( ( ord_less_eq_int @ Y3 @ X4 )
% 5.46/5.77 => ~ ( ord_less_eq_int @ X4 @ Z ) )
% 5.46/5.77 => ( ( ( ord_less_eq_int @ X4 @ Z )
% 5.46/5.77 => ~ ( ord_less_eq_int @ Z @ Y3 ) )
% 5.46/5.77 => ( ( ( ord_less_eq_int @ Z @ Y3 )
% 5.46/5.77 => ~ ( ord_less_eq_int @ Y3 @ X4 ) )
% 5.46/5.77 => ( ( ( ord_less_eq_int @ Y3 @ Z )
% 5.46/5.77 => ~ ( ord_less_eq_int @ Z @ X4 ) )
% 5.46/5.77 => ~ ( ( ord_less_eq_int @ Z @ X4 )
% 5.46/5.77 => ~ ( ord_less_eq_int @ X4 @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % le_cases3
% 5.46/5.77 thf(fact_7680_order__class_Oorder__eq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: set_nat,Z4: set_nat] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [X: set_nat,Y: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.46/5.77 & ( ord_less_eq_set_nat @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_class.order_eq_iff
% 5.46/5.77 thf(fact_7681_order__class_Oorder__eq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [X: rat,Y: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X @ Y )
% 5.46/5.77 & ( ord_less_eq_rat @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_class.order_eq_iff
% 5.46/5.77 thf(fact_7682_order__class_Oorder__eq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [X: num,Y: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X @ Y )
% 5.46/5.77 & ( ord_less_eq_num @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_class.order_eq_iff
% 5.46/5.77 thf(fact_7683_order__class_Oorder__eq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [X: nat,Y: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X @ Y )
% 5.46/5.77 & ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_class.order_eq_iff
% 5.46/5.77 thf(fact_7684_order__class_Oorder__eq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [X: int,Y: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ X @ Y )
% 5.46/5.77 & ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_class.order_eq_iff
% 5.46/5.77 thf(fact_7685_ord__eq__le__trans,axiom,
% 5.46/5.77 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 5.46/5.77 ( ( A = B2 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 5.46/5.77 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_trans
% 5.46/5.77 thf(fact_7686_ord__eq__le__trans,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( A = B2 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_trans
% 5.46/5.77 thf(fact_7687_ord__eq__le__trans,axiom,
% 5.46/5.77 ! [A: num,B2: num,C: num] :
% 5.46/5.77 ( ( A = B2 )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.77 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_trans
% 5.46/5.77 thf(fact_7688_ord__eq__le__trans,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.77 ( ( A = B2 )
% 5.46/5.77 => ( ( ord_less_eq_nat @ B2 @ C )
% 5.46/5.77 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_trans
% 5.46/5.77 thf(fact_7689_ord__eq__le__trans,axiom,
% 5.46/5.77 ! [A: int,B2: int,C: int] :
% 5.46/5.77 ( ( A = B2 )
% 5.46/5.77 => ( ( ord_less_eq_int @ B2 @ C )
% 5.46/5.77 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_trans
% 5.46/5.77 thf(fact_7690_ord__le__eq__trans,axiom,
% 5.46/5.77 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A @ B2 )
% 5.46/5.77 => ( ( B2 = C )
% 5.46/5.77 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_trans
% 5.46/5.77 thf(fact_7691_ord__le__eq__trans,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( B2 = C )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_trans
% 5.46/5.77 thf(fact_7692_ord__le__eq__trans,axiom,
% 5.46/5.77 ! [A: num,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( B2 = C )
% 5.46/5.77 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_trans
% 5.46/5.77 thf(fact_7693_ord__le__eq__trans,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.77 => ( ( B2 = C )
% 5.46/5.77 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_trans
% 5.46/5.77 thf(fact_7694_ord__le__eq__trans,axiom,
% 5.46/5.77 ! [A: int,B2: int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.77 => ( ( B2 = C )
% 5.46/5.77 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_trans
% 5.46/5.77 thf(fact_7695_order__antisym,axiom,
% 5.46/5.77 ! [X4: set_nat,Y3: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ Y3 @ X4 )
% 5.46/5.77 => ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_antisym
% 5.46/5.77 thf(fact_7696_order__antisym,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ Y3 @ X4 )
% 5.46/5.77 => ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_antisym
% 5.46/5.77 thf(fact_7697_order__antisym,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_num @ Y3 @ X4 )
% 5.46/5.77 => ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_antisym
% 5.46/5.77 thf(fact_7698_order__antisym,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_nat @ Y3 @ X4 )
% 5.46/5.77 => ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_antisym
% 5.46/5.77 thf(fact_7699_order__antisym,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_int @ Y3 @ X4 )
% 5.46/5.77 => ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_antisym
% 5.46/5.77 thf(fact_7700_order_Otrans,axiom,
% 5.46/5.77 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 5.46/5.77 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.trans
% 5.46/5.77 thf(fact_7701_order_Otrans,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.trans
% 5.46/5.77 thf(fact_7702_order_Otrans,axiom,
% 5.46/5.77 ! [A: num,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.77 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.trans
% 5.46/5.77 thf(fact_7703_order_Otrans,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_nat @ B2 @ C )
% 5.46/5.77 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.trans
% 5.46/5.77 thf(fact_7704_order_Otrans,axiom,
% 5.46/5.77 ! [A: int,B2: int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_int @ B2 @ C )
% 5.46/5.77 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.trans
% 5.46/5.77 thf(fact_7705_order__trans,axiom,
% 5.46/5.77 ! [X4: set_nat,Y3: set_nat,Z: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ Y3 @ Z )
% 5.46/5.77 => ( ord_less_eq_set_nat @ X4 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_trans
% 5.46/5.77 thf(fact_7706_order__trans,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat,Z: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ Y3 @ Z )
% 5.46/5.77 => ( ord_less_eq_rat @ X4 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_trans
% 5.46/5.77 thf(fact_7707_order__trans,axiom,
% 5.46/5.77 ! [X4: num,Y3: num,Z: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_num @ Y3 @ Z )
% 5.46/5.77 => ( ord_less_eq_num @ X4 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_trans
% 5.46/5.77 thf(fact_7708_order__trans,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat,Z: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_nat @ Y3 @ Z )
% 5.46/5.77 => ( ord_less_eq_nat @ X4 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_trans
% 5.46/5.77 thf(fact_7709_order__trans,axiom,
% 5.46/5.77 ! [X4: int,Y3: int,Z: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.46/5.77 => ( ord_less_eq_int @ X4 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_trans
% 5.46/5.77 thf(fact_7710_linorder__wlog,axiom,
% 5.46/5.77 ! [P: rat > rat > $o,A: rat,B2: rat] :
% 5.46/5.77 ( ! [A5: rat,B5: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( ! [A5: rat,B5: rat] :
% 5.46/5.77 ( ( P @ B5 @ A5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( P @ A @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_wlog
% 5.46/5.77 thf(fact_7711_linorder__wlog,axiom,
% 5.46/5.77 ! [P: num > num > $o,A: num,B2: num] :
% 5.46/5.77 ( ! [A5: num,B5: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( ! [A5: num,B5: num] :
% 5.46/5.77 ( ( P @ B5 @ A5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( P @ A @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_wlog
% 5.46/5.77 thf(fact_7712_linorder__wlog,axiom,
% 5.46/5.77 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 5.46/5.77 ( ! [A5: nat,B5: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( ! [A5: nat,B5: nat] :
% 5.46/5.77 ( ( P @ B5 @ A5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( P @ A @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_wlog
% 5.46/5.77 thf(fact_7713_linorder__wlog,axiom,
% 5.46/5.77 ! [P: int > int > $o,A: int,B2: int] :
% 5.46/5.77 ( ! [A5: int,B5: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( ! [A5: int,B5: int] :
% 5.46/5.77 ( ( P @ B5 @ A5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( P @ A @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_wlog
% 5.46/5.77 thf(fact_7714_dual__order_Oeq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: set_nat,Z4: set_nat] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [A4: set_nat,B3: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 5.46/5.77 & ( ord_less_eq_set_nat @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.eq_iff
% 5.46/5.77 thf(fact_7715_dual__order_Oeq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [A4: rat,B3: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.46/5.77 & ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.eq_iff
% 5.46/5.77 thf(fact_7716_dual__order_Oeq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [A4: num,B3: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.46/5.77 & ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.eq_iff
% 5.46/5.77 thf(fact_7717_dual__order_Oeq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [A4: nat,B3: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.46/5.77 & ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.eq_iff
% 5.46/5.77 thf(fact_7718_dual__order_Oeq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [A4: int,B3: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.46/5.77 & ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.eq_iff
% 5.46/5.77 thf(fact_7719_dual__order_Oantisym,axiom,
% 5.46/5.77 ! [B2: set_nat,A: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ A @ B2 )
% 5.46/5.77 => ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.antisym
% 5.46/5.77 thf(fact_7720_dual__order_Oantisym,axiom,
% 5.46/5.77 ! [B2: rat,A: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.antisym
% 5.46/5.77 thf(fact_7721_dual__order_Oantisym,axiom,
% 5.46/5.77 ! [B2: num,A: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.antisym
% 5.46/5.77 thf(fact_7722_dual__order_Oantisym,axiom,
% 5.46/5.77 ! [B2: nat,A: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.77 => ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.antisym
% 5.46/5.77 thf(fact_7723_dual__order_Oantisym,axiom,
% 5.46/5.77 ! [B2: int,A: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.77 => ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.antisym
% 5.46/5.77 thf(fact_7724_dual__order_Otrans,axiom,
% 5.46/5.77 ! [B2: set_nat,A: set_nat,C: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ C @ B2 )
% 5.46/5.77 => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.trans
% 5.46/5.77 thf(fact_7725_dual__order_Otrans,axiom,
% 5.46/5.77 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_rat @ C @ B2 )
% 5.46/5.77 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.trans
% 5.46/5.77 thf(fact_7726_dual__order_Otrans,axiom,
% 5.46/5.77 ! [B2: num,A: num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_num @ C @ B2 )
% 5.46/5.77 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.trans
% 5.46/5.77 thf(fact_7727_dual__order_Otrans,axiom,
% 5.46/5.77 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_nat @ C @ B2 )
% 5.46/5.77 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.trans
% 5.46/5.77 thf(fact_7728_dual__order_Otrans,axiom,
% 5.46/5.77 ! [B2: int,A: int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_int @ C @ B2 )
% 5.46/5.77 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.trans
% 5.46/5.77 thf(fact_7729_antisym,axiom,
% 5.46/5.77 ! [A: set_nat,B2: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ B2 @ A )
% 5.46/5.77 => ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym
% 5.46/5.77 thf(fact_7730_antisym,axiom,
% 5.46/5.77 ! [A: rat,B2: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ A )
% 5.46/5.77 => ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym
% 5.46/5.77 thf(fact_7731_antisym,axiom,
% 5.46/5.77 ! [A: num,B2: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ A )
% 5.46/5.77 => ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym
% 5.46/5.77 thf(fact_7732_antisym,axiom,
% 5.46/5.77 ! [A: nat,B2: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_nat @ B2 @ A )
% 5.46/5.77 => ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym
% 5.46/5.77 thf(fact_7733_antisym,axiom,
% 5.46/5.77 ! [A: int,B2: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_int @ B2 @ A )
% 5.46/5.77 => ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym
% 5.46/5.77 thf(fact_7734_Orderings_Oorder__eq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: set_nat,Z4: set_nat] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [A4: set_nat,B3: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 5.46/5.77 & ( ord_less_eq_set_nat @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Orderings.order_eq_iff
% 5.46/5.77 thf(fact_7735_Orderings_Oorder__eq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [A4: rat,B3: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.46/5.77 & ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Orderings.order_eq_iff
% 5.46/5.77 thf(fact_7736_Orderings_Oorder__eq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [A4: num,B3: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.46/5.77 & ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Orderings.order_eq_iff
% 5.46/5.77 thf(fact_7737_Orderings_Oorder__eq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [A4: nat,B3: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.46/5.77 & ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Orderings.order_eq_iff
% 5.46/5.77 thf(fact_7738_Orderings_Oorder__eq__iff,axiom,
% 5.46/5.77 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.77 = ( ^ [A4: int,B3: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.46/5.77 & ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Orderings.order_eq_iff
% 5.46/5.77 thf(fact_7739_order__subst1,axiom,
% 5.46/5.77 ! [A: rat,F: rat > rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst1
% 5.46/5.77 thf(fact_7740_order__subst1,axiom,
% 5.46/5.77 ! [A: rat,F: num > rat,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst1
% 5.46/5.77 thf(fact_7741_order__subst1,axiom,
% 5.46/5.77 ! [A: rat,F: nat > rat,B2: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_nat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst1
% 5.46/5.77 thf(fact_7742_order__subst1,axiom,
% 5.46/5.77 ! [A: rat,F: int > rat,B2: int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_int @ B2 @ C )
% 5.46/5.77 => ( ! [X3: int,Y4: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst1
% 5.46/5.77 thf(fact_7743_order__subst1,axiom,
% 5.46/5.77 ! [A: num,F: rat > num,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst1
% 5.46/5.77 thf(fact_7744_order__subst1,axiom,
% 5.46/5.77 ! [A: num,F: num > num,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst1
% 5.46/5.77 thf(fact_7745_order__subst1,axiom,
% 5.46/5.77 ! [A: num,F: nat > num,B2: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_nat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst1
% 5.46/5.77 thf(fact_7746_order__subst1,axiom,
% 5.46/5.77 ! [A: num,F: int > num,B2: int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_int @ B2 @ C )
% 5.46/5.77 => ( ! [X3: int,Y4: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst1
% 5.46/5.77 thf(fact_7747_order__subst1,axiom,
% 5.46/5.77 ! [A: nat,F: rat > nat,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst1
% 5.46/5.77 thf(fact_7748_order__subst1,axiom,
% 5.46/5.77 ! [A: nat,F: num > nat,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst1
% 5.46/5.77 thf(fact_7749_order__subst2,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst2
% 5.46/5.77 thf(fact_7750_order__subst2,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_num @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst2
% 5.46/5.77 thf(fact_7751_order__subst2,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst2
% 5.46/5.77 thf(fact_7752_order__subst2,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst2
% 5.46/5.77 thf(fact_7753_order__subst2,axiom,
% 5.46/5.77 ! [A: num,B2: num,F: num > rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst2
% 5.46/5.77 thf(fact_7754_order__subst2,axiom,
% 5.46/5.77 ! [A: num,B2: num,F: num > num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_num @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst2
% 5.46/5.77 thf(fact_7755_order__subst2,axiom,
% 5.46/5.77 ! [A: num,B2: num,F: num > nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst2
% 5.46/5.77 thf(fact_7756_order__subst2,axiom,
% 5.46/5.77 ! [A: num,B2: num,F: num > int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_int @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst2
% 5.46/5.77 thf(fact_7757_order__subst2,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,F: nat > rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst2
% 5.46/5.77 thf(fact_7758_order__subst2,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,F: nat > num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_num @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_subst2
% 5.46/5.77 thf(fact_7759_order__eq__refl,axiom,
% 5.46/5.77 ! [X4: set_nat,Y3: set_nat] :
% 5.46/5.77 ( ( X4 = Y3 )
% 5.46/5.77 => ( ord_less_eq_set_nat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_eq_refl
% 5.46/5.77 thf(fact_7760_order__eq__refl,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( X4 = Y3 )
% 5.46/5.77 => ( ord_less_eq_rat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_eq_refl
% 5.46/5.77 thf(fact_7761_order__eq__refl,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( X4 = Y3 )
% 5.46/5.77 => ( ord_less_eq_num @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_eq_refl
% 5.46/5.77 thf(fact_7762_order__eq__refl,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( X4 = Y3 )
% 5.46/5.77 => ( ord_less_eq_nat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_eq_refl
% 5.46/5.77 thf(fact_7763_order__eq__refl,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( X4 = Y3 )
% 5.46/5.77 => ( ord_less_eq_int @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_eq_refl
% 5.46/5.77 thf(fact_7764_linorder__linear,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.77 | ( ord_less_eq_rat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_linear
% 5.46/5.77 thf(fact_7765_linorder__linear,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.77 | ( ord_less_eq_num @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_linear
% 5.46/5.77 thf(fact_7766_linorder__linear,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.77 | ( ord_less_eq_nat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_linear
% 5.46/5.77 thf(fact_7767_linorder__linear,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.77 | ( ord_less_eq_int @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_linear
% 5.46/5.77 thf(fact_7768_ord__eq__le__subst,axiom,
% 5.46/5.77 ! [A: rat,F: rat > rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_subst
% 5.46/5.77 thf(fact_7769_ord__eq__le__subst,axiom,
% 5.46/5.77 ! [A: num,F: rat > num,B2: rat,C: rat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_subst
% 5.46/5.77 thf(fact_7770_ord__eq__le__subst,axiom,
% 5.46/5.77 ! [A: nat,F: rat > nat,B2: rat,C: rat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_subst
% 5.46/5.77 thf(fact_7771_ord__eq__le__subst,axiom,
% 5.46/5.77 ! [A: int,F: rat > int,B2: rat,C: rat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_subst
% 5.46/5.77 thf(fact_7772_ord__eq__le__subst,axiom,
% 5.46/5.77 ! [A: rat,F: num > rat,B2: num,C: num] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_subst
% 5.46/5.77 thf(fact_7773_ord__eq__le__subst,axiom,
% 5.46/5.77 ! [A: num,F: num > num,B2: num,C: num] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_subst
% 5.46/5.77 thf(fact_7774_ord__eq__le__subst,axiom,
% 5.46/5.77 ! [A: nat,F: num > nat,B2: num,C: num] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_subst
% 5.46/5.77 thf(fact_7775_ord__eq__le__subst,axiom,
% 5.46/5.77 ! [A: int,F: num > int,B2: num,C: num] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_subst
% 5.46/5.77 thf(fact_7776_ord__eq__le__subst,axiom,
% 5.46/5.77 ! [A: rat,F: nat > rat,B2: nat,C: nat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_nat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_subst
% 5.46/5.77 thf(fact_7777_ord__eq__le__subst,axiom,
% 5.46/5.77 ! [A: num,F: nat > num,B2: nat,C: nat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_eq_nat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_le_subst
% 5.46/5.77 thf(fact_7778_ord__le__eq__subst,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_subst
% 5.46/5.77 thf(fact_7779_ord__le__eq__subst,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_subst
% 5.46/5.77 thf(fact_7780_ord__le__eq__subst,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_subst
% 5.46/5.77 thf(fact_7781_ord__le__eq__subst,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_subst
% 5.46/5.77 thf(fact_7782_ord__le__eq__subst,axiom,
% 5.46/5.77 ! [A: num,B2: num,F: num > rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_subst
% 5.46/5.77 thf(fact_7783_ord__le__eq__subst,axiom,
% 5.46/5.77 ! [A: num,B2: num,F: num > num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_subst
% 5.46/5.77 thf(fact_7784_ord__le__eq__subst,axiom,
% 5.46/5.77 ! [A: num,B2: num,F: num > nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_subst
% 5.46/5.77 thf(fact_7785_ord__le__eq__subst,axiom,
% 5.46/5.77 ! [A: num,B2: num,F: num > int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_subst
% 5.46/5.77 thf(fact_7786_ord__le__eq__subst,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,F: nat > rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_subst
% 5.46/5.77 thf(fact_7787_ord__le__eq__subst,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,F: nat > num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_le_eq_subst
% 5.46/5.77 thf(fact_7788_linorder__le__cases,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ~ ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_rat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_le_cases
% 5.46/5.77 thf(fact_7789_linorder__le__cases,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ~ ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_num @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_le_cases
% 5.46/5.77 thf(fact_7790_linorder__le__cases,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ~ ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_nat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_le_cases
% 5.46/5.77 thf(fact_7791_linorder__le__cases,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ~ ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_int @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_le_cases
% 5.46/5.77 thf(fact_7792_order__antisym__conv,axiom,
% 5.46/5.77 ! [Y3: set_nat,X4: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ Y3 @ X4 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_antisym_conv
% 5.46/5.77 thf(fact_7793_order__antisym__conv,axiom,
% 5.46/5.77 ! [Y3: rat,X4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ Y3 @ X4 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_antisym_conv
% 5.46/5.77 thf(fact_7794_order__antisym__conv,axiom,
% 5.46/5.77 ! [Y3: num,X4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ Y3 @ X4 )
% 5.46/5.77 => ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_antisym_conv
% 5.46/5.77 thf(fact_7795_order__antisym__conv,axiom,
% 5.46/5.77 ! [Y3: nat,X4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ Y3 @ X4 )
% 5.46/5.77 => ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_antisym_conv
% 5.46/5.77 thf(fact_7796_order__antisym__conv,axiom,
% 5.46/5.77 ! [Y3: int,X4: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ Y3 @ X4 )
% 5.46/5.77 => ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_antisym_conv
% 5.46/5.77 thf(fact_7797_lt__ex,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ? [Y4: real] : ( ord_less_real @ Y4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % lt_ex
% 5.46/5.77 thf(fact_7798_lt__ex,axiom,
% 5.46/5.77 ! [X4: rat] :
% 5.46/5.77 ? [Y4: rat] : ( ord_less_rat @ Y4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % lt_ex
% 5.46/5.77 thf(fact_7799_lt__ex,axiom,
% 5.46/5.77 ! [X4: int] :
% 5.46/5.77 ? [Y4: int] : ( ord_less_int @ Y4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % lt_ex
% 5.46/5.77 thf(fact_7800_gt__ex,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ? [X_1: real] : ( ord_less_real @ X4 @ X_1 ) ).
% 5.46/5.77
% 5.46/5.77 % gt_ex
% 5.46/5.77 thf(fact_7801_gt__ex,axiom,
% 5.46/5.77 ! [X4: rat] :
% 5.46/5.77 ? [X_1: rat] : ( ord_less_rat @ X4 @ X_1 ) ).
% 5.46/5.77
% 5.46/5.77 % gt_ex
% 5.46/5.77 thf(fact_7802_gt__ex,axiom,
% 5.46/5.77 ! [X4: nat] :
% 5.46/5.77 ? [X_1: nat] : ( ord_less_nat @ X4 @ X_1 ) ).
% 5.46/5.77
% 5.46/5.77 % gt_ex
% 5.46/5.77 thf(fact_7803_gt__ex,axiom,
% 5.46/5.77 ! [X4: int] :
% 5.46/5.77 ? [X_1: int] : ( ord_less_int @ X4 @ X_1 ) ).
% 5.46/5.77
% 5.46/5.77 % gt_ex
% 5.46/5.77 thf(fact_7804_dense,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ? [Z2: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Z2 )
% 5.46/5.77 & ( ord_less_real @ Z2 @ Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dense
% 5.46/5.77 thf(fact_7805_dense,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ? [Z2: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Z2 )
% 5.46/5.77 & ( ord_less_rat @ Z2 @ Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dense
% 5.46/5.77 thf(fact_7806_less__imp__neq,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_imp_neq
% 5.46/5.77 thf(fact_7807_less__imp__neq,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_imp_neq
% 5.46/5.77 thf(fact_7808_less__imp__neq,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_imp_neq
% 5.46/5.77 thf(fact_7809_less__imp__neq,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_imp_neq
% 5.46/5.77 thf(fact_7810_less__imp__neq,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_imp_neq
% 5.46/5.77 thf(fact_7811_order_Oasym,axiom,
% 5.46/5.77 ! [A: real,B2: real] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ~ ( ord_less_real @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.asym
% 5.46/5.77 thf(fact_7812_order_Oasym,axiom,
% 5.46/5.77 ! [A: rat,B2: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ~ ( ord_less_rat @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.asym
% 5.46/5.77 thf(fact_7813_order_Oasym,axiom,
% 5.46/5.77 ! [A: num,B2: num] :
% 5.46/5.77 ( ( ord_less_num @ A @ B2 )
% 5.46/5.77 => ~ ( ord_less_num @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.asym
% 5.46/5.77 thf(fact_7814_order_Oasym,axiom,
% 5.46/5.77 ! [A: nat,B2: nat] :
% 5.46/5.77 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.77 => ~ ( ord_less_nat @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.asym
% 5.46/5.77 thf(fact_7815_order_Oasym,axiom,
% 5.46/5.77 ! [A: int,B2: int] :
% 5.46/5.77 ( ( ord_less_int @ A @ B2 )
% 5.46/5.77 => ~ ( ord_less_int @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.asym
% 5.46/5.77 thf(fact_7816_ord__eq__less__trans,axiom,
% 5.46/5.77 ! [A: real,B2: real,C: real] :
% 5.46/5.77 ( ( A = B2 )
% 5.46/5.77 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.77 => ( ord_less_real @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_trans
% 5.46/5.77 thf(fact_7817_ord__eq__less__trans,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( A = B2 )
% 5.46/5.77 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.77 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_trans
% 5.46/5.77 thf(fact_7818_ord__eq__less__trans,axiom,
% 5.46/5.77 ! [A: num,B2: num,C: num] :
% 5.46/5.77 ( ( A = B2 )
% 5.46/5.77 => ( ( ord_less_num @ B2 @ C )
% 5.46/5.77 => ( ord_less_num @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_trans
% 5.46/5.77 thf(fact_7819_ord__eq__less__trans,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.77 ( ( A = B2 )
% 5.46/5.77 => ( ( ord_less_nat @ B2 @ C )
% 5.46/5.77 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_trans
% 5.46/5.77 thf(fact_7820_ord__eq__less__trans,axiom,
% 5.46/5.77 ! [A: int,B2: int,C: int] :
% 5.46/5.77 ( ( A = B2 )
% 5.46/5.77 => ( ( ord_less_int @ B2 @ C )
% 5.46/5.77 => ( ord_less_int @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_trans
% 5.46/5.77 thf(fact_7821_ord__less__eq__trans,axiom,
% 5.46/5.77 ! [A: real,B2: real,C: real] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( B2 = C )
% 5.46/5.77 => ( ord_less_real @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_trans
% 5.46/5.77 thf(fact_7822_ord__less__eq__trans,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( B2 = C )
% 5.46/5.77 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_trans
% 5.46/5.77 thf(fact_7823_ord__less__eq__trans,axiom,
% 5.46/5.77 ! [A: num,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_num @ A @ B2 )
% 5.46/5.77 => ( ( B2 = C )
% 5.46/5.77 => ( ord_less_num @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_trans
% 5.46/5.77 thf(fact_7824_ord__less__eq__trans,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.77 => ( ( B2 = C )
% 5.46/5.77 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_trans
% 5.46/5.77 thf(fact_7825_ord__less__eq__trans,axiom,
% 5.46/5.77 ! [A: int,B2: int,C: int] :
% 5.46/5.77 ( ( ord_less_int @ A @ B2 )
% 5.46/5.77 => ( ( B2 = C )
% 5.46/5.77 => ( ord_less_int @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_trans
% 5.46/5.77 thf(fact_7826_less__induct,axiom,
% 5.46/5.77 ! [P: nat > $o,A: nat] :
% 5.46/5.77 ( ! [X3: nat] :
% 5.46/5.77 ( ! [Y5: nat] :
% 5.46/5.77 ( ( ord_less_nat @ Y5 @ X3 )
% 5.46/5.77 => ( P @ Y5 ) )
% 5.46/5.77 => ( P @ X3 ) )
% 5.46/5.77 => ( P @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_induct
% 5.46/5.77 thf(fact_7827_antisym__conv3,axiom,
% 5.46/5.77 ! [Y3: real,X4: real] :
% 5.46/5.77 ( ~ ( ord_less_real @ Y3 @ X4 )
% 5.46/5.77 => ( ( ~ ( ord_less_real @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv3
% 5.46/5.77 thf(fact_7828_antisym__conv3,axiom,
% 5.46/5.77 ! [Y3: rat,X4: rat] :
% 5.46/5.77 ( ~ ( ord_less_rat @ Y3 @ X4 )
% 5.46/5.77 => ( ( ~ ( ord_less_rat @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv3
% 5.46/5.77 thf(fact_7829_antisym__conv3,axiom,
% 5.46/5.77 ! [Y3: num,X4: num] :
% 5.46/5.77 ( ~ ( ord_less_num @ Y3 @ X4 )
% 5.46/5.77 => ( ( ~ ( ord_less_num @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv3
% 5.46/5.77 thf(fact_7830_antisym__conv3,axiom,
% 5.46/5.77 ! [Y3: nat,X4: nat] :
% 5.46/5.77 ( ~ ( ord_less_nat @ Y3 @ X4 )
% 5.46/5.77 => ( ( ~ ( ord_less_nat @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv3
% 5.46/5.77 thf(fact_7831_antisym__conv3,axiom,
% 5.46/5.77 ! [Y3: int,X4: int] :
% 5.46/5.77 ( ~ ( ord_less_int @ Y3 @ X4 )
% 5.46/5.77 => ( ( ~ ( ord_less_int @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv3
% 5.46/5.77 thf(fact_7832_linorder__cases,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ~ ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( ( X4 != Y3 )
% 5.46/5.77 => ( ord_less_real @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_cases
% 5.46/5.77 thf(fact_7833_linorder__cases,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ~ ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ( X4 != Y3 )
% 5.46/5.77 => ( ord_less_rat @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_cases
% 5.46/5.77 thf(fact_7834_linorder__cases,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ~ ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ( ( X4 != Y3 )
% 5.46/5.77 => ( ord_less_num @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_cases
% 5.46/5.77 thf(fact_7835_linorder__cases,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ~ ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( X4 != Y3 )
% 5.46/5.77 => ( ord_less_nat @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_cases
% 5.46/5.77 thf(fact_7836_linorder__cases,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ~ ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ( ( X4 != Y3 )
% 5.46/5.77 => ( ord_less_int @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_cases
% 5.46/5.77 thf(fact_7837_dual__order_Oasym,axiom,
% 5.46/5.77 ! [B2: real,A: real] :
% 5.46/5.77 ( ( ord_less_real @ B2 @ A )
% 5.46/5.77 => ~ ( ord_less_real @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.asym
% 5.46/5.77 thf(fact_7838_dual__order_Oasym,axiom,
% 5.46/5.77 ! [B2: rat,A: rat] :
% 5.46/5.77 ( ( ord_less_rat @ B2 @ A )
% 5.46/5.77 => ~ ( ord_less_rat @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.asym
% 5.46/5.77 thf(fact_7839_dual__order_Oasym,axiom,
% 5.46/5.77 ! [B2: num,A: num] :
% 5.46/5.77 ( ( ord_less_num @ B2 @ A )
% 5.46/5.77 => ~ ( ord_less_num @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.asym
% 5.46/5.77 thf(fact_7840_dual__order_Oasym,axiom,
% 5.46/5.77 ! [B2: nat,A: nat] :
% 5.46/5.77 ( ( ord_less_nat @ B2 @ A )
% 5.46/5.77 => ~ ( ord_less_nat @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.asym
% 5.46/5.77 thf(fact_7841_dual__order_Oasym,axiom,
% 5.46/5.77 ! [B2: int,A: int] :
% 5.46/5.77 ( ( ord_less_int @ B2 @ A )
% 5.46/5.77 => ~ ( ord_less_int @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.asym
% 5.46/5.77 thf(fact_7842_dual__order_Oirrefl,axiom,
% 5.46/5.77 ! [A: real] :
% 5.46/5.77 ~ ( ord_less_real @ A @ A ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.irrefl
% 5.46/5.77 thf(fact_7843_dual__order_Oirrefl,axiom,
% 5.46/5.77 ! [A: rat] :
% 5.46/5.77 ~ ( ord_less_rat @ A @ A ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.irrefl
% 5.46/5.77 thf(fact_7844_dual__order_Oirrefl,axiom,
% 5.46/5.77 ! [A: num] :
% 5.46/5.77 ~ ( ord_less_num @ A @ A ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.irrefl
% 5.46/5.77 thf(fact_7845_dual__order_Oirrefl,axiom,
% 5.46/5.77 ! [A: nat] :
% 5.46/5.77 ~ ( ord_less_nat @ A @ A ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.irrefl
% 5.46/5.77 thf(fact_7846_dual__order_Oirrefl,axiom,
% 5.46/5.77 ! [A: int] :
% 5.46/5.77 ~ ( ord_less_int @ A @ A ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.irrefl
% 5.46/5.77 thf(fact_7847_exists__least__iff,axiom,
% 5.46/5.77 ( ( ^ [P5: nat > $o] :
% 5.46/5.77 ? [X7: nat] : ( P5 @ X7 ) )
% 5.46/5.77 = ( ^ [P6: nat > $o] :
% 5.46/5.77 ? [N2: nat] :
% 5.46/5.77 ( ( P6 @ N2 )
% 5.46/5.77 & ! [M6: nat] :
% 5.46/5.77 ( ( ord_less_nat @ M6 @ N2 )
% 5.46/5.77 => ~ ( P6 @ M6 ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % exists_least_iff
% 5.46/5.77 thf(fact_7848_linorder__less__wlog,axiom,
% 5.46/5.77 ! [P: real > real > $o,A: real,B2: real] :
% 5.46/5.77 ( ! [A5: real,B5: real] :
% 5.46/5.77 ( ( ord_less_real @ A5 @ B5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( ! [A5: real] : ( P @ A5 @ A5 )
% 5.46/5.77 => ( ! [A5: real,B5: real] :
% 5.46/5.77 ( ( P @ B5 @ A5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( P @ A @ B2 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_less_wlog
% 5.46/5.77 thf(fact_7849_linorder__less__wlog,axiom,
% 5.46/5.77 ! [P: rat > rat > $o,A: rat,B2: rat] :
% 5.46/5.77 ( ! [A5: rat,B5: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A5 @ B5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 5.46/5.77 => ( ! [A5: rat,B5: rat] :
% 5.46/5.77 ( ( P @ B5 @ A5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( P @ A @ B2 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_less_wlog
% 5.46/5.77 thf(fact_7850_linorder__less__wlog,axiom,
% 5.46/5.77 ! [P: num > num > $o,A: num,B2: num] :
% 5.46/5.77 ( ! [A5: num,B5: num] :
% 5.46/5.77 ( ( ord_less_num @ A5 @ B5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( ! [A5: num] : ( P @ A5 @ A5 )
% 5.46/5.77 => ( ! [A5: num,B5: num] :
% 5.46/5.77 ( ( P @ B5 @ A5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( P @ A @ B2 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_less_wlog
% 5.46/5.77 thf(fact_7851_linorder__less__wlog,axiom,
% 5.46/5.77 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 5.46/5.77 ( ! [A5: nat,B5: nat] :
% 5.46/5.77 ( ( ord_less_nat @ A5 @ B5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 5.46/5.77 => ( ! [A5: nat,B5: nat] :
% 5.46/5.77 ( ( P @ B5 @ A5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( P @ A @ B2 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_less_wlog
% 5.46/5.77 thf(fact_7852_linorder__less__wlog,axiom,
% 5.46/5.77 ! [P: int > int > $o,A: int,B2: int] :
% 5.46/5.77 ( ! [A5: int,B5: int] :
% 5.46/5.77 ( ( ord_less_int @ A5 @ B5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( ! [A5: int] : ( P @ A5 @ A5 )
% 5.46/5.77 => ( ! [A5: int,B5: int] :
% 5.46/5.77 ( ( P @ B5 @ A5 )
% 5.46/5.77 => ( P @ A5 @ B5 ) )
% 5.46/5.77 => ( P @ A @ B2 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_less_wlog
% 5.46/5.77 thf(fact_7853_order_Ostrict__trans,axiom,
% 5.46/5.77 ! [A: real,B2: real,C: real] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.77 => ( ord_less_real @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans
% 5.46/5.77 thf(fact_7854_order_Ostrict__trans,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.77 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans
% 5.46/5.77 thf(fact_7855_order_Ostrict__trans,axiom,
% 5.46/5.77 ! [A: num,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_num @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_num @ B2 @ C )
% 5.46/5.77 => ( ord_less_num @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans
% 5.46/5.77 thf(fact_7856_order_Ostrict__trans,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_nat @ B2 @ C )
% 5.46/5.77 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans
% 5.46/5.77 thf(fact_7857_order_Ostrict__trans,axiom,
% 5.46/5.77 ! [A: int,B2: int,C: int] :
% 5.46/5.77 ( ( ord_less_int @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_int @ B2 @ C )
% 5.46/5.77 => ( ord_less_int @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans
% 5.46/5.77 thf(fact_7858_not__less__iff__gr__or__eq,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ~ ( ord_less_real @ X4 @ Y3 ) )
% 5.46/5.77 = ( ( ord_less_real @ Y3 @ X4 )
% 5.46/5.77 | ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_less_iff_gr_or_eq
% 5.46/5.77 thf(fact_7859_not__less__iff__gr__or__eq,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ~ ( ord_less_rat @ X4 @ Y3 ) )
% 5.46/5.77 = ( ( ord_less_rat @ Y3 @ X4 )
% 5.46/5.77 | ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_less_iff_gr_or_eq
% 5.46/5.77 thf(fact_7860_not__less__iff__gr__or__eq,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ~ ( ord_less_num @ X4 @ Y3 ) )
% 5.46/5.77 = ( ( ord_less_num @ Y3 @ X4 )
% 5.46/5.77 | ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_less_iff_gr_or_eq
% 5.46/5.77 thf(fact_7861_not__less__iff__gr__or__eq,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ~ ( ord_less_nat @ X4 @ Y3 ) )
% 5.46/5.77 = ( ( ord_less_nat @ Y3 @ X4 )
% 5.46/5.77 | ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_less_iff_gr_or_eq
% 5.46/5.77 thf(fact_7862_not__less__iff__gr__or__eq,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ~ ( ord_less_int @ X4 @ Y3 ) )
% 5.46/5.77 = ( ( ord_less_int @ Y3 @ X4 )
% 5.46/5.77 | ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_less_iff_gr_or_eq
% 5.46/5.77 thf(fact_7863_dual__order_Ostrict__trans,axiom,
% 5.46/5.77 ! [B2: real,A: real,C: real] :
% 5.46/5.77 ( ( ord_less_real @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_real @ C @ B2 )
% 5.46/5.77 => ( ord_less_real @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans
% 5.46/5.77 thf(fact_7864_dual__order_Ostrict__trans,axiom,
% 5.46/5.77 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_rat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_rat @ C @ B2 )
% 5.46/5.77 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans
% 5.46/5.77 thf(fact_7865_dual__order_Ostrict__trans,axiom,
% 5.46/5.77 ! [B2: num,A: num,C: num] :
% 5.46/5.77 ( ( ord_less_num @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_num @ C @ B2 )
% 5.46/5.77 => ( ord_less_num @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans
% 5.46/5.77 thf(fact_7866_dual__order_Ostrict__trans,axiom,
% 5.46/5.77 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_nat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_nat @ C @ B2 )
% 5.46/5.77 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans
% 5.46/5.77 thf(fact_7867_dual__order_Ostrict__trans,axiom,
% 5.46/5.77 ! [B2: int,A: int,C: int] :
% 5.46/5.77 ( ( ord_less_int @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_int @ C @ B2 )
% 5.46/5.77 => ( ord_less_int @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans
% 5.46/5.77 thf(fact_7868_order_Ostrict__implies__not__eq,axiom,
% 5.46/5.77 ! [A: real,B2: real] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( A != B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_not_eq
% 5.46/5.77 thf(fact_7869_order_Ostrict__implies__not__eq,axiom,
% 5.46/5.77 ! [A: rat,B2: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( A != B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_not_eq
% 5.46/5.77 thf(fact_7870_order_Ostrict__implies__not__eq,axiom,
% 5.46/5.77 ! [A: num,B2: num] :
% 5.46/5.77 ( ( ord_less_num @ A @ B2 )
% 5.46/5.77 => ( A != B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_not_eq
% 5.46/5.77 thf(fact_7871_order_Ostrict__implies__not__eq,axiom,
% 5.46/5.77 ! [A: nat,B2: nat] :
% 5.46/5.77 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.77 => ( A != B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_not_eq
% 5.46/5.77 thf(fact_7872_order_Ostrict__implies__not__eq,axiom,
% 5.46/5.77 ! [A: int,B2: int] :
% 5.46/5.77 ( ( ord_less_int @ A @ B2 )
% 5.46/5.77 => ( A != B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_not_eq
% 5.46/5.77 thf(fact_7873_dual__order_Ostrict__implies__not__eq,axiom,
% 5.46/5.77 ! [B2: real,A: real] :
% 5.46/5.77 ( ( ord_less_real @ B2 @ A )
% 5.46/5.77 => ( A != B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_not_eq
% 5.46/5.77 thf(fact_7874_dual__order_Ostrict__implies__not__eq,axiom,
% 5.46/5.77 ! [B2: rat,A: rat] :
% 5.46/5.77 ( ( ord_less_rat @ B2 @ A )
% 5.46/5.77 => ( A != B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_not_eq
% 5.46/5.77 thf(fact_7875_dual__order_Ostrict__implies__not__eq,axiom,
% 5.46/5.77 ! [B2: num,A: num] :
% 5.46/5.77 ( ( ord_less_num @ B2 @ A )
% 5.46/5.77 => ( A != B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_not_eq
% 5.46/5.77 thf(fact_7876_dual__order_Ostrict__implies__not__eq,axiom,
% 5.46/5.77 ! [B2: nat,A: nat] :
% 5.46/5.77 ( ( ord_less_nat @ B2 @ A )
% 5.46/5.77 => ( A != B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_not_eq
% 5.46/5.77 thf(fact_7877_dual__order_Ostrict__implies__not__eq,axiom,
% 5.46/5.77 ! [B2: int,A: int] :
% 5.46/5.77 ( ( ord_less_int @ B2 @ A )
% 5.46/5.77 => ( A != B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_not_eq
% 5.46/5.77 thf(fact_7878_linorder__neqE,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( X4 != Y3 )
% 5.46/5.77 => ( ~ ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_real @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_neqE
% 5.46/5.77 thf(fact_7879_linorder__neqE,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( X4 != Y3 )
% 5.46/5.77 => ( ~ ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_rat @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_neqE
% 5.46/5.77 thf(fact_7880_linorder__neqE,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( X4 != Y3 )
% 5.46/5.77 => ( ~ ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_num @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_neqE
% 5.46/5.77 thf(fact_7881_linorder__neqE,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( X4 != Y3 )
% 5.46/5.77 => ( ~ ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_nat @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_neqE
% 5.46/5.77 thf(fact_7882_linorder__neqE,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( X4 != Y3 )
% 5.46/5.77 => ( ~ ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_int @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_neqE
% 5.46/5.77 thf(fact_7883_order__less__asym,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_real @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_asym
% 5.46/5.77 thf(fact_7884_order__less__asym,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_rat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_asym
% 5.46/5.77 thf(fact_7885_order__less__asym,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_num @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_asym
% 5.46/5.77 thf(fact_7886_order__less__asym,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_nat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_asym
% 5.46/5.77 thf(fact_7887_order__less__asym,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_int @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_asym
% 5.46/5.77 thf(fact_7888_linorder__neq__iff,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( X4 != Y3 )
% 5.46/5.77 = ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 | ( ord_less_real @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_neq_iff
% 5.46/5.77 thf(fact_7889_linorder__neq__iff,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( X4 != Y3 )
% 5.46/5.77 = ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 | ( ord_less_rat @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_neq_iff
% 5.46/5.77 thf(fact_7890_linorder__neq__iff,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( X4 != Y3 )
% 5.46/5.77 = ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 | ( ord_less_num @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_neq_iff
% 5.46/5.77 thf(fact_7891_linorder__neq__iff,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( X4 != Y3 )
% 5.46/5.77 = ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 | ( ord_less_nat @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_neq_iff
% 5.46/5.77 thf(fact_7892_linorder__neq__iff,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( X4 != Y3 )
% 5.46/5.77 = ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 | ( ord_less_int @ Y3 @ X4 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_neq_iff
% 5.46/5.77 thf(fact_7893_order__less__asym_H,axiom,
% 5.46/5.77 ! [A: real,B2: real] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ~ ( ord_less_real @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_asym'
% 5.46/5.77 thf(fact_7894_order__less__asym_H,axiom,
% 5.46/5.77 ! [A: rat,B2: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ~ ( ord_less_rat @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_asym'
% 5.46/5.77 thf(fact_7895_order__less__asym_H,axiom,
% 5.46/5.77 ! [A: num,B2: num] :
% 5.46/5.77 ( ( ord_less_num @ A @ B2 )
% 5.46/5.77 => ~ ( ord_less_num @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_asym'
% 5.46/5.77 thf(fact_7896_order__less__asym_H,axiom,
% 5.46/5.77 ! [A: nat,B2: nat] :
% 5.46/5.77 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.77 => ~ ( ord_less_nat @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_asym'
% 5.46/5.77 thf(fact_7897_order__less__asym_H,axiom,
% 5.46/5.77 ! [A: int,B2: int] :
% 5.46/5.77 ( ( ord_less_int @ A @ B2 )
% 5.46/5.77 => ~ ( ord_less_int @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_asym'
% 5.46/5.77 thf(fact_7898_order__less__trans,axiom,
% 5.46/5.77 ! [X4: real,Y3: real,Z: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_real @ Y3 @ Z )
% 5.46/5.77 => ( ord_less_real @ X4 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_trans
% 5.46/5.77 thf(fact_7899_order__less__trans,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat,Z: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_rat @ Y3 @ Z )
% 5.46/5.77 => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_trans
% 5.46/5.77 thf(fact_7900_order__less__trans,axiom,
% 5.46/5.77 ! [X4: num,Y3: num,Z: num] :
% 5.46/5.77 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_num @ Y3 @ Z )
% 5.46/5.77 => ( ord_less_num @ X4 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_trans
% 5.46/5.77 thf(fact_7901_order__less__trans,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat,Z: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_nat @ Y3 @ Z )
% 5.46/5.77 => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_trans
% 5.46/5.77 thf(fact_7902_order__less__trans,axiom,
% 5.46/5.77 ! [X4: int,Y3: int,Z: int] :
% 5.46/5.77 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_int @ Y3 @ Z )
% 5.46/5.77 => ( ord_less_int @ X4 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_trans
% 5.46/5.77 thf(fact_7903_ord__eq__less__subst,axiom,
% 5.46/5.77 ! [A: real,F: real > real,B2: real,C: real] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_subst
% 5.46/5.77 thf(fact_7904_ord__eq__less__subst,axiom,
% 5.46/5.77 ! [A: rat,F: real > rat,B2: real,C: real] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_subst
% 5.46/5.77 thf(fact_7905_ord__eq__less__subst,axiom,
% 5.46/5.77 ! [A: num,F: real > num,B2: real,C: real] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_subst
% 5.46/5.77 thf(fact_7906_ord__eq__less__subst,axiom,
% 5.46/5.77 ! [A: nat,F: real > nat,B2: real,C: real] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_subst
% 5.46/5.77 thf(fact_7907_ord__eq__less__subst,axiom,
% 5.46/5.77 ! [A: int,F: real > int,B2: real,C: real] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_subst
% 5.46/5.77 thf(fact_7908_ord__eq__less__subst,axiom,
% 5.46/5.77 ! [A: real,F: rat > real,B2: rat,C: rat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_subst
% 5.46/5.77 thf(fact_7909_ord__eq__less__subst,axiom,
% 5.46/5.77 ! [A: rat,F: rat > rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_subst
% 5.46/5.77 thf(fact_7910_ord__eq__less__subst,axiom,
% 5.46/5.77 ! [A: num,F: rat > num,B2: rat,C: rat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_subst
% 5.46/5.77 thf(fact_7911_ord__eq__less__subst,axiom,
% 5.46/5.77 ! [A: nat,F: rat > nat,B2: rat,C: rat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_subst
% 5.46/5.77 thf(fact_7912_ord__eq__less__subst,axiom,
% 5.46/5.77 ! [A: int,F: rat > int,B2: rat,C: rat] :
% 5.46/5.77 ( ( A
% 5.46/5.77 = ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_eq_less_subst
% 5.46/5.77 thf(fact_7913_ord__less__eq__subst,axiom,
% 5.46/5.77 ! [A: real,B2: real,F: real > real,C: real] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_subst
% 5.46/5.77 thf(fact_7914_ord__less__eq__subst,axiom,
% 5.46/5.77 ! [A: real,B2: real,F: real > rat,C: rat] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_subst
% 5.46/5.77 thf(fact_7915_ord__less__eq__subst,axiom,
% 5.46/5.77 ! [A: real,B2: real,F: real > num,C: num] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_subst
% 5.46/5.77 thf(fact_7916_ord__less__eq__subst,axiom,
% 5.46/5.77 ! [A: real,B2: real,F: real > nat,C: nat] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_subst
% 5.46/5.77 thf(fact_7917_ord__less__eq__subst,axiom,
% 5.46/5.77 ! [A: real,B2: real,F: real > int,C: int] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_subst
% 5.46/5.77 thf(fact_7918_ord__less__eq__subst,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > real,C: real] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_subst
% 5.46/5.77 thf(fact_7919_ord__less__eq__subst,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > rat,C: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_subst
% 5.46/5.77 thf(fact_7920_ord__less__eq__subst,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > num,C: num] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_subst
% 5.46/5.77 thf(fact_7921_ord__less__eq__subst,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > nat,C: nat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_subst
% 5.46/5.77 thf(fact_7922_ord__less__eq__subst,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > int,C: int] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ( F @ B2 )
% 5.46/5.77 = C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % ord_less_eq_subst
% 5.46/5.77 thf(fact_7923_order__less__irrefl,axiom,
% 5.46/5.77 ! [X4: real] :
% 5.46/5.77 ~ ( ord_less_real @ X4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_irrefl
% 5.46/5.77 thf(fact_7924_order__less__irrefl,axiom,
% 5.46/5.77 ! [X4: rat] :
% 5.46/5.77 ~ ( ord_less_rat @ X4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_irrefl
% 5.46/5.77 thf(fact_7925_order__less__irrefl,axiom,
% 5.46/5.77 ! [X4: num] :
% 5.46/5.77 ~ ( ord_less_num @ X4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_irrefl
% 5.46/5.77 thf(fact_7926_order__less__irrefl,axiom,
% 5.46/5.77 ! [X4: nat] :
% 5.46/5.77 ~ ( ord_less_nat @ X4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_irrefl
% 5.46/5.77 thf(fact_7927_order__less__irrefl,axiom,
% 5.46/5.77 ! [X4: int] :
% 5.46/5.77 ~ ( ord_less_int @ X4 @ X4 ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_irrefl
% 5.46/5.77 thf(fact_7928_order__less__subst1,axiom,
% 5.46/5.77 ! [A: real,F: real > real,B2: real,C: real] :
% 5.46/5.77 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst1
% 5.46/5.77 thf(fact_7929_order__less__subst1,axiom,
% 5.46/5.77 ! [A: real,F: rat > real,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst1
% 5.46/5.77 thf(fact_7930_order__less__subst1,axiom,
% 5.46/5.77 ! [A: real,F: num > real,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_num @ B2 @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst1
% 5.46/5.77 thf(fact_7931_order__less__subst1,axiom,
% 5.46/5.77 ! [A: real,F: nat > real,B2: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_nat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst1
% 5.46/5.77 thf(fact_7932_order__less__subst1,axiom,
% 5.46/5.77 ! [A: real,F: int > real,B2: int,C: int] :
% 5.46/5.77 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_int @ B2 @ C )
% 5.46/5.77 => ( ! [X3: int,Y4: int] :
% 5.46/5.77 ( ( ord_less_int @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst1
% 5.46/5.77 thf(fact_7933_order__less__subst1,axiom,
% 5.46/5.77 ! [A: rat,F: real > rat,B2: real,C: real] :
% 5.46/5.77 ( ( ord_less_rat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst1
% 5.46/5.77 thf(fact_7934_order__less__subst1,axiom,
% 5.46/5.77 ! [A: rat,F: rat > rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst1
% 5.46/5.77 thf(fact_7935_order__less__subst1,axiom,
% 5.46/5.77 ! [A: rat,F: num > rat,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_rat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_num @ B2 @ C )
% 5.46/5.77 => ( ! [X3: num,Y4: num] :
% 5.46/5.77 ( ( ord_less_num @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst1
% 5.46/5.77 thf(fact_7936_order__less__subst1,axiom,
% 5.46/5.77 ! [A: rat,F: nat > rat,B2: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_nat @ B2 @ C )
% 5.46/5.77 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst1
% 5.46/5.77 thf(fact_7937_order__less__subst1,axiom,
% 5.46/5.77 ! [A: rat,F: int > rat,B2: int,C: int] :
% 5.46/5.77 ( ( ord_less_rat @ A @ ( F @ B2 ) )
% 5.46/5.77 => ( ( ord_less_int @ B2 @ C )
% 5.46/5.77 => ( ! [X3: int,Y4: int] :
% 5.46/5.77 ( ( ord_less_int @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst1
% 5.46/5.77 thf(fact_7938_order__less__subst2,axiom,
% 5.46/5.77 ! [A: real,B2: real,F: real > real,C: real] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_real @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst2
% 5.46/5.77 thf(fact_7939_order__less__subst2,axiom,
% 5.46/5.77 ! [A: real,B2: real,F: real > rat,C: rat] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_rat @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst2
% 5.46/5.77 thf(fact_7940_order__less__subst2,axiom,
% 5.46/5.77 ! [A: real,B2: real,F: real > num,C: num] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_num @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst2
% 5.46/5.77 thf(fact_7941_order__less__subst2,axiom,
% 5.46/5.77 ! [A: real,B2: real,F: real > nat,C: nat] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst2
% 5.46/5.77 thf(fact_7942_order__less__subst2,axiom,
% 5.46/5.77 ! [A: real,B2: real,F: real > int,C: int] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: real,Y4: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst2
% 5.46/5.77 thf(fact_7943_order__less__subst2,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > real,C: real] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_real @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst2
% 5.46/5.77 thf(fact_7944_order__less__subst2,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > rat,C: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_rat @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst2
% 5.46/5.77 thf(fact_7945_order__less__subst2,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > num,C: num] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_num @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst2
% 5.46/5.77 thf(fact_7946_order__less__subst2,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > nat,C: nat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst2
% 5.46/5.77 thf(fact_7947_order__less__subst2,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,F: rat > int,C: int] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 5.46/5.77 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.77 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.77 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_subst2
% 5.46/5.77 thf(fact_7948_order__less__not__sym,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_real @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_not_sym
% 5.46/5.77 thf(fact_7949_order__less__not__sym,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_rat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_not_sym
% 5.46/5.77 thf(fact_7950_order__less__not__sym,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_num @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_not_sym
% 5.46/5.77 thf(fact_7951_order__less__not__sym,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_nat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_not_sym
% 5.46/5.77 thf(fact_7952_order__less__not__sym,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_int @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_not_sym
% 5.46/5.77 thf(fact_7953_order__less__imp__triv,axiom,
% 5.46/5.77 ! [X4: real,Y3: real,P: $o] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_real @ Y3 @ X4 )
% 5.46/5.77 => P ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_triv
% 5.46/5.77 thf(fact_7954_order__less__imp__triv,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat,P: $o] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_rat @ Y3 @ X4 )
% 5.46/5.77 => P ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_triv
% 5.46/5.77 thf(fact_7955_order__less__imp__triv,axiom,
% 5.46/5.77 ! [X4: num,Y3: num,P: $o] :
% 5.46/5.77 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_num @ Y3 @ X4 )
% 5.46/5.77 => P ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_triv
% 5.46/5.77 thf(fact_7956_order__less__imp__triv,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat,P: $o] :
% 5.46/5.77 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_nat @ Y3 @ X4 )
% 5.46/5.77 => P ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_triv
% 5.46/5.77 thf(fact_7957_order__less__imp__triv,axiom,
% 5.46/5.77 ! [X4: int,Y3: int,P: $o] :
% 5.46/5.77 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_int @ Y3 @ X4 )
% 5.46/5.77 => P ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_triv
% 5.46/5.77 thf(fact_7958_linorder__less__linear,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 | ( X4 = Y3 )
% 5.46/5.77 | ( ord_less_real @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_less_linear
% 5.46/5.77 thf(fact_7959_linorder__less__linear,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 | ( X4 = Y3 )
% 5.46/5.77 | ( ord_less_rat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_less_linear
% 5.46/5.77 thf(fact_7960_linorder__less__linear,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 | ( X4 = Y3 )
% 5.46/5.77 | ( ord_less_num @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_less_linear
% 5.46/5.77 thf(fact_7961_linorder__less__linear,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 | ( X4 = Y3 )
% 5.46/5.77 | ( ord_less_nat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_less_linear
% 5.46/5.77 thf(fact_7962_linorder__less__linear,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 | ( X4 = Y3 )
% 5.46/5.77 | ( ord_less_int @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_less_linear
% 5.46/5.77 thf(fact_7963_order__less__imp__not__eq,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_eq
% 5.46/5.77 thf(fact_7964_order__less__imp__not__eq,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_eq
% 5.46/5.77 thf(fact_7965_order__less__imp__not__eq,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_eq
% 5.46/5.77 thf(fact_7966_order__less__imp__not__eq,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_eq
% 5.46/5.77 thf(fact_7967_order__less__imp__not__eq,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ( X4 != Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_eq
% 5.46/5.77 thf(fact_7968_order__less__imp__not__eq2,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( Y3 != X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_eq2
% 5.46/5.77 thf(fact_7969_order__less__imp__not__eq2,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( Y3 != X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_eq2
% 5.46/5.77 thf(fact_7970_order__less__imp__not__eq2,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ( Y3 != X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_eq2
% 5.46/5.77 thf(fact_7971_order__less__imp__not__eq2,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ( Y3 != X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_eq2
% 5.46/5.77 thf(fact_7972_order__less__imp__not__eq2,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ( Y3 != X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_eq2
% 5.46/5.77 thf(fact_7973_order__less__imp__not__less,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_real @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_less
% 5.46/5.77 thf(fact_7974_order__less__imp__not__less,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_rat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_less
% 5.46/5.77 thf(fact_7975_order__less__imp__not__less,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_num @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_less
% 5.46/5.77 thf(fact_7976_order__less__imp__not__less,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_nat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_less
% 5.46/5.77 thf(fact_7977_order__less__imp__not__less,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ~ ( ord_less_int @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_not_less
% 5.46/5.77 thf(fact_7978_take__bit__not__eq__mask__diff,axiom,
% 5.46/5.77 ! [N: nat,A: int] :
% 5.46/5.77 ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.46/5.77 = ( minus_minus_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % take_bit_not_eq_mask_diff
% 5.46/5.77 thf(fact_7979_minus__numeral__inc__eq,axiom,
% 5.46/5.77 ! [N: num] :
% 5.46/5.77 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) )
% 5.46/5.77 = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % minus_numeral_inc_eq
% 5.46/5.77 thf(fact_7980_minus__numeral__inc__eq,axiom,
% 5.46/5.77 ! [N: num] :
% 5.46/5.77 ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % minus_numeral_inc_eq
% 5.46/5.77 thf(fact_7981_unset__bit__int__def,axiom,
% 5.46/5.77 ( bit_se4203085406695923979it_int
% 5.46/5.77 = ( ^ [N2: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % unset_bit_int_def
% 5.46/5.77 thf(fact_7982_not__int__div__2,axiom,
% 5.46/5.77 ! [K: int] :
% 5.46/5.77 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_int_div_2
% 5.46/5.77 thf(fact_7983_even__not__iff__int,axiom,
% 5.46/5.77 ! [K: int] :
% 5.46/5.77 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.46/5.77 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % even_not_iff_int
% 5.46/5.77 thf(fact_7984_not__numeral__Bit0__eq,axiom,
% 5.46/5.77 ! [N: num] :
% 5.46/5.77 ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) )
% 5.46/5.77 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_numeral_Bit0_eq
% 5.46/5.77 thf(fact_7985_not__numeral__Bit0__eq,axiom,
% 5.46/5.77 ! [N: num] :
% 5.46/5.77 ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) )
% 5.46/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_numeral_Bit0_eq
% 5.46/5.77 thf(fact_7986_and__not__numerals_I2_J,axiom,
% 5.46/5.77 ! [N: num] :
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.77 = one_one_int ) ).
% 5.46/5.77
% 5.46/5.77 % and_not_numerals(2)
% 5.46/5.77 thf(fact_7987_and__not__numerals_I4_J,axiom,
% 5.46/5.77 ! [M: num] :
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.77 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % and_not_numerals(4)
% 5.46/5.77 thf(fact_7988_bit__minus__int__iff,axiom,
% 5.46/5.77 ! [K: int,N: nat] :
% 5.46/5.77 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.46/5.77 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit_minus_int_iff
% 5.46/5.77 thf(fact_7989_take__bit__not__mask__eq__0,axiom,
% 5.46/5.77 ! [M: nat,N: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.77 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) )
% 5.46/5.77 = zero_zero_int ) ) ).
% 5.46/5.77
% 5.46/5.77 % take_bit_not_mask_eq_0
% 5.46/5.77 thf(fact_7990_push__bit__mask__eq,axiom,
% 5.46/5.77 ! [M: nat,N: nat] :
% 5.46/5.77 ( ( bit_se545348938243370406it_int @ M @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.46/5.77 = ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ N @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ M ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % push_bit_mask_eq
% 5.46/5.77 thf(fact_7991_unset__bit__eq__and__not,axiom,
% 5.46/5.77 ( bit_se4203085406695923979it_int
% 5.46/5.77 = ( ^ [N2: nat,A4: int] : ( bit_se725231765392027082nd_int @ A4 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % unset_bit_eq_and_not
% 5.46/5.77 thf(fact_7992_and__not__numerals_I5_J,axiom,
% 5.46/5.77 ! [M: num,N: num] :
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.77 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % and_not_numerals(5)
% 5.46/5.77 thf(fact_7993_and__not__numerals_I7_J,axiom,
% 5.46/5.77 ! [M: num] :
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.77 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % and_not_numerals(7)
% 5.46/5.77 thf(fact_7994_and__not__numerals_I3_J,axiom,
% 5.46/5.77 ! [N: num] :
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.77 = zero_zero_int ) ).
% 5.46/5.77
% 5.46/5.77 % and_not_numerals(3)
% 5.46/5.77 thf(fact_7995_and__not__numerals_I9_J,axiom,
% 5.46/5.77 ! [M: num,N: num] :
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.77 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % and_not_numerals(9)
% 5.46/5.77 thf(fact_7996_and__not__numerals_I6_J,axiom,
% 5.46/5.77 ! [M: num,N: num] :
% 5.46/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.77 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % and_not_numerals(6)
% 5.46/5.77 thf(fact_7997_bit__not__iff__eq,axiom,
% 5.46/5.77 ! [A: int,N: nat] :
% 5.46/5.77 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ A ) @ N )
% 5.46/5.77 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.46/5.77 != zero_zero_int )
% 5.46/5.77 & ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % bit_not_iff_eq
% 5.46/5.77 thf(fact_7998_minus__exp__eq__not__mask,axiom,
% 5.46/5.77 ! [N: nat] :
% 5.46/5.77 ( ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.77 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % minus_exp_eq_not_mask
% 5.46/5.77 thf(fact_7999_minus__exp__eq__not__mask,axiom,
% 5.46/5.77 ! [N: nat] :
% 5.46/5.77 ( ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.77 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % minus_exp_eq_not_mask
% 5.46/5.77 thf(fact_8000_CauchyD,axiom,
% 5.46/5.77 ! [X8: nat > complex,E: real] :
% 5.46/5.77 ( ( topolo6517432010174082258omplex @ X8 )
% 5.46/5.77 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.77 => ? [M9: nat] :
% 5.46/5.77 ! [M5: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M9 @ M5 )
% 5.46/5.77 => ! [N6: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M9 @ N6 )
% 5.46/5.77 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M5 ) @ ( X8 @ N6 ) ) ) @ E ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % CauchyD
% 5.46/5.77 thf(fact_8001_CauchyD,axiom,
% 5.46/5.77 ! [X8: nat > real,E: real] :
% 5.46/5.77 ( ( topolo4055970368930404560y_real @ X8 )
% 5.46/5.77 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.46/5.77 => ? [M9: nat] :
% 5.46/5.77 ! [M5: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M9 @ M5 )
% 5.46/5.77 => ! [N6: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M9 @ N6 )
% 5.46/5.77 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M5 ) @ ( X8 @ N6 ) ) ) @ E ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % CauchyD
% 5.46/5.77 thf(fact_8002_CauchyI,axiom,
% 5.46/5.77 ! [X8: nat > complex] :
% 5.46/5.77 ( ! [E2: real] :
% 5.46/5.77 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.46/5.77 => ? [M10: nat] :
% 5.46/5.77 ! [M4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M10 @ M4 )
% 5.46/5.77 => ! [N4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M10 @ N4 )
% 5.46/5.77 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M4 ) @ ( X8 @ N4 ) ) ) @ E2 ) ) ) )
% 5.46/5.77 => ( topolo6517432010174082258omplex @ X8 ) ) ).
% 5.46/5.77
% 5.46/5.77 % CauchyI
% 5.46/5.77 thf(fact_8003_CauchyI,axiom,
% 5.46/5.77 ! [X8: nat > real] :
% 5.46/5.77 ( ! [E2: real] :
% 5.46/5.77 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.46/5.77 => ? [M10: nat] :
% 5.46/5.77 ! [M4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M10 @ M4 )
% 5.46/5.77 => ! [N4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M10 @ N4 )
% 5.46/5.77 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M4 ) @ ( X8 @ N4 ) ) ) @ E2 ) ) ) )
% 5.46/5.77 => ( topolo4055970368930404560y_real @ X8 ) ) ).
% 5.46/5.77
% 5.46/5.77 % CauchyI
% 5.46/5.77 thf(fact_8004_Cauchy__iff,axiom,
% 5.46/5.77 ( topolo6517432010174082258omplex
% 5.46/5.77 = ( ^ [X6: nat > complex] :
% 5.46/5.77 ! [E3: real] :
% 5.46/5.77 ( ( ord_less_real @ zero_zero_real @ E3 )
% 5.46/5.77 => ? [M8: nat] :
% 5.46/5.77 ! [M6: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M8 @ M6 )
% 5.46/5.77 => ! [N2: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M8 @ N2 )
% 5.46/5.77 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) ) @ E3 ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Cauchy_iff
% 5.46/5.77 thf(fact_8005_Cauchy__iff,axiom,
% 5.46/5.77 ( topolo4055970368930404560y_real
% 5.46/5.77 = ( ^ [X6: nat > real] :
% 5.46/5.77 ! [E3: real] :
% 5.46/5.77 ( ( ord_less_real @ zero_zero_real @ E3 )
% 5.46/5.77 => ? [M8: nat] :
% 5.46/5.77 ! [M6: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M8 @ M6 )
% 5.46/5.77 => ! [N2: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ M8 @ N2 )
% 5.46/5.77 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) ) @ E3 ) ) ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % Cauchy_iff
% 5.46/5.77 thf(fact_8006_leD,axiom,
% 5.46/5.77 ! [Y3: real,X4: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ Y3 @ X4 )
% 5.46/5.77 => ~ ( ord_less_real @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leD
% 5.46/5.77 thf(fact_8007_leD,axiom,
% 5.46/5.77 ! [Y3: set_nat,X4: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ Y3 @ X4 )
% 5.46/5.77 => ~ ( ord_less_set_nat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leD
% 5.46/5.77 thf(fact_8008_leD,axiom,
% 5.46/5.77 ! [Y3: rat,X4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ Y3 @ X4 )
% 5.46/5.77 => ~ ( ord_less_rat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leD
% 5.46/5.77 thf(fact_8009_leD,axiom,
% 5.46/5.77 ! [Y3: num,X4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ Y3 @ X4 )
% 5.46/5.77 => ~ ( ord_less_num @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leD
% 5.46/5.77 thf(fact_8010_leD,axiom,
% 5.46/5.77 ! [Y3: nat,X4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ Y3 @ X4 )
% 5.46/5.77 => ~ ( ord_less_nat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leD
% 5.46/5.77 thf(fact_8011_leD,axiom,
% 5.46/5.77 ! [Y3: int,X4: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ Y3 @ X4 )
% 5.46/5.77 => ~ ( ord_less_int @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leD
% 5.46/5.77 thf(fact_8012_leI,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ~ ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_real @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leI
% 5.46/5.77 thf(fact_8013_leI,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ~ ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_rat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leI
% 5.46/5.77 thf(fact_8014_leI,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ~ ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_num @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leI
% 5.46/5.77 thf(fact_8015_leI,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ~ ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_nat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leI
% 5.46/5.77 thf(fact_8016_leI,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ~ ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_int @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % leI
% 5.46/5.77 thf(fact_8017_nless__le,axiom,
% 5.46/5.77 ! [A: real,B2: real] :
% 5.46/5.77 ( ( ~ ( ord_less_real @ A @ B2 ) )
% 5.46/5.77 = ( ~ ( ord_less_eq_real @ A @ B2 )
% 5.46/5.77 | ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % nless_le
% 5.46/5.77 thf(fact_8018_nless__le,axiom,
% 5.46/5.77 ! [A: set_nat,B2: set_nat] :
% 5.46/5.77 ( ( ~ ( ord_less_set_nat @ A @ B2 ) )
% 5.46/5.77 = ( ~ ( ord_less_eq_set_nat @ A @ B2 )
% 5.46/5.77 | ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % nless_le
% 5.46/5.77 thf(fact_8019_nless__le,axiom,
% 5.46/5.77 ! [A: rat,B2: rat] :
% 5.46/5.77 ( ( ~ ( ord_less_rat @ A @ B2 ) )
% 5.46/5.77 = ( ~ ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 | ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % nless_le
% 5.46/5.77 thf(fact_8020_nless__le,axiom,
% 5.46/5.77 ! [A: num,B2: num] :
% 5.46/5.77 ( ( ~ ( ord_less_num @ A @ B2 ) )
% 5.46/5.77 = ( ~ ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 | ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % nless_le
% 5.46/5.77 thf(fact_8021_nless__le,axiom,
% 5.46/5.77 ! [A: nat,B2: nat] :
% 5.46/5.77 ( ( ~ ( ord_less_nat @ A @ B2 ) )
% 5.46/5.77 = ( ~ ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.77 | ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % nless_le
% 5.46/5.77 thf(fact_8022_nless__le,axiom,
% 5.46/5.77 ! [A: int,B2: int] :
% 5.46/5.77 ( ( ~ ( ord_less_int @ A @ B2 ) )
% 5.46/5.77 = ( ~ ( ord_less_eq_int @ A @ B2 )
% 5.46/5.77 | ( A = B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % nless_le
% 5.46/5.77 thf(fact_8023_antisym__conv1,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ~ ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv1
% 5.46/5.77 thf(fact_8024_antisym__conv1,axiom,
% 5.46/5.77 ! [X4: set_nat,Y3: set_nat] :
% 5.46/5.77 ( ~ ( ord_less_set_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv1
% 5.46/5.77 thf(fact_8025_antisym__conv1,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ~ ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv1
% 5.46/5.77 thf(fact_8026_antisym__conv1,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ~ ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv1
% 5.46/5.77 thf(fact_8027_antisym__conv1,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ~ ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv1
% 5.46/5.77 thf(fact_8028_antisym__conv1,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ~ ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv1
% 5.46/5.77 thf(fact_8029_antisym__conv2,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.77 => ( ( ~ ( ord_less_real @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv2
% 5.46/5.77 thf(fact_8030_antisym__conv2,axiom,
% 5.46/5.77 ! [X4: set_nat,Y3: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ~ ( ord_less_set_nat @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv2
% 5.46/5.77 thf(fact_8031_antisym__conv2,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ~ ( ord_less_rat @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv2
% 5.46/5.77 thf(fact_8032_antisym__conv2,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.77 => ( ( ~ ( ord_less_num @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv2
% 5.46/5.77 thf(fact_8033_antisym__conv2,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ( ~ ( ord_less_nat @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv2
% 5.46/5.77 thf(fact_8034_antisym__conv2,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.77 => ( ( ~ ( ord_less_int @ X4 @ Y3 ) )
% 5.46/5.77 = ( X4 = Y3 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % antisym_conv2
% 5.46/5.77 thf(fact_8035_dense__ge,axiom,
% 5.46/5.77 ! [Z: real,Y3: real] :
% 5.46/5.77 ( ! [X3: real] :
% 5.46/5.77 ( ( ord_less_real @ Z @ X3 )
% 5.46/5.77 => ( ord_less_eq_real @ Y3 @ X3 ) )
% 5.46/5.77 => ( ord_less_eq_real @ Y3 @ Z ) ) ).
% 5.46/5.77
% 5.46/5.77 % dense_ge
% 5.46/5.77 thf(fact_8036_dense__ge,axiom,
% 5.46/5.77 ! [Z: rat,Y3: rat] :
% 5.46/5.77 ( ! [X3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ Z @ X3 )
% 5.46/5.77 => ( ord_less_eq_rat @ Y3 @ X3 ) )
% 5.46/5.77 => ( ord_less_eq_rat @ Y3 @ Z ) ) ).
% 5.46/5.77
% 5.46/5.77 % dense_ge
% 5.46/5.77 thf(fact_8037_dense__le,axiom,
% 5.46/5.77 ! [Y3: real,Z: real] :
% 5.46/5.77 ( ! [X3: real] :
% 5.46/5.77 ( ( ord_less_real @ X3 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_real @ X3 @ Z ) )
% 5.46/5.77 => ( ord_less_eq_real @ Y3 @ Z ) ) ).
% 5.46/5.77
% 5.46/5.77 % dense_le
% 5.46/5.77 thf(fact_8038_dense__le,axiom,
% 5.46/5.77 ! [Y3: rat,Z: rat] :
% 5.46/5.77 ( ! [X3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X3 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_rat @ X3 @ Z ) )
% 5.46/5.77 => ( ord_less_eq_rat @ Y3 @ Z ) ) ).
% 5.46/5.77
% 5.46/5.77 % dense_le
% 5.46/5.77 thf(fact_8039_less__le__not__le,axiom,
% 5.46/5.77 ( ord_less_real
% 5.46/5.77 = ( ^ [X: real,Y: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ X @ Y )
% 5.46/5.77 & ~ ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_le_not_le
% 5.46/5.77 thf(fact_8040_less__le__not__le,axiom,
% 5.46/5.77 ( ord_less_set_nat
% 5.46/5.77 = ( ^ [X: set_nat,Y: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.46/5.77 & ~ ( ord_less_eq_set_nat @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_le_not_le
% 5.46/5.77 thf(fact_8041_less__le__not__le,axiom,
% 5.46/5.77 ( ord_less_rat
% 5.46/5.77 = ( ^ [X: rat,Y: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X @ Y )
% 5.46/5.77 & ~ ( ord_less_eq_rat @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_le_not_le
% 5.46/5.77 thf(fact_8042_less__le__not__le,axiom,
% 5.46/5.77 ( ord_less_num
% 5.46/5.77 = ( ^ [X: num,Y: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X @ Y )
% 5.46/5.77 & ~ ( ord_less_eq_num @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_le_not_le
% 5.46/5.77 thf(fact_8043_less__le__not__le,axiom,
% 5.46/5.77 ( ord_less_nat
% 5.46/5.77 = ( ^ [X: nat,Y: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X @ Y )
% 5.46/5.77 & ~ ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_le_not_le
% 5.46/5.77 thf(fact_8044_less__le__not__le,axiom,
% 5.46/5.77 ( ord_less_int
% 5.46/5.77 = ( ^ [X: int,Y: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ X @ Y )
% 5.46/5.77 & ~ ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % less_le_not_le
% 5.46/5.77 thf(fact_8045_not__le__imp__less,axiom,
% 5.46/5.77 ! [Y3: real,X4: real] :
% 5.46/5.77 ( ~ ( ord_less_eq_real @ Y3 @ X4 )
% 5.46/5.77 => ( ord_less_real @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_le_imp_less
% 5.46/5.77 thf(fact_8046_not__le__imp__less,axiom,
% 5.46/5.77 ! [Y3: rat,X4: rat] :
% 5.46/5.77 ( ~ ( ord_less_eq_rat @ Y3 @ X4 )
% 5.46/5.77 => ( ord_less_rat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_le_imp_less
% 5.46/5.77 thf(fact_8047_not__le__imp__less,axiom,
% 5.46/5.77 ! [Y3: num,X4: num] :
% 5.46/5.77 ( ~ ( ord_less_eq_num @ Y3 @ X4 )
% 5.46/5.77 => ( ord_less_num @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_le_imp_less
% 5.46/5.77 thf(fact_8048_not__le__imp__less,axiom,
% 5.46/5.77 ! [Y3: nat,X4: nat] :
% 5.46/5.77 ( ~ ( ord_less_eq_nat @ Y3 @ X4 )
% 5.46/5.77 => ( ord_less_nat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_le_imp_less
% 5.46/5.77 thf(fact_8049_not__le__imp__less,axiom,
% 5.46/5.77 ! [Y3: int,X4: int] :
% 5.46/5.77 ( ~ ( ord_less_eq_int @ Y3 @ X4 )
% 5.46/5.77 => ( ord_less_int @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % not_le_imp_less
% 5.46/5.77 thf(fact_8050_order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_real
% 5.46/5.77 = ( ^ [A4: real,B3: real] :
% 5.46/5.77 ( ( ord_less_real @ A4 @ B3 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.order_iff_strict
% 5.46/5.77 thf(fact_8051_order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_set_nat
% 5.46/5.77 = ( ^ [A4: set_nat,B3: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ A4 @ B3 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.order_iff_strict
% 5.46/5.77 thf(fact_8052_order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_rat
% 5.46/5.77 = ( ^ [A4: rat,B3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A4 @ B3 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.order_iff_strict
% 5.46/5.77 thf(fact_8053_order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_num
% 5.46/5.77 = ( ^ [A4: num,B3: num] :
% 5.46/5.77 ( ( ord_less_num @ A4 @ B3 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.order_iff_strict
% 5.46/5.77 thf(fact_8054_order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_nat
% 5.46/5.77 = ( ^ [A4: nat,B3: nat] :
% 5.46/5.77 ( ( ord_less_nat @ A4 @ B3 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.order_iff_strict
% 5.46/5.77 thf(fact_8055_order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_int
% 5.46/5.77 = ( ^ [A4: int,B3: int] :
% 5.46/5.77 ( ( ord_less_int @ A4 @ B3 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.order_iff_strict
% 5.46/5.77 thf(fact_8056_order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_real
% 5.46/5.77 = ( ^ [A4: real,B3: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ A4 @ B3 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_order
% 5.46/5.77 thf(fact_8057_order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_set_nat
% 5.46/5.77 = ( ^ [A4: set_nat,B3: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_order
% 5.46/5.77 thf(fact_8058_order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_rat
% 5.46/5.77 = ( ^ [A4: rat,B3: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_order
% 5.46/5.77 thf(fact_8059_order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_num
% 5.46/5.77 = ( ^ [A4: num,B3: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_order
% 5.46/5.77 thf(fact_8060_order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_nat
% 5.46/5.77 = ( ^ [A4: nat,B3: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_order
% 5.46/5.77 thf(fact_8061_order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_int
% 5.46/5.77 = ( ^ [A4: int,B3: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_order
% 5.46/5.77 thf(fact_8062_order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [A: real,B2: real,C: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.77 => ( ord_less_real @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans1
% 5.46/5.77 thf(fact_8063_order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_set_nat @ B2 @ C )
% 5.46/5.77 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans1
% 5.46/5.77 thf(fact_8064_order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.77 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans1
% 5.46/5.77 thf(fact_8065_order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [A: num,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_num @ B2 @ C )
% 5.46/5.77 => ( ord_less_num @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans1
% 5.46/5.77 thf(fact_8066_order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_nat @ B2 @ C )
% 5.46/5.77 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans1
% 5.46/5.77 thf(fact_8067_order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [A: int,B2: int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_int @ B2 @ C )
% 5.46/5.77 => ( ord_less_int @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans1
% 5.46/5.77 thf(fact_8068_order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [A: real,B2: real,C: real] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_real @ B2 @ C )
% 5.46/5.77 => ( ord_less_real @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans2
% 5.46/5.77 thf(fact_8069_order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ B2 @ C )
% 5.46/5.77 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans2
% 5.46/5.77 thf(fact_8070_order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [A: rat,B2: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.77 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans2
% 5.46/5.77 thf(fact_8071_order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [A: num,B2: num,C: num] :
% 5.46/5.77 ( ( ord_less_num @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.77 => ( ord_less_num @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans2
% 5.46/5.77 thf(fact_8072_order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [A: nat,B2: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_nat @ B2 @ C )
% 5.46/5.77 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans2
% 5.46/5.77 thf(fact_8073_order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [A: int,B2: int,C: int] :
% 5.46/5.77 ( ( ord_less_int @ A @ B2 )
% 5.46/5.77 => ( ( ord_less_eq_int @ B2 @ C )
% 5.46/5.77 => ( ord_less_int @ A @ C ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_trans2
% 5.46/5.77 thf(fact_8074_order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_real
% 5.46/5.77 = ( ^ [A4: real,B3: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ A4 @ B3 )
% 5.46/5.77 & ~ ( ord_less_eq_real @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_not
% 5.46/5.77 thf(fact_8075_order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_set_nat
% 5.46/5.77 = ( ^ [A4: set_nat,B3: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A4 @ B3 )
% 5.46/5.77 & ~ ( ord_less_eq_set_nat @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_not
% 5.46/5.77 thf(fact_8076_order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_rat
% 5.46/5.77 = ( ^ [A4: rat,B3: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.46/5.77 & ~ ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_not
% 5.46/5.77 thf(fact_8077_order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_num
% 5.46/5.77 = ( ^ [A4: num,B3: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.46/5.77 & ~ ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_not
% 5.46/5.77 thf(fact_8078_order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_nat
% 5.46/5.77 = ( ^ [A4: nat,B3: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.46/5.77 & ~ ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_not
% 5.46/5.77 thf(fact_8079_order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_int
% 5.46/5.77 = ( ^ [A4: int,B3: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.46/5.77 & ~ ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_iff_not
% 5.46/5.77 thf(fact_8080_dense__ge__bounded,axiom,
% 5.46/5.77 ! [Z: real,X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ Z @ X4 )
% 5.46/5.77 => ( ! [W3: real] :
% 5.46/5.77 ( ( ord_less_real @ Z @ W3 )
% 5.46/5.77 => ( ( ord_less_real @ W3 @ X4 )
% 5.46/5.77 => ( ord_less_eq_real @ Y3 @ W3 ) ) )
% 5.46/5.77 => ( ord_less_eq_real @ Y3 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dense_ge_bounded
% 5.46/5.77 thf(fact_8081_dense__ge__bounded,axiom,
% 5.46/5.77 ! [Z: rat,X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ Z @ X4 )
% 5.46/5.77 => ( ! [W3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ Z @ W3 )
% 5.46/5.77 => ( ( ord_less_rat @ W3 @ X4 )
% 5.46/5.77 => ( ord_less_eq_rat @ Y3 @ W3 ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dense_ge_bounded
% 5.46/5.77 thf(fact_8082_dense__le__bounded,axiom,
% 5.46/5.77 ! [X4: real,Y3: real,Z: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( ! [W3: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ W3 )
% 5.46/5.77 => ( ( ord_less_real @ W3 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_real @ W3 @ Z ) ) )
% 5.46/5.77 => ( ord_less_eq_real @ Y3 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dense_le_bounded
% 5.46/5.77 thf(fact_8083_dense__le__bounded,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat,Z: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ! [W3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ W3 )
% 5.46/5.77 => ( ( ord_less_rat @ W3 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_rat @ W3 @ Z ) ) )
% 5.46/5.77 => ( ord_less_eq_rat @ Y3 @ Z ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dense_le_bounded
% 5.46/5.77 thf(fact_8084_dual__order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_real
% 5.46/5.77 = ( ^ [B3: real,A4: real] :
% 5.46/5.77 ( ( ord_less_real @ B3 @ A4 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.order_iff_strict
% 5.46/5.77 thf(fact_8085_dual__order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_set_nat
% 5.46/5.77 = ( ^ [B3: set_nat,A4: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ B3 @ A4 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.order_iff_strict
% 5.46/5.77 thf(fact_8086_dual__order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_rat
% 5.46/5.77 = ( ^ [B3: rat,A4: rat] :
% 5.46/5.77 ( ( ord_less_rat @ B3 @ A4 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.order_iff_strict
% 5.46/5.77 thf(fact_8087_dual__order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_num
% 5.46/5.77 = ( ^ [B3: num,A4: num] :
% 5.46/5.77 ( ( ord_less_num @ B3 @ A4 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.order_iff_strict
% 5.46/5.77 thf(fact_8088_dual__order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_nat
% 5.46/5.77 = ( ^ [B3: nat,A4: nat] :
% 5.46/5.77 ( ( ord_less_nat @ B3 @ A4 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.order_iff_strict
% 5.46/5.77 thf(fact_8089_dual__order_Oorder__iff__strict,axiom,
% 5.46/5.77 ( ord_less_eq_int
% 5.46/5.77 = ( ^ [B3: int,A4: int] :
% 5.46/5.77 ( ( ord_less_int @ B3 @ A4 )
% 5.46/5.77 | ( A4 = B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.order_iff_strict
% 5.46/5.77 thf(fact_8090_dual__order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_real
% 5.46/5.77 = ( ^ [B3: real,A4: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ B3 @ A4 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_order
% 5.46/5.77 thf(fact_8091_dual__order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_set_nat
% 5.46/5.77 = ( ^ [B3: set_nat,A4: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_order
% 5.46/5.77 thf(fact_8092_dual__order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_rat
% 5.46/5.77 = ( ^ [B3: rat,A4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_order
% 5.46/5.77 thf(fact_8093_dual__order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_num
% 5.46/5.77 = ( ^ [B3: num,A4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_order
% 5.46/5.77 thf(fact_8094_dual__order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_nat
% 5.46/5.77 = ( ^ [B3: nat,A4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_order
% 5.46/5.77 thf(fact_8095_dual__order_Ostrict__iff__order,axiom,
% 5.46/5.77 ( ord_less_int
% 5.46/5.77 = ( ^ [B3: int,A4: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.46/5.77 & ( A4 != B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_order
% 5.46/5.77 thf(fact_8096_dual__order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [B2: real,A: real,C: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_real @ C @ B2 )
% 5.46/5.77 => ( ord_less_real @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans1
% 5.46/5.77 thf(fact_8097_dual__order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [B2: set_nat,A: set_nat,C: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_set_nat @ C @ B2 )
% 5.46/5.77 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans1
% 5.46/5.77 thf(fact_8098_dual__order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_rat @ C @ B2 )
% 5.46/5.77 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans1
% 5.46/5.77 thf(fact_8099_dual__order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [B2: num,A: num,C: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_num @ C @ B2 )
% 5.46/5.77 => ( ord_less_num @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans1
% 5.46/5.77 thf(fact_8100_dual__order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_nat @ C @ B2 )
% 5.46/5.77 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans1
% 5.46/5.77 thf(fact_8101_dual__order_Ostrict__trans1,axiom,
% 5.46/5.77 ! [B2: int,A: int,C: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_int @ C @ B2 )
% 5.46/5.77 => ( ord_less_int @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans1
% 5.46/5.77 thf(fact_8102_dual__order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [B2: real,A: real,C: real] :
% 5.46/5.77 ( ( ord_less_real @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_real @ C @ B2 )
% 5.46/5.77 => ( ord_less_real @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans2
% 5.46/5.77 thf(fact_8103_dual__order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [B2: set_nat,A: set_nat,C: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_set_nat @ C @ B2 )
% 5.46/5.77 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans2
% 5.46/5.77 thf(fact_8104_dual__order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [B2: rat,A: rat,C: rat] :
% 5.46/5.77 ( ( ord_less_rat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_rat @ C @ B2 )
% 5.46/5.77 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans2
% 5.46/5.77 thf(fact_8105_dual__order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [B2: num,A: num,C: num] :
% 5.46/5.77 ( ( ord_less_num @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_num @ C @ B2 )
% 5.46/5.77 => ( ord_less_num @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans2
% 5.46/5.77 thf(fact_8106_dual__order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [B2: nat,A: nat,C: nat] :
% 5.46/5.77 ( ( ord_less_nat @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_nat @ C @ B2 )
% 5.46/5.77 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans2
% 5.46/5.77 thf(fact_8107_dual__order_Ostrict__trans2,axiom,
% 5.46/5.77 ! [B2: int,A: int,C: int] :
% 5.46/5.77 ( ( ord_less_int @ B2 @ A )
% 5.46/5.77 => ( ( ord_less_eq_int @ C @ B2 )
% 5.46/5.77 => ( ord_less_int @ C @ A ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_trans2
% 5.46/5.77 thf(fact_8108_dual__order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_real
% 5.46/5.77 = ( ^ [B3: real,A4: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ B3 @ A4 )
% 5.46/5.77 & ~ ( ord_less_eq_real @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_not
% 5.46/5.77 thf(fact_8109_dual__order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_set_nat
% 5.46/5.77 = ( ^ [B3: set_nat,A4: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ B3 @ A4 )
% 5.46/5.77 & ~ ( ord_less_eq_set_nat @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_not
% 5.46/5.77 thf(fact_8110_dual__order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_rat
% 5.46/5.77 = ( ^ [B3: rat,A4: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.46/5.77 & ~ ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_not
% 5.46/5.77 thf(fact_8111_dual__order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_num
% 5.46/5.77 = ( ^ [B3: num,A4: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.46/5.77 & ~ ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_not
% 5.46/5.77 thf(fact_8112_dual__order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_nat
% 5.46/5.77 = ( ^ [B3: nat,A4: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.46/5.77 & ~ ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_not
% 5.46/5.77 thf(fact_8113_dual__order_Ostrict__iff__not,axiom,
% 5.46/5.77 ( ord_less_int
% 5.46/5.77 = ( ^ [B3: int,A4: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.46/5.77 & ~ ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_iff_not
% 5.46/5.77 thf(fact_8114_order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [A: real,B2: real] :
% 5.46/5.77 ( ( ord_less_real @ A @ B2 )
% 5.46/5.77 => ( ord_less_eq_real @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_order
% 5.46/5.77 thf(fact_8115_order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [A: set_nat,B2: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ A @ B2 )
% 5.46/5.77 => ( ord_less_eq_set_nat @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_order
% 5.46/5.77 thf(fact_8116_order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [A: rat,B2: rat] :
% 5.46/5.77 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.77 => ( ord_less_eq_rat @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_order
% 5.46/5.77 thf(fact_8117_order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [A: num,B2: num] :
% 5.46/5.77 ( ( ord_less_num @ A @ B2 )
% 5.46/5.77 => ( ord_less_eq_num @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_order
% 5.46/5.77 thf(fact_8118_order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [A: nat,B2: nat] :
% 5.46/5.77 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.77 => ( ord_less_eq_nat @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_order
% 5.46/5.77 thf(fact_8119_order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [A: int,B2: int] :
% 5.46/5.77 ( ( ord_less_int @ A @ B2 )
% 5.46/5.77 => ( ord_less_eq_int @ A @ B2 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order.strict_implies_order
% 5.46/5.77 thf(fact_8120_dual__order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [B2: real,A: real] :
% 5.46/5.77 ( ( ord_less_real @ B2 @ A )
% 5.46/5.77 => ( ord_less_eq_real @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_order
% 5.46/5.77 thf(fact_8121_dual__order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [B2: set_nat,A: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ B2 @ A )
% 5.46/5.77 => ( ord_less_eq_set_nat @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_order
% 5.46/5.77 thf(fact_8122_dual__order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [B2: rat,A: rat] :
% 5.46/5.77 ( ( ord_less_rat @ B2 @ A )
% 5.46/5.77 => ( ord_less_eq_rat @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_order
% 5.46/5.77 thf(fact_8123_dual__order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [B2: num,A: num] :
% 5.46/5.77 ( ( ord_less_num @ B2 @ A )
% 5.46/5.77 => ( ord_less_eq_num @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_order
% 5.46/5.77 thf(fact_8124_dual__order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [B2: nat,A: nat] :
% 5.46/5.77 ( ( ord_less_nat @ B2 @ A )
% 5.46/5.77 => ( ord_less_eq_nat @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_order
% 5.46/5.77 thf(fact_8125_dual__order_Ostrict__implies__order,axiom,
% 5.46/5.77 ! [B2: int,A: int] :
% 5.46/5.77 ( ( ord_less_int @ B2 @ A )
% 5.46/5.77 => ( ord_less_eq_int @ B2 @ A ) ) ).
% 5.46/5.77
% 5.46/5.77 % dual_order.strict_implies_order
% 5.46/5.77 thf(fact_8126_order__le__less,axiom,
% 5.46/5.77 ( ord_less_eq_real
% 5.46/5.77 = ( ^ [X: real,Y: real] :
% 5.46/5.77 ( ( ord_less_real @ X @ Y )
% 5.46/5.77 | ( X = Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_le_less
% 5.46/5.77 thf(fact_8127_order__le__less,axiom,
% 5.46/5.77 ( ord_less_eq_set_nat
% 5.46/5.77 = ( ^ [X: set_nat,Y: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ X @ Y )
% 5.46/5.77 | ( X = Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_le_less
% 5.46/5.77 thf(fact_8128_order__le__less,axiom,
% 5.46/5.77 ( ord_less_eq_rat
% 5.46/5.77 = ( ^ [X: rat,Y: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X @ Y )
% 5.46/5.77 | ( X = Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_le_less
% 5.46/5.77 thf(fact_8129_order__le__less,axiom,
% 5.46/5.77 ( ord_less_eq_num
% 5.46/5.77 = ( ^ [X: num,Y: num] :
% 5.46/5.77 ( ( ord_less_num @ X @ Y )
% 5.46/5.77 | ( X = Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_le_less
% 5.46/5.77 thf(fact_8130_order__le__less,axiom,
% 5.46/5.77 ( ord_less_eq_nat
% 5.46/5.77 = ( ^ [X: nat,Y: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X @ Y )
% 5.46/5.77 | ( X = Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_le_less
% 5.46/5.77 thf(fact_8131_order__le__less,axiom,
% 5.46/5.77 ( ord_less_eq_int
% 5.46/5.77 = ( ^ [X: int,Y: int] :
% 5.46/5.77 ( ( ord_less_int @ X @ Y )
% 5.46/5.77 | ( X = Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_le_less
% 5.46/5.77 thf(fact_8132_order__less__le,axiom,
% 5.46/5.77 ( ord_less_real
% 5.46/5.77 = ( ^ [X: real,Y: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ X @ Y )
% 5.46/5.77 & ( X != Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_le
% 5.46/5.77 thf(fact_8133_order__less__le,axiom,
% 5.46/5.77 ( ord_less_set_nat
% 5.46/5.77 = ( ^ [X: set_nat,Y: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.46/5.77 & ( X != Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_le
% 5.46/5.77 thf(fact_8134_order__less__le,axiom,
% 5.46/5.77 ( ord_less_rat
% 5.46/5.77 = ( ^ [X: rat,Y: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ X @ Y )
% 5.46/5.77 & ( X != Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_le
% 5.46/5.77 thf(fact_8135_order__less__le,axiom,
% 5.46/5.77 ( ord_less_num
% 5.46/5.77 = ( ^ [X: num,Y: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ X @ Y )
% 5.46/5.77 & ( X != Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_le
% 5.46/5.77 thf(fact_8136_order__less__le,axiom,
% 5.46/5.77 ( ord_less_nat
% 5.46/5.77 = ( ^ [X: nat,Y: nat] :
% 5.46/5.77 ( ( ord_less_eq_nat @ X @ Y )
% 5.46/5.77 & ( X != Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_le
% 5.46/5.77 thf(fact_8137_order__less__le,axiom,
% 5.46/5.77 ( ord_less_int
% 5.46/5.77 = ( ^ [X: int,Y: int] :
% 5.46/5.77 ( ( ord_less_eq_int @ X @ Y )
% 5.46/5.77 & ( X != Y ) ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_le
% 5.46/5.77 thf(fact_8138_linorder__not__le,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ~ ( ord_less_eq_real @ X4 @ Y3 ) )
% 5.46/5.77 = ( ord_less_real @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_not_le
% 5.46/5.77 thf(fact_8139_linorder__not__le,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ~ ( ord_less_eq_rat @ X4 @ Y3 ) )
% 5.46/5.77 = ( ord_less_rat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_not_le
% 5.46/5.77 thf(fact_8140_linorder__not__le,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ~ ( ord_less_eq_num @ X4 @ Y3 ) )
% 5.46/5.77 = ( ord_less_num @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_not_le
% 5.46/5.77 thf(fact_8141_linorder__not__le,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ~ ( ord_less_eq_nat @ X4 @ Y3 ) )
% 5.46/5.77 = ( ord_less_nat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_not_le
% 5.46/5.77 thf(fact_8142_linorder__not__le,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ~ ( ord_less_eq_int @ X4 @ Y3 ) )
% 5.46/5.77 = ( ord_less_int @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_not_le
% 5.46/5.77 thf(fact_8143_linorder__not__less,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ~ ( ord_less_real @ X4 @ Y3 ) )
% 5.46/5.77 = ( ord_less_eq_real @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_not_less
% 5.46/5.77 thf(fact_8144_linorder__not__less,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ~ ( ord_less_rat @ X4 @ Y3 ) )
% 5.46/5.77 = ( ord_less_eq_rat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_not_less
% 5.46/5.77 thf(fact_8145_linorder__not__less,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ~ ( ord_less_num @ X4 @ Y3 ) )
% 5.46/5.77 = ( ord_less_eq_num @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_not_less
% 5.46/5.77 thf(fact_8146_linorder__not__less,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ~ ( ord_less_nat @ X4 @ Y3 ) )
% 5.46/5.77 = ( ord_less_eq_nat @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_not_less
% 5.46/5.77 thf(fact_8147_linorder__not__less,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ~ ( ord_less_int @ X4 @ Y3 ) )
% 5.46/5.77 = ( ord_less_eq_int @ Y3 @ X4 ) ) ).
% 5.46/5.77
% 5.46/5.77 % linorder_not_less
% 5.46/5.77 thf(fact_8148_order__less__imp__le,axiom,
% 5.46/5.77 ! [X4: real,Y3: real] :
% 5.46/5.77 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_real @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_le
% 5.46/5.77 thf(fact_8149_order__less__imp__le,axiom,
% 5.46/5.77 ! [X4: set_nat,Y3: set_nat] :
% 5.46/5.77 ( ( ord_less_set_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_set_nat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_le
% 5.46/5.77 thf(fact_8150_order__less__imp__le,axiom,
% 5.46/5.77 ! [X4: rat,Y3: rat] :
% 5.46/5.77 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_rat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_le
% 5.46/5.77 thf(fact_8151_order__less__imp__le,axiom,
% 5.46/5.77 ! [X4: num,Y3: num] :
% 5.46/5.77 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_num @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_le
% 5.46/5.77 thf(fact_8152_order__less__imp__le,axiom,
% 5.46/5.77 ! [X4: nat,Y3: nat] :
% 5.46/5.77 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_nat @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_le
% 5.46/5.77 thf(fact_8153_order__less__imp__le,axiom,
% 5.46/5.77 ! [X4: int,Y3: int] :
% 5.46/5.77 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.77 => ( ord_less_eq_int @ X4 @ Y3 ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_less_imp_le
% 5.46/5.77 thf(fact_8154_order__le__neq__trans,axiom,
% 5.46/5.77 ! [A: real,B2: real] :
% 5.46/5.77 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.77 => ( ( A != B2 )
% 5.46/5.77 => ( ord_less_real @ A @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_le_neq_trans
% 5.46/5.77 thf(fact_8155_order__le__neq__trans,axiom,
% 5.46/5.77 ! [A: set_nat,B2: set_nat] :
% 5.46/5.77 ( ( ord_less_eq_set_nat @ A @ B2 )
% 5.46/5.77 => ( ( A != B2 )
% 5.46/5.77 => ( ord_less_set_nat @ A @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_le_neq_trans
% 5.46/5.77 thf(fact_8156_order__le__neq__trans,axiom,
% 5.46/5.77 ! [A: rat,B2: rat] :
% 5.46/5.77 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.77 => ( ( A != B2 )
% 5.46/5.77 => ( ord_less_rat @ A @ B2 ) ) ) ).
% 5.46/5.77
% 5.46/5.77 % order_le_neq_trans
% 5.46/5.77 thf(fact_8157_order__le__neq__trans,axiom,
% 5.46/5.77 ! [A: num,B2: num] :
% 5.46/5.77 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.78 => ( ( A != B2 )
% 5.46/5.78 => ( ord_less_num @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_neq_trans
% 5.46/5.78 thf(fact_8158_order__le__neq__trans,axiom,
% 5.46/5.78 ! [A: nat,B2: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.78 => ( ( A != B2 )
% 5.46/5.78 => ( ord_less_nat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_neq_trans
% 5.46/5.78 thf(fact_8159_order__le__neq__trans,axiom,
% 5.46/5.78 ! [A: int,B2: int] :
% 5.46/5.78 ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.78 => ( ( A != B2 )
% 5.46/5.78 => ( ord_less_int @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_neq_trans
% 5.46/5.78 thf(fact_8160_order__neq__le__trans,axiom,
% 5.46/5.78 ! [A: real,B2: real] :
% 5.46/5.78 ( ( A != B2 )
% 5.46/5.78 => ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.78 => ( ord_less_real @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_neq_le_trans
% 5.46/5.78 thf(fact_8161_order__neq__le__trans,axiom,
% 5.46/5.78 ! [A: set_nat,B2: set_nat] :
% 5.46/5.78 ( ( A != B2 )
% 5.46/5.78 => ( ( ord_less_eq_set_nat @ A @ B2 )
% 5.46/5.78 => ( ord_less_set_nat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_neq_le_trans
% 5.46/5.78 thf(fact_8162_order__neq__le__trans,axiom,
% 5.46/5.78 ! [A: rat,B2: rat] :
% 5.46/5.78 ( ( A != B2 )
% 5.46/5.78 => ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.78 => ( ord_less_rat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_neq_le_trans
% 5.46/5.78 thf(fact_8163_order__neq__le__trans,axiom,
% 5.46/5.78 ! [A: num,B2: num] :
% 5.46/5.78 ( ( A != B2 )
% 5.46/5.78 => ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.78 => ( ord_less_num @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_neq_le_trans
% 5.46/5.78 thf(fact_8164_order__neq__le__trans,axiom,
% 5.46/5.78 ! [A: nat,B2: nat] :
% 5.46/5.78 ( ( A != B2 )
% 5.46/5.78 => ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.78 => ( ord_less_nat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_neq_le_trans
% 5.46/5.78 thf(fact_8165_order__neq__le__trans,axiom,
% 5.46/5.78 ! [A: int,B2: int] :
% 5.46/5.78 ( ( A != B2 )
% 5.46/5.78 => ( ( ord_less_eq_int @ A @ B2 )
% 5.46/5.78 => ( ord_less_int @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_neq_le_trans
% 5.46/5.78 thf(fact_8166_order__le__less__trans,axiom,
% 5.46/5.78 ! [X4: real,Y3: real,Z: real] :
% 5.46/5.78 ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_real @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_real @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_trans
% 5.46/5.78 thf(fact_8167_order__le__less__trans,axiom,
% 5.46/5.78 ! [X4: set_nat,Y3: set_nat,Z: set_nat] :
% 5.46/5.78 ( ( ord_less_eq_set_nat @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_set_nat @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_set_nat @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_trans
% 5.46/5.78 thf(fact_8168_order__le__less__trans,axiom,
% 5.46/5.78 ! [X4: rat,Y3: rat,Z: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_rat @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_trans
% 5.46/5.78 thf(fact_8169_order__le__less__trans,axiom,
% 5.46/5.78 ! [X4: num,Y3: num,Z: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_num @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_num @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_trans
% 5.46/5.78 thf(fact_8170_order__le__less__trans,axiom,
% 5.46/5.78 ! [X4: nat,Y3: nat,Z: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_nat @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_trans
% 5.46/5.78 thf(fact_8171_order__le__less__trans,axiom,
% 5.46/5.78 ! [X4: int,Y3: int,Z: int] :
% 5.46/5.78 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_int @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_int @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_trans
% 5.46/5.78 thf(fact_8172_order__less__le__trans,axiom,
% 5.46/5.78 ! [X4: real,Y3: real,Z: real] :
% 5.46/5.78 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_eq_real @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_real @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_trans
% 5.46/5.78 thf(fact_8173_order__less__le__trans,axiom,
% 5.46/5.78 ! [X4: set_nat,Y3: set_nat,Z: set_nat] :
% 5.46/5.78 ( ( ord_less_set_nat @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_eq_set_nat @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_set_nat @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_trans
% 5.46/5.78 thf(fact_8174_order__less__le__trans,axiom,
% 5.46/5.78 ! [X4: rat,Y3: rat,Z: rat] :
% 5.46/5.78 ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_eq_rat @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_trans
% 5.46/5.78 thf(fact_8175_order__less__le__trans,axiom,
% 5.46/5.78 ! [X4: num,Y3: num,Z: num] :
% 5.46/5.78 ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_eq_num @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_num @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_trans
% 5.46/5.78 thf(fact_8176_order__less__le__trans,axiom,
% 5.46/5.78 ! [X4: nat,Y3: nat,Z: nat] :
% 5.46/5.78 ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_eq_nat @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_trans
% 5.46/5.78 thf(fact_8177_order__less__le__trans,axiom,
% 5.46/5.78 ! [X4: int,Y3: int,Z: int] :
% 5.46/5.78 ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_eq_int @ Y3 @ Z )
% 5.46/5.78 => ( ord_less_int @ X4 @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_trans
% 5.46/5.78 thf(fact_8178_order__le__less__subst1,axiom,
% 5.46/5.78 ! [A: real,F: real > real,B2: real,C: real] :
% 5.46/5.78 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.78 => ( ! [X3: real,Y4: real] :
% 5.46/5.78 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst1
% 5.46/5.78 thf(fact_8179_order__le__less__subst1,axiom,
% 5.46/5.78 ! [A: real,F: rat > real,B2: rat,C: rat] :
% 5.46/5.78 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst1
% 5.46/5.78 thf(fact_8180_order__le__less__subst1,axiom,
% 5.46/5.78 ! [A: real,F: num > real,B2: num,C: num] :
% 5.46/5.78 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_num @ B2 @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst1
% 5.46/5.78 thf(fact_8181_order__le__less__subst1,axiom,
% 5.46/5.78 ! [A: real,F: nat > real,B2: nat,C: nat] :
% 5.46/5.78 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_nat @ B2 @ C )
% 5.46/5.78 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.78 ( ( ord_less_nat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst1
% 5.46/5.78 thf(fact_8182_order__le__less__subst1,axiom,
% 5.46/5.78 ! [A: real,F: int > real,B2: int,C: int] :
% 5.46/5.78 ( ( ord_less_eq_real @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_int @ B2 @ C )
% 5.46/5.78 => ( ! [X3: int,Y4: int] :
% 5.46/5.78 ( ( ord_less_int @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst1
% 5.46/5.78 thf(fact_8183_order__le__less__subst1,axiom,
% 5.46/5.78 ! [A: rat,F: real > rat,B2: real,C: real] :
% 5.46/5.78 ( ( ord_less_eq_rat @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_real @ B2 @ C )
% 5.46/5.78 => ( ! [X3: real,Y4: real] :
% 5.46/5.78 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst1
% 5.46/5.78 thf(fact_8184_order__le__less__subst1,axiom,
% 5.46/5.78 ! [A: rat,F: rat > rat,B2: rat,C: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_rat @ B2 @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst1
% 5.46/5.78 thf(fact_8185_order__le__less__subst1,axiom,
% 5.46/5.78 ! [A: rat,F: num > rat,B2: num,C: num] :
% 5.46/5.78 ( ( ord_less_eq_rat @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_num @ B2 @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst1
% 5.46/5.78 thf(fact_8186_order__le__less__subst1,axiom,
% 5.46/5.78 ! [A: rat,F: nat > rat,B2: nat,C: nat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_nat @ B2 @ C )
% 5.46/5.78 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.78 ( ( ord_less_nat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst1
% 5.46/5.78 thf(fact_8187_order__le__less__subst1,axiom,
% 5.46/5.78 ! [A: rat,F: int > rat,B2: int,C: int] :
% 5.46/5.78 ( ( ord_less_eq_rat @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_int @ B2 @ C )
% 5.46/5.78 => ( ! [X3: int,Y4: int] :
% 5.46/5.78 ( ( ord_less_int @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst1
% 5.46/5.78 thf(fact_8188_order__le__less__subst2,axiom,
% 5.46/5.78 ! [A: rat,B2: rat,F: rat > real,C: real] :
% 5.46/5.78 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_real @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst2
% 5.46/5.78 thf(fact_8189_order__le__less__subst2,axiom,
% 5.46/5.78 ! [A: rat,B2: rat,F: rat > rat,C: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_rat @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst2
% 5.46/5.78 thf(fact_8190_order__le__less__subst2,axiom,
% 5.46/5.78 ! [A: rat,B2: rat,F: rat > num,C: num] :
% 5.46/5.78 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_num @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst2
% 5.46/5.78 thf(fact_8191_order__le__less__subst2,axiom,
% 5.46/5.78 ! [A: rat,B2: rat,F: rat > nat,C: nat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst2
% 5.46/5.78 thf(fact_8192_order__le__less__subst2,axiom,
% 5.46/5.78 ! [A: rat,B2: rat,F: rat > int,C: int] :
% 5.46/5.78 ( ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst2
% 5.46/5.78 thf(fact_8193_order__le__less__subst2,axiom,
% 5.46/5.78 ! [A: num,B2: num,F: num > real,C: real] :
% 5.46/5.78 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_real @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst2
% 5.46/5.78 thf(fact_8194_order__le__less__subst2,axiom,
% 5.46/5.78 ! [A: num,B2: num,F: num > rat,C: rat] :
% 5.46/5.78 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_rat @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst2
% 5.46/5.78 thf(fact_8195_order__le__less__subst2,axiom,
% 5.46/5.78 ! [A: num,B2: num,F: num > num,C: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_num @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst2
% 5.46/5.78 thf(fact_8196_order__le__less__subst2,axiom,
% 5.46/5.78 ! [A: num,B2: num,F: num > nat,C: nat] :
% 5.46/5.78 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst2
% 5.46/5.78 thf(fact_8197_order__le__less__subst2,axiom,
% 5.46/5.78 ! [A: num,B2: num,F: num > int,C: int] :
% 5.46/5.78 ( ( ord_less_eq_num @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_less_subst2
% 5.46/5.78 thf(fact_8198_order__less__le__subst1,axiom,
% 5.46/5.78 ! [A: real,F: rat > real,B2: rat,C: rat] :
% 5.46/5.78 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst1
% 5.46/5.78 thf(fact_8199_order__less__le__subst1,axiom,
% 5.46/5.78 ! [A: rat,F: rat > rat,B2: rat,C: rat] :
% 5.46/5.78 ( ( ord_less_rat @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst1
% 5.46/5.78 thf(fact_8200_order__less__le__subst1,axiom,
% 5.46/5.78 ! [A: num,F: rat > num,B2: rat,C: rat] :
% 5.46/5.78 ( ( ord_less_num @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst1
% 5.46/5.78 thf(fact_8201_order__less__le__subst1,axiom,
% 5.46/5.78 ! [A: nat,F: rat > nat,B2: rat,C: rat] :
% 5.46/5.78 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst1
% 5.46/5.78 thf(fact_8202_order__less__le__subst1,axiom,
% 5.46/5.78 ! [A: int,F: rat > int,B2: rat,C: rat] :
% 5.46/5.78 ( ( ord_less_int @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_eq_rat @ B2 @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst1
% 5.46/5.78 thf(fact_8203_order__less__le__subst1,axiom,
% 5.46/5.78 ! [A: real,F: num > real,B2: num,C: num] :
% 5.46/5.78 ( ( ord_less_real @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst1
% 5.46/5.78 thf(fact_8204_order__less__le__subst1,axiom,
% 5.46/5.78 ! [A: rat,F: num > rat,B2: num,C: num] :
% 5.46/5.78 ( ( ord_less_rat @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst1
% 5.46/5.78 thf(fact_8205_order__less__le__subst1,axiom,
% 5.46/5.78 ! [A: num,F: num > num,B2: num,C: num] :
% 5.46/5.78 ( ( ord_less_num @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst1
% 5.46/5.78 thf(fact_8206_order__less__le__subst1,axiom,
% 5.46/5.78 ! [A: nat,F: num > nat,B2: num,C: num] :
% 5.46/5.78 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst1
% 5.46/5.78 thf(fact_8207_order__less__le__subst1,axiom,
% 5.46/5.78 ! [A: int,F: num > int,B2: num,C: num] :
% 5.46/5.78 ( ( ord_less_int @ A @ ( F @ B2 ) )
% 5.46/5.78 => ( ( ord_less_eq_num @ B2 @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst1
% 5.46/5.78 thf(fact_8208_order__less__le__subst2,axiom,
% 5.46/5.78 ! [A: real,B2: real,F: real > real,C: real] :
% 5.46/5.78 ( ( ord_less_real @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: real,Y4: real] :
% 5.46/5.78 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst2
% 5.46/5.78 thf(fact_8209_order__less__le__subst2,axiom,
% 5.46/5.78 ! [A: rat,B2: rat,F: rat > real,C: real] :
% 5.46/5.78 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst2
% 5.46/5.78 thf(fact_8210_order__less__le__subst2,axiom,
% 5.46/5.78 ! [A: num,B2: num,F: num > real,C: real] :
% 5.46/5.78 ( ( ord_less_num @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst2
% 5.46/5.78 thf(fact_8211_order__less__le__subst2,axiom,
% 5.46/5.78 ! [A: nat,B2: nat,F: nat > real,C: real] :
% 5.46/5.78 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.78 ( ( ord_less_nat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst2
% 5.46/5.78 thf(fact_8212_order__less__le__subst2,axiom,
% 5.46/5.78 ! [A: int,B2: int,F: int > real,C: real] :
% 5.46/5.78 ( ( ord_less_int @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_eq_real @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: int,Y4: int] :
% 5.46/5.78 ( ( ord_less_int @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst2
% 5.46/5.78 thf(fact_8213_order__less__le__subst2,axiom,
% 5.46/5.78 ! [A: real,B2: real,F: real > rat,C: rat] :
% 5.46/5.78 ( ( ord_less_real @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: real,Y4: real] :
% 5.46/5.78 ( ( ord_less_real @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst2
% 5.46/5.78 thf(fact_8214_order__less__le__subst2,axiom,
% 5.46/5.78 ! [A: rat,B2: rat,F: rat > rat,C: rat] :
% 5.46/5.78 ( ( ord_less_rat @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: rat,Y4: rat] :
% 5.46/5.78 ( ( ord_less_rat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst2
% 5.46/5.78 thf(fact_8215_order__less__le__subst2,axiom,
% 5.46/5.78 ! [A: num,B2: num,F: num > rat,C: rat] :
% 5.46/5.78 ( ( ord_less_num @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: num,Y4: num] :
% 5.46/5.78 ( ( ord_less_num @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst2
% 5.46/5.78 thf(fact_8216_order__less__le__subst2,axiom,
% 5.46/5.78 ! [A: nat,B2: nat,F: nat > rat,C: rat] :
% 5.46/5.78 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: nat,Y4: nat] :
% 5.46/5.78 ( ( ord_less_nat @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst2
% 5.46/5.78 thf(fact_8217_order__less__le__subst2,axiom,
% 5.46/5.78 ! [A: int,B2: int,F: int > rat,C: rat] :
% 5.46/5.78 ( ( ord_less_int @ A @ B2 )
% 5.46/5.78 => ( ( ord_less_eq_rat @ ( F @ B2 ) @ C )
% 5.46/5.78 => ( ! [X3: int,Y4: int] :
% 5.46/5.78 ( ( ord_less_int @ X3 @ Y4 )
% 5.46/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 5.46/5.78 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_less_le_subst2
% 5.46/5.78 thf(fact_8218_linorder__le__less__linear,axiom,
% 5.46/5.78 ! [X4: real,Y3: real] :
% 5.46/5.78 ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.78 | ( ord_less_real @ Y3 @ X4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % linorder_le_less_linear
% 5.46/5.78 thf(fact_8219_linorder__le__less__linear,axiom,
% 5.46/5.78 ! [X4: rat,Y3: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.78 | ( ord_less_rat @ Y3 @ X4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % linorder_le_less_linear
% 5.46/5.78 thf(fact_8220_linorder__le__less__linear,axiom,
% 5.46/5.78 ! [X4: num,Y3: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.78 | ( ord_less_num @ Y3 @ X4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % linorder_le_less_linear
% 5.46/5.78 thf(fact_8221_linorder__le__less__linear,axiom,
% 5.46/5.78 ! [X4: nat,Y3: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.78 | ( ord_less_nat @ Y3 @ X4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % linorder_le_less_linear
% 5.46/5.78 thf(fact_8222_linorder__le__less__linear,axiom,
% 5.46/5.78 ! [X4: int,Y3: int] :
% 5.46/5.78 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.78 | ( ord_less_int @ Y3 @ X4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % linorder_le_less_linear
% 5.46/5.78 thf(fact_8223_order__le__imp__less__or__eq,axiom,
% 5.46/5.78 ! [X4: real,Y3: real] :
% 5.46/5.78 ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.78 | ( X4 = Y3 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_imp_less_or_eq
% 5.46/5.78 thf(fact_8224_order__le__imp__less__or__eq,axiom,
% 5.46/5.78 ! [X4: set_nat,Y3: set_nat] :
% 5.46/5.78 ( ( ord_less_eq_set_nat @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_set_nat @ X4 @ Y3 )
% 5.46/5.78 | ( X4 = Y3 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_imp_less_or_eq
% 5.46/5.78 thf(fact_8225_order__le__imp__less__or__eq,axiom,
% 5.46/5.78 ! [X4: rat,Y3: rat] :
% 5.46/5.78 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_rat @ X4 @ Y3 )
% 5.46/5.78 | ( X4 = Y3 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_imp_less_or_eq
% 5.46/5.78 thf(fact_8226_order__le__imp__less__or__eq,axiom,
% 5.46/5.78 ! [X4: num,Y3: num] :
% 5.46/5.78 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_num @ X4 @ Y3 )
% 5.46/5.78 | ( X4 = Y3 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_imp_less_or_eq
% 5.46/5.78 thf(fact_8227_order__le__imp__less__or__eq,axiom,
% 5.46/5.78 ! [X4: nat,Y3: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.78 | ( X4 = Y3 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_imp_less_or_eq
% 5.46/5.78 thf(fact_8228_order__le__imp__less__or__eq,axiom,
% 5.46/5.78 ! [X4: int,Y3: int] :
% 5.46/5.78 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.46/5.78 => ( ( ord_less_int @ X4 @ Y3 )
% 5.46/5.78 | ( X4 = Y3 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % order_le_imp_less_or_eq
% 5.46/5.78 thf(fact_8229_and__not__numerals_I8_J,axiom,
% 5.46/5.78 ! [M: num,N: num] :
% 5.46/5.78 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.78 = ( 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 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % and_not_numerals(8)
% 5.46/5.78 thf(fact_8230_not__int__rec,axiom,
% 5.46/5.78 ( bit_ri7919022796975470100ot_int
% 5.46/5.78 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % not_int_rec
% 5.46/5.78 thf(fact_8231__C5_Ohyps_C_I11_J,axiom,
% 5.46/5.78 ( ( mi != ma )
% 5.46/5.78 => ! [I4: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.46/5.78 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.46/5.78 = I4 )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.46/5.78 & ! [X5: nat] :
% 5.46/5.78 ( ( ( ( vEBT_VEBT_high @ X5 @ na )
% 5.46/5.78 = I4 )
% 5.46/5.78 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ ( vEBT_VEBT_low @ X5 @ na ) ) )
% 5.46/5.78 => ( ( ord_less_nat @ mi @ X5 )
% 5.46/5.78 & ( ord_less_eq_nat @ X5 @ ma ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % "5.hyps"(11)
% 5.46/5.78 thf(fact_8232__C20_C,axiom,
% 5.46/5.78 ( ( za = mi )
% 5.46/5.78 | ( za = ma )
% 5.46/5.78 | ( ( ord_less_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
% 5.46/5.78 & ( 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 ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % "20"
% 5.46/5.78 thf(fact_8233_abd,axiom,
% 5.46/5.78 ( ( za = ma )
% 5.46/5.78 => ( 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 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % abd
% 5.46/5.78 thf(fact_8234_aaa,axiom,
% 5.46/5.78 ( ( ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.78 = ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 => ( 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 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aaa
% 5.46/5.78 thf(fact_8235__C33_C,axiom,
% 5.46/5.78 ~ ? [U2: nat] :
% 5.46/5.78 ( ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U2 )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ U2 ) ) ).
% 5.46/5.78
% 5.46/5.78 % "33"
% 5.46/5.78 thf(fact_8236__092_060open_062_092_060exists_062miny_O_Aboth__member__options_A_ItreeList_A_B_Asc_J_Aminy_092_060close_062,axiom,
% 5.46/5.78 ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ sc ) @ X_1 ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>\<exists>miny. both_member_options (treeList ! sc) miny\<close>
% 5.46/5.78 thf(fact_8237_abf,axiom,
% 5.46/5.78 vEBT_V8194947554948674370ptions @ ( 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 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % abf
% 5.46/5.78 thf(fact_8238_abe,axiom,
% 5.46/5.78 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 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % abe
% 5.46/5.78 thf(fact_8239_aa,axiom,
% 5.46/5.78 ( ( za = ma )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ ( 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 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aa
% 5.46/5.78 thf(fact_8240_nth__equalityI,axiom,
% 5.46/5.78 ! [Xs2: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.46/5.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.46/5.78 = ( size_s6755466524823107622T_VEBT @ Ys2 ) )
% 5.46/5.78 => ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.78 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 5.46/5.78 = ( nth_VEBT_VEBT @ Ys2 @ I3 ) ) )
% 5.46/5.78 => ( Xs2 = Ys2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_equalityI
% 5.46/5.78 thf(fact_8241_nth__equalityI,axiom,
% 5.46/5.78 ! [Xs2: list_o,Ys2: list_o] :
% 5.46/5.78 ( ( ( size_size_list_o @ Xs2 )
% 5.46/5.78 = ( size_size_list_o @ Ys2 ) )
% 5.46/5.78 => ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.78 => ( ( nth_o @ Xs2 @ I3 )
% 5.46/5.78 = ( nth_o @ Ys2 @ I3 ) ) )
% 5.46/5.78 => ( Xs2 = Ys2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_equalityI
% 5.46/5.78 thf(fact_8242_nth__equalityI,axiom,
% 5.46/5.78 ! [Xs2: list_nat,Ys2: list_nat] :
% 5.46/5.78 ( ( ( size_size_list_nat @ Xs2 )
% 5.46/5.78 = ( size_size_list_nat @ Ys2 ) )
% 5.46/5.78 => ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.78 => ( ( nth_nat @ Xs2 @ I3 )
% 5.46/5.78 = ( nth_nat @ Ys2 @ I3 ) ) )
% 5.46/5.78 => ( Xs2 = Ys2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_equalityI
% 5.46/5.78 thf(fact_8243_nth__equalityI,axiom,
% 5.46/5.78 ! [Xs2: list_int,Ys2: list_int] :
% 5.46/5.78 ( ( ( size_size_list_int @ Xs2 )
% 5.46/5.78 = ( size_size_list_int @ Ys2 ) )
% 5.46/5.78 => ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.78 => ( ( nth_int @ Xs2 @ I3 )
% 5.46/5.78 = ( nth_int @ Ys2 @ I3 ) ) )
% 5.46/5.78 => ( Xs2 = Ys2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_equalityI
% 5.46/5.78 thf(fact_8244_Skolem__list__nth,axiom,
% 5.46/5.78 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.46/5.78 ( ( ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ K )
% 5.46/5.78 => ? [X6: vEBT_VEBT] : ( P @ I2 @ X6 ) ) )
% 5.46/5.78 = ( ? [Xs: list_VEBT_VEBT] :
% 5.46/5.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.46/5.78 = K )
% 5.46/5.78 & ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ K )
% 5.46/5.78 => ( P @ I2 @ ( nth_VEBT_VEBT @ Xs @ I2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % Skolem_list_nth
% 5.46/5.78 thf(fact_8245_Skolem__list__nth,axiom,
% 5.46/5.78 ! [K: nat,P: nat > $o > $o] :
% 5.46/5.78 ( ( ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ K )
% 5.46/5.78 => ? [X6: $o] : ( P @ I2 @ X6 ) ) )
% 5.46/5.78 = ( ? [Xs: list_o] :
% 5.46/5.78 ( ( ( size_size_list_o @ Xs )
% 5.46/5.78 = K )
% 5.46/5.78 & ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ K )
% 5.46/5.78 => ( P @ I2 @ ( nth_o @ Xs @ I2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % Skolem_list_nth
% 5.46/5.78 thf(fact_8246_Skolem__list__nth,axiom,
% 5.46/5.78 ! [K: nat,P: nat > nat > $o] :
% 5.46/5.78 ( ( ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ K )
% 5.46/5.78 => ? [X6: nat] : ( P @ I2 @ X6 ) ) )
% 5.46/5.78 = ( ? [Xs: list_nat] :
% 5.46/5.78 ( ( ( size_size_list_nat @ Xs )
% 5.46/5.78 = K )
% 5.46/5.78 & ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ K )
% 5.46/5.78 => ( P @ I2 @ ( nth_nat @ Xs @ I2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % Skolem_list_nth
% 5.46/5.78 thf(fact_8247_Skolem__list__nth,axiom,
% 5.46/5.78 ! [K: nat,P: nat > int > $o] :
% 5.46/5.78 ( ( ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ K )
% 5.46/5.78 => ? [X6: int] : ( P @ I2 @ X6 ) ) )
% 5.46/5.78 = ( ? [Xs: list_int] :
% 5.46/5.78 ( ( ( size_size_list_int @ Xs )
% 5.46/5.78 = K )
% 5.46/5.78 & ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ K )
% 5.46/5.78 => ( P @ I2 @ ( nth_int @ Xs @ I2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % Skolem_list_nth
% 5.46/5.78 thf(fact_8248_list__eq__iff__nth__eq,axiom,
% 5.46/5.78 ( ( ^ [Y6: list_VEBT_VEBT,Z4: list_VEBT_VEBT] : ( Y6 = Z4 ) )
% 5.46/5.78 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.46/5.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.46/5.78 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.46/5.78 & ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.46/5.78 => ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 5.46/5.78 = ( nth_VEBT_VEBT @ Ys3 @ I2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % list_eq_iff_nth_eq
% 5.46/5.78 thf(fact_8249_list__eq__iff__nth__eq,axiom,
% 5.46/5.78 ( ( ^ [Y6: list_o,Z4: list_o] : ( Y6 = Z4 ) )
% 5.46/5.78 = ( ^ [Xs: list_o,Ys3: list_o] :
% 5.46/5.78 ( ( ( size_size_list_o @ Xs )
% 5.46/5.78 = ( size_size_list_o @ Ys3 ) )
% 5.46/5.78 & ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 5.46/5.78 => ( ( nth_o @ Xs @ I2 )
% 5.46/5.78 = ( nth_o @ Ys3 @ I2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % list_eq_iff_nth_eq
% 5.46/5.78 thf(fact_8250_list__eq__iff__nth__eq,axiom,
% 5.46/5.78 ( ( ^ [Y6: list_nat,Z4: list_nat] : ( Y6 = Z4 ) )
% 5.46/5.78 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 5.46/5.78 ( ( ( size_size_list_nat @ Xs )
% 5.46/5.78 = ( size_size_list_nat @ Ys3 ) )
% 5.46/5.78 & ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 5.46/5.78 => ( ( nth_nat @ Xs @ I2 )
% 5.46/5.78 = ( nth_nat @ Ys3 @ I2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % list_eq_iff_nth_eq
% 5.46/5.78 thf(fact_8251_list__eq__iff__nth__eq,axiom,
% 5.46/5.78 ( ( ^ [Y6: list_int,Z4: list_int] : ( Y6 = Z4 ) )
% 5.46/5.78 = ( ^ [Xs: list_int,Ys3: list_int] :
% 5.46/5.78 ( ( ( size_size_list_int @ Xs )
% 5.46/5.78 = ( size_size_list_int @ Ys3 ) )
% 5.46/5.78 & ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 5.46/5.78 => ( ( nth_int @ Xs @ I2 )
% 5.46/5.78 = ( nth_int @ Ys3 @ I2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % list_eq_iff_nth_eq
% 5.46/5.78 thf(fact_8252_num_Osize_I4_J,axiom,
% 5.46/5.78 ( ( size_size_num @ one )
% 5.46/5.78 = zero_zero_nat ) ).
% 5.46/5.78
% 5.46/5.78 % num.size(4)
% 5.46/5.78 thf(fact_8253_num_Osize_I5_J,axiom,
% 5.46/5.78 ! [X2: num] :
% 5.46/5.78 ( ( size_size_num @ ( bit0 @ X2 ) )
% 5.46/5.78 = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % num.size(5)
% 5.46/5.78 thf(fact_8254_num_Osize_I6_J,axiom,
% 5.46/5.78 ! [X32: num] :
% 5.46/5.78 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.46/5.78 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % num.size(6)
% 5.46/5.78 thf(fact_8255_in__children__def,axiom,
% 5.46/5.78 ( vEBT_V5917875025757280293ildren
% 5.46/5.78 = ( ^ [N2: nat,TreeList: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ N2 ) ) @ ( vEBT_VEBT_low @ X @ N2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % in_children_def
% 5.46/5.78 thf(fact_8256_abc,axiom,
% 5.46/5.78 vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ na ).
% 5.46/5.78
% 5.46/5.78 % abc
% 5.46/5.78 thf(fact_8257__092_060open_062invar__vebt_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_An_092_060close_062,axiom,
% 5.46/5.78 vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ na ).
% 5.46/5.78
% 5.46/5.78 % \<open>invar_vebt (treeList ! high x (deg div 2)) n\<close>
% 5.46/5.78 thf(fact_8258_abh,axiom,
% 5.46/5.78 vEBT_vebt_member @ summary @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % abh
% 5.46/5.78 thf(fact_8259_valid__0__not,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT] :
% 5.46/5.78 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.46/5.78
% 5.46/5.78 % valid_0_not
% 5.46/5.78 thf(fact_8260_valid__tree__deg__neq__0,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT] :
% 5.46/5.78 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.46/5.78
% 5.46/5.78 % valid_tree_deg_neq_0
% 5.46/5.78 thf(fact_8261__C5_Ohyps_C_I2_J,axiom,
% 5.46/5.78 vEBT_invar_vebt @ summary @ m ).
% 5.46/5.78
% 5.46/5.78 % "5.hyps"(2)
% 5.46/5.78 thf(fact_8262_deg__not__0,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.46/5.78
% 5.46/5.78 % deg_not_0
% 5.46/5.78 thf(fact_8263_both__member__options__equiv__member,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( vEBT_V8194947554948674370ptions @ T @ X4 )
% 5.46/5.78 = ( vEBT_vebt_member @ T @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % both_member_options_equiv_member
% 5.46/5.78 thf(fact_8264_valid__member__both__member__options,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( vEBT_V8194947554948674370ptions @ T @ X4 )
% 5.46/5.78 => ( vEBT_vebt_member @ T @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % valid_member_both_member_options
% 5.46/5.78 thf(fact_8265__092_060open_062both__member__options_Asummary_Asc_092_060close_062,axiom,
% 5.46/5.78 vEBT_V8194947554948674370ptions @ summary @ sc ).
% 5.46/5.78
% 5.46/5.78 % \<open>both_member_options summary sc\<close>
% 5.46/5.78 thf(fact_8266__092_060open_062vebt__member_Asummary_Asc_092_060close_062,axiom,
% 5.46/5.78 vEBT_vebt_member @ summary @ sc ).
% 5.46/5.78
% 5.46/5.78 % \<open>vebt_member summary sc\<close>
% 5.46/5.78 thf(fact_8267_member__correct,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( vEBT_vebt_member @ T @ X4 )
% 5.46/5.78 = ( member_nat @ X4 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % member_correct
% 5.46/5.78 thf(fact_8268_member__bound,axiom,
% 5.46/5.78 ! [Tree: vEBT_VEBT,X4: nat,N: nat] :
% 5.46/5.78 ( ( vEBT_vebt_member @ Tree @ X4 )
% 5.46/5.78 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.46/5.78 => ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % member_bound
% 5.46/5.78 thf(fact_8269_abg,axiom,
% 5.46/5.78 vEBT_V8194947554948674370ptions @ summary @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % abg
% 5.46/5.78 thf(fact_8270__092_060open_062length_AtreeList_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_Am_092_060close_062,axiom,
% 5.46/5.78 ( ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.46/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.46/5.78 & ( vEBT_invar_vebt @ summary @ m ) ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>length treeList = 2 ^ m \<and> invar_vebt summary m\<close>
% 5.46/5.78 thf(fact_8271__C5_Ohyps_C_I7_J,axiom,
% 5.46/5.78 ! [I4: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.46/5.78 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I4 ) @ X6 ) )
% 5.46/5.78 = ( vEBT_V8194947554948674370ptions @ summary @ I4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % "5.hyps"(7)
% 5.46/5.78 thf(fact_8272_post__member__pre__member,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,X4: nat,Y3: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.78 => ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.78 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X4 ) @ Y3 )
% 5.46/5.78 => ( ( vEBT_vebt_member @ T @ Y3 )
% 5.46/5.78 | ( X4 = Y3 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % post_member_pre_member
% 5.46/5.78 thf(fact_8273_valid__insert__both__member__options__pres,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,X4: nat,Y3: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.78 => ( ( ord_less_nat @ Y3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.78 => ( ( vEBT_V8194947554948674370ptions @ T @ X4 )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y3 ) @ X4 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % valid_insert_both_member_options_pres
% 5.46/5.78 thf(fact_8274_valid__insert__both__member__options__add,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X4 ) @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % valid_insert_both_member_options_add
% 5.46/5.78 thf(fact_8275_both__member__options__ding,axiom,
% 5.46/5.78 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 5.46/5.78 => ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.46/5.78 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % both_member_options_ding
% 5.46/5.78 thf(fact_8276_deg__deg__n,axiom,
% 5.46/5.78 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 5.46/5.78 => ( Deg = N ) ) ).
% 5.46/5.78
% 5.46/5.78 % deg_deg_n
% 5.46/5.78 thf(fact_8277_deg__SUcn__Node,axiom,
% 5.46/5.78 ! [Tree: vEBT_VEBT,N: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.46/5.78 => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.78 ( Tree
% 5.46/5.78 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList3 @ S3 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % deg_SUcn_Node
% 5.46/5.78 thf(fact_8278__C5_Ohyps_C_I8_J,axiom,
% 5.46/5.78 ( ( mi = ma )
% 5.46/5.78 => ! [X5: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.46/5.78 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % "5.hyps"(8)
% 5.46/5.78 thf(fact_8279_set__vebt__set__vebt_H__valid,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( vEBT_set_vebt @ T )
% 5.46/5.78 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_vebt_set_vebt'_valid
% 5.46/5.78 thf(fact_8280_buildup__gives__valid,axiom,
% 5.46/5.78 ! [N: nat] :
% 5.46/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.78 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.46/5.78
% 5.46/5.78 % buildup_gives_valid
% 5.46/5.78 thf(fact_8281__092_060open_062is__succ__in__set_A_Iset__vebt_H_Asummary_J_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_Asc_092_060close_062,axiom,
% 5.46/5.78 vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ sc ).
% 5.46/5.78
% 5.46/5.78 % \<open>is_succ_in_set (set_vebt' summary) (high x (deg div 2)) sc\<close>
% 5.46/5.78 thf(fact_8282_set__n__deg__not__0,axiom,
% 5.46/5.78 ! [TreeList2: list_VEBT_VEBT,N: nat,M: nat] :
% 5.46/5.78 ( ! [X3: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.78 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.46/5.78 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.78 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_n_deg_not_0
% 5.46/5.78 thf(fact_8283_inthall,axiom,
% 5.46/5.78 ! [Xs2: list_Extended_enat,P: extended_enat > $o,N: nat] :
% 5.46/5.78 ( ! [X3: extended_enat] :
% 5.46/5.78 ( ( member_Extended_enat @ X3 @ ( set_Extended_enat2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( ( ord_less_nat @ N @ ( size_s3941691890525107288d_enat @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_Extended_enat @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % inthall
% 5.46/5.78 thf(fact_8284_inthall,axiom,
% 5.46/5.78 ! [Xs2: list_complex,P: complex > $o,N: nat] :
% 5.46/5.78 ( ! [X3: complex] :
% 5.46/5.78 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % inthall
% 5.46/5.78 thf(fact_8285_inthall,axiom,
% 5.46/5.78 ! [Xs2: list_real,P: real > $o,N: nat] :
% 5.46/5.78 ( ! [X3: real] :
% 5.46/5.78 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % inthall
% 5.46/5.78 thf(fact_8286_inthall,axiom,
% 5.46/5.78 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.46/5.78 ( ! [X3: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % inthall
% 5.46/5.78 thf(fact_8287_inthall,axiom,
% 5.46/5.78 ! [Xs2: list_o,P: $o > $o,N: nat] :
% 5.46/5.78 ( ! [X3: $o] :
% 5.46/5.78 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % inthall
% 5.46/5.78 thf(fact_8288_inthall,axiom,
% 5.46/5.78 ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 5.46/5.78 ( ! [X3: nat] :
% 5.46/5.78 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % inthall
% 5.46/5.78 thf(fact_8289_inthall,axiom,
% 5.46/5.78 ! [Xs2: list_int,P: int > $o,N: nat] :
% 5.46/5.78 ( ! [X3: int] :
% 5.46/5.78 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % inthall
% 5.46/5.78 thf(fact_8290_succ__member,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,X4: nat,Y3: nat] :
% 5.46/5.78 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X4 @ Y3 )
% 5.46/5.78 = ( ( vEBT_vebt_member @ T @ Y3 )
% 5.46/5.78 & ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.78 & ! [Z5: nat] :
% 5.46/5.78 ( ( ( vEBT_vebt_member @ T @ Z5 )
% 5.46/5.78 & ( ord_less_nat @ X4 @ Z5 ) )
% 5.46/5.78 => ( ord_less_eq_nat @ Y3 @ Z5 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % succ_member
% 5.46/5.78 thf(fact_8291_length__pos__if__in__set,axiom,
% 5.46/5.78 ! [X4: extended_enat,Xs2: list_Extended_enat] :
% 5.46/5.78 ( ( member_Extended_enat @ X4 @ ( set_Extended_enat2 @ Xs2 ) )
% 5.46/5.78 => ( ord_less_nat @ zero_zero_nat @ ( size_s3941691890525107288d_enat @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % length_pos_if_in_set
% 5.46/5.78 thf(fact_8292_length__pos__if__in__set,axiom,
% 5.46/5.78 ! [X4: complex,Xs2: list_complex] :
% 5.46/5.78 ( ( member_complex @ X4 @ ( set_complex2 @ Xs2 ) )
% 5.46/5.78 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % length_pos_if_in_set
% 5.46/5.78 thf(fact_8293_length__pos__if__in__set,axiom,
% 5.46/5.78 ! [X4: real,Xs2: list_real] :
% 5.46/5.78 ( ( member_real @ X4 @ ( set_real2 @ Xs2 ) )
% 5.46/5.78 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % length_pos_if_in_set
% 5.46/5.78 thf(fact_8294_length__pos__if__in__set,axiom,
% 5.46/5.78 ! [X4: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.46/5.78 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % length_pos_if_in_set
% 5.46/5.78 thf(fact_8295_length__pos__if__in__set,axiom,
% 5.46/5.78 ! [X4: $o,Xs2: list_o] :
% 5.46/5.78 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 5.46/5.78 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % length_pos_if_in_set
% 5.46/5.78 thf(fact_8296_length__pos__if__in__set,axiom,
% 5.46/5.78 ! [X4: nat,Xs2: list_nat] :
% 5.46/5.78 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 5.46/5.78 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % length_pos_if_in_set
% 5.46/5.78 thf(fact_8297_length__pos__if__in__set,axiom,
% 5.46/5.78 ! [X4: int,Xs2: list_int] :
% 5.46/5.78 ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 5.46/5.78 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % length_pos_if_in_set
% 5.46/5.78 thf(fact_8298_nth__mem,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_Extended_enat] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_s3941691890525107288d_enat @ Xs2 ) )
% 5.46/5.78 => ( member_Extended_enat @ ( nth_Extended_enat @ Xs2 @ N ) @ ( set_Extended_enat2 @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_mem
% 5.46/5.78 thf(fact_8299_nth__mem,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_complex] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.46/5.78 => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_mem
% 5.46/5.78 thf(fact_8300_nth__mem,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_real] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.46/5.78 => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_mem
% 5.46/5.78 thf(fact_8301_nth__mem,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.78 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_mem
% 5.46/5.78 thf(fact_8302_nth__mem,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_o] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.78 => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_mem
% 5.46/5.78 thf(fact_8303_nth__mem,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_nat] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.78 => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_mem
% 5.46/5.78 thf(fact_8304_nth__mem,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_int] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.78 => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nth_mem
% 5.46/5.78 thf(fact_8305_list__ball__nth,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.78 => ( ! [X3: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % list_ball_nth
% 5.46/5.78 thf(fact_8306_list__ball__nth,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_o,P: $o > $o] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.78 => ( ! [X3: $o] :
% 5.46/5.78 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % list_ball_nth
% 5.46/5.78 thf(fact_8307_list__ball__nth,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.78 => ( ! [X3: nat] :
% 5.46/5.78 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % list_ball_nth
% 5.46/5.78 thf(fact_8308_list__ball__nth,axiom,
% 5.46/5.78 ! [N: nat,Xs2: list_int,P: int > $o] :
% 5.46/5.78 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.78 => ( ! [X3: int] :
% 5.46/5.78 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X3 ) )
% 5.46/5.78 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % list_ball_nth
% 5.46/5.78 thf(fact_8309_in__set__conv__nth,axiom,
% 5.46/5.78 ! [X4: extended_enat,Xs2: list_Extended_enat] :
% 5.46/5.78 ( ( member_Extended_enat @ X4 @ ( set_Extended_enat2 @ Xs2 ) )
% 5.46/5.78 = ( ? [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_s3941691890525107288d_enat @ Xs2 ) )
% 5.46/5.78 & ( ( nth_Extended_enat @ Xs2 @ I2 )
% 5.46/5.78 = X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % in_set_conv_nth
% 5.46/5.78 thf(fact_8310_in__set__conv__nth,axiom,
% 5.46/5.78 ! [X4: complex,Xs2: list_complex] :
% 5.46/5.78 ( ( member_complex @ X4 @ ( set_complex2 @ Xs2 ) )
% 5.46/5.78 = ( ? [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.46/5.78 & ( ( nth_complex @ Xs2 @ I2 )
% 5.46/5.78 = X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % in_set_conv_nth
% 5.46/5.78 thf(fact_8311_in__set__conv__nth,axiom,
% 5.46/5.78 ! [X4: real,Xs2: list_real] :
% 5.46/5.78 ( ( member_real @ X4 @ ( set_real2 @ Xs2 ) )
% 5.46/5.78 = ( ? [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs2 ) )
% 5.46/5.78 & ( ( nth_real @ Xs2 @ I2 )
% 5.46/5.78 = X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % in_set_conv_nth
% 5.46/5.78 thf(fact_8312_in__set__conv__nth,axiom,
% 5.46/5.78 ! [X4: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.46/5.78 = ( ? [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.78 & ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 5.46/5.78 = X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % in_set_conv_nth
% 5.46/5.78 thf(fact_8313_in__set__conv__nth,axiom,
% 5.46/5.78 ! [X4: $o,Xs2: list_o] :
% 5.46/5.78 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 5.46/5.78 = ( ? [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.78 & ( ( nth_o @ Xs2 @ I2 )
% 5.46/5.78 = X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % in_set_conv_nth
% 5.46/5.78 thf(fact_8314_in__set__conv__nth,axiom,
% 5.46/5.78 ! [X4: nat,Xs2: list_nat] :
% 5.46/5.78 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 5.46/5.78 = ( ? [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.78 & ( ( nth_nat @ Xs2 @ I2 )
% 5.46/5.78 = X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % in_set_conv_nth
% 5.46/5.78 thf(fact_8315_in__set__conv__nth,axiom,
% 5.46/5.78 ! [X4: int,Xs2: list_int] :
% 5.46/5.78 ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 5.46/5.78 = ( ? [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.78 & ( ( nth_int @ Xs2 @ I2 )
% 5.46/5.78 = X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % in_set_conv_nth
% 5.46/5.78 thf(fact_8316_all__nth__imp__all__set,axiom,
% 5.46/5.78 ! [Xs2: list_Extended_enat,P: extended_enat > $o,X4: extended_enat] :
% 5.46/5.78 ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_s3941691890525107288d_enat @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_Extended_enat @ Xs2 @ I3 ) ) )
% 5.46/5.78 => ( ( member_Extended_enat @ X4 @ ( set_Extended_enat2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_nth_imp_all_set
% 5.46/5.78 thf(fact_8317_all__nth__imp__all__set,axiom,
% 5.46/5.78 ! [Xs2: list_complex,P: complex > $o,X4: complex] :
% 5.46/5.78 ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_complex @ Xs2 @ I3 ) ) )
% 5.46/5.78 => ( ( member_complex @ X4 @ ( set_complex2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_nth_imp_all_set
% 5.46/5.78 thf(fact_8318_all__nth__imp__all__set,axiom,
% 5.46/5.78 ! [Xs2: list_real,P: real > $o,X4: real] :
% 5.46/5.78 ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_real @ Xs2 @ I3 ) ) )
% 5.46/5.78 => ( ( member_real @ X4 @ ( set_real2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_nth_imp_all_set
% 5.46/5.78 thf(fact_8319_all__nth__imp__all__set,axiom,
% 5.46/5.78 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X4: vEBT_VEBT] :
% 5.46/5.78 ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) )
% 5.46/5.78 => ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_nth_imp_all_set
% 5.46/5.78 thf(fact_8320_all__nth__imp__all__set,axiom,
% 5.46/5.78 ! [Xs2: list_o,P: $o > $o,X4: $o] :
% 5.46/5.78 ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_o @ Xs2 @ I3 ) ) )
% 5.46/5.78 => ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_nth_imp_all_set
% 5.46/5.78 thf(fact_8321_all__nth__imp__all__set,axiom,
% 5.46/5.78 ! [Xs2: list_nat,P: nat > $o,X4: nat] :
% 5.46/5.78 ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_nat @ Xs2 @ I3 ) ) )
% 5.46/5.78 => ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_nth_imp_all_set
% 5.46/5.78 thf(fact_8322_all__nth__imp__all__set,axiom,
% 5.46/5.78 ! [Xs2: list_int,P: int > $o,X4: int] :
% 5.46/5.78 ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_int @ Xs2 @ I3 ) ) )
% 5.46/5.78 => ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_nth_imp_all_set
% 5.46/5.78 thf(fact_8323_all__set__conv__all__nth,axiom,
% 5.46/5.78 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.46/5.78 ( ( ! [X: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X ) ) )
% 5.46/5.78 = ( ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_set_conv_all_nth
% 5.46/5.78 thf(fact_8324_all__set__conv__all__nth,axiom,
% 5.46/5.78 ! [Xs2: list_o,P: $o > $o] :
% 5.46/5.78 ( ( ! [X: $o] :
% 5.46/5.78 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X ) ) )
% 5.46/5.78 = ( ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_o @ Xs2 @ I2 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_set_conv_all_nth
% 5.46/5.78 thf(fact_8325_all__set__conv__all__nth,axiom,
% 5.46/5.78 ! [Xs2: list_nat,P: nat > $o] :
% 5.46/5.78 ( ( ! [X: nat] :
% 5.46/5.78 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X ) ) )
% 5.46/5.78 = ( ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_set_conv_all_nth
% 5.46/5.78 thf(fact_8326_all__set__conv__all__nth,axiom,
% 5.46/5.78 ! [Xs2: list_int,P: int > $o] :
% 5.46/5.78 ( ( ! [X: int] :
% 5.46/5.78 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.46/5.78 => ( P @ X ) ) )
% 5.46/5.78 = ( ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.46/5.78 => ( P @ ( nth_int @ Xs2 @ I2 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_set_conv_all_nth
% 5.46/5.78 thf(fact_8327_is__succ__in__set__def,axiom,
% 5.46/5.78 ( vEBT_is_succ_in_set
% 5.46/5.78 = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 5.46/5.78 ( ( member_nat @ Y @ Xs )
% 5.46/5.78 & ( ord_less_nat @ X @ Y )
% 5.46/5.78 & ! [Z5: nat] :
% 5.46/5.78 ( ( member_nat @ Z5 @ Xs )
% 5.46/5.78 => ( ( ord_less_nat @ X @ Z5 )
% 5.46/5.78 => ( ord_less_eq_nat @ Y @ Z5 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % is_succ_in_set_def
% 5.46/5.78 thf(fact_8328_inrange,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( 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 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % inrange
% 5.46/5.78 thf(fact_8329_fgh,axiom,
% 5.46/5.78 ( ( vEBT_VEBT_set_vebt @ ( nth_VEBT_VEBT @ treeList @ sc ) )
% 5.46/5.78 != bot_bot_set_nat ) ).
% 5.46/5.78
% 5.46/5.78 % fgh
% 5.46/5.78 thf(fact_8330__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Az_A_092_060and_062_Ax_A_060_Az_092_060close_062,axiom,
% 5.46/5.78 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ za )
% 5.46/5.78 & ( ord_less_nat @ xa @ za ) ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>vebt_member (Node (Some (mi, ma)) deg treeList summary) z \<and> x < z\<close>
% 5.46/5.78 thf(fact_8331__092_060open_062vebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Asc_092_060close_062,axiom,
% 5.46/5.78 ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 = ( some_nat @ sc ) ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>vebt_succ summary (high x (deg div 2)) = Some sc\<close>
% 5.46/5.78 thf(fact_8332_buildup__gives__empty,axiom,
% 5.46/5.78 ! [N: nat] :
% 5.46/5.78 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.46/5.78 = bot_bot_set_nat ) ).
% 5.46/5.78
% 5.46/5.78 % buildup_gives_empty
% 5.46/5.78 thf(fact_8333_power__shift,axiom,
% 5.46/5.78 ! [X4: nat,Y3: nat,Z: nat] :
% 5.46/5.78 ( ( ( power_power_nat @ X4 @ Y3 )
% 5.46/5.78 = Z )
% 5.46/5.78 = ( ( vEBT_VEBT_power @ ( some_nat @ X4 ) @ ( some_nat @ Y3 ) )
% 5.46/5.78 = ( some_nat @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_shift
% 5.46/5.78 thf(fact_8334__C5_Ohyps_C_I1_J,axiom,
% 5.46/5.78 ! [X5: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.46/5.78 => ( ( vEBT_invar_vebt @ X5 @ na )
% 5.46/5.78 & ! [Xa2: nat,Xb2: nat] :
% 5.46/5.78 ( ( ( vEBT_vebt_succ @ X5 @ Xa2 )
% 5.46/5.78 = ( some_nat @ Xb2 ) )
% 5.46/5.78 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ X5 ) @ Xa2 @ Xb2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % "5.hyps"(1)
% 5.46/5.78 thf(fact_8335_mi__eq__ma__no__ch,axiom,
% 5.46/5.78 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.46/5.78 => ( ( Mi = Ma )
% 5.46/5.78 => ( ! [X5: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.78 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 5.46/5.78 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % mi_eq_ma_no_ch
% 5.46/5.78 thf(fact_8336__C5_Ohyps_C_I3_J,axiom,
% 5.46/5.78 ! [X4: nat,Sx: nat] :
% 5.46/5.78 ( ( ( vEBT_vebt_succ @ summary @ X4 )
% 5.46/5.78 = ( some_nat @ Sx ) )
% 5.46/5.78 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ summary ) @ X4 @ Sx ) ) ).
% 5.46/5.78
% 5.46/5.78 % "5.hyps"(3)
% 5.46/5.78 thf(fact_8337_atLeastAtMost__iff,axiom,
% 5.46/5.78 ! [I: extended_enat,L2: extended_enat,U: extended_enat] :
% 5.46/5.78 ( ( member_Extended_enat @ I @ ( set_or5403411693681687835d_enat @ L2 @ U ) )
% 5.46/5.78 = ( ( ord_le2932123472753598470d_enat @ L2 @ I )
% 5.46/5.78 & ( ord_le2932123472753598470d_enat @ I @ U ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastAtMost_iff
% 5.46/5.78 thf(fact_8338_atLeastAtMost__iff,axiom,
% 5.46/5.78 ! [I: set_nat,L2: set_nat,U: set_nat] :
% 5.46/5.78 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L2 @ U ) )
% 5.46/5.78 = ( ( ord_less_eq_set_nat @ L2 @ I )
% 5.46/5.78 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastAtMost_iff
% 5.46/5.78 thf(fact_8339_atLeastAtMost__iff,axiom,
% 5.46/5.78 ! [I: rat,L2: rat,U: rat] :
% 5.46/5.78 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L2 @ U ) )
% 5.46/5.78 = ( ( ord_less_eq_rat @ L2 @ I )
% 5.46/5.78 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastAtMost_iff
% 5.46/5.78 thf(fact_8340_atLeastAtMost__iff,axiom,
% 5.46/5.78 ! [I: num,L2: num,U: num] :
% 5.46/5.78 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 5.46/5.78 = ( ( ord_less_eq_num @ L2 @ I )
% 5.46/5.78 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastAtMost_iff
% 5.46/5.78 thf(fact_8341_atLeastAtMost__iff,axiom,
% 5.46/5.78 ! [I: nat,L2: nat,U: nat] :
% 5.46/5.78 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.46/5.78 = ( ( ord_less_eq_nat @ L2 @ I )
% 5.46/5.78 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastAtMost_iff
% 5.46/5.78 thf(fact_8342_atLeastAtMost__iff,axiom,
% 5.46/5.78 ! [I: int,L2: int,U: int] :
% 5.46/5.78 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.46/5.78 = ( ( ord_less_eq_int @ L2 @ I )
% 5.46/5.78 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastAtMost_iff
% 5.46/5.78 thf(fact_8343_atLeastAtMost__iff,axiom,
% 5.46/5.78 ! [I: real,L2: real,U: real] :
% 5.46/5.78 ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 5.46/5.78 = ( ( ord_less_eq_real @ L2 @ I )
% 5.46/5.78 & ( ord_less_eq_real @ I @ U ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastAtMost_iff
% 5.46/5.78 thf(fact_8344_Icc__eq__Icc,axiom,
% 5.46/5.78 ! [L2: set_nat,H2: set_nat,L4: set_nat,H3: set_nat] :
% 5.46/5.78 ( ( ( set_or4548717258645045905et_nat @ L2 @ H2 )
% 5.46/5.78 = ( set_or4548717258645045905et_nat @ L4 @ H3 ) )
% 5.46/5.78 = ( ( ( L2 = L4 )
% 5.46/5.78 & ( H2 = H3 ) )
% 5.46/5.78 | ( ~ ( ord_less_eq_set_nat @ L2 @ H2 )
% 5.46/5.78 & ~ ( ord_less_eq_set_nat @ L4 @ H3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % Icc_eq_Icc
% 5.46/5.78 thf(fact_8345_Icc__eq__Icc,axiom,
% 5.46/5.78 ! [L2: rat,H2: rat,L4: rat,H3: rat] :
% 5.46/5.78 ( ( ( set_or633870826150836451st_rat @ L2 @ H2 )
% 5.46/5.78 = ( set_or633870826150836451st_rat @ L4 @ H3 ) )
% 5.46/5.78 = ( ( ( L2 = L4 )
% 5.46/5.78 & ( H2 = H3 ) )
% 5.46/5.78 | ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.46/5.78 & ~ ( ord_less_eq_rat @ L4 @ H3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % Icc_eq_Icc
% 5.46/5.78 thf(fact_8346_Icc__eq__Icc,axiom,
% 5.46/5.78 ! [L2: num,H2: num,L4: num,H3: num] :
% 5.46/5.78 ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 5.46/5.78 = ( set_or7049704709247886629st_num @ L4 @ H3 ) )
% 5.46/5.78 = ( ( ( L2 = L4 )
% 5.46/5.78 & ( H2 = H3 ) )
% 5.46/5.78 | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.46/5.78 & ~ ( ord_less_eq_num @ L4 @ H3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % Icc_eq_Icc
% 5.46/5.78 thf(fact_8347_Icc__eq__Icc,axiom,
% 5.46/5.78 ! [L2: nat,H2: nat,L4: nat,H3: nat] :
% 5.46/5.78 ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 5.46/5.78 = ( set_or1269000886237332187st_nat @ L4 @ H3 ) )
% 5.46/5.78 = ( ( ( L2 = L4 )
% 5.46/5.78 & ( H2 = H3 ) )
% 5.46/5.78 | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.46/5.78 & ~ ( ord_less_eq_nat @ L4 @ H3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % Icc_eq_Icc
% 5.46/5.78 thf(fact_8348_Icc__eq__Icc,axiom,
% 5.46/5.78 ! [L2: int,H2: int,L4: int,H3: int] :
% 5.46/5.78 ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 5.46/5.78 = ( set_or1266510415728281911st_int @ L4 @ H3 ) )
% 5.46/5.78 = ( ( ( L2 = L4 )
% 5.46/5.78 & ( H2 = H3 ) )
% 5.46/5.78 | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.46/5.78 & ~ ( ord_less_eq_int @ L4 @ H3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % Icc_eq_Icc
% 5.46/5.78 thf(fact_8349_Icc__eq__Icc,axiom,
% 5.46/5.78 ! [L2: real,H2: real,L4: real,H3: real] :
% 5.46/5.78 ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 5.46/5.78 = ( set_or1222579329274155063t_real @ L4 @ H3 ) )
% 5.46/5.78 = ( ( ( L2 = L4 )
% 5.46/5.78 & ( H2 = H3 ) )
% 5.46/5.78 | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.46/5.78 & ~ ( ord_less_eq_real @ L4 @ H3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % Icc_eq_Icc
% 5.46/5.78 thf(fact_8350_insert__simp__mima,axiom,
% 5.46/5.78 ! [X4: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.46/5.78 ( ( ( X4 = Mi )
% 5.46/5.78 | ( X4 = Ma ) )
% 5.46/5.78 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.46/5.78 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % insert_simp_mima
% 5.46/5.78 thf(fact_8351_Diff__cancel,axiom,
% 5.46/5.78 ! [A3: set_Extended_enat] :
% 5.46/5.78 ( ( minus_925952699566721837d_enat @ A3 @ A3 )
% 5.46/5.78 = bot_bo7653980558646680370d_enat ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_cancel
% 5.46/5.78 thf(fact_8352_Diff__cancel,axiom,
% 5.46/5.78 ! [A3: set_real] :
% 5.46/5.78 ( ( minus_minus_set_real @ A3 @ A3 )
% 5.46/5.78 = bot_bot_set_real ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_cancel
% 5.46/5.78 thf(fact_8353_Diff__cancel,axiom,
% 5.46/5.78 ! [A3: set_int] :
% 5.46/5.78 ( ( minus_minus_set_int @ A3 @ A3 )
% 5.46/5.78 = bot_bot_set_int ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_cancel
% 5.46/5.78 thf(fact_8354_Diff__cancel,axiom,
% 5.46/5.78 ! [A3: set_nat] :
% 5.46/5.78 ( ( minus_minus_set_nat @ A3 @ A3 )
% 5.46/5.78 = bot_bot_set_nat ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_cancel
% 5.46/5.78 thf(fact_8355_empty__Diff,axiom,
% 5.46/5.78 ! [A3: set_Extended_enat] :
% 5.46/5.78 ( ( minus_925952699566721837d_enat @ bot_bo7653980558646680370d_enat @ A3 )
% 5.46/5.78 = bot_bo7653980558646680370d_enat ) ).
% 5.46/5.78
% 5.46/5.78 % empty_Diff
% 5.46/5.78 thf(fact_8356_empty__Diff,axiom,
% 5.46/5.78 ! [A3: set_real] :
% 5.46/5.78 ( ( minus_minus_set_real @ bot_bot_set_real @ A3 )
% 5.46/5.78 = bot_bot_set_real ) ).
% 5.46/5.78
% 5.46/5.78 % empty_Diff
% 5.46/5.78 thf(fact_8357_empty__Diff,axiom,
% 5.46/5.78 ! [A3: set_int] :
% 5.46/5.78 ( ( minus_minus_set_int @ bot_bot_set_int @ A3 )
% 5.46/5.78 = bot_bot_set_int ) ).
% 5.46/5.78
% 5.46/5.78 % empty_Diff
% 5.46/5.78 thf(fact_8358_empty__Diff,axiom,
% 5.46/5.78 ! [A3: set_nat] :
% 5.46/5.78 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A3 )
% 5.46/5.78 = bot_bot_set_nat ) ).
% 5.46/5.78
% 5.46/5.78 % empty_Diff
% 5.46/5.78 thf(fact_8359_Diff__empty,axiom,
% 5.46/5.78 ! [A3: set_Extended_enat] :
% 5.46/5.78 ( ( minus_925952699566721837d_enat @ A3 @ bot_bo7653980558646680370d_enat )
% 5.46/5.78 = A3 ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_empty
% 5.46/5.78 thf(fact_8360_Diff__empty,axiom,
% 5.46/5.78 ! [A3: set_real] :
% 5.46/5.78 ( ( minus_minus_set_real @ A3 @ bot_bot_set_real )
% 5.46/5.78 = A3 ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_empty
% 5.46/5.78 thf(fact_8361_Diff__empty,axiom,
% 5.46/5.78 ! [A3: set_int] :
% 5.46/5.78 ( ( minus_minus_set_int @ A3 @ bot_bot_set_int )
% 5.46/5.78 = A3 ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_empty
% 5.46/5.78 thf(fact_8362_Diff__empty,axiom,
% 5.46/5.78 ! [A3: set_nat] :
% 5.46/5.78 ( ( minus_minus_set_nat @ A3 @ bot_bot_set_nat )
% 5.46/5.78 = A3 ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_empty
% 5.46/5.78 thf(fact_8363_mi__ma__2__deg,axiom,
% 5.46/5.78 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.46/5.78 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.46/5.78 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % mi_ma_2_deg
% 5.46/5.78 thf(fact_8364_succ__min,axiom,
% 5.46/5.78 ! [Deg: nat,X4: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.46/5.78 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.46/5.78 => ( ( ord_less_nat @ X4 @ Mi )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 = ( some_nat @ Mi ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % succ_min
% 5.46/5.78 thf(fact_8365_atLeastatMost__empty__iff,axiom,
% 5.46/5.78 ! [A: extended_enat,B2: extended_enat] :
% 5.46/5.78 ( ( ( set_or5403411693681687835d_enat @ A @ B2 )
% 5.46/5.78 = bot_bo7653980558646680370d_enat )
% 5.46/5.78 = ( ~ ( ord_le2932123472753598470d_enat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff
% 5.46/5.78 thf(fact_8366_atLeastatMost__empty__iff,axiom,
% 5.46/5.78 ! [A: set_nat,B2: set_nat] :
% 5.46/5.78 ( ( ( set_or4548717258645045905et_nat @ A @ B2 )
% 5.46/5.78 = bot_bot_set_set_nat )
% 5.46/5.78 = ( ~ ( ord_less_eq_set_nat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff
% 5.46/5.78 thf(fact_8367_atLeastatMost__empty__iff,axiom,
% 5.46/5.78 ! [A: rat,B2: rat] :
% 5.46/5.78 ( ( ( set_or633870826150836451st_rat @ A @ B2 )
% 5.46/5.78 = bot_bot_set_rat )
% 5.46/5.78 = ( ~ ( ord_less_eq_rat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff
% 5.46/5.78 thf(fact_8368_atLeastatMost__empty__iff,axiom,
% 5.46/5.78 ! [A: num,B2: num] :
% 5.46/5.78 ( ( ( set_or7049704709247886629st_num @ A @ B2 )
% 5.46/5.78 = bot_bot_set_num )
% 5.46/5.78 = ( ~ ( ord_less_eq_num @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff
% 5.46/5.78 thf(fact_8369_atLeastatMost__empty__iff,axiom,
% 5.46/5.78 ! [A: nat,B2: nat] :
% 5.46/5.78 ( ( ( set_or1269000886237332187st_nat @ A @ B2 )
% 5.46/5.78 = bot_bot_set_nat )
% 5.46/5.78 = ( ~ ( ord_less_eq_nat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff
% 5.46/5.78 thf(fact_8370_atLeastatMost__empty__iff,axiom,
% 5.46/5.78 ! [A: int,B2: int] :
% 5.46/5.78 ( ( ( set_or1266510415728281911st_int @ A @ B2 )
% 5.46/5.78 = bot_bot_set_int )
% 5.46/5.78 = ( ~ ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff
% 5.46/5.78 thf(fact_8371_atLeastatMost__empty__iff,axiom,
% 5.46/5.78 ! [A: real,B2: real] :
% 5.46/5.78 ( ( ( set_or1222579329274155063t_real @ A @ B2 )
% 5.46/5.78 = bot_bot_set_real )
% 5.46/5.78 = ( ~ ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff
% 5.46/5.78 thf(fact_8372_atLeastatMost__empty__iff2,axiom,
% 5.46/5.78 ! [A: extended_enat,B2: extended_enat] :
% 5.46/5.78 ( ( bot_bo7653980558646680370d_enat
% 5.46/5.78 = ( set_or5403411693681687835d_enat @ A @ B2 ) )
% 5.46/5.78 = ( ~ ( ord_le2932123472753598470d_enat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff2
% 5.46/5.78 thf(fact_8373_atLeastatMost__empty__iff2,axiom,
% 5.46/5.78 ! [A: set_nat,B2: set_nat] :
% 5.46/5.78 ( ( bot_bot_set_set_nat
% 5.46/5.78 = ( set_or4548717258645045905et_nat @ A @ B2 ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_set_nat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff2
% 5.46/5.78 thf(fact_8374_atLeastatMost__empty__iff2,axiom,
% 5.46/5.78 ! [A: rat,B2: rat] :
% 5.46/5.78 ( ( bot_bot_set_rat
% 5.46/5.78 = ( set_or633870826150836451st_rat @ A @ B2 ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_rat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff2
% 5.46/5.78 thf(fact_8375_atLeastatMost__empty__iff2,axiom,
% 5.46/5.78 ! [A: num,B2: num] :
% 5.46/5.78 ( ( bot_bot_set_num
% 5.46/5.78 = ( set_or7049704709247886629st_num @ A @ B2 ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_num @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff2
% 5.46/5.78 thf(fact_8376_atLeastatMost__empty__iff2,axiom,
% 5.46/5.78 ! [A: nat,B2: nat] :
% 5.46/5.78 ( ( bot_bot_set_nat
% 5.46/5.78 = ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_nat @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff2
% 5.46/5.78 thf(fact_8377_atLeastatMost__empty__iff2,axiom,
% 5.46/5.78 ! [A: int,B2: int] :
% 5.46/5.78 ( ( bot_bot_set_int
% 5.46/5.78 = ( set_or1266510415728281911st_int @ A @ B2 ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff2
% 5.46/5.78 thf(fact_8378_atLeastatMost__empty__iff2,axiom,
% 5.46/5.78 ! [A: real,B2: real] :
% 5.46/5.78 ( ( bot_bot_set_real
% 5.46/5.78 = ( set_or1222579329274155063t_real @ A @ B2 ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_real @ A @ B2 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty_iff2
% 5.46/5.78 thf(fact_8379_atLeastatMost__subset__iff,axiom,
% 5.46/5.78 ! [A: set_nat,B2: set_nat,C: set_nat,D: set_nat] :
% 5.46/5.78 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B2 ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_set_nat @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.46/5.78 & ( ord_less_eq_set_nat @ B2 @ D ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_subset_iff
% 5.46/5.78 thf(fact_8380_atLeastatMost__subset__iff,axiom,
% 5.46/5.78 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.78 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B2 ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_rat @ C @ A )
% 5.46/5.78 & ( ord_less_eq_rat @ B2 @ D ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_subset_iff
% 5.46/5.78 thf(fact_8381_atLeastatMost__subset__iff,axiom,
% 5.46/5.78 ! [A: num,B2: num,C: num,D: num] :
% 5.46/5.78 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B2 ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_num @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_num @ C @ A )
% 5.46/5.78 & ( ord_less_eq_num @ B2 @ D ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_subset_iff
% 5.46/5.78 thf(fact_8382_atLeastatMost__subset__iff,axiom,
% 5.46/5.78 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.78 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B2 ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_nat @ C @ A )
% 5.46/5.78 & ( ord_less_eq_nat @ B2 @ D ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_subset_iff
% 5.46/5.78 thf(fact_8383_atLeastatMost__subset__iff,axiom,
% 5.46/5.78 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.78 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B2 ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_int @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_int @ C @ A )
% 5.46/5.78 & ( ord_less_eq_int @ B2 @ D ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_subset_iff
% 5.46/5.78 thf(fact_8384_atLeastatMost__subset__iff,axiom,
% 5.46/5.78 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.78 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.46/5.78 = ( ~ ( ord_less_eq_real @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_real @ C @ A )
% 5.46/5.78 & ( ord_less_eq_real @ B2 @ D ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_subset_iff
% 5.46/5.78 thf(fact_8385_atLeastatMost__empty,axiom,
% 5.46/5.78 ! [B2: extended_enat,A: extended_enat] :
% 5.46/5.78 ( ( ord_le72135733267957522d_enat @ B2 @ A )
% 5.46/5.78 => ( ( set_or5403411693681687835d_enat @ A @ B2 )
% 5.46/5.78 = bot_bo7653980558646680370d_enat ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty
% 5.46/5.78 thf(fact_8386_atLeastatMost__empty,axiom,
% 5.46/5.78 ! [B2: rat,A: rat] :
% 5.46/5.78 ( ( ord_less_rat @ B2 @ A )
% 5.46/5.78 => ( ( set_or633870826150836451st_rat @ A @ B2 )
% 5.46/5.78 = bot_bot_set_rat ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty
% 5.46/5.78 thf(fact_8387_atLeastatMost__empty,axiom,
% 5.46/5.78 ! [B2: num,A: num] :
% 5.46/5.78 ( ( ord_less_num @ B2 @ A )
% 5.46/5.78 => ( ( set_or7049704709247886629st_num @ A @ B2 )
% 5.46/5.78 = bot_bot_set_num ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty
% 5.46/5.78 thf(fact_8388_atLeastatMost__empty,axiom,
% 5.46/5.78 ! [B2: nat,A: nat] :
% 5.46/5.78 ( ( ord_less_nat @ B2 @ A )
% 5.46/5.78 => ( ( set_or1269000886237332187st_nat @ A @ B2 )
% 5.46/5.78 = bot_bot_set_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty
% 5.46/5.78 thf(fact_8389_atLeastatMost__empty,axiom,
% 5.46/5.78 ! [B2: int,A: int] :
% 5.46/5.78 ( ( ord_less_int @ B2 @ A )
% 5.46/5.78 => ( ( set_or1266510415728281911st_int @ A @ B2 )
% 5.46/5.78 = bot_bot_set_int ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty
% 5.46/5.78 thf(fact_8390_atLeastatMost__empty,axiom,
% 5.46/5.78 ! [B2: real,A: real] :
% 5.46/5.78 ( ( ord_less_real @ B2 @ A )
% 5.46/5.78 => ( ( set_or1222579329274155063t_real @ A @ B2 )
% 5.46/5.78 = bot_bot_set_real ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_empty
% 5.46/5.78 thf(fact_8391_Diff__eq__empty__iff,axiom,
% 5.46/5.78 ! [A3: set_Extended_enat,B4: set_Extended_enat] :
% 5.46/5.78 ( ( ( minus_925952699566721837d_enat @ A3 @ B4 )
% 5.46/5.78 = bot_bo7653980558646680370d_enat )
% 5.46/5.78 = ( ord_le7203529160286727270d_enat @ A3 @ B4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_eq_empty_iff
% 5.46/5.78 thf(fact_8392_Diff__eq__empty__iff,axiom,
% 5.46/5.78 ! [A3: set_real,B4: set_real] :
% 5.46/5.78 ( ( ( minus_minus_set_real @ A3 @ B4 )
% 5.46/5.78 = bot_bot_set_real )
% 5.46/5.78 = ( ord_less_eq_set_real @ A3 @ B4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_eq_empty_iff
% 5.46/5.78 thf(fact_8393_Diff__eq__empty__iff,axiom,
% 5.46/5.78 ! [A3: set_int,B4: set_int] :
% 5.46/5.78 ( ( ( minus_minus_set_int @ A3 @ B4 )
% 5.46/5.78 = bot_bot_set_int )
% 5.46/5.78 = ( ord_less_eq_set_int @ A3 @ B4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_eq_empty_iff
% 5.46/5.78 thf(fact_8394_Diff__eq__empty__iff,axiom,
% 5.46/5.78 ! [A3: set_nat,B4: set_nat] :
% 5.46/5.78 ( ( ( minus_minus_set_nat @ A3 @ B4 )
% 5.46/5.78 = bot_bot_set_nat )
% 5.46/5.78 = ( ord_less_eq_set_nat @ A3 @ B4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % Diff_eq_empty_iff
% 5.46/5.78 thf(fact_8395__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062sc_O_Avebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Asc_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.46/5.78 ~ ! [Sc: nat] :
% 5.46/5.78 ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 != ( some_nat @ Sc ) ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>\<And>thesis. (\<And>sc. vebt_succ summary (high x (deg div 2)) = Some sc \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.46/5.78 thf(fact_8396_both__member__options__from__complete__tree__to__child,axiom,
% 5.46/5.78 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X4: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.46/5.78 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 | ( X4 = Mi )
% 5.46/5.78 | ( X4 = Ma ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % both_member_options_from_complete_tree_to_child
% 5.46/5.78 thf(fact_8397_member__inv,axiom,
% 5.46/5.78 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X4: nat] :
% 5.46/5.78 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.46/5.78 & ( ( X4 = Mi )
% 5.46/5.78 | ( X4 = Ma )
% 5.46/5.78 | ( ( ord_less_nat @ X4 @ Ma )
% 5.46/5.78 & ( ord_less_nat @ Mi @ X4 )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.78 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % member_inv
% 5.46/5.78 thf(fact_8398_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.46/5.78 ! [X4: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.46/5.78 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.78 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.46/5.78 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % both_member_options_from_chilf_to_complete_tree
% 5.46/5.78 thf(fact_8399__092_060open_062Some_Aminy_A_061_Avebt__mint_A_ItreeList_A_B_Asc_J_092_060close_062,axiom,
% 5.46/5.78 ( ( some_nat @ miny )
% 5.46/5.78 = ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ sc ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>Some miny = vebt_mint (treeList ! sc)\<close>
% 5.46/5.78 thf(fact_8400_greater__shift,axiom,
% 5.46/5.78 ( ord_less_nat
% 5.46/5.78 = ( ^ [Y: nat,X: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % greater_shift
% 5.46/5.78 thf(fact_8401_lesseq__shift,axiom,
% 5.46/5.78 ( ord_less_eq_nat
% 5.46/5.78 = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % lesseq_shift
% 5.46/5.78 thf(fact_8402_False,axiom,
% 5.46/5.78 ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 != none_nat ) ).
% 5.46/5.78
% 5.46/5.78 % False
% 5.46/5.78 thf(fact_8403_not__psubset__empty,axiom,
% 5.46/5.78 ! [A3: set_Extended_enat] :
% 5.46/5.78 ~ ( ord_le2529575680413868914d_enat @ A3 @ bot_bo7653980558646680370d_enat ) ).
% 5.46/5.78
% 5.46/5.78 % not_psubset_empty
% 5.46/5.78 thf(fact_8404_not__psubset__empty,axiom,
% 5.46/5.78 ! [A3: set_real] :
% 5.46/5.78 ~ ( ord_less_set_real @ A3 @ bot_bot_set_real ) ).
% 5.46/5.78
% 5.46/5.78 % not_psubset_empty
% 5.46/5.78 thf(fact_8405_not__psubset__empty,axiom,
% 5.46/5.78 ! [A3: set_nat] :
% 5.46/5.78 ~ ( ord_less_set_nat @ A3 @ bot_bot_set_nat ) ).
% 5.46/5.78
% 5.46/5.78 % not_psubset_empty
% 5.46/5.78 thf(fact_8406_not__psubset__empty,axiom,
% 5.46/5.78 ! [A3: set_int] :
% 5.46/5.78 ~ ( ord_less_set_int @ A3 @ bot_bot_set_int ) ).
% 5.46/5.78
% 5.46/5.78 % not_psubset_empty
% 5.46/5.78 thf(fact_8407_bot_Onot__eq__extremum,axiom,
% 5.46/5.78 ! [A: set_Extended_enat] :
% 5.46/5.78 ( ( A != bot_bo7653980558646680370d_enat )
% 5.46/5.78 = ( ord_le2529575680413868914d_enat @ bot_bo7653980558646680370d_enat @ A ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.not_eq_extremum
% 5.46/5.78 thf(fact_8408_bot_Onot__eq__extremum,axiom,
% 5.46/5.78 ! [A: set_real] :
% 5.46/5.78 ( ( A != bot_bot_set_real )
% 5.46/5.78 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.not_eq_extremum
% 5.46/5.78 thf(fact_8409_bot_Onot__eq__extremum,axiom,
% 5.46/5.78 ! [A: set_nat] :
% 5.46/5.78 ( ( A != bot_bot_set_nat )
% 5.46/5.78 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.not_eq_extremum
% 5.46/5.78 thf(fact_8410_bot_Onot__eq__extremum,axiom,
% 5.46/5.78 ! [A: set_int] :
% 5.46/5.78 ( ( A != bot_bot_set_int )
% 5.46/5.78 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.not_eq_extremum
% 5.46/5.78 thf(fact_8411_bot_Onot__eq__extremum,axiom,
% 5.46/5.78 ! [A: nat] :
% 5.46/5.78 ( ( A != bot_bot_nat )
% 5.46/5.78 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.not_eq_extremum
% 5.46/5.78 thf(fact_8412_bot_Oextremum__strict,axiom,
% 5.46/5.78 ! [A: set_Extended_enat] :
% 5.46/5.78 ~ ( ord_le2529575680413868914d_enat @ A @ bot_bo7653980558646680370d_enat ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_strict
% 5.46/5.78 thf(fact_8413_bot_Oextremum__strict,axiom,
% 5.46/5.78 ! [A: set_real] :
% 5.46/5.78 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_strict
% 5.46/5.78 thf(fact_8414_bot_Oextremum__strict,axiom,
% 5.46/5.78 ! [A: set_nat] :
% 5.46/5.78 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_strict
% 5.46/5.78 thf(fact_8415_bot_Oextremum__strict,axiom,
% 5.46/5.78 ! [A: set_int] :
% 5.46/5.78 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_strict
% 5.46/5.78 thf(fact_8416_bot_Oextremum__strict,axiom,
% 5.46/5.78 ! [A: nat] :
% 5.46/5.78 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_strict
% 5.46/5.78 thf(fact_8417_bot_Oextremum,axiom,
% 5.46/5.78 ! [A: set_Extended_enat] : ( ord_le7203529160286727270d_enat @ bot_bo7653980558646680370d_enat @ A ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum
% 5.46/5.78 thf(fact_8418_bot_Oextremum,axiom,
% 5.46/5.78 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum
% 5.46/5.78 thf(fact_8419_bot_Oextremum,axiom,
% 5.46/5.78 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum
% 5.46/5.78 thf(fact_8420_bot_Oextremum,axiom,
% 5.46/5.78 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum
% 5.46/5.78 thf(fact_8421_bot_Oextremum,axiom,
% 5.46/5.78 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum
% 5.46/5.78 thf(fact_8422_bot_Oextremum__unique,axiom,
% 5.46/5.78 ! [A: set_Extended_enat] :
% 5.46/5.78 ( ( ord_le7203529160286727270d_enat @ A @ bot_bo7653980558646680370d_enat )
% 5.46/5.78 = ( A = bot_bo7653980558646680370d_enat ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_unique
% 5.46/5.78 thf(fact_8423_bot_Oextremum__unique,axiom,
% 5.46/5.78 ! [A: set_real] :
% 5.46/5.78 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.46/5.78 = ( A = bot_bot_set_real ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_unique
% 5.46/5.78 thf(fact_8424_bot_Oextremum__unique,axiom,
% 5.46/5.78 ! [A: set_int] :
% 5.46/5.78 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.46/5.78 = ( A = bot_bot_set_int ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_unique
% 5.46/5.78 thf(fact_8425_bot_Oextremum__unique,axiom,
% 5.46/5.78 ! [A: set_nat] :
% 5.46/5.78 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.46/5.78 = ( A = bot_bot_set_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_unique
% 5.46/5.78 thf(fact_8426_bot_Oextremum__unique,axiom,
% 5.46/5.78 ! [A: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.46/5.78 = ( A = bot_bot_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_unique
% 5.46/5.78 thf(fact_8427_bot_Oextremum__uniqueI,axiom,
% 5.46/5.78 ! [A: set_Extended_enat] :
% 5.46/5.78 ( ( ord_le7203529160286727270d_enat @ A @ bot_bo7653980558646680370d_enat )
% 5.46/5.78 => ( A = bot_bo7653980558646680370d_enat ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_uniqueI
% 5.46/5.78 thf(fact_8428_bot_Oextremum__uniqueI,axiom,
% 5.46/5.78 ! [A: set_real] :
% 5.46/5.78 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.46/5.78 => ( A = bot_bot_set_real ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_uniqueI
% 5.46/5.78 thf(fact_8429_bot_Oextremum__uniqueI,axiom,
% 5.46/5.78 ! [A: set_int] :
% 5.46/5.78 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.46/5.78 => ( A = bot_bot_set_int ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_uniqueI
% 5.46/5.78 thf(fact_8430_bot_Oextremum__uniqueI,axiom,
% 5.46/5.78 ! [A: set_nat] :
% 5.46/5.78 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.46/5.78 => ( A = bot_bot_set_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_uniqueI
% 5.46/5.78 thf(fact_8431_bot_Oextremum__uniqueI,axiom,
% 5.46/5.78 ! [A: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.46/5.78 => ( A = bot_bot_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % bot.extremum_uniqueI
% 5.46/5.78 thf(fact_8432_diff__shunt__var,axiom,
% 5.46/5.78 ! [X4: set_Extended_enat,Y3: set_Extended_enat] :
% 5.46/5.78 ( ( ( minus_925952699566721837d_enat @ X4 @ Y3 )
% 5.46/5.78 = bot_bo7653980558646680370d_enat )
% 5.46/5.78 = ( ord_le7203529160286727270d_enat @ X4 @ Y3 ) ) ).
% 5.46/5.78
% 5.46/5.78 % diff_shunt_var
% 5.46/5.78 thf(fact_8433_diff__shunt__var,axiom,
% 5.46/5.78 ! [X4: set_real,Y3: set_real] :
% 5.46/5.78 ( ( ( minus_minus_set_real @ X4 @ Y3 )
% 5.46/5.78 = bot_bot_set_real )
% 5.46/5.78 = ( ord_less_eq_set_real @ X4 @ Y3 ) ) ).
% 5.46/5.78
% 5.46/5.78 % diff_shunt_var
% 5.46/5.78 thf(fact_8434_diff__shunt__var,axiom,
% 5.46/5.78 ! [X4: set_int,Y3: set_int] :
% 5.46/5.78 ( ( ( minus_minus_set_int @ X4 @ Y3 )
% 5.46/5.78 = bot_bot_set_int )
% 5.46/5.78 = ( ord_less_eq_set_int @ X4 @ Y3 ) ) ).
% 5.46/5.78
% 5.46/5.78 % diff_shunt_var
% 5.46/5.78 thf(fact_8435_diff__shunt__var,axiom,
% 5.46/5.78 ! [X4: set_nat,Y3: set_nat] :
% 5.46/5.78 ( ( ( minus_minus_set_nat @ X4 @ Y3 )
% 5.46/5.78 = bot_bot_set_nat )
% 5.46/5.78 = ( ord_less_eq_set_nat @ X4 @ Y3 ) ) ).
% 5.46/5.78
% 5.46/5.78 % diff_shunt_var
% 5.46/5.78 thf(fact_8436_ex__nat__less,axiom,
% 5.46/5.78 ! [N: nat,P: nat > $o] :
% 5.46/5.78 ( ( ? [M6: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M6 @ N )
% 5.46/5.78 & ( P @ M6 ) ) )
% 5.46/5.78 = ( ? [X: nat] :
% 5.46/5.78 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.78 & ( P @ X ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % ex_nat_less
% 5.46/5.78 thf(fact_8437_all__nat__less,axiom,
% 5.46/5.78 ! [N: nat,P: nat > $o] :
% 5.46/5.78 ( ( ! [M6: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M6 @ N )
% 5.46/5.78 => ( P @ M6 ) ) )
% 5.46/5.78 = ( ! [X: nat] :
% 5.46/5.78 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.78 => ( P @ X ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % all_nat_less
% 5.46/5.78 thf(fact_8438_atLeastatMost__psubset__iff,axiom,
% 5.46/5.78 ! [A: set_nat,B2: set_nat,C: set_nat,D: set_nat] :
% 5.46/5.78 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B2 ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.46/5.78 = ( ( ~ ( ord_less_eq_set_nat @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.46/5.78 & ( ord_less_eq_set_nat @ B2 @ D )
% 5.46/5.78 & ( ( ord_less_set_nat @ C @ A )
% 5.46/5.78 | ( ord_less_set_nat @ B2 @ D ) ) ) )
% 5.46/5.78 & ( ord_less_eq_set_nat @ C @ D ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_psubset_iff
% 5.46/5.78 thf(fact_8439_atLeastatMost__psubset__iff,axiom,
% 5.46/5.78 ! [A: rat,B2: rat,C: rat,D: rat] :
% 5.46/5.78 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B2 ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.46/5.78 = ( ( ~ ( ord_less_eq_rat @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_rat @ C @ A )
% 5.46/5.78 & ( ord_less_eq_rat @ B2 @ D )
% 5.46/5.78 & ( ( ord_less_rat @ C @ A )
% 5.46/5.78 | ( ord_less_rat @ B2 @ D ) ) ) )
% 5.46/5.78 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_psubset_iff
% 5.46/5.78 thf(fact_8440_atLeastatMost__psubset__iff,axiom,
% 5.46/5.78 ! [A: num,B2: num,C: num,D: num] :
% 5.46/5.78 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B2 ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.46/5.78 = ( ( ~ ( ord_less_eq_num @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_num @ C @ A )
% 5.46/5.78 & ( ord_less_eq_num @ B2 @ D )
% 5.46/5.78 & ( ( ord_less_num @ C @ A )
% 5.46/5.78 | ( ord_less_num @ B2 @ D ) ) ) )
% 5.46/5.78 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_psubset_iff
% 5.46/5.78 thf(fact_8441_atLeastatMost__psubset__iff,axiom,
% 5.46/5.78 ! [A: nat,B2: nat,C: nat,D: nat] :
% 5.46/5.78 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B2 ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.46/5.78 = ( ( ~ ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_nat @ C @ A )
% 5.46/5.78 & ( ord_less_eq_nat @ B2 @ D )
% 5.46/5.78 & ( ( ord_less_nat @ C @ A )
% 5.46/5.78 | ( ord_less_nat @ B2 @ D ) ) ) )
% 5.46/5.78 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_psubset_iff
% 5.46/5.78 thf(fact_8442_atLeastatMost__psubset__iff,axiom,
% 5.46/5.78 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.78 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B2 ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.46/5.78 = ( ( ~ ( ord_less_eq_int @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_int @ C @ A )
% 5.46/5.78 & ( ord_less_eq_int @ B2 @ D )
% 5.46/5.78 & ( ( ord_less_int @ C @ A )
% 5.46/5.78 | ( ord_less_int @ B2 @ D ) ) ) )
% 5.46/5.78 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_psubset_iff
% 5.46/5.78 thf(fact_8443_atLeastatMost__psubset__iff,axiom,
% 5.46/5.78 ! [A: real,B2: real,C: real,D: real] :
% 5.46/5.78 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.46/5.78 = ( ( ~ ( ord_less_eq_real @ A @ B2 )
% 5.46/5.78 | ( ( ord_less_eq_real @ C @ A )
% 5.46/5.78 & ( ord_less_eq_real @ B2 @ D )
% 5.46/5.78 & ( ( ord_less_real @ C @ A )
% 5.46/5.78 | ( ord_less_real @ B2 @ D ) ) ) )
% 5.46/5.78 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % atLeastatMost_psubset_iff
% 5.46/5.78 thf(fact_8444_invar__vebt_Ointros_I4_J,axiom,
% 5.46/5.78 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.46/5.78 ( ! [X3: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.78 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.46/5.78 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.46/5.78 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.78 => ( ( M = N )
% 5.46/5.78 => ( ( Deg
% 5.46/5.78 = ( plus_plus_nat @ N @ M ) )
% 5.46/5.78 => ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.78 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X6 ) )
% 5.46/5.78 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.46/5.78 => ( ( ( Mi = Ma )
% 5.46/5.78 => ! [X3: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.78 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.46/5.78 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.46/5.78 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.46/5.78 => ( ( ( Mi != Ma )
% 5.46/5.78 => ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.78 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.46/5.78 = I3 )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.46/5.78 & ! [X3: nat] :
% 5.46/5.78 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.46/5.78 = I3 )
% 5.46/5.78 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.46/5.78 => ( ( ord_less_nat @ Mi @ X3 )
% 5.46/5.78 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.46/5.78 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % invar_vebt.intros(4)
% 5.46/5.78 thf(fact_8445_invar__vebt_Ointros_I5_J,axiom,
% 5.46/5.78 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.46/5.78 ( ! [X3: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.78 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.46/5.78 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.46/5.78 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.78 => ( ( M
% 5.46/5.78 = ( suc @ N ) )
% 5.46/5.78 => ( ( Deg
% 5.46/5.78 = ( plus_plus_nat @ N @ M ) )
% 5.46/5.78 => ( ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.78 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X6 ) )
% 5.46/5.78 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.46/5.78 => ( ( ( Mi = Ma )
% 5.46/5.78 => ! [X3: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.78 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.46/5.78 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.46/5.78 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.46/5.78 => ( ( ( Mi != Ma )
% 5.46/5.78 => ! [I3: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.78 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.46/5.78 = I3 )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.46/5.78 & ! [X3: nat] :
% 5.46/5.78 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 5.46/5.78 = I3 )
% 5.46/5.78 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 5.46/5.78 => ( ( ord_less_nat @ Mi @ X3 )
% 5.46/5.78 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.46/5.78 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % invar_vebt.intros(5)
% 5.46/5.78 thf(fact_8446_mintlistlength,axiom,
% 5.46/5.78 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.46/5.78 => ( ( Mi != Ma )
% 5.46/5.78 => ( ( ord_less_nat @ Mi @ Ma )
% 5.46/5.78 & ? [M4: nat] :
% 5.46/5.78 ( ( ( some_nat @ M4 )
% 5.46/5.78 = ( vEBT_vebt_mint @ Summary ) )
% 5.46/5.78 & ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % mintlistlength
% 5.46/5.78 thf(fact_8447__092_060open_062min__in__set_A_Iset__vebt_H_A_ItreeList_A_B_Athe_A_Ivebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_J_Aminy_092_060close_062,axiom,
% 5.46/5.78 vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ miny ).
% 5.46/5.78
% 5.46/5.78 % \<open>min_in_set (set_vebt' (treeList ! the (vebt_succ summary (high x (deg div 2))))) miny\<close>
% 5.46/5.78 thf(fact_8448_scmem,axiom,
% 5.46/5.78 vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ miny ).
% 5.46/5.78
% 5.46/5.78 % scmem
% 5.46/5.78 thf(fact_8449__092_060open_062invar__vebt_A_ItreeList_A_B_Athe_A_Ivebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_An_092_060close_062,axiom,
% 5.46/5.78 vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ na ).
% 5.46/5.78
% 5.46/5.78 % \<open>invar_vebt (treeList ! the (vebt_succ summary (high x (deg div 2)))) n\<close>
% 5.46/5.78 thf(fact_8450_mint__member,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ( vEBT_vebt_mint @ T )
% 5.46/5.78 = ( some_nat @ Maxi ) )
% 5.46/5.78 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % mint_member
% 5.46/5.78 thf(fact_8451_mint__corr__help,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,Mini: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ( vEBT_vebt_mint @ T )
% 5.46/5.78 = ( some_nat @ Mini ) )
% 5.46/5.78 => ( ( vEBT_vebt_member @ T @ X4 )
% 5.46/5.78 => ( ord_less_eq_nat @ Mini @ X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % mint_corr_help
% 5.46/5.78 thf(fact_8452_mint__corr__help__empty,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ( vEBT_vebt_mint @ T )
% 5.46/5.78 = none_nat )
% 5.46/5.78 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.46/5.78 = bot_bot_set_nat ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % mint_corr_help_empty
% 5.46/5.78 thf(fact_8453_mint__sound,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X4 )
% 5.46/5.78 => ( ( vEBT_vebt_mint @ T )
% 5.46/5.78 = ( some_nat @ X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % mint_sound
% 5.46/5.78 thf(fact_8454_mint__corr,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ( vEBT_vebt_mint @ T )
% 5.46/5.78 = ( some_nat @ X4 ) )
% 5.46/5.78 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % mint_corr
% 5.46/5.78 thf(fact_8455__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062miny_O_ASome_Aminy_A_061_Avebt__mint_A_ItreeList_A_B_Asc_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.46/5.78 ~ ! [Miny: nat] :
% 5.46/5.78 ( ( some_nat @ Miny )
% 5.46/5.78 != ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ sc ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>\<And>thesis. (\<And>miny. Some miny = vebt_mint (treeList ! sc) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.46/5.78 thf(fact_8456_misiz,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ( some_nat @ M )
% 5.46/5.78 = ( vEBT_vebt_mint @ T ) )
% 5.46/5.78 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % misiz
% 5.46/5.78 thf(fact_8457_bit__0__eq,axiom,
% 5.46/5.78 ( ( bit_se1146084159140164899it_int @ zero_zero_int )
% 5.46/5.78 = bot_bot_nat_o ) ).
% 5.46/5.78
% 5.46/5.78 % bit_0_eq
% 5.46/5.78 thf(fact_8458_bit__0__eq,axiom,
% 5.46/5.78 ( ( bit_se1148574629649215175it_nat @ zero_zero_nat )
% 5.46/5.78 = bot_bot_nat_o ) ).
% 5.46/5.78
% 5.46/5.78 % bit_0_eq
% 5.46/5.78 thf(fact_8459_succ__list__to__short,axiom,
% 5.46/5.78 ! [Deg: nat,Mi: nat,X4: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.46/5.78 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.46/5.78 => ( ( ord_less_eq_nat @ Mi @ X4 )
% 5.46/5.78 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 = none_nat ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % succ_list_to_short
% 5.46/5.78 thf(fact_8460_nested__mint,axiom,
% 5.46/5.78 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va2: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.46/5.78 => ( ( N
% 5.46/5.78 = ( suc @ ( suc @ Va2 ) ) )
% 5.46/5.78 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.46/5.78 => ( ( Ma != Mi )
% 5.46/5.78 => ( 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 @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nested_mint
% 5.46/5.78 thf(fact_8461__092_060open_062Some_Aminy_A_061_Avebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_092_060close_062,axiom,
% 5.46/5.78 ( ( some_nat @ miny )
% 5.46/5.78 = ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>Some miny = vebt_mint (treeList ! the (vebt_succ summary (high x (deg div 2))))\<close>
% 5.46/5.78 thf(fact_8462_local_Opower__def,axiom,
% 5.46/5.78 ( vEBT_VEBT_power
% 5.46/5.78 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % local.power_def
% 5.46/5.78 thf(fact_8463_bot__enat__def,axiom,
% 5.46/5.78 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.46/5.78
% 5.46/5.78 % bot_enat_def
% 5.46/5.78 thf(fact_8464_bot__nat__def,axiom,
% 5.46/5.78 bot_bot_nat = zero_zero_nat ).
% 5.46/5.78
% 5.46/5.78 % bot_nat_def
% 5.46/5.78 thf(fact_8465_aset_I2_J,axiom,
% 5.46/5.78 ! [D4: int,A3: set_int,P: int > $o,Q: int > $o] :
% 5.46/5.78 ( ! [X3: int] :
% 5.46/5.78 ( ! [Xa2: int] :
% 5.46/5.78 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb2: int] :
% 5.46/5.78 ( ( member_int @ Xb2 @ A3 )
% 5.46/5.78 => ( X3
% 5.46/5.78 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.46/5.78 => ( ( P @ X3 )
% 5.46/5.78 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.46/5.78 => ( ! [X3: int] :
% 5.46/5.78 ( ! [Xa2: int] :
% 5.46/5.78 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb2: int] :
% 5.46/5.78 ( ( member_int @ Xb2 @ A3 )
% 5.46/5.78 => ( X3
% 5.46/5.78 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.46/5.78 => ( ( Q @ X3 )
% 5.46/5.78 => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ A3 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ( P @ X5 )
% 5.46/5.78 | ( Q @ X5 ) )
% 5.46/5.78 => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 5.46/5.78 | ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aset(2)
% 5.46/5.78 thf(fact_8466_aset_I1_J,axiom,
% 5.46/5.78 ! [D4: int,A3: set_int,P: int > $o,Q: int > $o] :
% 5.46/5.78 ( ! [X3: int] :
% 5.46/5.78 ( ! [Xa2: int] :
% 5.46/5.78 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb2: int] :
% 5.46/5.78 ( ( member_int @ Xb2 @ A3 )
% 5.46/5.78 => ( X3
% 5.46/5.78 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.46/5.78 => ( ( P @ X3 )
% 5.46/5.78 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.46/5.78 => ( ! [X3: int] :
% 5.46/5.78 ( ! [Xa2: int] :
% 5.46/5.78 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb2: int] :
% 5.46/5.78 ( ( member_int @ Xb2 @ A3 )
% 5.46/5.78 => ( X3
% 5.46/5.78 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.46/5.78 => ( ( Q @ X3 )
% 5.46/5.78 => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ A3 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ( P @ X5 )
% 5.46/5.78 & ( Q @ X5 ) )
% 5.46/5.78 => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 5.46/5.78 & ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aset(1)
% 5.46/5.78 thf(fact_8467_bset_I2_J,axiom,
% 5.46/5.78 ! [D4: int,B4: set_int,P: int > $o,Q: int > $o] :
% 5.46/5.78 ( ! [X3: int] :
% 5.46/5.78 ( ! [Xa2: int] :
% 5.46/5.78 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb2: int] :
% 5.46/5.78 ( ( member_int @ Xb2 @ B4 )
% 5.46/5.78 => ( X3
% 5.46/5.78 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.46/5.78 => ( ( P @ X3 )
% 5.46/5.78 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.46/5.78 => ( ! [X3: int] :
% 5.46/5.78 ( ! [Xa2: int] :
% 5.46/5.78 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb2: int] :
% 5.46/5.78 ( ( member_int @ Xb2 @ B4 )
% 5.46/5.78 => ( X3
% 5.46/5.78 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.46/5.78 => ( ( Q @ X3 )
% 5.46/5.78 => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ( P @ X5 )
% 5.46/5.78 | ( Q @ X5 ) )
% 5.46/5.78 => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 5.46/5.78 | ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % bset(2)
% 5.46/5.78 thf(fact_8468_bset_I1_J,axiom,
% 5.46/5.78 ! [D4: int,B4: set_int,P: int > $o,Q: int > $o] :
% 5.46/5.78 ( ! [X3: int] :
% 5.46/5.78 ( ! [Xa2: int] :
% 5.46/5.78 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb2: int] :
% 5.46/5.78 ( ( member_int @ Xb2 @ B4 )
% 5.46/5.78 => ( X3
% 5.46/5.78 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.46/5.78 => ( ( P @ X3 )
% 5.46/5.78 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.46/5.78 => ( ! [X3: int] :
% 5.46/5.78 ( ! [Xa2: int] :
% 5.46/5.78 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb2: int] :
% 5.46/5.78 ( ( member_int @ Xb2 @ B4 )
% 5.46/5.78 => ( X3
% 5.46/5.78 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.46/5.78 => ( ( Q @ X3 )
% 5.46/5.78 => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ( P @ X5 )
% 5.46/5.78 & ( Q @ X5 ) )
% 5.46/5.78 => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 5.46/5.78 & ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % bset(1)
% 5.46/5.78 thf(fact_8469_bset_I9_J,axiom,
% 5.46/5.78 ! [D: int,D4: int,B4: set_int,T: int] :
% 5.46/5.78 ( ( dvd_dvd_int @ D @ D4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.46/5.78 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % bset(9)
% 5.46/5.78 thf(fact_8470_bset_I10_J,axiom,
% 5.46/5.78 ! [D: int,D4: int,B4: set_int,T: int] :
% 5.46/5.78 ( ( dvd_dvd_int @ D @ D4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.46/5.78 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % bset(10)
% 5.46/5.78 thf(fact_8471_aset_I9_J,axiom,
% 5.46/5.78 ! [D: int,D4: int,A3: set_int,T: int] :
% 5.46/5.78 ( ( dvd_dvd_int @ D @ D4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ A3 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.46/5.78 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aset(9)
% 5.46/5.78 thf(fact_8472_aset_I10_J,axiom,
% 5.46/5.78 ! [D: int,D4: int,A3: set_int,T: int] :
% 5.46/5.78 ( ( dvd_dvd_int @ D @ D4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ A3 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.46/5.78 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aset(10)
% 5.46/5.78 thf(fact_8473_vebt__succ_Osimps_I4_J,axiom,
% 5.46/5.78 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 5.46/5.78 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 5.46/5.78 = none_nat ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_succ.simps(4)
% 5.46/5.78 thf(fact_8474_periodic__finite__ex,axiom,
% 5.46/5.78 ! [D: int,P: int > $o] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D )
% 5.46/5.78 => ( ! [X3: int,K2: int] :
% 5.46/5.78 ( ( P @ X3 )
% 5.46/5.78 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.46/5.78 => ( ( ? [X6: int] : ( P @ X6 ) )
% 5.46/5.78 = ( ? [X: int] :
% 5.46/5.78 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.46/5.78 & ( P @ X ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % periodic_finite_ex
% 5.46/5.78 thf(fact_8475_aset_I7_J,axiom,
% 5.46/5.78 ! [D4: int,A3: set_int,T: int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ A3 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ord_less_int @ T @ X5 )
% 5.46/5.78 => ( ord_less_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aset(7)
% 5.46/5.78 thf(fact_8476_aset_I5_J,axiom,
% 5.46/5.78 ! [D4: int,T: int,A3: set_int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ( ( member_int @ T @ A3 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ A3 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ord_less_int @ X5 @ T )
% 5.46/5.78 => ( ord_less_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aset(5)
% 5.46/5.78 thf(fact_8477_aset_I4_J,axiom,
% 5.46/5.78 ! [D4: int,T: int,A3: set_int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ( ( member_int @ T @ A3 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ A3 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( X5 != T )
% 5.46/5.78 => ( ( plus_plus_int @ X5 @ D4 )
% 5.46/5.78 != T ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aset(4)
% 5.46/5.78 thf(fact_8478_aset_I3_J,axiom,
% 5.46/5.78 ! [D4: int,T: int,A3: set_int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A3 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ A3 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( X5 = T )
% 5.46/5.78 => ( ( plus_plus_int @ X5 @ D4 )
% 5.46/5.78 = T ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aset(3)
% 5.46/5.78 thf(fact_8479_bset_I7_J,axiom,
% 5.46/5.78 ! [D4: int,T: int,B4: set_int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ( ( member_int @ T @ B4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ord_less_int @ T @ X5 )
% 5.46/5.78 => ( ord_less_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % bset(7)
% 5.46/5.78 thf(fact_8480_bset_I5_J,axiom,
% 5.46/5.78 ! [D4: int,B4: set_int,T: int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ord_less_int @ X5 @ T )
% 5.46/5.78 => ( ord_less_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % bset(5)
% 5.46/5.78 thf(fact_8481_bset_I4_J,axiom,
% 5.46/5.78 ! [D4: int,T: int,B4: set_int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ( ( member_int @ T @ B4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( X5 != T )
% 5.46/5.78 => ( ( minus_minus_int @ X5 @ D4 )
% 5.46/5.78 != T ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % bset(4)
% 5.46/5.78 thf(fact_8482_bset_I3_J,axiom,
% 5.46/5.78 ! [D4: int,T: int,B4: set_int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( X5 = T )
% 5.46/5.78 => ( ( minus_minus_int @ X5 @ D4 )
% 5.46/5.78 = T ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % bset(3)
% 5.46/5.78 thf(fact_8483_vebt__succ_Osimps_I5_J,axiom,
% 5.46/5.78 ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.46/5.78 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 5.46/5.78 = none_nat ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_succ.simps(5)
% 5.46/5.78 thf(fact_8484_aset_I8_J,axiom,
% 5.46/5.78 ! [D4: int,A3: set_int,T: int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ A3 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ord_less_eq_int @ T @ X5 )
% 5.46/5.78 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aset(8)
% 5.46/5.78 thf(fact_8485_aset_I6_J,axiom,
% 5.46/5.78 ! [D4: int,T: int,A3: set_int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A3 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ A3 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ord_less_eq_int @ X5 @ T )
% 5.46/5.78 => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % aset(6)
% 5.46/5.78 thf(fact_8486_bset_I8_J,axiom,
% 5.46/5.78 ! [D4: int,T: int,B4: set_int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ord_less_eq_int @ T @ X5 )
% 5.46/5.78 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % bset(8)
% 5.46/5.78 thf(fact_8487_bset_I6_J,axiom,
% 5.46/5.78 ! [D4: int,B4: set_int,T: int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ! [X5: int] :
% 5.46/5.78 ( ! [Xa3: int] :
% 5.46/5.78 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb3: int] :
% 5.46/5.78 ( ( member_int @ Xb3 @ B4 )
% 5.46/5.78 => ( X5
% 5.46/5.78 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.46/5.78 => ( ( ord_less_eq_int @ X5 @ T )
% 5.46/5.78 => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % bset(6)
% 5.46/5.78 thf(fact_8488_cpmi,axiom,
% 5.46/5.78 ! [D4: int,P: int > $o,P4: int > $o,B4: set_int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ( ? [Z3: int] :
% 5.46/5.78 ! [X3: int] :
% 5.46/5.78 ( ( ord_less_int @ X3 @ Z3 )
% 5.46/5.78 => ( ( P @ X3 )
% 5.46/5.78 = ( P4 @ X3 ) ) )
% 5.46/5.78 => ( ! [X3: int] :
% 5.46/5.78 ( ! [Xa2: int] :
% 5.46/5.78 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb2: int] :
% 5.46/5.78 ( ( member_int @ Xb2 @ B4 )
% 5.46/5.78 => ( X3
% 5.46/5.78 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.46/5.78 => ( ( P @ X3 )
% 5.46/5.78 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 5.46/5.78 => ( ! [X3: int,K2: int] :
% 5.46/5.78 ( ( P4 @ X3 )
% 5.46/5.78 = ( P4 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.46/5.78 => ( ( ? [X6: int] : ( P @ X6 ) )
% 5.46/5.78 = ( ? [X: int] :
% 5.46/5.78 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 & ( P4 @ X ) )
% 5.46/5.78 | ? [X: int] :
% 5.46/5.78 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 & ? [Y: int] :
% 5.46/5.78 ( ( member_int @ Y @ B4 )
% 5.46/5.78 & ( P @ ( plus_plus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % cpmi
% 5.46/5.78 thf(fact_8489_cppi,axiom,
% 5.46/5.78 ! [D4: int,P: int > $o,P4: int > $o,A3: set_int] :
% 5.46/5.78 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.46/5.78 => ( ? [Z3: int] :
% 5.46/5.78 ! [X3: int] :
% 5.46/5.78 ( ( ord_less_int @ Z3 @ X3 )
% 5.46/5.78 => ( ( P @ X3 )
% 5.46/5.78 = ( P4 @ X3 ) ) )
% 5.46/5.78 => ( ! [X3: int] :
% 5.46/5.78 ( ! [Xa2: int] :
% 5.46/5.78 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 => ! [Xb2: int] :
% 5.46/5.78 ( ( member_int @ Xb2 @ A3 )
% 5.46/5.78 => ( X3
% 5.46/5.78 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.46/5.78 => ( ( P @ X3 )
% 5.46/5.78 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 5.46/5.78 => ( ! [X3: int,K2: int] :
% 5.46/5.78 ( ( P4 @ X3 )
% 5.46/5.78 = ( P4 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.46/5.78 => ( ( ? [X6: int] : ( P @ X6 ) )
% 5.46/5.78 = ( ? [X: int] :
% 5.46/5.78 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 & ( P4 @ X ) )
% 5.46/5.78 | ? [X: int] :
% 5.46/5.78 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.46/5.78 & ? [Y: int] :
% 5.46/5.78 ( ( member_int @ Y @ A3 )
% 5.46/5.78 & ( P @ ( minus_minus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % cppi
% 5.46/5.78 thf(fact_8490__092_060open_062res_A_061_Athe_A_ISome_A_I2_A_094_A_Ideg_Adiv_A2_J_J_A_K_092_060_094sub_062o_Avebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_L_092_060_094sub_062o_Avebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_J_092_060close_062,axiom,
% 5.46/5.78 ( res
% 5.46/5.78 = ( 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_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>res = the (Some (2 ^ (deg div 2)) *\<^sub>o vebt_succ summary (high x (deg div 2)) +\<^sub>o vebt_mint (treeList ! the (vebt_succ summary (high x (deg div 2)))))\<close>
% 5.46/5.78 thf(fact_8491_summaxma,axiom,
% 5.46/5.78 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.46/5.78 => ( ( Mi != Ma )
% 5.46/5.78 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.46/5.78 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % summaxma
% 5.46/5.78 thf(fact_8492_maxt__sound,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X4 )
% 5.46/5.78 => ( ( vEBT_vebt_maxt @ T )
% 5.46/5.78 = ( some_nat @ X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % maxt_sound
% 5.46/5.78 thf(fact_8493_maxt__corr,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ( vEBT_vebt_maxt @ T )
% 5.46/5.78 = ( some_nat @ X4 ) )
% 5.46/5.78 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X4 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % maxt_corr
% 5.46/5.78 thf(fact_8494_add__shift,axiom,
% 5.46/5.78 ! [X4: nat,Y3: nat,Z: nat] :
% 5.46/5.78 ( ( ( plus_plus_nat @ X4 @ Y3 )
% 5.46/5.78 = Z )
% 5.46/5.78 = ( ( vEBT_VEBT_add @ ( some_nat @ X4 ) @ ( some_nat @ Y3 ) )
% 5.46/5.78 = ( some_nat @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % add_shift
% 5.46/5.78 thf(fact_8495_mul__shift,axiom,
% 5.46/5.78 ! [X4: nat,Y3: nat,Z: nat] :
% 5.46/5.78 ( ( ( times_times_nat @ X4 @ Y3 )
% 5.46/5.78 = Z )
% 5.46/5.78 = ( ( vEBT_VEBT_mul @ ( some_nat @ X4 ) @ ( some_nat @ Y3 ) )
% 5.46/5.78 = ( some_nat @ Z ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % mul_shift
% 5.46/5.78 thf(fact_8496_maxbmo,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,X4: nat] :
% 5.46/5.78 ( ( ( vEBT_vebt_maxt @ T )
% 5.46/5.78 = ( some_nat @ X4 ) )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ T @ X4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % maxbmo
% 5.46/5.78 thf(fact_8497_add__def,axiom,
% 5.46/5.78 ( vEBT_VEBT_add
% 5.46/5.78 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % add_def
% 5.46/5.78 thf(fact_8498_mul__def,axiom,
% 5.46/5.78 ( vEBT_VEBT_mul
% 5.46/5.78 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % mul_def
% 5.46/5.78 thf(fact_8499_maxt__member,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ( vEBT_vebt_maxt @ T )
% 5.46/5.78 = ( some_nat @ Maxi ) )
% 5.46/5.78 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % maxt_member
% 5.46/5.78 thf(fact_8500_maxt__corr__help,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ( vEBT_vebt_maxt @ T )
% 5.46/5.78 = ( some_nat @ Maxi ) )
% 5.46/5.78 => ( ( vEBT_vebt_member @ T @ X4 )
% 5.46/5.78 => ( ord_less_eq_nat @ X4 @ Maxi ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % maxt_corr_help
% 5.46/5.78 thf(fact_8501_maxt__corr__help__empty,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( ( vEBT_vebt_maxt @ T )
% 5.46/5.78 = none_nat )
% 5.46/5.78 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.46/5.78 = bot_bot_set_nat ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % maxt_corr_help_empty
% 5.46/5.78 thf(fact_8502__092_060open_062vebt__succ_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ax_A_061_ASome_A_I2_A_094_A_Ideg_Adiv_A2_J_J_A_K_092_060_094sub_062o_Avebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_L_092_060_094sub_062o_Avebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_092_060close_062,axiom,
% 5.46/5.78 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.46/5.78 = ( 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_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>vebt_succ (Node (Some (mi, ma)) deg treeList summary) x = Some (2 ^ (deg div 2)) *\<^sub>o vebt_succ summary (high x (deg div 2)) +\<^sub>o vebt_mint (treeList ! the (vebt_succ summary (high x (deg div 2))))\<close>
% 5.46/5.78 thf(fact_8503__C2_C,axiom,
% 5.46/5.78 ( ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 = none_nat )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.46/5.78 = none_nat ) )
% 5.46/5.78 & ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 != none_nat )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.46/5.78 = ( 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_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % "2"
% 5.46/5.78 thf(fact_8504__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_A_Ithe_A_ISome_A_I2_A_094_A_Ideg_Adiv_A2_J_J_A_K_092_060_094sub_062o_Avebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_L_092_060_094sub_062o_Avebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__succ_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_J_J_092_060close_062,axiom,
% 5.46/5.78 vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ ( 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_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % \<open>vebt_member (Node (Some (mi, ma)) deg treeList summary) (the (Some (2 ^ (deg div 2)) *\<^sub>o vebt_succ summary (high x (deg div 2)) +\<^sub>o vebt_mint (treeList ! the (vebt_succ summary (high x (deg div 2))))))\<close>
% 5.46/5.78 thf(fact_8505__C1_C,axiom,
% 5.46/5.78 ( ( ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 != none_nat )
% 5.46/5.78 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.46/5.78 = ( 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_succ @ ( 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 ) ) ) ) ) ) ) )
% 5.46/5.78 & ( ~ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 != none_nat )
% 5.46/5.78 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.46/5.78 => ( ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 = none_nat )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.46/5.78 = none_nat ) )
% 5.46/5.78 & ( ( ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 != none_nat )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.46/5.78 = ( 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_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_succ @ summary @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % "1"
% 5.46/5.78 thf(fact_8506_i1,axiom,
% 5.46/5.78 ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 = none_nat )
% 5.46/5.78 | ~ ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % i1
% 5.46/5.78 thf(fact_8507_divmod__step__eq,axiom,
% 5.46/5.78 ! [L2: num,R2: nat,Q2: nat] :
% 5.46/5.78 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 )
% 5.46/5.78 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.46/5.78 = ( 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 ) ) ) ) )
% 5.46/5.78 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 )
% 5.46/5.78 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.46/5.78 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % divmod_step_eq
% 5.46/5.78 thf(fact_8508_divmod__step__eq,axiom,
% 5.46/5.78 ! [L2: num,R2: int,Q2: int] :
% 5.46/5.78 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 )
% 5.46/5.78 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.78 = ( 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 ) ) ) ) )
% 5.46/5.78 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 )
% 5.46/5.78 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.78 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % divmod_step_eq
% 5.46/5.78 thf(fact_8509_divmod__step__eq,axiom,
% 5.46/5.78 ! [L2: num,R2: code_integer,Q2: code_integer] :
% 5.46/5.78 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 )
% 5.46/5.78 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.46/5.78 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 5.46/5.78 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 )
% 5.46/5.78 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.46/5.78 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % divmod_step_eq
% 5.46/5.78 thf(fact_8510_less__shift,axiom,
% 5.46/5.78 ( ord_less_nat
% 5.46/5.78 = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % less_shift
% 5.46/5.78 thf(fact_8511_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.46/5.78 ! [X4: produc3368934014287244435at_num] :
% 5.46/5.78 ~ ! [F3: nat > num > num,A5: nat,B5: nat,Acc2: num] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc851828971589881931at_num @ F3 @ ( produc1195630363706982562at_num @ A5 @ ( product_Pair_nat_num @ B5 @ Acc2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % fold_atLeastAtMost_nat.cases
% 5.46/5.78 thf(fact_8512_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.46/5.78 ! [X4: produc4471711990508489141at_nat] :
% 5.46/5.78 ~ ! [F3: nat > nat > nat,A5: nat,B5: nat,Acc2: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc3209952032786966637at_nat @ F3 @ ( produc487386426758144856at_nat @ A5 @ ( product_Pair_nat_nat @ B5 @ Acc2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % fold_atLeastAtMost_nat.cases
% 5.46/5.78 thf(fact_8513_xor__num_Ocases,axiom,
% 5.46/5.78 ! [X4: product_prod_num_num] :
% 5.46/5.78 ( ( X4
% 5.46/5.78 != ( product_Pair_num_num @ one @ one ) )
% 5.46/5.78 => ( ! [N4: num] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( product_Pair_num_num @ one @ ( bit0 @ N4 ) ) )
% 5.46/5.78 => ( ! [N4: num] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( product_Pair_num_num @ one @ ( bit1 @ N4 ) ) )
% 5.46/5.78 => ( ! [M4: num] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 5.46/5.78 => ( ! [M4: num,N4: num] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N4 ) ) )
% 5.46/5.78 => ( ! [M4: num,N4: num] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N4 ) ) )
% 5.46/5.78 => ( ! [M4: num] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 5.46/5.78 => ( ! [M4: num,N4: num] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N4 ) ) )
% 5.46/5.78 => ~ ! [M4: num,N4: num] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N4 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % xor_num.cases
% 5.46/5.78 thf(fact_8514_minNullmin,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT] :
% 5.46/5.78 ( ( vEBT_VEBT_minNull @ T )
% 5.46/5.78 => ( ( vEBT_vebt_mint @ T )
% 5.46/5.78 = none_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % minNullmin
% 5.46/5.78 thf(fact_8515_minminNull,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT] :
% 5.46/5.78 ( ( ( vEBT_vebt_mint @ T )
% 5.46/5.78 = none_nat )
% 5.46/5.78 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.46/5.78
% 5.46/5.78 % minminNull
% 5.46/5.78 thf(fact_8516_vebt__member_Osimps_I4_J,axiom,
% 5.46/5.78 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X4: nat] :
% 5.46/5.78 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X4 ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_member.simps(4)
% 5.46/5.78 thf(fact_8517_succ__less__length__list,axiom,
% 5.46/5.78 ! [Deg: nat,Mi: nat,X4: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.46/5.78 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.46/5.78 => ( ( ord_less_eq_nat @ Mi @ X4 )
% 5.46/5.78 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 = ( if_option_nat
% 5.46/5.78 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 != none_nat )
% 5.46/5.78 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.46/5.78 @ ( 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 @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 @ ( if_option_nat
% 5.46/5.78 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 = none_nat )
% 5.46/5.78 @ none_nat
% 5.46/5.78 @ ( 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_succ @ Summary @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % succ_less_length_list
% 5.46/5.78 thf(fact_8518_not__min__Null__member,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT] :
% 5.46/5.78 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.46/5.78 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.46/5.78
% 5.46/5.78 % not_min_Null_member
% 5.46/5.78 thf(fact_8519_min__Null__member,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,X4: nat] :
% 5.46/5.78 ( ( vEBT_VEBT_minNull @ T )
% 5.46/5.78 => ~ ( vEBT_vebt_member @ T @ X4 ) ) ).
% 5.46/5.78
% 5.46/5.78 % min_Null_member
% 5.46/5.78 thf(fact_8520_set__vebt_H__def,axiom,
% 5.46/5.78 ( vEBT_VEBT_set_vebt
% 5.46/5.78 = ( ^ [T3: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_vebt'_def
% 5.46/5.78 thf(fact_8521_succ__greatereq__min,axiom,
% 5.46/5.78 ! [Deg: nat,Mi: nat,X4: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.46/5.78 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.46/5.78 => ( ( ord_less_eq_nat @ Mi @ X4 )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.78 @ ( if_option_nat
% 5.46/5.78 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 != none_nat )
% 5.46/5.78 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.46/5.78 @ ( 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 @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 @ ( if_option_nat
% 5.46/5.78 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 = none_nat )
% 5.46/5.78 @ none_nat
% 5.46/5.78 @ ( 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_succ @ Summary @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.78 @ none_nat ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % succ_greatereq_min
% 5.46/5.78 thf(fact_8522_nat__less__as__int,axiom,
% 5.46/5.78 ( ord_less_nat
% 5.46/5.78 = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nat_less_as_int
% 5.46/5.78 thf(fact_8523_less__set__def,axiom,
% 5.46/5.78 ( ord_le2529575680413868914d_enat
% 5.46/5.78 = ( ^ [A6: set_Extended_enat,B7: set_Extended_enat] :
% 5.46/5.78 ( ord_le8499522857272258027enat_o
% 5.46/5.78 @ ^ [X: extended_enat] : ( member_Extended_enat @ X @ A6 )
% 5.46/5.78 @ ^ [X: extended_enat] : ( member_Extended_enat @ X @ B7 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % less_set_def
% 5.46/5.78 thf(fact_8524_less__set__def,axiom,
% 5.46/5.78 ( ord_less_set_complex
% 5.46/5.78 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.46/5.78 ( ord_less_complex_o
% 5.46/5.78 @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 5.46/5.78 @ ^ [X: complex] : ( member_complex @ X @ B7 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % less_set_def
% 5.46/5.78 thf(fact_8525_less__set__def,axiom,
% 5.46/5.78 ( ord_less_set_real
% 5.46/5.78 = ( ^ [A6: set_real,B7: set_real] :
% 5.46/5.78 ( ord_less_real_o
% 5.46/5.78 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.46/5.78 @ ^ [X: real] : ( member_real @ X @ B7 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % less_set_def
% 5.46/5.78 thf(fact_8526_less__set__def,axiom,
% 5.46/5.78 ( ord_less_set_nat
% 5.46/5.78 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.46/5.78 ( ord_less_nat_o
% 5.46/5.78 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.46/5.78 @ ^ [X: nat] : ( member_nat @ X @ B7 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % less_set_def
% 5.46/5.78 thf(fact_8527_less__set__def,axiom,
% 5.46/5.78 ( ord_less_set_int
% 5.46/5.78 = ( ^ [A6: set_int,B7: set_int] :
% 5.46/5.78 ( ord_less_int_o
% 5.46/5.78 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.46/5.78 @ ^ [X: int] : ( member_int @ X @ B7 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % less_set_def
% 5.46/5.78 thf(fact_8528_strict__subset__divisors__dvd,axiom,
% 5.46/5.78 ! [A: complex,B2: complex] :
% 5.46/5.78 ( ( ord_less_set_complex
% 5.46/5.78 @ ( collect_complex
% 5.46/5.78 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 5.46/5.78 @ ( collect_complex
% 5.46/5.78 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B2 ) ) )
% 5.46/5.78 = ( ( dvd_dvd_complex @ A @ B2 )
% 5.46/5.78 & ~ ( dvd_dvd_complex @ B2 @ A ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % strict_subset_divisors_dvd
% 5.46/5.78 thf(fact_8529_strict__subset__divisors__dvd,axiom,
% 5.46/5.78 ! [A: real,B2: real] :
% 5.46/5.78 ( ( ord_less_set_real
% 5.46/5.78 @ ( collect_real
% 5.46/5.78 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 5.46/5.78 @ ( collect_real
% 5.46/5.78 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B2 ) ) )
% 5.46/5.78 = ( ( dvd_dvd_real @ A @ B2 )
% 5.46/5.78 & ~ ( dvd_dvd_real @ B2 @ A ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % strict_subset_divisors_dvd
% 5.46/5.78 thf(fact_8530_strict__subset__divisors__dvd,axiom,
% 5.46/5.78 ! [A: nat,B2: nat] :
% 5.46/5.78 ( ( ord_less_set_nat
% 5.46/5.78 @ ( collect_nat
% 5.46/5.78 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 5.46/5.78 @ ( collect_nat
% 5.46/5.78 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B2 ) ) )
% 5.46/5.78 = ( ( dvd_dvd_nat @ A @ B2 )
% 5.46/5.78 & ~ ( dvd_dvd_nat @ B2 @ A ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % strict_subset_divisors_dvd
% 5.46/5.78 thf(fact_8531_strict__subset__divisors__dvd,axiom,
% 5.46/5.78 ! [A: int,B2: int] :
% 5.46/5.78 ( ( ord_less_set_int
% 5.46/5.78 @ ( collect_int
% 5.46/5.78 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 5.46/5.78 @ ( collect_int
% 5.46/5.78 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B2 ) ) )
% 5.46/5.78 = ( ( dvd_dvd_int @ A @ B2 )
% 5.46/5.78 & ~ ( dvd_dvd_int @ B2 @ A ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % strict_subset_divisors_dvd
% 5.46/5.78 thf(fact_8532_strict__subset__divisors__dvd,axiom,
% 5.46/5.78 ! [A: code_integer,B2: code_integer] :
% 5.46/5.78 ( ( ord_le1307284697595431911nteger
% 5.46/5.78 @ ( collect_Code_integer
% 5.46/5.78 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 5.46/5.78 @ ( collect_Code_integer
% 5.46/5.78 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B2 ) ) )
% 5.46/5.78 = ( ( dvd_dvd_Code_integer @ A @ B2 )
% 5.46/5.78 & ~ ( dvd_dvd_Code_integer @ B2 @ A ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % strict_subset_divisors_dvd
% 5.46/5.78 thf(fact_8533_set__diff__eq,axiom,
% 5.46/5.78 ( minus_925952699566721837d_enat
% 5.46/5.78 = ( ^ [A6: set_Extended_enat,B7: set_Extended_enat] :
% 5.46/5.78 ( collec4429806609662206161d_enat
% 5.46/5.78 @ ^ [X: extended_enat] :
% 5.46/5.78 ( ( member_Extended_enat @ X @ A6 )
% 5.46/5.78 & ~ ( member_Extended_enat @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_diff_eq
% 5.46/5.78 thf(fact_8534_set__diff__eq,axiom,
% 5.46/5.78 ( minus_811609699411566653omplex
% 5.46/5.78 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.46/5.78 ( collect_complex
% 5.46/5.78 @ ^ [X: complex] :
% 5.46/5.78 ( ( member_complex @ X @ A6 )
% 5.46/5.78 & ~ ( member_complex @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_diff_eq
% 5.46/5.78 thf(fact_8535_set__diff__eq,axiom,
% 5.46/5.78 ( minus_minus_set_real
% 5.46/5.78 = ( ^ [A6: set_real,B7: set_real] :
% 5.46/5.78 ( collect_real
% 5.46/5.78 @ ^ [X: real] :
% 5.46/5.78 ( ( member_real @ X @ A6 )
% 5.46/5.78 & ~ ( member_real @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_diff_eq
% 5.46/5.78 thf(fact_8536_set__diff__eq,axiom,
% 5.46/5.78 ( minus_7954133019191499631st_nat
% 5.46/5.78 = ( ^ [A6: set_list_nat,B7: set_list_nat] :
% 5.46/5.78 ( collect_list_nat
% 5.46/5.78 @ ^ [X: list_nat] :
% 5.46/5.78 ( ( member_list_nat @ X @ A6 )
% 5.46/5.78 & ~ ( member_list_nat @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_diff_eq
% 5.46/5.78 thf(fact_8537_set__diff__eq,axiom,
% 5.46/5.78 ( minus_minus_set_int
% 5.46/5.78 = ( ^ [A6: set_int,B7: set_int] :
% 5.46/5.78 ( collect_int
% 5.46/5.78 @ ^ [X: int] :
% 5.46/5.78 ( ( member_int @ X @ A6 )
% 5.46/5.78 & ~ ( member_int @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_diff_eq
% 5.46/5.78 thf(fact_8538_set__diff__eq,axiom,
% 5.46/5.78 ( minus_minus_set_nat
% 5.46/5.78 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.46/5.78 ( collect_nat
% 5.46/5.78 @ ^ [X: nat] :
% 5.46/5.78 ( ( member_nat @ X @ A6 )
% 5.46/5.78 & ~ ( member_nat @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_diff_eq
% 5.46/5.78 thf(fact_8539_minus__set__def,axiom,
% 5.46/5.78 ( minus_925952699566721837d_enat
% 5.46/5.78 = ( ^ [A6: set_Extended_enat,B7: set_Extended_enat] :
% 5.46/5.78 ( collec4429806609662206161d_enat
% 5.46/5.78 @ ( minus_2020553357622893040enat_o
% 5.46/5.78 @ ^ [X: extended_enat] : ( member_Extended_enat @ X @ A6 )
% 5.46/5.78 @ ^ [X: extended_enat] : ( member_Extended_enat @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % minus_set_def
% 5.46/5.78 thf(fact_8540_minus__set__def,axiom,
% 5.46/5.78 ( minus_811609699411566653omplex
% 5.46/5.78 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.46/5.78 ( collect_complex
% 5.46/5.78 @ ( minus_8727706125548526216plex_o
% 5.46/5.78 @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 5.46/5.78 @ ^ [X: complex] : ( member_complex @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % minus_set_def
% 5.46/5.78 thf(fact_8541_minus__set__def,axiom,
% 5.46/5.78 ( minus_minus_set_real
% 5.46/5.78 = ( ^ [A6: set_real,B7: set_real] :
% 5.46/5.78 ( collect_real
% 5.46/5.78 @ ( minus_minus_real_o
% 5.46/5.78 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.46/5.78 @ ^ [X: real] : ( member_real @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % minus_set_def
% 5.46/5.78 thf(fact_8542_minus__set__def,axiom,
% 5.46/5.78 ( minus_7954133019191499631st_nat
% 5.46/5.78 = ( ^ [A6: set_list_nat,B7: set_list_nat] :
% 5.46/5.78 ( collect_list_nat
% 5.46/5.78 @ ( minus_1139252259498527702_nat_o
% 5.46/5.78 @ ^ [X: list_nat] : ( member_list_nat @ X @ A6 )
% 5.46/5.78 @ ^ [X: list_nat] : ( member_list_nat @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % minus_set_def
% 5.46/5.78 thf(fact_8543_minus__set__def,axiom,
% 5.46/5.78 ( minus_minus_set_int
% 5.46/5.78 = ( ^ [A6: set_int,B7: set_int] :
% 5.46/5.78 ( collect_int
% 5.46/5.78 @ ( minus_minus_int_o
% 5.46/5.78 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.46/5.78 @ ^ [X: int] : ( member_int @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % minus_set_def
% 5.46/5.78 thf(fact_8544_minus__set__def,axiom,
% 5.46/5.78 ( minus_minus_set_nat
% 5.46/5.78 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.46/5.78 ( collect_nat
% 5.46/5.78 @ ( minus_minus_nat_o
% 5.46/5.78 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.46/5.78 @ ^ [X: nat] : ( member_nat @ X @ B7 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % minus_set_def
% 5.46/5.78 thf(fact_8545_numeral__code_I2_J,axiom,
% 5.46/5.78 ! [N: num] :
% 5.46/5.78 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.46/5.78 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % numeral_code(2)
% 5.46/5.78 thf(fact_8546_numeral__code_I2_J,axiom,
% 5.46/5.78 ! [N: num] :
% 5.46/5.78 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.46/5.78 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % numeral_code(2)
% 5.46/5.78 thf(fact_8547_numeral__code_I2_J,axiom,
% 5.46/5.78 ! [N: num] :
% 5.46/5.78 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.46/5.78 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % numeral_code(2)
% 5.46/5.78 thf(fact_8548_numeral__code_I2_J,axiom,
% 5.46/5.78 ! [N: num] :
% 5.46/5.78 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.46/5.78 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % numeral_code(2)
% 5.46/5.78 thf(fact_8549_numeral__code_I2_J,axiom,
% 5.46/5.78 ! [N: num] :
% 5.46/5.78 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.46/5.78 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % numeral_code(2)
% 5.46/5.78 thf(fact_8550_lambda__zero,axiom,
% 5.46/5.78 ( ( ^ [H: real] : zero_zero_real )
% 5.46/5.78 = ( times_times_real @ zero_zero_real ) ) ).
% 5.46/5.78
% 5.46/5.78 % lambda_zero
% 5.46/5.78 thf(fact_8551_lambda__zero,axiom,
% 5.46/5.78 ( ( ^ [H: rat] : zero_zero_rat )
% 5.46/5.78 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.46/5.78
% 5.46/5.78 % lambda_zero
% 5.46/5.78 thf(fact_8552_lambda__zero,axiom,
% 5.46/5.78 ( ( ^ [H: nat] : zero_zero_nat )
% 5.46/5.78 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % lambda_zero
% 5.46/5.78 thf(fact_8553_lambda__zero,axiom,
% 5.46/5.78 ( ( ^ [H: int] : zero_zero_int )
% 5.46/5.78 = ( times_times_int @ zero_zero_int ) ) ).
% 5.46/5.78
% 5.46/5.78 % lambda_zero
% 5.46/5.78 thf(fact_8554_mult__commute__abs,axiom,
% 5.46/5.78 ! [C: real] :
% 5.46/5.78 ( ( ^ [X: real] : ( times_times_real @ X @ C ) )
% 5.46/5.78 = ( times_times_real @ C ) ) ).
% 5.46/5.78
% 5.46/5.78 % mult_commute_abs
% 5.46/5.78 thf(fact_8555_mult__commute__abs,axiom,
% 5.46/5.78 ! [C: rat] :
% 5.46/5.78 ( ( ^ [X: rat] : ( times_times_rat @ X @ C ) )
% 5.46/5.78 = ( times_times_rat @ C ) ) ).
% 5.46/5.78
% 5.46/5.78 % mult_commute_abs
% 5.46/5.78 thf(fact_8556_mult__commute__abs,axiom,
% 5.46/5.78 ! [C: nat] :
% 5.46/5.78 ( ( ^ [X: nat] : ( times_times_nat @ X @ C ) )
% 5.46/5.78 = ( times_times_nat @ C ) ) ).
% 5.46/5.78
% 5.46/5.78 % mult_commute_abs
% 5.46/5.78 thf(fact_8557_mult__commute__abs,axiom,
% 5.46/5.78 ! [C: int] :
% 5.46/5.78 ( ( ^ [X: int] : ( times_times_int @ X @ C ) )
% 5.46/5.78 = ( times_times_int @ C ) ) ).
% 5.46/5.78
% 5.46/5.78 % mult_commute_abs
% 5.46/5.78 thf(fact_8558_lambda__one,axiom,
% 5.46/5.78 ( ( ^ [X: complex] : X )
% 5.46/5.78 = ( times_times_complex @ one_one_complex ) ) ).
% 5.46/5.78
% 5.46/5.78 % lambda_one
% 5.46/5.78 thf(fact_8559_lambda__one,axiom,
% 5.46/5.78 ( ( ^ [X: real] : X )
% 5.46/5.78 = ( times_times_real @ one_one_real ) ) ).
% 5.46/5.78
% 5.46/5.78 % lambda_one
% 5.46/5.78 thf(fact_8560_lambda__one,axiom,
% 5.46/5.78 ( ( ^ [X: rat] : X )
% 5.46/5.78 = ( times_times_rat @ one_one_rat ) ) ).
% 5.46/5.78
% 5.46/5.78 % lambda_one
% 5.46/5.78 thf(fact_8561_lambda__one,axiom,
% 5.46/5.78 ( ( ^ [X: nat] : X )
% 5.46/5.78 = ( times_times_nat @ one_one_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % lambda_one
% 5.46/5.78 thf(fact_8562_lambda__one,axiom,
% 5.46/5.78 ( ( ^ [X: int] : X )
% 5.46/5.78 = ( times_times_int @ one_one_int ) ) ).
% 5.46/5.78
% 5.46/5.78 % lambda_one
% 5.46/5.78 thf(fact_8563_subset__divisors__dvd,axiom,
% 5.46/5.78 ! [A: complex,B2: complex] :
% 5.46/5.78 ( ( ord_le211207098394363844omplex
% 5.46/5.78 @ ( collect_complex
% 5.46/5.78 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 5.46/5.78 @ ( collect_complex
% 5.46/5.78 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B2 ) ) )
% 5.46/5.78 = ( dvd_dvd_complex @ A @ B2 ) ) ).
% 5.46/5.78
% 5.46/5.78 % subset_divisors_dvd
% 5.46/5.78 thf(fact_8564_subset__divisors__dvd,axiom,
% 5.46/5.78 ! [A: real,B2: real] :
% 5.46/5.78 ( ( ord_less_eq_set_real
% 5.46/5.78 @ ( collect_real
% 5.46/5.78 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 5.46/5.78 @ ( collect_real
% 5.46/5.78 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B2 ) ) )
% 5.46/5.78 = ( dvd_dvd_real @ A @ B2 ) ) ).
% 5.46/5.78
% 5.46/5.78 % subset_divisors_dvd
% 5.46/5.78 thf(fact_8565_subset__divisors__dvd,axiom,
% 5.46/5.78 ! [A: int,B2: int] :
% 5.46/5.78 ( ( ord_less_eq_set_int
% 5.46/5.78 @ ( collect_int
% 5.46/5.78 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 5.46/5.78 @ ( collect_int
% 5.46/5.78 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B2 ) ) )
% 5.46/5.78 = ( dvd_dvd_int @ A @ B2 ) ) ).
% 5.46/5.78
% 5.46/5.78 % subset_divisors_dvd
% 5.46/5.78 thf(fact_8566_subset__divisors__dvd,axiom,
% 5.46/5.78 ! [A: code_integer,B2: code_integer] :
% 5.46/5.78 ( ( ord_le7084787975880047091nteger
% 5.46/5.78 @ ( collect_Code_integer
% 5.46/5.78 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 5.46/5.78 @ ( collect_Code_integer
% 5.46/5.78 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B2 ) ) )
% 5.46/5.78 = ( dvd_dvd_Code_integer @ A @ B2 ) ) ).
% 5.46/5.78
% 5.46/5.78 % subset_divisors_dvd
% 5.46/5.78 thf(fact_8567_subset__divisors__dvd,axiom,
% 5.46/5.78 ! [A: nat,B2: nat] :
% 5.46/5.78 ( ( ord_less_eq_set_nat
% 5.46/5.78 @ ( collect_nat
% 5.46/5.78 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 5.46/5.78 @ ( collect_nat
% 5.46/5.78 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B2 ) ) )
% 5.46/5.78 = ( dvd_dvd_nat @ A @ B2 ) ) ).
% 5.46/5.78
% 5.46/5.78 % subset_divisors_dvd
% 5.46/5.78 thf(fact_8568_nat__leq__as__int,axiom,
% 5.46/5.78 ( ord_less_eq_nat
% 5.46/5.78 = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nat_leq_as_int
% 5.46/5.78 thf(fact_8569_power__numeral__even,axiom,
% 5.46/5.78 ! [Z: complex,W: num] :
% 5.46/5.78 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.46/5.78 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_numeral_even
% 5.46/5.78 thf(fact_8570_power__numeral__even,axiom,
% 5.46/5.78 ! [Z: real,W: num] :
% 5.46/5.78 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.46/5.78 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_numeral_even
% 5.46/5.78 thf(fact_8571_power__numeral__even,axiom,
% 5.46/5.78 ! [Z: rat,W: num] :
% 5.46/5.78 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.46/5.78 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_numeral_even
% 5.46/5.78 thf(fact_8572_power__numeral__even,axiom,
% 5.46/5.78 ! [Z: nat,W: num] :
% 5.46/5.78 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.46/5.78 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_numeral_even
% 5.46/5.78 thf(fact_8573_power__numeral__even,axiom,
% 5.46/5.78 ! [Z: int,W: num] :
% 5.46/5.78 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.46/5.78 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_numeral_even
% 5.46/5.78 thf(fact_8574_numeral__code_I3_J,axiom,
% 5.46/5.78 ! [N: num] :
% 5.46/5.78 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.46/5.78 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.46/5.78
% 5.46/5.78 % numeral_code(3)
% 5.46/5.78 thf(fact_8575_numeral__code_I3_J,axiom,
% 5.46/5.78 ! [N: num] :
% 5.46/5.78 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.46/5.78 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.46/5.78
% 5.46/5.78 % numeral_code(3)
% 5.46/5.78 thf(fact_8576_numeral__code_I3_J,axiom,
% 5.46/5.78 ! [N: num] :
% 5.46/5.78 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.46/5.78 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.46/5.78
% 5.46/5.78 % numeral_code(3)
% 5.46/5.78 thf(fact_8577_numeral__code_I3_J,axiom,
% 5.46/5.78 ! [N: num] :
% 5.46/5.78 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.46/5.78 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % numeral_code(3)
% 5.46/5.78 thf(fact_8578_numeral__code_I3_J,axiom,
% 5.46/5.78 ! [N: num] :
% 5.46/5.78 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.46/5.78 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.46/5.78
% 5.46/5.78 % numeral_code(3)
% 5.46/5.78 thf(fact_8579_power__numeral__odd,axiom,
% 5.46/5.78 ! [Z: complex,W: num] :
% 5.46/5.78 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.46/5.78 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_numeral_odd
% 5.46/5.78 thf(fact_8580_power__numeral__odd,axiom,
% 5.46/5.78 ! [Z: real,W: num] :
% 5.46/5.78 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.46/5.78 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_numeral_odd
% 5.46/5.78 thf(fact_8581_power__numeral__odd,axiom,
% 5.46/5.78 ! [Z: rat,W: num] :
% 5.46/5.78 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.46/5.78 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_numeral_odd
% 5.46/5.78 thf(fact_8582_power__numeral__odd,axiom,
% 5.46/5.78 ! [Z: nat,W: num] :
% 5.46/5.78 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.46/5.78 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_numeral_odd
% 5.46/5.78 thf(fact_8583_power__numeral__odd,axiom,
% 5.46/5.78 ! [Z: int,W: num] :
% 5.46/5.78 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.46/5.78 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % power_numeral_odd
% 5.46/5.78 thf(fact_8584_nat__plus__as__int,axiom,
% 5.46/5.78 ( plus_plus_nat
% 5.46/5.78 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nat_plus_as_int
% 5.46/5.78 thf(fact_8585_nat__times__as__int,axiom,
% 5.46/5.78 ( times_times_nat
% 5.46/5.78 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nat_times_as_int
% 5.46/5.78 thf(fact_8586_nat__minus__as__int,axiom,
% 5.46/5.78 ( minus_minus_nat
% 5.46/5.78 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nat_minus_as_int
% 5.46/5.78 thf(fact_8587_nat__div__as__int,axiom,
% 5.46/5.78 ( divide_divide_nat
% 5.46/5.78 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nat_div_as_int
% 5.46/5.78 thf(fact_8588_nat__mod__as__int,axiom,
% 5.46/5.78 ( modulo_modulo_nat
% 5.46/5.78 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % nat_mod_as_int
% 5.46/5.78 thf(fact_8589_set__conv__nth,axiom,
% 5.46/5.78 ( set_complex2
% 5.46/5.78 = ( ^ [Xs: list_complex] :
% 5.46/5.78 ( collect_complex
% 5.46/5.78 @ ^ [Uu: complex] :
% 5.46/5.78 ? [I2: nat] :
% 5.46/5.78 ( ( Uu
% 5.46/5.78 = ( nth_complex @ Xs @ I2 ) )
% 5.46/5.78 & ( ord_less_nat @ I2 @ ( size_s3451745648224563538omplex @ Xs ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_conv_nth
% 5.46/5.78 thf(fact_8590_set__conv__nth,axiom,
% 5.46/5.78 ( set_real2
% 5.46/5.78 = ( ^ [Xs: list_real] :
% 5.46/5.78 ( collect_real
% 5.46/5.78 @ ^ [Uu: real] :
% 5.46/5.78 ? [I2: nat] :
% 5.46/5.78 ( ( Uu
% 5.46/5.78 = ( nth_real @ Xs @ I2 ) )
% 5.46/5.78 & ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_conv_nth
% 5.46/5.78 thf(fact_8591_set__conv__nth,axiom,
% 5.46/5.78 ( set_list_nat2
% 5.46/5.78 = ( ^ [Xs: list_list_nat] :
% 5.46/5.78 ( collect_list_nat
% 5.46/5.78 @ ^ [Uu: list_nat] :
% 5.46/5.78 ? [I2: nat] :
% 5.46/5.78 ( ( Uu
% 5.46/5.78 = ( nth_list_nat @ Xs @ I2 ) )
% 5.46/5.78 & ( ord_less_nat @ I2 @ ( size_s3023201423986296836st_nat @ Xs ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_conv_nth
% 5.46/5.78 thf(fact_8592_set__conv__nth,axiom,
% 5.46/5.78 ( set_VEBT_VEBT2
% 5.46/5.78 = ( ^ [Xs: list_VEBT_VEBT] :
% 5.46/5.78 ( collect_VEBT_VEBT
% 5.46/5.78 @ ^ [Uu: vEBT_VEBT] :
% 5.46/5.78 ? [I2: nat] :
% 5.46/5.78 ( ( Uu
% 5.46/5.78 = ( nth_VEBT_VEBT @ Xs @ I2 ) )
% 5.46/5.78 & ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_conv_nth
% 5.46/5.78 thf(fact_8593_set__conv__nth,axiom,
% 5.46/5.78 ( set_o2
% 5.46/5.78 = ( ^ [Xs: list_o] :
% 5.46/5.78 ( collect_o
% 5.46/5.78 @ ^ [Uu: $o] :
% 5.46/5.78 ? [I2: nat] :
% 5.46/5.78 ( ( Uu
% 5.46/5.78 = ( nth_o @ Xs @ I2 ) )
% 5.46/5.78 & ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_conv_nth
% 5.46/5.78 thf(fact_8594_set__conv__nth,axiom,
% 5.46/5.78 ( set_nat2
% 5.46/5.78 = ( ^ [Xs: list_nat] :
% 5.46/5.78 ( collect_nat
% 5.46/5.78 @ ^ [Uu: nat] :
% 5.46/5.78 ? [I2: nat] :
% 5.46/5.78 ( ( Uu
% 5.46/5.78 = ( nth_nat @ Xs @ I2 ) )
% 5.46/5.78 & ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_conv_nth
% 5.46/5.78 thf(fact_8595_set__conv__nth,axiom,
% 5.46/5.78 ( set_int2
% 5.46/5.78 = ( ^ [Xs: list_int] :
% 5.46/5.78 ( collect_int
% 5.46/5.78 @ ^ [Uu: int] :
% 5.46/5.78 ? [I2: nat] :
% 5.46/5.78 ( ( Uu
% 5.46/5.78 = ( nth_int @ Xs @ I2 ) )
% 5.46/5.78 & ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_conv_nth
% 5.46/5.78 thf(fact_8596_diff__nat__eq__if,axiom,
% 5.46/5.78 ! [Z6: int,Z: int] :
% 5.46/5.78 ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 5.46/5.78 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 5.46/5.78 = ( nat2 @ Z ) ) )
% 5.46/5.78 & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 5.46/5.78 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 5.46/5.78 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z6 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % diff_nat_eq_if
% 5.46/5.78 thf(fact_8597_set__decode__def,axiom,
% 5.46/5.78 ( nat_set_decode
% 5.46/5.78 = ( ^ [X: nat] :
% 5.46/5.78 ( collect_nat
% 5.46/5.78 @ ^ [N2: nat] :
% 5.46/5.78 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % set_decode_def
% 5.46/5.78 thf(fact_8598_signed__take__bit__code,axiom,
% 5.46/5.78 ( bit_ri6519982836138164636nteger
% 5.46/5.78 = ( ^ [N2: nat,A4: code_integer] : ( if_Code_integer @ ( bit_se9216721137139052372nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A4 ) @ N2 ) @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A4 ) @ ( bit_se7788150548672797655nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) @ ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % signed_take_bit_code
% 5.46/5.78 thf(fact_8599_signed__take__bit__code,axiom,
% 5.46/5.78 ( bit_ri631733984087533419it_int
% 5.46/5.78 = ( ^ [N2: nat,A4: int] : ( if_int @ ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A4 ) @ N2 ) @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A4 ) @ ( bit_se545348938243370406it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ one_one_int ) ) ) @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % signed_take_bit_code
% 5.46/5.78 thf(fact_8600_pochhammer__code,axiom,
% 5.46/5.78 ( comm_s2602460028002588243omplex
% 5.46/5.78 = ( ^ [A4: complex,N2: nat] :
% 5.46/5.78 ( if_complex @ ( N2 = zero_zero_nat ) @ one_one_complex
% 5.46/5.78 @ ( set_fo1517530859248394432omplex
% 5.46/5.78 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.46/5.78 @ zero_zero_nat
% 5.46/5.78 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.46/5.78 @ one_one_complex ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_code
% 5.46/5.78 thf(fact_8601_pochhammer__code,axiom,
% 5.46/5.78 ( comm_s7457072308508201937r_real
% 5.46/5.78 = ( ^ [A4: real,N2: nat] :
% 5.46/5.78 ( if_real @ ( N2 = zero_zero_nat ) @ one_one_real
% 5.46/5.78 @ ( set_fo3111899725591712190t_real
% 5.46/5.78 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.46/5.78 @ zero_zero_nat
% 5.46/5.78 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.46/5.78 @ one_one_real ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_code
% 5.46/5.78 thf(fact_8602_pochhammer__code,axiom,
% 5.46/5.78 ( comm_s4028243227959126397er_rat
% 5.46/5.78 = ( ^ [A4: rat,N2: nat] :
% 5.46/5.78 ( if_rat @ ( N2 = zero_zero_nat ) @ one_one_rat
% 5.46/5.78 @ ( set_fo1949268297981939178at_rat
% 5.46/5.78 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.46/5.78 @ zero_zero_nat
% 5.46/5.78 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.46/5.78 @ one_one_rat ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_code
% 5.46/5.78 thf(fact_8603_pochhammer__code,axiom,
% 5.46/5.78 ( comm_s4660882817536571857er_int
% 5.46/5.78 = ( ^ [A4: int,N2: nat] :
% 5.46/5.78 ( if_int @ ( N2 = zero_zero_nat ) @ one_one_int
% 5.46/5.78 @ ( set_fo2581907887559384638at_int
% 5.46/5.78 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.46/5.78 @ zero_zero_nat
% 5.46/5.78 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.46/5.78 @ one_one_int ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_code
% 5.46/5.78 thf(fact_8604_pochhammer__code,axiom,
% 5.46/5.78 ( comm_s4663373288045622133er_nat
% 5.46/5.78 = ( ^ [A4: nat,N2: nat] :
% 5.46/5.78 ( if_nat @ ( N2 = zero_zero_nat ) @ one_one_nat
% 5.46/5.78 @ ( set_fo2584398358068434914at_nat
% 5.46/5.78 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.46/5.78 @ zero_zero_nat
% 5.46/5.78 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.46/5.78 @ one_one_nat ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_code
% 5.46/5.78 thf(fact_8605_gbinomial__code,axiom,
% 5.46/5.78 ( gbinomial_complex
% 5.46/5.78 = ( ^ [A4: complex,K3: nat] :
% 5.46/5.78 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 5.46/5.78 @ ( divide1717551699836669952omplex
% 5.46/5.78 @ ( set_fo1517530859248394432omplex
% 5.46/5.78 @ ^ [L: nat] : ( times_times_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ L ) ) )
% 5.46/5.78 @ zero_zero_nat
% 5.46/5.78 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.46/5.78 @ one_one_complex )
% 5.46/5.78 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % gbinomial_code
% 5.46/5.78 thf(fact_8606_gbinomial__code,axiom,
% 5.46/5.78 ( gbinomial_rat
% 5.46/5.78 = ( ^ [A4: rat,K3: nat] :
% 5.46/5.78 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 5.46/5.78 @ ( divide_divide_rat
% 5.46/5.78 @ ( set_fo1949268297981939178at_rat
% 5.46/5.78 @ ^ [L: nat] : ( times_times_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ L ) ) )
% 5.46/5.78 @ zero_zero_nat
% 5.46/5.78 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.46/5.78 @ one_one_rat )
% 5.46/5.78 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % gbinomial_code
% 5.46/5.78 thf(fact_8607_gbinomial__code,axiom,
% 5.46/5.78 ( gbinomial_real
% 5.46/5.78 = ( ^ [A4: real,K3: nat] :
% 5.46/5.78 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 5.46/5.78 @ ( divide_divide_real
% 5.46/5.78 @ ( set_fo3111899725591712190t_real
% 5.46/5.78 @ ^ [L: nat] : ( times_times_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ L ) ) )
% 5.46/5.78 @ zero_zero_nat
% 5.46/5.78 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.46/5.78 @ one_one_real )
% 5.46/5.78 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % gbinomial_code
% 5.46/5.78 thf(fact_8608_vebt__member_Osimps_I5_J,axiom,
% 5.46/5.78 ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X4: nat] :
% 5.46/5.78 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 = ( ( X4 != Mi )
% 5.46/5.78 => ( ( X4 != Ma )
% 5.46/5.78 => ( ~ ( ord_less_nat @ X4 @ Mi )
% 5.46/5.78 & ( ~ ( ord_less_nat @ X4 @ Mi )
% 5.46/5.78 => ( ~ ( ord_less_nat @ Ma @ X4 )
% 5.46/5.78 & ( ~ ( ord_less_nat @ Ma @ X4 )
% 5.46/5.78 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.78 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_member.simps(5)
% 5.46/5.78 thf(fact_8609_vebt__succ_Osimps_I6_J,axiom,
% 5.46/5.78 ! [X4: nat,Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.46/5.78 ( ( ( ord_less_nat @ X4 @ Mi )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 = ( some_nat @ Mi ) ) )
% 5.46/5.78 & ( ~ ( ord_less_nat @ X4 @ Mi )
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.78 @ ( if_option_nat
% 5.46/5.78 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 != none_nat )
% 5.46/5.78 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.46/5.78 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 @ ( if_option_nat
% 5.46/5.78 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 = none_nat )
% 5.46/5.78 @ none_nat
% 5.46/5.78 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.78 @ none_nat ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_succ.simps(6)
% 5.46/5.78 thf(fact_8610_of__int__code__if,axiom,
% 5.46/5.78 ( ring_1_of_int_real
% 5.46/5.78 = ( ^ [K3: int] :
% 5.46/5.78 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 5.46/5.78 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 5.46/5.78 @ ( if_real
% 5.46/5.78 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.78 = zero_zero_int )
% 5.46/5.78 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 @ ( 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 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % of_int_code_if
% 5.46/5.78 thf(fact_8611_of__int__code__if,axiom,
% 5.46/5.78 ( ring_1_of_int_int
% 5.46/5.78 = ( ^ [K3: int] :
% 5.46/5.78 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 5.46/5.78 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.46/5.78 @ ( if_int
% 5.46/5.78 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.78 = zero_zero_int )
% 5.46/5.78 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 @ ( 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 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % of_int_code_if
% 5.46/5.78 thf(fact_8612_of__int__code__if,axiom,
% 5.46/5.78 ( ring_17405671764205052669omplex
% 5.46/5.78 = ( ^ [K3: int] :
% 5.46/5.78 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 5.46/5.78 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 5.46/5.78 @ ( if_complex
% 5.46/5.78 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.78 = zero_zero_int )
% 5.46/5.78 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % of_int_code_if
% 5.46/5.78 thf(fact_8613_of__int__code__if,axiom,
% 5.46/5.78 ( ring_18347121197199848620nteger
% 5.46/5.78 = ( ^ [K3: int] :
% 5.46/5.78 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.46/5.78 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 5.46/5.78 @ ( if_Code_integer
% 5.46/5.78 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.78 = zero_zero_int )
% 5.46/5.78 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % of_int_code_if
% 5.46/5.78 thf(fact_8614_of__int__code__if,axiom,
% 5.46/5.78 ( ring_1_of_int_rat
% 5.46/5.78 = ( ^ [K3: int] :
% 5.46/5.78 ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 5.46/5.78 @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 5.46/5.78 @ ( if_rat
% 5.46/5.78 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.78 = zero_zero_int )
% 5.46/5.78 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.78 @ ( 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 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % of_int_code_if
% 5.46/5.78 thf(fact_8615_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.46/5.78 ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X4: nat] :
% 5.46/5.78 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X4 )
% 5.46/5.78 = ( ( X4 = Mi )
% 5.46/5.78 | ( X4 = Ma )
% 5.46/5.78 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.78 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % VEBT_internal.membermima.simps(4)
% 5.46/5.78 thf(fact_8616_monoseq__arctan__series,axiom,
% 5.46/5.78 ! [X4: real] :
% 5.46/5.78 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.78 => ( topolo6980174941875973593q_real
% 5.46/5.78 @ ^ [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 @ X4 @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % monoseq_arctan_series
% 5.46/5.78 thf(fact_8617_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.46/5.78 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X4: nat] :
% 5.46/5.78 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X4 )
% 5.46/5.78 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.78 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % VEBT_internal.naive_member.simps(3)
% 5.46/5.78 thf(fact_8618_buildup__nothing__in__min__max,axiom,
% 5.46/5.78 ! [N: nat,X4: nat] :
% 5.46/5.78 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X4 ) ).
% 5.46/5.78
% 5.46/5.78 % buildup_nothing_in_min_max
% 5.46/5.78 thf(fact_8619_buildup__nothing__in__leaf,axiom,
% 5.46/5.78 ! [N: nat,X4: nat] :
% 5.46/5.78 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X4 ) ).
% 5.46/5.78
% 5.46/5.78 % buildup_nothing_in_leaf
% 5.46/5.78 thf(fact_8620_both__member__options__def,axiom,
% 5.46/5.78 ( vEBT_V8194947554948674370ptions
% 5.46/5.78 = ( ^ [T3: vEBT_VEBT,X: nat] :
% 5.46/5.78 ( ( vEBT_V5719532721284313246member @ T3 @ X )
% 5.46/5.78 | ( vEBT_VEBT_membermima @ T3 @ X ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % both_member_options_def
% 5.46/5.78 thf(fact_8621_member__valid__both__member__options,axiom,
% 5.46/5.78 ! [Tree: vEBT_VEBT,N: nat,X4: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.46/5.78 => ( ( vEBT_vebt_member @ Tree @ X4 )
% 5.46/5.78 => ( ( vEBT_V5719532721284313246member @ Tree @ X4 )
% 5.46/5.78 | ( vEBT_VEBT_membermima @ Tree @ X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % member_valid_both_member_options
% 5.46/5.78 thf(fact_8622_monoseq__realpow,axiom,
% 5.46/5.78 ! [X4: real] :
% 5.46/5.78 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.78 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.78 => ( topolo6980174941875973593q_real @ ( power_power_real @ X4 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % monoseq_realpow
% 5.46/5.78 thf(fact_8623_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.46/5.78 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.78 ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.46/5.78 => ( ! [Mi2: nat,Ma2: nat] :
% 5.46/5.78 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.46/5.78 => ~ ( ( Xa = Mi2 )
% 5.46/5.78 | ( Xa = Ma2 ) ) )
% 5.46/5.78 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.78 ( ? [Vc2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 5.46/5.78 => ~ ( ( Xa = Mi2 )
% 5.46/5.78 | ( Xa = Ma2 )
% 5.46/5.78 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.78 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.46/5.78 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.78 ( ? [Vd2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 5.46/5.78 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.78 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % VEBT_internal.membermima.elims(2)
% 5.46/5.78 thf(fact_8624_vebt__member_Oelims_I2_J,axiom,
% 5.46/5.78 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.78 ( ( vEBT_vebt_member @ X4 @ Xa )
% 5.46/5.78 => ( ! [A5: $o,B5: $o] :
% 5.46/5.78 ( ( X4
% 5.46/5.78 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.78 => ~ ( ( ( Xa = zero_zero_nat )
% 5.46/5.78 => A5 )
% 5.46/5.78 & ( ( Xa != zero_zero_nat )
% 5.46/5.78 => ( ( ( Xa = one_one_nat )
% 5.46/5.78 => B5 )
% 5.46/5.78 & ( Xa = one_one_nat ) ) ) ) )
% 5.46/5.78 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.78 ( ? [Summary2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.78 => ~ ( ( Xa != Mi2 )
% 5.46/5.78 => ( ( Xa != Ma2 )
% 5.46/5.78 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.78 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.78 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.78 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.78 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.78 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_member.elims(2)
% 5.46/5.78 thf(fact_8625_vebt__insert_Osimps_I3_J,axiom,
% 5.46/5.78 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X4: nat] :
% 5.46/5.78 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X4 )
% 5.46/5.78 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_insert.simps(3)
% 5.46/5.78 thf(fact_8626_pochhammer__times__pochhammer__half,axiom,
% 5.46/5.78 ! [Z: complex,N: nat] :
% 5.46/5.78 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.46/5.78 = ( groups6464643781859351333omplex
% 5.46/5.78 @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_times_pochhammer_half
% 5.46/5.78 thf(fact_8627_pochhammer__times__pochhammer__half,axiom,
% 5.46/5.78 ! [Z: real,N: nat] :
% 5.46/5.78 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.46/5.78 = ( groups129246275422532515t_real
% 5.46/5.78 @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_times_pochhammer_half
% 5.46/5.78 thf(fact_8628_pochhammer__times__pochhammer__half,axiom,
% 5.46/5.78 ! [Z: rat,N: nat] :
% 5.46/5.78 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.46/5.78 = ( groups73079841787564623at_rat
% 5.46/5.78 @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_times_pochhammer_half
% 5.46/5.78 thf(fact_8629_Leaf__0__not,axiom,
% 5.46/5.78 ! [A: $o,B2: $o] :
% 5.46/5.78 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B2 ) @ zero_zero_nat ) ).
% 5.46/5.78
% 5.46/5.78 % Leaf_0_not
% 5.46/5.78 thf(fact_8630_deg__1__Leafy,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT,N: nat] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.78 => ( ( N = one_one_nat )
% 5.46/5.78 => ? [A5: $o,B5: $o] :
% 5.46/5.78 ( T
% 5.46/5.78 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % deg_1_Leafy
% 5.46/5.78 thf(fact_8631_deg__1__Leaf,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.46/5.78 => ? [A5: $o,B5: $o] :
% 5.46/5.78 ( T
% 5.46/5.78 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % deg_1_Leaf
% 5.46/5.78 thf(fact_8632_deg1Leaf,axiom,
% 5.46/5.78 ! [T: vEBT_VEBT] :
% 5.46/5.78 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.46/5.78 = ( ? [A4: $o,B3: $o] :
% 5.46/5.78 ( T
% 5.46/5.78 = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % deg1Leaf
% 5.46/5.78 thf(fact_8633_prod_Ocl__ivl__Suc,axiom,
% 5.46/5.78 ! [N: nat,M: nat,G: nat > complex] :
% 5.46/5.78 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.78 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = one_one_complex ) )
% 5.46/5.78 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.78 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.cl_ivl_Suc
% 5.46/5.78 thf(fact_8634_prod_Ocl__ivl__Suc,axiom,
% 5.46/5.78 ! [N: nat,M: nat,G: nat > real] :
% 5.46/5.78 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.78 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = one_one_real ) )
% 5.46/5.78 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.78 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.cl_ivl_Suc
% 5.46/5.78 thf(fact_8635_prod_Ocl__ivl__Suc,axiom,
% 5.46/5.78 ! [N: nat,M: nat,G: nat > rat] :
% 5.46/5.78 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.78 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = one_one_rat ) )
% 5.46/5.78 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.78 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.cl_ivl_Suc
% 5.46/5.78 thf(fact_8636_prod_Ocl__ivl__Suc,axiom,
% 5.46/5.78 ! [N: nat,M: nat,G: nat > nat] :
% 5.46/5.78 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.78 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = one_one_nat ) )
% 5.46/5.78 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.78 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.cl_ivl_Suc
% 5.46/5.78 thf(fact_8637_prod_Ocl__ivl__Suc,axiom,
% 5.46/5.78 ! [N: nat,M: nat,G: nat > int] :
% 5.46/5.78 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.78 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = one_one_int ) )
% 5.46/5.78 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.46/5.78 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.cl_ivl_Suc
% 5.46/5.78 thf(fact_8638_mod__prod__eq,axiom,
% 5.46/5.78 ! [F: nat > nat,A: nat,A3: set_nat] :
% 5.46/5.78 ( ( modulo_modulo_nat
% 5.46/5.78 @ ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [I2: nat] : ( modulo_modulo_nat @ ( F @ I2 ) @ A )
% 5.46/5.78 @ A3 )
% 5.46/5.78 @ A )
% 5.46/5.78 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ A ) ) ).
% 5.46/5.78
% 5.46/5.78 % mod_prod_eq
% 5.46/5.78 thf(fact_8639_mod__prod__eq,axiom,
% 5.46/5.78 ! [F: nat > int,A: int,A3: set_nat] :
% 5.46/5.78 ( ( modulo_modulo_int
% 5.46/5.78 @ ( groups705719431365010083at_int
% 5.46/5.78 @ ^ [I2: nat] : ( modulo_modulo_int @ ( F @ I2 ) @ A )
% 5.46/5.78 @ A3 )
% 5.46/5.78 @ A )
% 5.46/5.78 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A3 ) @ A ) ) ).
% 5.46/5.78
% 5.46/5.78 % mod_prod_eq
% 5.46/5.78 thf(fact_8640_mod__prod__eq,axiom,
% 5.46/5.78 ! [F: int > int,A: int,A3: set_int] :
% 5.46/5.78 ( ( modulo_modulo_int
% 5.46/5.78 @ ( groups1705073143266064639nt_int
% 5.46/5.78 @ ^ [I2: int] : ( modulo_modulo_int @ ( F @ I2 ) @ A )
% 5.46/5.78 @ A3 )
% 5.46/5.78 @ A )
% 5.46/5.78 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A3 ) @ A ) ) ).
% 5.46/5.78
% 5.46/5.78 % mod_prod_eq
% 5.46/5.78 thf(fact_8641_vebt__insert_Ocases,axiom,
% 5.46/5.78 ! [X4: produc9072475918466114483BT_nat] :
% 5.46/5.78 ( ! [A5: $o,B5: $o,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X3 ) )
% 5.46/5.78 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ X3 ) )
% 5.46/5.78 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ X3 ) )
% 5.46/5.78 => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) @ X3 ) )
% 5.46/5.78 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_insert.cases
% 5.46/5.78 thf(fact_8642_vebt__insert_Osimps_I1_J,axiom,
% 5.46/5.78 ! [X4: nat,A: $o,B2: $o] :
% 5.46/5.78 ( ( ( X4 = zero_zero_nat )
% 5.46/5.78 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B2 ) @ X4 )
% 5.46/5.78 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 5.46/5.78 & ( ( X4 != zero_zero_nat )
% 5.46/5.78 => ( ( ( X4 = one_one_nat )
% 5.46/5.78 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B2 ) @ X4 )
% 5.46/5.78 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.46/5.78 & ( ( X4 != one_one_nat )
% 5.46/5.78 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B2 ) @ X4 )
% 5.46/5.78 = ( vEBT_Leaf @ A @ B2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_insert.simps(1)
% 5.46/5.78 thf(fact_8643_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.46/5.78 ! [G: nat > nat,M: nat,N: nat] :
% 5.46/5.78 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.46/5.78 = ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.shift_bounds_cl_Suc_ivl
% 5.46/5.78 thf(fact_8644_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.46/5.78 ! [G: nat > int,M: nat,N: nat] :
% 5.46/5.78 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.46/5.78 = ( groups705719431365010083at_int
% 5.46/5.78 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.shift_bounds_cl_Suc_ivl
% 5.46/5.78 thf(fact_8645_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.46/5.78 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.46/5.78 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.46/5.78 = ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [I2: nat] : ( G @ ( plus_plus_nat @ I2 @ K ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.shift_bounds_cl_nat_ivl
% 5.46/5.78 thf(fact_8646_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.46/5.78 ! [G: nat > int,M: nat,K: nat,N: nat] :
% 5.46/5.78 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.46/5.78 = ( groups705719431365010083at_int
% 5.46/5.78 @ ^ [I2: nat] : ( G @ ( plus_plus_nat @ I2 @ K ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.shift_bounds_cl_nat_ivl
% 5.46/5.78 thf(fact_8647_vebt__member_Ocases,axiom,
% 5.46/5.78 ! [X4: produc9072475918466114483BT_nat] :
% 5.46/5.78 ( ! [A5: $o,B5: $o,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X3 ) )
% 5.46/5.78 => ( ! [Uu2: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) @ X3 ) )
% 5.46/5.78 => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz ) @ X3 ) )
% 5.46/5.78 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 5.46/5.78 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_member.cases
% 5.46/5.78 thf(fact_8648_vebt__succ_Ocases,axiom,
% 5.46/5.78 ! [X4: produc9072475918466114483BT_nat] :
% 5.46/5.78 ( ! [Uu2: $o,B5: $o] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) )
% 5.46/5.78 => ( ! [Uv: $o,Uw: $o,N4: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N4 ) ) )
% 5.46/5.78 => ( ! [Ux: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,Va3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy2 @ Uz ) @ Va3 ) )
% 5.46/5.78 => ( ! [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 5.46/5.78 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 ) )
% 5.46/5.78 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_succ.cases
% 5.46/5.78 thf(fact_8649_VEBT__internal_Omembermima_Ocases,axiom,
% 5.46/5.78 ! [X4: produc9072475918466114483BT_nat] :
% 5.46/5.78 ( ! [Uu2: $o,Uv: $o,Uw: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv ) @ Uw ) )
% 5.46/5.78 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) @ Uz ) )
% 5.46/5.78 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X3 ) )
% 5.46/5.78 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ X3 ) )
% 5.46/5.78 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ X3 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % VEBT_internal.membermima.cases
% 5.46/5.78 thf(fact_8650_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.46/5.78 ! [X4: produc9072475918466114483BT_nat] :
% 5.46/5.78 ( ! [A5: $o,B5: $o,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X3 ) )
% 5.46/5.78 => ( ! [Uu2: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv @ Uw ) @ Ux ) )
% 5.46/5.78 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X3: nat] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ X3 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % VEBT_internal.naive_member.cases
% 5.46/5.78 thf(fact_8651_invar__vebt_Ointros_I1_J,axiom,
% 5.46/5.78 ! [A: $o,B2: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B2 ) @ ( suc @ zero_zero_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % invar_vebt.intros(1)
% 5.46/5.78 thf(fact_8652_vebt__member_Osimps_I1_J,axiom,
% 5.46/5.78 ! [A: $o,B2: $o,X4: nat] :
% 5.46/5.78 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B2 ) @ X4 )
% 5.46/5.78 = ( ( ( X4 = zero_zero_nat )
% 5.46/5.78 => A )
% 5.46/5.78 & ( ( X4 != zero_zero_nat )
% 5.46/5.78 => ( ( ( X4 = one_one_nat )
% 5.46/5.78 => B2 )
% 5.46/5.78 & ( X4 = one_one_nat ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_member.simps(1)
% 5.46/5.78 thf(fact_8653_vebt__buildup_Osimps_I2_J,axiom,
% 5.46/5.78 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.46/5.78 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_buildup.simps(2)
% 5.46/5.78 thf(fact_8654_vebt__succ_Osimps_I2_J,axiom,
% 5.46/5.78 ! [Uv2: $o,Uw2: $o,N: nat] :
% 5.46/5.78 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N ) )
% 5.46/5.78 = none_nat ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_succ.simps(2)
% 5.46/5.78 thf(fact_8655_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.46/5.78 ! [A: $o,B2: $o,X4: nat] :
% 5.46/5.78 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B2 ) @ X4 )
% 5.46/5.78 = ( ( ( X4 = zero_zero_nat )
% 5.46/5.78 => A )
% 5.46/5.78 & ( ( X4 != zero_zero_nat )
% 5.46/5.78 => ( ( ( X4 = one_one_nat )
% 5.46/5.78 => B2 )
% 5.46/5.78 & ( X4 = one_one_nat ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % VEBT_internal.naive_member.simps(1)
% 5.46/5.78 thf(fact_8656_prod_OatLeastAtMost__rev,axiom,
% 5.46/5.78 ! [G: nat > nat,N: nat,M: nat] :
% 5.46/5.78 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.46/5.78 = ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [I2: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.atLeastAtMost_rev
% 5.46/5.78 thf(fact_8657_prod_OatLeastAtMost__rev,axiom,
% 5.46/5.78 ! [G: nat > int,N: nat,M: nat] :
% 5.46/5.78 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.46/5.78 = ( groups705719431365010083at_int
% 5.46/5.78 @ ^ [I2: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.atLeastAtMost_rev
% 5.46/5.78 thf(fact_8658_vebt__succ_Osimps_I3_J,axiom,
% 5.46/5.78 ! [Ux2: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va2: nat] :
% 5.46/5.78 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy @ Uz2 ) @ Va2 )
% 5.46/5.78 = none_nat ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_succ.simps(3)
% 5.46/5.78 thf(fact_8659_prod_OatLeast0__atMost__Suc,axiom,
% 5.46/5.78 ! [G: nat > real,N: nat] :
% 5.46/5.78 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.atLeast0_atMost_Suc
% 5.46/5.78 thf(fact_8660_prod_OatLeast0__atMost__Suc,axiom,
% 5.46/5.78 ! [G: nat > rat,N: nat] :
% 5.46/5.78 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.atLeast0_atMost_Suc
% 5.46/5.78 thf(fact_8661_prod_OatLeast0__atMost__Suc,axiom,
% 5.46/5.78 ! [G: nat > nat,N: nat] :
% 5.46/5.78 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.atLeast0_atMost_Suc
% 5.46/5.78 thf(fact_8662_prod_OatLeast0__atMost__Suc,axiom,
% 5.46/5.78 ! [G: nat > int,N: nat] :
% 5.46/5.78 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.atLeast0_atMost_Suc
% 5.46/5.78 thf(fact_8663_prod_OatLeast__Suc__atMost,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > real] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.78 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.78 = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.atLeast_Suc_atMost
% 5.46/5.78 thf(fact_8664_prod_OatLeast__Suc__atMost,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > rat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.78 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.78 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.atLeast_Suc_atMost
% 5.46/5.78 thf(fact_8665_prod_OatLeast__Suc__atMost,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.78 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.78 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.atLeast_Suc_atMost
% 5.46/5.78 thf(fact_8666_prod_OatLeast__Suc__atMost,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > int] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.78 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.78 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.atLeast_Suc_atMost
% 5.46/5.78 thf(fact_8667_prod_Onat__ivl__Suc_H,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > real] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.78 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.nat_ivl_Suc'
% 5.46/5.78 thf(fact_8668_prod_Onat__ivl__Suc_H,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > rat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.78 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_rat @ ( G @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.nat_ivl_Suc'
% 5.46/5.78 thf(fact_8669_prod_Onat__ivl__Suc_H,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.78 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.nat_ivl_Suc'
% 5.46/5.78 thf(fact_8670_prod_Onat__ivl__Suc_H,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > int] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.78 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.nat_ivl_Suc'
% 5.46/5.78 thf(fact_8671_vebt__insert_Osimps_I4_J,axiom,
% 5.46/5.78 ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X4: nat] :
% 5.46/5.78 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X4 @ X4 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_insert.simps(4)
% 5.46/5.78 thf(fact_8672_prod_OSuc__reindex__ivl,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > real] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.78 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_real @ ( G @ M )
% 5.46/5.78 @ ( groups129246275422532515t_real
% 5.46/5.78 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.Suc_reindex_ivl
% 5.46/5.78 thf(fact_8673_prod_OSuc__reindex__ivl,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > rat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.78 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_rat @ ( G @ M )
% 5.46/5.78 @ ( groups73079841787564623at_rat
% 5.46/5.78 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.Suc_reindex_ivl
% 5.46/5.78 thf(fact_8674_prod_OSuc__reindex__ivl,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.78 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_nat @ ( G @ M )
% 5.46/5.78 @ ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.Suc_reindex_ivl
% 5.46/5.78 thf(fact_8675_prod_OSuc__reindex__ivl,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > int] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.78 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.46/5.78 = ( times_times_int @ ( G @ M )
% 5.46/5.78 @ ( groups705719431365010083at_int
% 5.46/5.78 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.Suc_reindex_ivl
% 5.46/5.78 thf(fact_8676_fact__prod,axiom,
% 5.46/5.78 ( semiri5044797733671781792omplex
% 5.46/5.78 = ( ^ [N2: nat] :
% 5.46/5.78 ( semiri8010041392384452111omplex
% 5.46/5.78 @ ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [X: nat] : X
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % fact_prod
% 5.46/5.78 thf(fact_8677_fact__prod,axiom,
% 5.46/5.78 ( semiri773545260158071498ct_rat
% 5.46/5.78 = ( ^ [N2: nat] :
% 5.46/5.78 ( semiri681578069525770553at_rat
% 5.46/5.78 @ ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [X: nat] : X
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % fact_prod
% 5.46/5.78 thf(fact_8678_fact__prod,axiom,
% 5.46/5.78 ( semiri1406184849735516958ct_int
% 5.46/5.78 = ( ^ [N2: nat] :
% 5.46/5.78 ( semiri1314217659103216013at_int
% 5.46/5.78 @ ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [X: nat] : X
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % fact_prod
% 5.46/5.78 thf(fact_8679_fact__prod,axiom,
% 5.46/5.78 ( semiri1408675320244567234ct_nat
% 5.46/5.78 = ( ^ [N2: nat] :
% 5.46/5.78 ( semiri1316708129612266289at_nat
% 5.46/5.78 @ ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [X: nat] : X
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % fact_prod
% 5.46/5.78 thf(fact_8680_fact__prod,axiom,
% 5.46/5.78 ( semiri2265585572941072030t_real
% 5.46/5.78 = ( ^ [N2: nat] :
% 5.46/5.78 ( semiri5074537144036343181t_real
% 5.46/5.78 @ ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [X: nat] : X
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % fact_prod
% 5.46/5.78 thf(fact_8681_prod__atLeastAtMost__code,axiom,
% 5.46/5.78 ! [F: nat > complex,A: nat,B2: nat] :
% 5.46/5.78 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 5.46/5.78 = ( set_fo1517530859248394432omplex
% 5.46/5.78 @ ^ [A4: nat] : ( times_times_complex @ ( F @ A4 ) )
% 5.46/5.78 @ A
% 5.46/5.78 @ B2
% 5.46/5.78 @ one_one_complex ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod_atLeastAtMost_code
% 5.46/5.78 thf(fact_8682_prod__atLeastAtMost__code,axiom,
% 5.46/5.78 ! [F: nat > real,A: nat,B2: nat] :
% 5.46/5.78 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 5.46/5.78 = ( set_fo3111899725591712190t_real
% 5.46/5.78 @ ^ [A4: nat] : ( times_times_real @ ( F @ A4 ) )
% 5.46/5.78 @ A
% 5.46/5.78 @ B2
% 5.46/5.78 @ one_one_real ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod_atLeastAtMost_code
% 5.46/5.78 thf(fact_8683_prod__atLeastAtMost__code,axiom,
% 5.46/5.78 ! [F: nat > rat,A: nat,B2: nat] :
% 5.46/5.78 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 5.46/5.78 = ( set_fo1949268297981939178at_rat
% 5.46/5.78 @ ^ [A4: nat] : ( times_times_rat @ ( F @ A4 ) )
% 5.46/5.78 @ A
% 5.46/5.78 @ B2
% 5.46/5.78 @ one_one_rat ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod_atLeastAtMost_code
% 5.46/5.78 thf(fact_8684_prod__atLeastAtMost__code,axiom,
% 5.46/5.78 ! [F: nat > nat,A: nat,B2: nat] :
% 5.46/5.78 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 5.46/5.78 = ( set_fo2584398358068434914at_nat
% 5.46/5.78 @ ^ [A4: nat] : ( times_times_nat @ ( F @ A4 ) )
% 5.46/5.78 @ A
% 5.46/5.78 @ B2
% 5.46/5.78 @ one_one_nat ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod_atLeastAtMost_code
% 5.46/5.78 thf(fact_8685_prod__atLeastAtMost__code,axiom,
% 5.46/5.78 ! [F: nat > int,A: nat,B2: nat] :
% 5.46/5.78 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 5.46/5.78 = ( set_fo2581907887559384638at_int
% 5.46/5.78 @ ^ [A4: nat] : ( times_times_int @ ( F @ A4 ) )
% 5.46/5.78 @ A
% 5.46/5.78 @ B2
% 5.46/5.78 @ one_one_int ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod_atLeastAtMost_code
% 5.46/5.78 thf(fact_8686_prod_Oub__add__nat,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > real,P2: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.46/5.78 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.46/5.78 = ( 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 @ P2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.ub_add_nat
% 5.46/5.78 thf(fact_8687_prod_Oub__add__nat,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > rat,P2: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.46/5.78 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.46/5.78 = ( 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 @ P2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.ub_add_nat
% 5.46/5.78 thf(fact_8688_prod_Oub__add__nat,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > nat,P2: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.46/5.78 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.46/5.78 = ( 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 @ P2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.ub_add_nat
% 5.46/5.78 thf(fact_8689_prod_Oub__add__nat,axiom,
% 5.46/5.78 ! [M: nat,N: nat,G: nat > int,P2: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.46/5.78 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.46/5.78 = ( 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 @ P2 ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.ub_add_nat
% 5.46/5.78 thf(fact_8690_vebt__succ_Osimps_I1_J,axiom,
% 5.46/5.78 ! [B2: $o,Uu3: $o] :
% 5.46/5.78 ( ( B2
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu3 @ B2 ) @ zero_zero_nat )
% 5.46/5.78 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.78 & ( ~ B2
% 5.46/5.78 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu3 @ B2 ) @ zero_zero_nat )
% 5.46/5.78 = none_nat ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_succ.simps(1)
% 5.46/5.78 thf(fact_8691_fact__eq__fact__times,axiom,
% 5.46/5.78 ! [N: nat,M: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.78 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.46/5.78 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.46/5.78 @ ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [X: nat] : X
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % fact_eq_fact_times
% 5.46/5.78 thf(fact_8692_pochhammer__Suc__prod,axiom,
% 5.46/5.78 ! [A: complex,N: nat] :
% 5.46/5.78 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.46/5.78 = ( groups6464643781859351333omplex
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_Suc_prod
% 5.46/5.78 thf(fact_8693_pochhammer__Suc__prod,axiom,
% 5.46/5.78 ! [A: real,N: nat] :
% 5.46/5.78 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.46/5.78 = ( groups129246275422532515t_real
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_Suc_prod
% 5.46/5.78 thf(fact_8694_pochhammer__Suc__prod,axiom,
% 5.46/5.78 ! [A: rat,N: nat] :
% 5.46/5.78 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.46/5.78 = ( groups73079841787564623at_rat
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_Suc_prod
% 5.46/5.78 thf(fact_8695_pochhammer__Suc__prod,axiom,
% 5.46/5.78 ! [A: nat,N: nat] :
% 5.46/5.78 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.46/5.78 = ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_Suc_prod
% 5.46/5.78 thf(fact_8696_pochhammer__Suc__prod,axiom,
% 5.46/5.78 ! [A: int,N: nat] :
% 5.46/5.78 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.46/5.78 = ( groups705719431365010083at_int
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_Suc_prod
% 5.46/5.78 thf(fact_8697_pochhammer__prod__rev,axiom,
% 5.46/5.78 ( comm_s2602460028002588243omplex
% 5.46/5.78 = ( ^ [A4: complex,N2: nat] :
% 5.46/5.78 ( groups6464643781859351333omplex
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N2 @ I2 ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_prod_rev
% 5.46/5.78 thf(fact_8698_pochhammer__prod__rev,axiom,
% 5.46/5.78 ( comm_s7457072308508201937r_real
% 5.46/5.78 = ( ^ [A4: real,N2: nat] :
% 5.46/5.78 ( groups129246275422532515t_real
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I2 ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_prod_rev
% 5.46/5.78 thf(fact_8699_pochhammer__prod__rev,axiom,
% 5.46/5.78 ( comm_s4028243227959126397er_rat
% 5.46/5.78 = ( ^ [A4: rat,N2: nat] :
% 5.46/5.78 ( groups73079841787564623at_rat
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I2 ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_prod_rev
% 5.46/5.78 thf(fact_8700_pochhammer__prod__rev,axiom,
% 5.46/5.78 ( comm_s4663373288045622133er_nat
% 5.46/5.78 = ( ^ [A4: nat,N2: nat] :
% 5.46/5.78 ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I2 ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_prod_rev
% 5.46/5.78 thf(fact_8701_pochhammer__prod__rev,axiom,
% 5.46/5.78 ( comm_s4660882817536571857er_int
% 5.46/5.78 = ( ^ [A4: int,N2: nat] :
% 5.46/5.78 ( groups705719431365010083at_int
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I2 ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_prod_rev
% 5.46/5.78 thf(fact_8702_fact__div__fact,axiom,
% 5.46/5.78 ! [N: nat,M: nat] :
% 5.46/5.78 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.78 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.46/5.78 = ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [X: nat] : X
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % fact_div_fact
% 5.46/5.78 thf(fact_8703_prod_Oin__pairs,axiom,
% 5.46/5.78 ! [G: nat > real,M: nat,N: nat] :
% 5.46/5.78 ( ( 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 ) ) ) )
% 5.46/5.78 = ( groups129246275422532515t_real
% 5.46/5.78 @ ^ [I2: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.in_pairs
% 5.46/5.78 thf(fact_8704_prod_Oin__pairs,axiom,
% 5.46/5.78 ! [G: nat > rat,M: nat,N: nat] :
% 5.46/5.78 ( ( 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 ) ) ) )
% 5.46/5.78 = ( groups73079841787564623at_rat
% 5.46/5.78 @ ^ [I2: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.in_pairs
% 5.46/5.78 thf(fact_8705_prod_Oin__pairs,axiom,
% 5.46/5.78 ! [G: nat > nat,M: nat,N: nat] :
% 5.46/5.78 ( ( 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 ) ) ) )
% 5.46/5.78 = ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [I2: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.in_pairs
% 5.46/5.78 thf(fact_8706_prod_Oin__pairs,axiom,
% 5.46/5.78 ! [G: nat > int,M: nat,N: nat] :
% 5.46/5.78 ( ( 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 ) ) ) )
% 5.46/5.78 = ( groups705719431365010083at_int
% 5.46/5.78 @ ^ [I2: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % prod.in_pairs
% 5.46/5.78 thf(fact_8707_pochhammer__Suc__prod__rev,axiom,
% 5.46/5.78 ! [A: complex,N: nat] :
% 5.46/5.78 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.46/5.78 = ( groups6464643781859351333omplex
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N @ I2 ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_Suc_prod_rev
% 5.46/5.78 thf(fact_8708_pochhammer__Suc__prod__rev,axiom,
% 5.46/5.78 ! [A: real,N: nat] :
% 5.46/5.78 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.46/5.78 = ( groups129246275422532515t_real
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I2 ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_Suc_prod_rev
% 5.46/5.78 thf(fact_8709_pochhammer__Suc__prod__rev,axiom,
% 5.46/5.78 ! [A: rat,N: nat] :
% 5.46/5.78 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.46/5.78 = ( groups73079841787564623at_rat
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I2 ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_Suc_prod_rev
% 5.46/5.78 thf(fact_8710_pochhammer__Suc__prod__rev,axiom,
% 5.46/5.78 ! [A: nat,N: nat] :
% 5.46/5.78 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.46/5.78 = ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I2 ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_Suc_prod_rev
% 5.46/5.78 thf(fact_8711_pochhammer__Suc__prod__rev,axiom,
% 5.46/5.78 ! [A: int,N: nat] :
% 5.46/5.78 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.46/5.78 = ( groups705719431365010083at_int
% 5.46/5.78 @ ^ [I2: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I2 ) ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % pochhammer_Suc_prod_rev
% 5.46/5.78 thf(fact_8712_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.46/5.78 ! [X4: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.46/5.78 ( ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.46/5.78 = Y3 )
% 5.46/5.78 => ( ( ? [Uu2: $o,Uv: $o] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Leaf @ Uu2 @ Uv ) )
% 5.46/5.78 => Y3 )
% 5.46/5.78 => ( ( ? [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 5.46/5.78 => Y3 )
% 5.46/5.78 => ( ! [Mi2: nat,Ma2: nat] :
% 5.46/5.78 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.46/5.78 => ( Y3
% 5.46/5.78 = ( ~ ( ( Xa = Mi2 )
% 5.46/5.78 | ( Xa = Ma2 ) ) ) ) )
% 5.46/5.78 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.78 ( ? [Vc2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 5.46/5.78 => ( Y3
% 5.46/5.78 = ( ~ ( ( Xa = Mi2 )
% 5.46/5.78 | ( Xa = Ma2 )
% 5.46/5.78 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.78 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 5.46/5.78 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.78 ( ? [Vd2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 5.46/5.78 => ( Y3
% 5.46/5.78 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.78 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % VEBT_internal.membermima.elims(1)
% 5.46/5.78 thf(fact_8713_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.46/5.78 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.78 ( ~ ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.46/5.78 => ( ! [Uu2: $o,Uv: $o] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( vEBT_Leaf @ Uu2 @ Uv ) )
% 5.46/5.78 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 5.46/5.78 => ( ! [Mi2: nat,Ma2: nat] :
% 5.46/5.78 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.46/5.78 => ( ( Xa = Mi2 )
% 5.46/5.78 | ( Xa = Ma2 ) ) )
% 5.46/5.78 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.78 ( ? [Vc2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 5.46/5.78 => ( ( Xa = Mi2 )
% 5.46/5.78 | ( Xa = Ma2 )
% 5.46/5.78 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.78 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.46/5.78 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.78 ( ? [Vd2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 5.46/5.78 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.78 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % VEBT_internal.membermima.elims(3)
% 5.46/5.78 thf(fact_8714_gbinomial__Suc,axiom,
% 5.46/5.78 ! [A: complex,K: nat] :
% 5.46/5.78 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.46/5.78 = ( divide1717551699836669952omplex
% 5.46/5.78 @ ( groups6464643781859351333omplex
% 5.46/5.78 @ ^ [I2: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.46/5.78 @ ( semiri5044797733671781792omplex @ ( suc @ K ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % gbinomial_Suc
% 5.46/5.78 thf(fact_8715_gbinomial__Suc,axiom,
% 5.46/5.78 ! [A: rat,K: nat] :
% 5.46/5.78 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.46/5.78 = ( divide_divide_rat
% 5.46/5.78 @ ( groups73079841787564623at_rat
% 5.46/5.78 @ ^ [I2: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.46/5.78 @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % gbinomial_Suc
% 5.46/5.78 thf(fact_8716_gbinomial__Suc,axiom,
% 5.46/5.78 ! [A: real,K: nat] :
% 5.46/5.78 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.46/5.78 = ( divide_divide_real
% 5.46/5.78 @ ( groups129246275422532515t_real
% 5.46/5.78 @ ^ [I2: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.46/5.78 @ ( semiri2265585572941072030t_real @ ( suc @ K ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % gbinomial_Suc
% 5.46/5.78 thf(fact_8717_gbinomial__Suc,axiom,
% 5.46/5.78 ! [A: nat,K: nat] :
% 5.46/5.78 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 5.46/5.78 = ( divide_divide_nat
% 5.46/5.78 @ ( groups708209901874060359at_nat
% 5.46/5.78 @ ^ [I2: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.46/5.78 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % gbinomial_Suc
% 5.46/5.78 thf(fact_8718_gbinomial__Suc,axiom,
% 5.46/5.78 ! [A: int,K: nat] :
% 5.46/5.78 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 5.46/5.78 = ( divide_divide_int
% 5.46/5.78 @ ( groups705719431365010083at_int
% 5.46/5.78 @ ^ [I2: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I2 ) )
% 5.46/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.46/5.78 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % gbinomial_Suc
% 5.46/5.78 thf(fact_8719_vebt__member_Oelims_I1_J,axiom,
% 5.46/5.78 ! [X4: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.46/5.78 ( ( ( vEBT_vebt_member @ X4 @ Xa )
% 5.46/5.78 = Y3 )
% 5.46/5.78 => ( ! [A5: $o,B5: $o] :
% 5.46/5.78 ( ( X4
% 5.46/5.78 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.78 => ( Y3
% 5.46/5.78 = ( ~ ( ( ( Xa = zero_zero_nat )
% 5.46/5.78 => A5 )
% 5.46/5.78 & ( ( Xa != zero_zero_nat )
% 5.46/5.78 => ( ( ( Xa = one_one_nat )
% 5.46/5.78 => B5 )
% 5.46/5.78 & ( Xa = one_one_nat ) ) ) ) ) ) )
% 5.46/5.78 => ( ( ? [Uu2: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) )
% 5.46/5.78 => Y3 )
% 5.46/5.78 => ( ( ? [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz ) )
% 5.46/5.78 => Y3 )
% 5.46/5.78 => ( ( ? [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.78 => Y3 )
% 5.46/5.78 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.78 ( ? [Summary2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.78 => ( Y3
% 5.46/5.78 = ( ~ ( ( Xa != Mi2 )
% 5.46/5.78 => ( ( Xa != Ma2 )
% 5.46/5.78 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.78 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.78 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.78 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.78 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.78 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_member.elims(1)
% 5.46/5.78 thf(fact_8720_vebt__member_Oelims_I3_J,axiom,
% 5.46/5.78 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.78 ( ~ ( vEBT_vebt_member @ X4 @ Xa )
% 5.46/5.78 => ( ! [A5: $o,B5: $o] :
% 5.46/5.78 ( ( X4
% 5.46/5.78 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.78 => ( ( ( Xa = zero_zero_nat )
% 5.46/5.78 => A5 )
% 5.46/5.78 & ( ( Xa != zero_zero_nat )
% 5.46/5.78 => ( ( ( Xa = one_one_nat )
% 5.46/5.78 => B5 )
% 5.46/5.78 & ( Xa = one_one_nat ) ) ) ) )
% 5.46/5.78 => ( ! [Uu2: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) )
% 5.46/5.78 => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz ) )
% 5.46/5.78 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.78 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.78 ( ? [Summary2: vEBT_VEBT] :
% 5.46/5.78 ( X4
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.78 => ( ( Xa != Mi2 )
% 5.46/5.78 => ( ( Xa != Ma2 )
% 5.46/5.78 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.78 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.78 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.78 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.78 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.78 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.78 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.78
% 5.46/5.78 % vebt_member.elims(3)
% 5.46/5.78 thf(fact_8721_invar__vebt_Osimps,axiom,
% 5.46/5.78 ( vEBT_invar_vebt
% 5.46/5.78 = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 5.46/5.78 ( ( ? [A4: $o,B3: $o] :
% 5.46/5.78 ( A1
% 5.46/5.78 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.46/5.78 & ( A22
% 5.46/5.78 = ( suc @ zero_zero_nat ) ) )
% 5.46/5.78 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.46/5.78 ( ( A1
% 5.46/5.78 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 5.46/5.78 & ! [X: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.78 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.46/5.78 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.46/5.78 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.46/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.46/5.78 & ( A22
% 5.46/5.78 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.46/5.78 & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 5.46/5.78 & ! [X: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.78 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.78 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.46/5.78 ( ( A1
% 5.46/5.78 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 5.46/5.78 & ! [X: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.78 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.46/5.78 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.46/5.78 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.46/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.46/5.78 & ( A22
% 5.46/5.78 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.46/5.78 & ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X6 )
% 5.46/5.78 & ! [X: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.78 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.78 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.46/5.78 ( ( A1
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 5.46/5.78 & ! [X: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.78 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.46/5.78 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.46/5.78 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.46/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.46/5.78 & ( A22
% 5.46/5.78 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.46/5.78 & ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.46/5.78 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X6 ) )
% 5.46/5.78 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I2 ) ) )
% 5.46/5.78 & ( ( Mi3 = Ma3 )
% 5.46/5.78 => ! [X: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.78 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.78 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.78 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.46/5.78 & ( ( Mi3 != Ma3 )
% 5.46/5.78 => ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.46/5.78 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.46/5.78 = I2 )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.46/5.78 & ! [X: nat] :
% 5.46/5.78 ( ( ( ( vEBT_VEBT_high @ X @ N2 )
% 5.46/5.78 = I2 )
% 5.46/5.78 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X @ N2 ) ) )
% 5.46/5.78 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.78 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) )
% 5.46/5.78 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.46/5.78 ( ( A1
% 5.46/5.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 5.46/5.78 & ! [X: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.78 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.46/5.78 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.46/5.78 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.46/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.46/5.78 & ( A22
% 5.46/5.78 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.46/5.78 & ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.46/5.78 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X6 ) )
% 5.46/5.78 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I2 ) ) )
% 5.46/5.78 & ( ( Mi3 = Ma3 )
% 5.46/5.78 => ! [X: vEBT_VEBT] :
% 5.46/5.78 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.46/5.78 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.78 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.78 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.46/5.78 & ( ( Mi3 != Ma3 )
% 5.46/5.78 => ! [I2: nat] :
% 5.46/5.78 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.46/5.78 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.46/5.78 = I2 )
% 5.46/5.78 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.46/5.78 & ! [X: nat] :
% 5.46/5.78 ( ( ( ( vEBT_VEBT_high @ X @ N2 )
% 5.46/5.79 = I2 )
% 5.46/5.79 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X @ N2 ) ) )
% 5.46/5.79 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.79 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % invar_vebt.simps
% 5.46/5.79 thf(fact_8722_invar__vebt_Ocases,axiom,
% 5.46/5.79 ! [A12: vEBT_VEBT,A23: nat] :
% 5.46/5.79 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 5.46/5.79 => ( ( ? [A5: $o,B5: $o] :
% 5.46/5.79 ( A12
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ( A23
% 5.46/5.79 != ( suc @ zero_zero_nat ) ) )
% 5.46/5.79 => ( ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.46/5.79 ( ( A12
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( ( A23 = Deg2 )
% 5.46/5.79 => ( ! [X5: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_invar_vebt @ X5 @ N4 ) )
% 5.46/5.79 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.46/5.79 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.79 => ( ( M4 = N4 )
% 5.46/5.79 => ( ( Deg2
% 5.46/5.79 = ( plus_plus_nat @ N4 @ M4 ) )
% 5.46/5.79 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.46/5.79 => ~ ! [X5: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.79 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.46/5.79 => ( ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.46/5.79 ( ( A12
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( ( A23 = Deg2 )
% 5.46/5.79 => ( ! [X5: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_invar_vebt @ X5 @ N4 ) )
% 5.46/5.79 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.46/5.79 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.79 => ( ( M4
% 5.46/5.79 = ( suc @ N4 ) )
% 5.46/5.79 => ( ( Deg2
% 5.46/5.79 = ( plus_plus_nat @ N4 @ M4 ) )
% 5.46/5.79 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.46/5.79 => ~ ! [X5: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.79 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.46/5.79 => ( ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.46/5.79 ( ( A12
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( ( A23 = Deg2 )
% 5.46/5.79 => ( ! [X5: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_invar_vebt @ X5 @ N4 ) )
% 5.46/5.79 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.46/5.79 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.79 => ( ( M4 = N4 )
% 5.46/5.79 => ( ( Deg2
% 5.46/5.79 = ( plus_plus_nat @ N4 @ M4 ) )
% 5.46/5.79 => ( ! [I4: nat] :
% 5.46/5.79 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.79 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 5.46/5.79 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.46/5.79 => ( ( ( Mi2 = Ma2 )
% 5.46/5.79 => ! [X5: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.79 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.46/5.79 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.46/5.79 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.79 => ~ ( ( Mi2 != Ma2 )
% 5.46/5.79 => ! [I4: nat] :
% 5.46/5.79 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.79 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N4 )
% 5.46/5.79 = I4 )
% 5.46/5.79 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N4 ) ) )
% 5.46/5.79 & ! [X5: nat] :
% 5.46/5.79 ( ( ( ( vEBT_VEBT_high @ X5 @ N4 )
% 5.46/5.79 = I4 )
% 5.46/5.79 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N4 ) ) )
% 5.46/5.79 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.46/5.79 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.79 => ~ ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.46/5.79 ( ( A12
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( ( A23 = Deg2 )
% 5.46/5.79 => ( ! [X5: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_invar_vebt @ X5 @ N4 ) )
% 5.46/5.79 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.46/5.79 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.79 => ( ( M4
% 5.46/5.79 = ( suc @ N4 ) )
% 5.46/5.79 => ( ( Deg2
% 5.46/5.79 = ( plus_plus_nat @ N4 @ M4 ) )
% 5.46/5.79 => ( ! [I4: nat] :
% 5.46/5.79 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.79 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X6 ) )
% 5.46/5.79 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.46/5.79 => ( ( ( Mi2 = Ma2 )
% 5.46/5.79 => ! [X5: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.79 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.46/5.79 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.46/5.79 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.79 => ~ ( ( Mi2 != Ma2 )
% 5.46/5.79 => ! [I4: nat] :
% 5.46/5.79 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.46/5.79 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N4 )
% 5.46/5.79 = I4 )
% 5.46/5.79 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N4 ) ) )
% 5.46/5.79 & ! [X5: nat] :
% 5.46/5.79 ( ( ( ( vEBT_VEBT_high @ X5 @ N4 )
% 5.46/5.79 = I4 )
% 5.46/5.79 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N4 ) ) )
% 5.46/5.79 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.46/5.79 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % invar_vebt.cases
% 5.46/5.79 thf(fact_8723_invar__vebt_Ointros_I2_J,axiom,
% 5.46/5.79 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.46/5.79 ( ! [X3: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.79 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.46/5.79 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.46/5.79 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.79 => ( ( M = N )
% 5.46/5.79 => ( ( Deg
% 5.46/5.79 = ( plus_plus_nat @ N @ M ) )
% 5.46/5.79 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.46/5.79 => ( ! [X3: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.79 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.46/5.79 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % invar_vebt.intros(2)
% 5.46/5.79 thf(fact_8724_invar__vebt_Ointros_I3_J,axiom,
% 5.46/5.79 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.46/5.79 ( ! [X3: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.79 => ( vEBT_invar_vebt @ X3 @ N ) )
% 5.46/5.79 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.46/5.79 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.46/5.79 => ( ( M
% 5.46/5.79 = ( suc @ N ) )
% 5.46/5.79 => ( ( Deg
% 5.46/5.79 = ( plus_plus_nat @ N @ M ) )
% 5.46/5.79 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.46/5.79 => ( ! [X3: vEBT_VEBT] :
% 5.46/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.79 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.46/5.79 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % invar_vebt.intros(3)
% 5.46/5.79 thf(fact_8725_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.46/5.79 ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X4: nat] :
% 5.46/5.79 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X4 )
% 5.46/5.79 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.79 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.membermima.simps(5)
% 5.46/5.79 thf(fact_8726_vebt__succ_Oelims,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 5.46/5.79 ( ( ( vEBT_vebt_succ @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ! [Uu2: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 5.46/5.79 => ( ( Xa = zero_zero_nat )
% 5.46/5.79 => ~ ( ( B5
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.79 & ( ~ B5
% 5.46/5.79 => ( Y3 = none_nat ) ) ) ) )
% 5.46/5.79 => ( ( ? [Uv: $o,Uw: $o] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Leaf @ Uv @ Uw ) )
% 5.46/5.79 => ( ? [N4: nat] :
% 5.46/5.79 ( Xa
% 5.46/5.79 = ( suc @ N4 ) )
% 5.46/5.79 => ( Y3 != none_nat ) ) )
% 5.46/5.79 => ( ( ? [Ux: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy2 @ Uz ) )
% 5.46/5.79 => ( Y3 != none_nat ) )
% 5.46/5.79 => ( ( ? [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.46/5.79 => ( Y3 != none_nat ) )
% 5.46/5.79 => ( ( ? [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 5.46/5.79 => ( Y3 != none_nat ) )
% 5.46/5.79 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ~ ( ( ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( some_nat @ Mi2 ) ) )
% 5.46/5.79 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 @ ( if_option_nat
% 5.46/5.79 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 != none_nat )
% 5.46/5.79 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.46/5.79 @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 @ ( if_option_nat
% 5.46/5.79 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.79 = none_nat )
% 5.46/5.79 @ none_nat
% 5.46/5.79 @ ( 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_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.79 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_succ.elims
% 5.46/5.79 thf(fact_8727_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.79 ( ~ ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => A5 )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => B5 )
% 5.46/5.79 & ( Xa = one_one_nat ) ) ) ) )
% 5.46/5.79 => ( ! [Uu2: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv @ Uw ) )
% 5.46/5.79 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.79 ( ? [S3: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 5.46/5.79 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.naive_member.elims(3)
% 5.46/5.79 thf(fact_8728_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.79 ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ~ ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => A5 )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => B5 )
% 5.46/5.79 & ( Xa = one_one_nat ) ) ) ) )
% 5.46/5.79 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.79 ( ? [S3: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 5.46/5.79 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.naive_member.elims(2)
% 5.46/5.79 thf(fact_8729_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.46/5.79 ( ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( ~ ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => A5 )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => B5 )
% 5.46/5.79 & ( Xa = one_one_nat ) ) ) ) ) ) )
% 5.46/5.79 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv @ Uw ) )
% 5.46/5.79 => Y3 )
% 5.46/5.79 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT] :
% 5.46/5.79 ( ? [S3: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.naive_member.elims(1)
% 5.46/5.79 thf(fact_8730_vebt__maxt_Oelims,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Y3: option_nat] :
% 5.46/5.79 ( ( ( vEBT_vebt_maxt @ X4 )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ~ ( ( B5
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.79 & ( ~ B5
% 5.46/5.79 => ( ( A5
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.79 & ( ~ A5
% 5.46/5.79 => ( Y3 = none_nat ) ) ) ) ) )
% 5.46/5.79 => ( ( ? [Uu2: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) )
% 5.46/5.79 => ( Y3 != none_nat ) )
% 5.46/5.79 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.46/5.79 ( ? [Ux: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy2 @ Uz ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_maxt.elims
% 5.46/5.79 thf(fact_8731_vebt__mint_Oelims,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Y3: option_nat] :
% 5.46/5.79 ( ( ( vEBT_vebt_mint @ X4 )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ~ ( ( A5
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.79 & ( ~ A5
% 5.46/5.79 => ( ( B5
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.79 & ( ~ B5
% 5.46/5.79 => ( Y3 = none_nat ) ) ) ) ) )
% 5.46/5.79 => ( ( ? [Uu2: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) )
% 5.46/5.79 => ( Y3 != none_nat ) )
% 5.46/5.79 => ~ ! [Mi2: nat] :
% 5.46/5.79 ( ? [Ma2: nat,Ux: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy2 @ Uz ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_mint.elims
% 5.46/5.79 thf(fact_8732_prod_Oempty,axiom,
% 5.46/5.79 ! [G: extended_enat > complex] :
% 5.46/5.79 ( ( groups4622424608036095791omplex @ G @ bot_bo7653980558646680370d_enat )
% 5.46/5.79 = one_one_complex ) ).
% 5.46/5.79
% 5.46/5.79 % prod.empty
% 5.46/5.79 thf(fact_8733_prod_Oempty,axiom,
% 5.46/5.79 ! [G: extended_enat > real] :
% 5.46/5.79 ( ( groups97031904164794029t_real @ G @ bot_bo7653980558646680370d_enat )
% 5.46/5.79 = one_one_real ) ).
% 5.46/5.79
% 5.46/5.79 % prod.empty
% 5.46/5.79 thf(fact_8734_prod_Oempty,axiom,
% 5.46/5.79 ! [G: extended_enat > rat] :
% 5.46/5.79 ( ( groups2245840878043517529at_rat @ G @ bot_bo7653980558646680370d_enat )
% 5.46/5.79 = one_one_rat ) ).
% 5.46/5.79
% 5.46/5.79 % prod.empty
% 5.46/5.79 thf(fact_8735_prod_Oempty,axiom,
% 5.46/5.79 ! [G: extended_enat > nat] :
% 5.46/5.79 ( ( groups2880970938130013265at_nat @ G @ bot_bo7653980558646680370d_enat )
% 5.46/5.79 = one_one_nat ) ).
% 5.46/5.79
% 5.46/5.79 % prod.empty
% 5.46/5.79 thf(fact_8736_prod_Oempty,axiom,
% 5.46/5.79 ! [G: extended_enat > int] :
% 5.46/5.79 ( ( groups2878480467620962989at_int @ G @ bot_bo7653980558646680370d_enat )
% 5.46/5.79 = one_one_int ) ).
% 5.46/5.79
% 5.46/5.79 % prod.empty
% 5.46/5.79 thf(fact_8737_prod_Oempty,axiom,
% 5.46/5.79 ! [G: real > complex] :
% 5.46/5.79 ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 5.46/5.79 = one_one_complex ) ).
% 5.46/5.79
% 5.46/5.79 % prod.empty
% 5.46/5.79 thf(fact_8738_prod_Oempty,axiom,
% 5.46/5.79 ! [G: real > real] :
% 5.46/5.79 ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 5.46/5.79 = one_one_real ) ).
% 5.46/5.79
% 5.46/5.79 % prod.empty
% 5.46/5.79 thf(fact_8739_prod_Oempty,axiom,
% 5.46/5.79 ! [G: real > rat] :
% 5.46/5.79 ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 5.46/5.79 = one_one_rat ) ).
% 5.46/5.79
% 5.46/5.79 % prod.empty
% 5.46/5.79 thf(fact_8740_prod_Oempty,axiom,
% 5.46/5.79 ! [G: real > nat] :
% 5.46/5.79 ( ( groups4696554848551431203al_nat @ G @ bot_bot_set_real )
% 5.46/5.79 = one_one_nat ) ).
% 5.46/5.79
% 5.46/5.79 % prod.empty
% 5.46/5.79 thf(fact_8741_prod_Oempty,axiom,
% 5.46/5.79 ! [G: real > int] :
% 5.46/5.79 ( ( groups4694064378042380927al_int @ G @ bot_bot_set_real )
% 5.46/5.79 = one_one_int ) ).
% 5.46/5.79
% 5.46/5.79 % prod.empty
% 5.46/5.79 thf(fact_8742_vebt__maxt_Osimps_I1_J,axiom,
% 5.46/5.79 ! [B2: $o,A: $o] :
% 5.46/5.79 ( ( B2
% 5.46/5.79 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B2 ) )
% 5.46/5.79 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.79 & ( ~ B2
% 5.46/5.79 => ( ( A
% 5.46/5.79 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B2 ) )
% 5.46/5.79 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.79 & ( ~ A
% 5.46/5.79 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B2 ) )
% 5.46/5.79 = none_nat ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_maxt.simps(1)
% 5.46/5.79 thf(fact_8743_prod_Oneutral__const,axiom,
% 5.46/5.79 ! [A3: set_nat] :
% 5.46/5.79 ( ( groups708209901874060359at_nat
% 5.46/5.79 @ ^ [Uu: nat] : one_one_nat
% 5.46/5.79 @ A3 )
% 5.46/5.79 = one_one_nat ) ).
% 5.46/5.79
% 5.46/5.79 % prod.neutral_const
% 5.46/5.79 thf(fact_8744_prod_Oneutral__const,axiom,
% 5.46/5.79 ! [A3: set_nat] :
% 5.46/5.79 ( ( groups705719431365010083at_int
% 5.46/5.79 @ ^ [Uu: nat] : one_one_int
% 5.46/5.79 @ A3 )
% 5.46/5.79 = one_one_int ) ).
% 5.46/5.79
% 5.46/5.79 % prod.neutral_const
% 5.46/5.79 thf(fact_8745_prod_Oneutral__const,axiom,
% 5.46/5.79 ! [A3: set_int] :
% 5.46/5.79 ( ( groups1705073143266064639nt_int
% 5.46/5.79 @ ^ [Uu: int] : one_one_int
% 5.46/5.79 @ A3 )
% 5.46/5.79 = one_one_int ) ).
% 5.46/5.79
% 5.46/5.79 % prod.neutral_const
% 5.46/5.79 thf(fact_8746_prod__int__eq,axiom,
% 5.46/5.79 ! [I: nat,J: nat] :
% 5.46/5.79 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.46/5.79 = ( groups1705073143266064639nt_int
% 5.46/5.79 @ ^ [X: int] : X
% 5.46/5.79 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_int_eq
% 5.46/5.79 thf(fact_8747_prod__int__plus__eq,axiom,
% 5.46/5.79 ! [I: nat,J: nat] :
% 5.46/5.79 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 5.46/5.79 = ( groups1705073143266064639nt_int
% 5.46/5.79 @ ^ [X: int] : X
% 5.46/5.79 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_int_plus_eq
% 5.46/5.79 thf(fact_8748_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.79 ! [G: extended_enat > complex,A3: set_Extended_enat] :
% 5.46/5.79 ( ( ( groups4622424608036095791omplex @ G @ A3 )
% 5.46/5.79 != one_one_complex )
% 5.46/5.79 => ~ ! [A5: extended_enat] :
% 5.46/5.79 ( ( member_Extended_enat @ A5 @ A3 )
% 5.46/5.79 => ( ( G @ A5 )
% 5.46/5.79 = one_one_complex ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.not_neutral_contains_not_neutral
% 5.46/5.79 thf(fact_8749_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.79 ! [G: complex > complex,A3: set_complex] :
% 5.46/5.79 ( ( ( groups3708469109370488835omplex @ G @ A3 )
% 5.46/5.79 != one_one_complex )
% 5.46/5.79 => ~ ! [A5: complex] :
% 5.46/5.79 ( ( member_complex @ A5 @ A3 )
% 5.46/5.79 => ( ( G @ A5 )
% 5.46/5.79 = one_one_complex ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.not_neutral_contains_not_neutral
% 5.46/5.79 thf(fact_8750_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.79 ! [G: real > complex,A3: set_real] :
% 5.46/5.79 ( ( ( groups713298508707869441omplex @ G @ A3 )
% 5.46/5.79 != one_one_complex )
% 5.46/5.79 => ~ ! [A5: real] :
% 5.46/5.79 ( ( member_real @ A5 @ A3 )
% 5.46/5.79 => ( ( G @ A5 )
% 5.46/5.79 = one_one_complex ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.not_neutral_contains_not_neutral
% 5.46/5.79 thf(fact_8751_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.79 ! [G: nat > complex,A3: set_nat] :
% 5.46/5.79 ( ( ( groups6464643781859351333omplex @ G @ A3 )
% 5.46/5.79 != one_one_complex )
% 5.46/5.79 => ~ ! [A5: nat] :
% 5.46/5.79 ( ( member_nat @ A5 @ A3 )
% 5.46/5.79 => ( ( G @ A5 )
% 5.46/5.79 = one_one_complex ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.not_neutral_contains_not_neutral
% 5.46/5.79 thf(fact_8752_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.79 ! [G: int > complex,A3: set_int] :
% 5.46/5.79 ( ( ( groups7440179247065528705omplex @ G @ A3 )
% 5.46/5.79 != one_one_complex )
% 5.46/5.79 => ~ ! [A5: int] :
% 5.46/5.79 ( ( member_int @ A5 @ A3 )
% 5.46/5.79 => ( ( G @ A5 )
% 5.46/5.79 = one_one_complex ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.not_neutral_contains_not_neutral
% 5.46/5.79 thf(fact_8753_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.79 ! [G: extended_enat > real,A3: set_Extended_enat] :
% 5.46/5.79 ( ( ( groups97031904164794029t_real @ G @ A3 )
% 5.46/5.79 != one_one_real )
% 5.46/5.79 => ~ ! [A5: extended_enat] :
% 5.46/5.79 ( ( member_Extended_enat @ A5 @ A3 )
% 5.46/5.79 => ( ( G @ A5 )
% 5.46/5.79 = one_one_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.not_neutral_contains_not_neutral
% 5.46/5.79 thf(fact_8754_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.79 ! [G: complex > real,A3: set_complex] :
% 5.46/5.79 ( ( ( groups766887009212190081x_real @ G @ A3 )
% 5.46/5.79 != one_one_real )
% 5.46/5.79 => ~ ! [A5: complex] :
% 5.46/5.79 ( ( member_complex @ A5 @ A3 )
% 5.46/5.79 => ( ( G @ A5 )
% 5.46/5.79 = one_one_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.not_neutral_contains_not_neutral
% 5.46/5.79 thf(fact_8755_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.79 ! [G: real > real,A3: set_real] :
% 5.46/5.79 ( ( ( groups1681761925125756287l_real @ G @ A3 )
% 5.46/5.79 != one_one_real )
% 5.46/5.79 => ~ ! [A5: real] :
% 5.46/5.79 ( ( member_real @ A5 @ A3 )
% 5.46/5.79 => ( ( G @ A5 )
% 5.46/5.79 = one_one_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.not_neutral_contains_not_neutral
% 5.46/5.79 thf(fact_8756_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.79 ! [G: nat > real,A3: set_nat] :
% 5.46/5.79 ( ( ( groups129246275422532515t_real @ G @ A3 )
% 5.46/5.79 != one_one_real )
% 5.46/5.79 => ~ ! [A5: nat] :
% 5.46/5.79 ( ( member_nat @ A5 @ A3 )
% 5.46/5.79 => ( ( G @ A5 )
% 5.46/5.79 = one_one_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.not_neutral_contains_not_neutral
% 5.46/5.79 thf(fact_8757_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.46/5.79 ! [G: int > real,A3: set_int] :
% 5.46/5.79 ( ( ( groups2316167850115554303t_real @ G @ A3 )
% 5.46/5.79 != one_one_real )
% 5.46/5.79 => ~ ! [A5: int] :
% 5.46/5.79 ( ( member_int @ A5 @ A3 )
% 5.46/5.79 => ( ( G @ A5 )
% 5.46/5.79 = one_one_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.not_neutral_contains_not_neutral
% 5.46/5.79 thf(fact_8758_prod_Oneutral,axiom,
% 5.46/5.79 ! [A3: set_nat,G: nat > nat] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ A3 )
% 5.46/5.79 => ( ( G @ X3 )
% 5.46/5.79 = one_one_nat ) )
% 5.46/5.79 => ( ( groups708209901874060359at_nat @ G @ A3 )
% 5.46/5.79 = one_one_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.neutral
% 5.46/5.79 thf(fact_8759_prod_Oneutral,axiom,
% 5.46/5.79 ! [A3: set_nat,G: nat > int] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ A3 )
% 5.46/5.79 => ( ( G @ X3 )
% 5.46/5.79 = one_one_int ) )
% 5.46/5.79 => ( ( groups705719431365010083at_int @ G @ A3 )
% 5.46/5.79 = one_one_int ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.neutral
% 5.46/5.79 thf(fact_8760_prod_Oneutral,axiom,
% 5.46/5.79 ! [A3: set_int,G: int > int] :
% 5.46/5.79 ( ! [X3: int] :
% 5.46/5.79 ( ( member_int @ X3 @ A3 )
% 5.46/5.79 => ( ( G @ X3 )
% 5.46/5.79 = one_one_int ) )
% 5.46/5.79 => ( ( groups1705073143266064639nt_int @ G @ A3 )
% 5.46/5.79 = one_one_int ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.neutral
% 5.46/5.79 thf(fact_8761_prod_Odistrib,axiom,
% 5.46/5.79 ! [G: nat > nat,H2: nat > nat,A3: set_nat] :
% 5.46/5.79 ( ( groups708209901874060359at_nat
% 5.46/5.79 @ ^ [X: nat] : ( times_times_nat @ ( G @ X ) @ ( H2 @ X ) )
% 5.46/5.79 @ A3 )
% 5.46/5.79 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A3 ) @ ( groups708209901874060359at_nat @ H2 @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.distrib
% 5.46/5.79 thf(fact_8762_prod_Odistrib,axiom,
% 5.46/5.79 ! [G: nat > int,H2: nat > int,A3: set_nat] :
% 5.46/5.79 ( ( groups705719431365010083at_int
% 5.46/5.79 @ ^ [X: nat] : ( times_times_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.46/5.79 @ A3 )
% 5.46/5.79 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A3 ) @ ( groups705719431365010083at_int @ H2 @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.distrib
% 5.46/5.79 thf(fact_8763_prod_Odistrib,axiom,
% 5.46/5.79 ! [G: int > int,H2: int > int,A3: set_int] :
% 5.46/5.79 ( ( groups1705073143266064639nt_int
% 5.46/5.79 @ ^ [X: int] : ( times_times_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.46/5.79 @ A3 )
% 5.46/5.79 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A3 ) @ ( groups1705073143266064639nt_int @ H2 @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod.distrib
% 5.46/5.79 thf(fact_8764_prod__power__distrib,axiom,
% 5.46/5.79 ! [F: nat > nat,A3: set_nat,N: nat] :
% 5.46/5.79 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ N )
% 5.46/5.79 = ( groups708209901874060359at_nat
% 5.46/5.79 @ ^ [X: nat] : ( power_power_nat @ ( F @ X ) @ N )
% 5.46/5.79 @ A3 ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_power_distrib
% 5.46/5.79 thf(fact_8765_prod__power__distrib,axiom,
% 5.46/5.79 ! [F: nat > int,A3: set_nat,N: nat] :
% 5.46/5.79 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A3 ) @ N )
% 5.46/5.79 = ( groups705719431365010083at_int
% 5.46/5.79 @ ^ [X: nat] : ( power_power_int @ ( F @ X ) @ N )
% 5.46/5.79 @ A3 ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_power_distrib
% 5.46/5.79 thf(fact_8766_prod__power__distrib,axiom,
% 5.46/5.79 ! [F: int > int,A3: set_int,N: nat] :
% 5.46/5.79 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A3 ) @ N )
% 5.46/5.79 = ( groups1705073143266064639nt_int
% 5.46/5.79 @ ^ [X: int] : ( power_power_int @ ( F @ X ) @ N )
% 5.46/5.79 @ A3 ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_power_distrib
% 5.46/5.79 thf(fact_8767_prod__nonneg,axiom,
% 5.46/5.79 ! [A3: set_nat,F: nat > nat] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_nonneg
% 5.46/5.79 thf(fact_8768_prod__nonneg,axiom,
% 5.46/5.79 ! [A3: set_nat,F: nat > int] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_nonneg
% 5.46/5.79 thf(fact_8769_prod__nonneg,axiom,
% 5.46/5.79 ! [A3: set_int,F: int > int] :
% 5.46/5.79 ( ! [X3: int] :
% 5.46/5.79 ( ( member_int @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_nonneg
% 5.46/5.79 thf(fact_8770_prod__mono,axiom,
% 5.46/5.79 ! [A3: set_Extended_enat,F: extended_enat > real,G: extended_enat > real] :
% 5.46/5.79 ( ! [I3: extended_enat] :
% 5.46/5.79 ( ( member_Extended_enat @ I3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.46/5.79 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( groups97031904164794029t_real @ F @ A3 ) @ ( groups97031904164794029t_real @ G @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_mono
% 5.46/5.79 thf(fact_8771_prod__mono,axiom,
% 5.46/5.79 ! [A3: set_complex,F: complex > real,G: complex > real] :
% 5.46/5.79 ( ! [I3: complex] :
% 5.46/5.79 ( ( member_complex @ I3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.46/5.79 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A3 ) @ ( groups766887009212190081x_real @ G @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_mono
% 5.46/5.79 thf(fact_8772_prod__mono,axiom,
% 5.46/5.79 ! [A3: set_real,F: real > real,G: real > real] :
% 5.46/5.79 ( ! [I3: real] :
% 5.46/5.79 ( ( member_real @ I3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.46/5.79 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ ( groups1681761925125756287l_real @ G @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_mono
% 5.46/5.79 thf(fact_8773_prod__mono,axiom,
% 5.46/5.79 ! [A3: set_nat,F: nat > real,G: nat > real] :
% 5.46/5.79 ( ! [I3: nat] :
% 5.46/5.79 ( ( member_nat @ I3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.46/5.79 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A3 ) @ ( groups129246275422532515t_real @ G @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_mono
% 5.46/5.79 thf(fact_8774_prod__mono,axiom,
% 5.46/5.79 ! [A3: set_int,F: int > real,G: int > real] :
% 5.46/5.79 ( ! [I3: int] :
% 5.46/5.79 ( ( member_int @ I3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.46/5.79 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ ( groups2316167850115554303t_real @ G @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_mono
% 5.46/5.79 thf(fact_8775_prod__mono,axiom,
% 5.46/5.79 ! [A3: set_Extended_enat,F: extended_enat > rat,G: extended_enat > rat] :
% 5.46/5.79 ( ! [I3: extended_enat] :
% 5.46/5.79 ( ( member_Extended_enat @ I3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.46/5.79 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ ( groups2245840878043517529at_rat @ F @ A3 ) @ ( groups2245840878043517529at_rat @ G @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_mono
% 5.46/5.79 thf(fact_8776_prod__mono,axiom,
% 5.46/5.79 ! [A3: set_complex,F: complex > rat,G: complex > rat] :
% 5.46/5.79 ( ! [I3: complex] :
% 5.46/5.79 ( ( member_complex @ I3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.46/5.79 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A3 ) @ ( groups225925009352817453ex_rat @ G @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_mono
% 5.46/5.79 thf(fact_8777_prod__mono,axiom,
% 5.46/5.79 ! [A3: set_real,F: real > rat,G: real > rat] :
% 5.46/5.79 ( ! [I3: real] :
% 5.46/5.79 ( ( member_real @ I3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.46/5.79 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ ( groups4061424788464935467al_rat @ G @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_mono
% 5.46/5.79 thf(fact_8778_prod__mono,axiom,
% 5.46/5.79 ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 5.46/5.79 ( ! [I3: nat] :
% 5.46/5.79 ( ( member_nat @ I3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.46/5.79 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ ( groups73079841787564623at_rat @ G @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_mono
% 5.46/5.79 thf(fact_8779_prod__mono,axiom,
% 5.46/5.79 ! [A3: set_int,F: int > rat,G: int > rat] :
% 5.46/5.79 ( ! [I3: int] :
% 5.46/5.79 ( ( member_int @ I3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.46/5.79 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ G @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_mono
% 5.46/5.79 thf(fact_8780_prod__pos,axiom,
% 5.46/5.79 ! [A3: set_nat,F: nat > nat] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_pos
% 5.46/5.79 thf(fact_8781_prod__pos,axiom,
% 5.46/5.79 ! [A3: set_nat,F: nat > int] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_pos
% 5.46/5.79 thf(fact_8782_prod__pos,axiom,
% 5.46/5.79 ! [A3: set_int,F: int > int] :
% 5.46/5.79 ( ! [X3: int] :
% 5.46/5.79 ( ( member_int @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_pos
% 5.46/5.79 thf(fact_8783_prod__ge__1,axiom,
% 5.46/5.79 ! [A3: set_Extended_enat,F: extended_enat > real] :
% 5.46/5.79 ( ! [X3: extended_enat] :
% 5.46/5.79 ( ( member_Extended_enat @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ one_one_real @ ( groups97031904164794029t_real @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_ge_1
% 5.46/5.79 thf(fact_8784_prod__ge__1,axiom,
% 5.46/5.79 ! [A3: set_complex,F: complex > real] :
% 5.46/5.79 ( ! [X3: complex] :
% 5.46/5.79 ( ( member_complex @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_ge_1
% 5.46/5.79 thf(fact_8785_prod__ge__1,axiom,
% 5.46/5.79 ! [A3: set_real,F: real > real] :
% 5.46/5.79 ( ! [X3: real] :
% 5.46/5.79 ( ( member_real @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_ge_1
% 5.46/5.79 thf(fact_8786_prod__ge__1,axiom,
% 5.46/5.79 ! [A3: set_nat,F: nat > real] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_ge_1
% 5.46/5.79 thf(fact_8787_prod__ge__1,axiom,
% 5.46/5.79 ! [A3: set_int,F: int > real] :
% 5.46/5.79 ( ! [X3: int] :
% 5.46/5.79 ( ( member_int @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_ge_1
% 5.46/5.79 thf(fact_8788_prod__ge__1,axiom,
% 5.46/5.79 ! [A3: set_Extended_enat,F: extended_enat > rat] :
% 5.46/5.79 ( ! [X3: extended_enat] :
% 5.46/5.79 ( ( member_Extended_enat @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( groups2245840878043517529at_rat @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_ge_1
% 5.46/5.79 thf(fact_8789_prod__ge__1,axiom,
% 5.46/5.79 ! [A3: set_complex,F: complex > rat] :
% 5.46/5.79 ( ! [X3: complex] :
% 5.46/5.79 ( ( member_complex @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_ge_1
% 5.46/5.79 thf(fact_8790_prod__ge__1,axiom,
% 5.46/5.79 ! [A3: set_real,F: real > rat] :
% 5.46/5.79 ( ! [X3: real] :
% 5.46/5.79 ( ( member_real @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_ge_1
% 5.46/5.79 thf(fact_8791_prod__ge__1,axiom,
% 5.46/5.79 ! [A3: set_nat,F: nat > rat] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_ge_1
% 5.46/5.79 thf(fact_8792_prod__ge__1,axiom,
% 5.46/5.79 ! [A3: set_int,F: int > rat] :
% 5.46/5.79 ( ! [X3: int] :
% 5.46/5.79 ( ( member_int @ X3 @ A3 )
% 5.46/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_ge_1
% 5.46/5.79 thf(fact_8793_prod__le__1,axiom,
% 5.46/5.79 ! [A3: set_Extended_enat,F: extended_enat > real] :
% 5.46/5.79 ( ! [X3: extended_enat] :
% 5.46/5.79 ( ( member_Extended_enat @ X3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.79 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( groups97031904164794029t_real @ F @ A3 ) @ one_one_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_le_1
% 5.46/5.79 thf(fact_8794_prod__le__1,axiom,
% 5.46/5.79 ! [A3: set_complex,F: complex > real] :
% 5.46/5.79 ( ! [X3: complex] :
% 5.46/5.79 ( ( member_complex @ X3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.79 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A3 ) @ one_one_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_le_1
% 5.46/5.79 thf(fact_8795_prod__le__1,axiom,
% 5.46/5.79 ! [A3: set_real,F: real > real] :
% 5.46/5.79 ( ! [X3: real] :
% 5.46/5.79 ( ( member_real @ X3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.79 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ one_one_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_le_1
% 5.46/5.79 thf(fact_8796_prod__le__1,axiom,
% 5.46/5.79 ! [A3: set_nat,F: nat > real] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.79 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A3 ) @ one_one_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_le_1
% 5.46/5.79 thf(fact_8797_prod__le__1,axiom,
% 5.46/5.79 ! [A3: set_int,F: int > real] :
% 5.46/5.79 ( ! [X3: int] :
% 5.46/5.79 ( ( member_int @ X3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.79 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ one_one_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_le_1
% 5.46/5.79 thf(fact_8798_prod__le__1,axiom,
% 5.46/5.79 ! [A3: set_Extended_enat,F: extended_enat > rat] :
% 5.46/5.79 ( ! [X3: extended_enat] :
% 5.46/5.79 ( ( member_Extended_enat @ X3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.46/5.79 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ ( groups2245840878043517529at_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_le_1
% 5.46/5.79 thf(fact_8799_prod__le__1,axiom,
% 5.46/5.79 ! [A3: set_complex,F: complex > rat] :
% 5.46/5.79 ( ! [X3: complex] :
% 5.46/5.79 ( ( member_complex @ X3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.46/5.79 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_le_1
% 5.46/5.79 thf(fact_8800_prod__le__1,axiom,
% 5.46/5.79 ! [A3: set_real,F: real > rat] :
% 5.46/5.79 ( ! [X3: real] :
% 5.46/5.79 ( ( member_real @ X3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.46/5.79 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_le_1
% 5.46/5.79 thf(fact_8801_prod__le__1,axiom,
% 5.46/5.79 ! [A3: set_nat,F: nat > rat] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.46/5.79 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_le_1
% 5.46/5.79 thf(fact_8802_prod__le__1,axiom,
% 5.46/5.79 ! [A3: set_int,F: int > rat] :
% 5.46/5.79 ( ! [X3: int] :
% 5.46/5.79 ( ( member_int @ X3 @ A3 )
% 5.46/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.46/5.79 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.46/5.79 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_le_1
% 5.46/5.79 thf(fact_8803_vebt__mint_Osimps_I1_J,axiom,
% 5.46/5.79 ! [A: $o,B2: $o] :
% 5.46/5.79 ( ( A
% 5.46/5.79 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B2 ) )
% 5.46/5.79 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.79 & ( ~ A
% 5.46/5.79 => ( ( B2
% 5.46/5.79 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B2 ) )
% 5.46/5.79 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.79 & ( ~ B2
% 5.46/5.79 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B2 ) )
% 5.46/5.79 = none_nat ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_mint.simps(1)
% 5.46/5.79 thf(fact_8804_vebt__succ_Opelims,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat,Y3: option_nat] :
% 5.46/5.79 ( ( ( vEBT_vebt_succ @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [Uu2: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 5.46/5.79 => ( ( Xa = zero_zero_nat )
% 5.46/5.79 => ( ( ( B5
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.79 & ( ~ B5
% 5.46/5.79 => ( Y3 = none_nat ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) ) ) ) )
% 5.46/5.79 => ( ! [Uv: $o,Uw: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ Uv @ Uw ) )
% 5.46/5.79 => ! [N4: nat] :
% 5.46/5.79 ( ( Xa
% 5.46/5.79 = ( suc @ N4 ) )
% 5.46/5.79 => ( ( Y3 = none_nat )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N4 ) ) ) ) ) )
% 5.46/5.79 => ( ! [Ux: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy2 @ Uz ) )
% 5.46/5.79 => ( ( Y3 = none_nat )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy2 @ Uz ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [V3: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.46/5.79 => ( ( Y3 = none_nat )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 5.46/5.79 => ( ( Y3 = none_nat )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa ) ) ) )
% 5.46/5.79 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( ( ( ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( some_nat @ Mi2 ) ) )
% 5.46/5.79 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 @ ( if_option_nat
% 5.46/5.79 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 != none_nat )
% 5.46/5.79 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.46/5.79 @ ( 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 @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 @ ( if_option_nat
% 5.46/5.79 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.79 = none_nat )
% 5.46/5.79 @ none_nat
% 5.46/5.79 @ ( 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_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.79 @ none_nat ) ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_succ.pelims
% 5.46/5.79 thf(fact_8805_ln__series,axiom,
% 5.46/5.79 ! [X4: real] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.79 => ( ( ln_ln_real @ X4 )
% 5.46/5.79 = ( suminf_real
% 5.46/5.79 @ ^ [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 @ X4 @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % ln_series
% 5.46/5.79 thf(fact_8806_arctan__series,axiom,
% 5.46/5.79 ! [X4: real] :
% 5.46/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.79 => ( ( arctan @ X4 )
% 5.46/5.79 = ( suminf_real
% 5.46/5.79 @ ^ [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 @ X4 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % arctan_series
% 5.46/5.79 thf(fact_8807_divmod__algorithm__code_I7_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( ( ord_less_eq_num @ M @ N )
% 5.46/5.79 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.46/5.79 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.46/5.79 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(7)
% 5.46/5.79 thf(fact_8808_divmod__algorithm__code_I7_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( ( ord_less_eq_num @ M @ N )
% 5.46/5.79 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.46/5.79 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.46/5.79 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(7)
% 5.46/5.79 thf(fact_8809_divmod__algorithm__code_I7_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( ( ord_less_eq_num @ M @ N )
% 5.46/5.79 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.46/5.79 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.46/5.79 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(7)
% 5.46/5.79 thf(fact_8810_divmod__algorithm__code_I2_J,axiom,
% 5.46/5.79 ! [M: num] :
% 5.46/5.79 ( ( unique5052692396658037445od_int @ M @ one )
% 5.46/5.79 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(2)
% 5.46/5.79 thf(fact_8811_divmod__algorithm__code_I2_J,axiom,
% 5.46/5.79 ! [M: num] :
% 5.46/5.79 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.46/5.79 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(2)
% 5.46/5.79 thf(fact_8812_divmod__algorithm__code_I2_J,axiom,
% 5.46/5.79 ! [M: num] :
% 5.46/5.79 ( ( unique3479559517661332726nteger @ M @ one )
% 5.46/5.79 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(2)
% 5.46/5.79 thf(fact_8813_powser__zero,axiom,
% 5.46/5.79 ! [F: nat > complex] :
% 5.46/5.79 ( ( suminf_complex
% 5.46/5.79 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 5.46/5.79 = ( F @ zero_zero_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % powser_zero
% 5.46/5.79 thf(fact_8814_powser__zero,axiom,
% 5.46/5.79 ! [F: nat > real] :
% 5.46/5.79 ( ( suminf_real
% 5.46/5.79 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 5.46/5.79 = ( F @ zero_zero_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % powser_zero
% 5.46/5.79 thf(fact_8815_divmod__algorithm__code_I3_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.46/5.79 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(3)
% 5.46/5.79 thf(fact_8816_divmod__algorithm__code_I3_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.46/5.79 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(3)
% 5.46/5.79 thf(fact_8817_divmod__algorithm__code_I3_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.46/5.79 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(3)
% 5.46/5.79 thf(fact_8818_divmod__algorithm__code_I4_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.46/5.79 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(4)
% 5.46/5.79 thf(fact_8819_divmod__algorithm__code_I4_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.46/5.79 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(4)
% 5.46/5.79 thf(fact_8820_divmod__algorithm__code_I4_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.46/5.79 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(4)
% 5.46/5.79 thf(fact_8821_divmod__algorithm__code_I8_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( ( ord_less_num @ M @ N )
% 5.46/5.79 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.46/5.79 & ( ~ ( ord_less_num @ M @ N )
% 5.46/5.79 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(8)
% 5.46/5.79 thf(fact_8822_divmod__algorithm__code_I8_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( ( ord_less_num @ M @ N )
% 5.46/5.79 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.46/5.79 & ( ~ ( ord_less_num @ M @ N )
% 5.46/5.79 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(8)
% 5.46/5.79 thf(fact_8823_divmod__algorithm__code_I8_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( ( ord_less_num @ M @ N )
% 5.46/5.79 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.46/5.79 & ( ~ ( ord_less_num @ M @ N )
% 5.46/5.79 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.79 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_algorithm_code(8)
% 5.46/5.79 thf(fact_8824_divmod__int__def,axiom,
% 5.46/5.79 ( unique5052692396658037445od_int
% 5.46/5.79 = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_int_def
% 5.46/5.79 thf(fact_8825_divmod__def,axiom,
% 5.46/5.79 ( unique5052692396658037445od_int
% 5.46/5.79 = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_def
% 5.46/5.79 thf(fact_8826_divmod__def,axiom,
% 5.46/5.79 ( unique5055182867167087721od_nat
% 5.46/5.79 = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_def
% 5.46/5.79 thf(fact_8827_divmod__def,axiom,
% 5.46/5.79 ( unique3479559517661332726nteger
% 5.46/5.79 = ( ^ [M6: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_def
% 5.46/5.79 thf(fact_8828_divmod_H__nat__def,axiom,
% 5.46/5.79 ( unique5055182867167087721od_nat
% 5.46/5.79 = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod'_nat_def
% 5.46/5.79 thf(fact_8829_divmod__divmod__step,axiom,
% 5.46/5.79 ( unique5055182867167087721od_nat
% 5.46/5.79 = ( ^ [M6: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_divmod_step
% 5.46/5.79 thf(fact_8830_divmod__divmod__step,axiom,
% 5.46/5.79 ( unique5052692396658037445od_int
% 5.46/5.79 = ( ^ [M6: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_divmod_step
% 5.46/5.79 thf(fact_8831_divmod__divmod__step,axiom,
% 5.46/5.79 ( unique3479559517661332726nteger
% 5.46/5.79 = ( ^ [M6: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_divmod_step
% 5.46/5.79 thf(fact_8832_pi__series,axiom,
% 5.46/5.79 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.46/5.79 = ( suminf_real
% 5.46/5.79 @ ^ [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 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % pi_series
% 5.46/5.79 thf(fact_8833_vebt__member_Opelims_I3_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.79 ( ~ ( vEBT_vebt_member @ X4 @ Xa )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) )
% 5.46/5.79 => ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => A5 )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => B5 )
% 5.46/5.79 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.46/5.79 => ( ! [Uu2: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) @ Xa ) ) )
% 5.46/5.79 => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz ) @ Xa ) ) )
% 5.46/5.79 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa ) ) )
% 5.46/5.79 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) )
% 5.46/5.79 => ( ( Xa != Mi2 )
% 5.46/5.79 => ( ( Xa != Ma2 )
% 5.46/5.79 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.79 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.79 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.79 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.79 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_member.pelims(3)
% 5.46/5.79 thf(fact_8834_vebt__member_Opelims_I1_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.46/5.79 ( ( ( vEBT_vebt_member @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => A5 )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => B5 )
% 5.46/5.79 & ( Xa = one_one_nat ) ) ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [Uu2: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) )
% 5.46/5.79 => ( ~ Y3
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz ) )
% 5.46/5.79 => ( ~ Y3
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.46/5.79 => ( ~ Y3
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa ) ) ) )
% 5.46/5.79 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( ( Xa != Mi2 )
% 5.46/5.79 => ( ( Xa != Ma2 )
% 5.46/5.79 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.79 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.79 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.79 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.79 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_member.pelims(1)
% 5.46/5.79 thf(fact_8835_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.46/5.79 ( ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => A5 )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => B5 )
% 5.46/5.79 & ( Xa = one_one_nat ) ) ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [Uu2: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv @ Uw ) )
% 5.46/5.79 => ( ~ Y3
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv @ Uw ) @ Xa ) ) ) )
% 5.46/5.79 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ Xa ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.naive_member.pelims(1)
% 5.46/5.79 thf(fact_8836_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.79 ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) )
% 5.46/5.79 => ~ ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => A5 )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => B5 )
% 5.46/5.79 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.46/5.79 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ Xa ) )
% 5.46/5.79 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.naive_member.pelims(2)
% 5.46/5.79 thf(fact_8837_vebt__member_Opelims_I2_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.79 ( ( vEBT_vebt_member @ X4 @ Xa )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) )
% 5.46/5.79 => ~ ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => A5 )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => B5 )
% 5.46/5.79 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.46/5.79 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) )
% 5.46/5.79 => ~ ( ( Xa != Mi2 )
% 5.46/5.79 => ( ( Xa != Ma2 )
% 5.46/5.79 => ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.79 & ( ~ ( ord_less_nat @ Xa @ Mi2 )
% 5.46/5.79 => ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.79 & ( ~ ( ord_less_nat @ Ma2 @ Xa )
% 5.46/5.79 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_member.pelims(2)
% 5.46/5.79 thf(fact_8838_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.79 ( ~ ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) )
% 5.46/5.79 => ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => A5 )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => B5 )
% 5.46/5.79 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.46/5.79 => ( ! [Uu2: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv @ Uw ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv @ Uw ) @ Xa ) ) )
% 5.46/5.79 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList3 @ S3 ) @ Xa ) )
% 5.46/5.79 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.naive_member.pelims(3)
% 5.46/5.79 thf(fact_8839_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.46/5.79 ( ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [Uu2: $o,Uv: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ Uu2 @ Uv ) )
% 5.46/5.79 => ( ~ Y3
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 5.46/5.79 => ( ~ Y3
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( ( Xa = Mi2 )
% 5.46/5.79 | ( Xa = Ma2 ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( ( Xa = Mi2 )
% 5.46/5.79 | ( Xa = Ma2 )
% 5.46/5.79 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ Xa ) ) ) )
% 5.46/5.79 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.membermima.pelims(1)
% 5.46/5.79 thf(fact_8840_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.79 ( ~ ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [Uu2: $o,Uv: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ Uu2 @ Uv ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv ) @ Xa ) ) )
% 5.46/5.79 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) @ Xa ) ) )
% 5.46/5.79 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 5.46/5.79 => ( ( Xa = Mi2 )
% 5.46/5.79 | ( Xa = Ma2 ) ) ) )
% 5.46/5.79 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ Xa ) )
% 5.46/5.79 => ( ( Xa = Mi2 )
% 5.46/5.79 | ( Xa = Ma2 )
% 5.46/5.79 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.46/5.79 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ Xa ) )
% 5.46/5.79 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.membermima.pelims(3)
% 5.46/5.79 thf(fact_8841_suminf__geometric,axiom,
% 5.46/5.79 ! [C: real] :
% 5.46/5.79 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.46/5.79 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.46/5.79 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % suminf_geometric
% 5.46/5.79 thf(fact_8842_suminf__geometric,axiom,
% 5.46/5.79 ! [C: complex] :
% 5.46/5.79 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.46/5.79 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.46/5.79 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % suminf_geometric
% 5.46/5.79 thf(fact_8843_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.79 ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 5.46/5.79 => ~ ( ( Xa = Mi2 )
% 5.46/5.79 | ( Xa = Ma2 ) ) ) )
% 5.46/5.79 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList3 @ Vc2 ) @ Xa ) )
% 5.46/5.79 => ~ ( ( Xa = Mi2 )
% 5.46/5.79 | ( Xa = Ma2 )
% 5.46/5.79 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.46/5.79 => ~ ! [V3: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList3 @ Vd2 ) @ Xa ) )
% 5.46/5.79 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.79 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.membermima.pelims(2)
% 5.46/5.79 thf(fact_8844_minus__one__div__numeral,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % minus_one_div_numeral
% 5.46/5.79 thf(fact_8845_one__div__minus__numeral,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % one_div_minus_numeral
% 5.46/5.79 thf(fact_8846_dvd__numeral__simp,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.79 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % dvd_numeral_simp
% 5.46/5.79 thf(fact_8847_dvd__numeral__simp,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.79 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % dvd_numeral_simp
% 5.46/5.79 thf(fact_8848_dvd__numeral__simp,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.46/5.79 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % dvd_numeral_simp
% 5.46/5.79 thf(fact_8849_minus__numeral__div__numeral,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % minus_numeral_div_numeral
% 5.46/5.79 thf(fact_8850_divides__aux__eq,axiom,
% 5.46/5.79 ! [Q2: nat,R2: nat] :
% 5.46/5.79 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.46/5.79 = ( R2 = zero_zero_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % divides_aux_eq
% 5.46/5.79 thf(fact_8851_divides__aux__eq,axiom,
% 5.46/5.79 ! [Q2: int,R2: int] :
% 5.46/5.79 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.79 = ( R2 = zero_zero_int ) ) ).
% 5.46/5.79
% 5.46/5.79 % divides_aux_eq
% 5.46/5.79 thf(fact_8852_Divides_Oadjust__div__eq,axiom,
% 5.46/5.79 ! [Q2: int,R2: int] :
% 5.46/5.79 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.79 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Divides.adjust_div_eq
% 5.46/5.79 thf(fact_8853_numeral__div__minus__numeral,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % numeral_div_minus_numeral
% 5.46/5.79 thf(fact_8854_neg__eucl__rel__int__mult__2,axiom,
% 5.46/5.79 ! [B2: int,A: int,Q2: int,R2: int] :
% 5.46/5.79 ( ( ord_less_eq_int @ B2 @ zero_zero_int )
% 5.46/5.79 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.79 => ( 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 ) ) @ B2 ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % neg_eucl_rel_int_mult_2
% 5.46/5.79 thf(fact_8855_summable__arctan__series,axiom,
% 5.46/5.79 ! [X4: real] :
% 5.46/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.79 => ( summable_real
% 5.46/5.79 @ ^ [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 @ X4 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % summable_arctan_series
% 5.46/5.79 thf(fact_8856_pos__eucl__rel__int__mult__2,axiom,
% 5.46/5.79 ! [B2: int,A: int,Q2: int,R2: int] :
% 5.46/5.79 ( ( ord_less_eq_int @ zero_zero_int @ B2 )
% 5.46/5.79 => ( ( eucl_rel_int @ A @ B2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.79 => ( 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 ) ) @ B2 ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % pos_eucl_rel_int_mult_2
% 5.46/5.79 thf(fact_8857_product__nth,axiom,
% 5.46/5.79 ! [N: nat,Xs2: list_num,Ys2: list_num] :
% 5.46/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys2 ) ) )
% 5.46/5.79 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys2 ) @ N )
% 5.46/5.79 = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys2 ) ) ) @ ( nth_num @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % product_nth
% 5.46/5.79 thf(fact_8858_product__nth,axiom,
% 5.46/5.79 ! [N: nat,Xs2: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.46/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 5.46/5.79 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys2 ) @ N )
% 5.46/5.79 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) @ ( nth_VEBT_VEBT @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % product_nth
% 5.46/5.79 thf(fact_8859_product__nth,axiom,
% 5.46/5.79 ! [N: nat,Xs2: list_VEBT_VEBT,Ys2: list_o] :
% 5.46/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys2 ) ) )
% 5.46/5.79 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys2 ) @ N )
% 5.46/5.79 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) @ ( nth_o @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % product_nth
% 5.46/5.79 thf(fact_8860_product__nth,axiom,
% 5.46/5.79 ! [N: nat,Xs2: list_VEBT_VEBT,Ys2: list_nat] :
% 5.46/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys2 ) ) )
% 5.46/5.79 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys2 ) @ N )
% 5.46/5.79 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) @ ( nth_nat @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % product_nth
% 5.46/5.79 thf(fact_8861_product__nth,axiom,
% 5.46/5.79 ! [N: nat,Xs2: list_VEBT_VEBT,Ys2: list_int] :
% 5.46/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys2 ) ) )
% 5.46/5.79 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys2 ) @ N )
% 5.46/5.79 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) @ ( nth_int @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % product_nth
% 5.46/5.79 thf(fact_8862_product__nth,axiom,
% 5.46/5.79 ! [N: nat,Xs2: list_o,Ys2: list_VEBT_VEBT] :
% 5.46/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) )
% 5.46/5.79 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys2 ) @ N )
% 5.46/5.79 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) @ ( nth_VEBT_VEBT @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % product_nth
% 5.46/5.79 thf(fact_8863_product__nth,axiom,
% 5.46/5.79 ! [N: nat,Xs2: list_o,Ys2: list_o] :
% 5.46/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys2 ) ) )
% 5.46/5.79 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys2 ) @ N )
% 5.46/5.79 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) @ ( nth_o @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % product_nth
% 5.46/5.79 thf(fact_8864_product__nth,axiom,
% 5.46/5.79 ! [N: nat,Xs2: list_o,Ys2: list_nat] :
% 5.46/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys2 ) ) )
% 5.46/5.79 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys2 ) @ N )
% 5.46/5.79 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) @ ( nth_nat @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % product_nth
% 5.46/5.79 thf(fact_8865_product__nth,axiom,
% 5.46/5.79 ! [N: nat,Xs2: list_o,Ys2: list_int] :
% 5.46/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys2 ) ) )
% 5.46/5.79 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys2 ) @ N )
% 5.46/5.79 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) @ ( nth_int @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % product_nth
% 5.46/5.79 thf(fact_8866_product__nth,axiom,
% 5.46/5.79 ! [N: nat,Xs2: list_nat,Ys2: list_num] :
% 5.46/5.79 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_num @ Ys2 ) ) )
% 5.46/5.79 => ( ( nth_Pr8326237132889035090at_num @ ( product_nat_num @ Xs2 @ Ys2 ) @ N )
% 5.46/5.79 = ( product_Pair_nat_num @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys2 ) ) ) @ ( nth_num @ Ys2 @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % product_nth
% 5.46/5.79 thf(fact_8867_summable__iff__shift,axiom,
% 5.46/5.79 ! [F: nat > real,K: nat] :
% 5.46/5.79 ( ( summable_real
% 5.46/5.79 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.46/5.79 = ( summable_real @ F ) ) ).
% 5.46/5.79
% 5.46/5.79 % summable_iff_shift
% 5.46/5.79 thf(fact_8868_summable__cmult__iff,axiom,
% 5.46/5.79 ! [C: real,F: nat > real] :
% 5.46/5.79 ( ( summable_real
% 5.46/5.79 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.46/5.79 = ( ( C = zero_zero_real )
% 5.46/5.79 | ( summable_real @ F ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % summable_cmult_iff
% 5.46/5.79 thf(fact_8869_summable__divide__iff,axiom,
% 5.46/5.79 ! [F: nat > complex,C: complex] :
% 5.46/5.79 ( ( summable_complex
% 5.46/5.79 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.46/5.79 = ( ( C = zero_zero_complex )
% 5.46/5.79 | ( summable_complex @ F ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % summable_divide_iff
% 5.46/5.79 thf(fact_8870_summable__divide__iff,axiom,
% 5.46/5.79 ! [F: nat > real,C: real] :
% 5.46/5.79 ( ( summable_real
% 5.46/5.79 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.46/5.79 = ( ( C = zero_zero_real )
% 5.46/5.79 | ( summable_real @ F ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % summable_divide_iff
% 5.46/5.79 thf(fact_8871_length__product,axiom,
% 5.46/5.79 ! [Xs2: list_VEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 5.46/5.79 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys2 ) )
% 5.46/5.79 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % length_product
% 5.46/5.79 thf(fact_8872_length__product,axiom,
% 5.46/5.79 ! [Xs2: list_VEBT_VEBT,Ys2: list_o] :
% 5.46/5.79 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys2 ) )
% 5.46/5.79 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % length_product
% 5.46/5.79 thf(fact_8873_length__product,axiom,
% 5.46/5.79 ! [Xs2: list_VEBT_VEBT,Ys2: list_nat] :
% 5.46/5.79 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys2 ) )
% 5.46/5.79 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % length_product
% 5.46/5.79 thf(fact_8874_length__product,axiom,
% 5.46/5.79 ! [Xs2: list_VEBT_VEBT,Ys2: list_int] :
% 5.46/5.79 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys2 ) )
% 5.46/5.79 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % length_product
% 5.46/5.79 thf(fact_8875_length__product,axiom,
% 5.46/5.79 ! [Xs2: list_o,Ys2: list_VEBT_VEBT] :
% 5.46/5.79 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys2 ) )
% 5.46/5.79 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % length_product
% 5.46/5.79 thf(fact_8876_length__product,axiom,
% 5.46/5.79 ! [Xs2: list_o,Ys2: list_o] :
% 5.46/5.79 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys2 ) )
% 5.46/5.79 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % length_product
% 5.46/5.79 thf(fact_8877_length__product,axiom,
% 5.46/5.79 ! [Xs2: list_o,Ys2: list_nat] :
% 5.46/5.79 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys2 ) )
% 5.46/5.79 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % length_product
% 5.46/5.79 thf(fact_8878_length__product,axiom,
% 5.46/5.79 ! [Xs2: list_o,Ys2: list_int] :
% 5.46/5.79 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys2 ) )
% 5.46/5.79 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % length_product
% 5.46/5.79 thf(fact_8879_length__product,axiom,
% 5.46/5.79 ! [Xs2: list_nat,Ys2: list_VEBT_VEBT] :
% 5.46/5.79 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys2 ) )
% 5.46/5.79 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % length_product
% 5.46/5.79 thf(fact_8880_length__product,axiom,
% 5.46/5.79 ! [Xs2: list_nat,Ys2: list_o] :
% 5.46/5.79 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys2 ) )
% 5.46/5.79 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % length_product
% 5.46/5.79 thf(fact_8881_summable__geometric__iff,axiom,
% 5.46/5.79 ! [C: complex] :
% 5.46/5.79 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.46/5.79 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % summable_geometric_iff
% 5.46/5.79 thf(fact_8882_unique__quotient,axiom,
% 5.46/5.79 ! [A: int,B2: int,Q2: int,R2: int,Q5: int,R4: int] :
% 5.46/5.79 ( ( eucl_rel_int @ A @ B2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.79 => ( ( eucl_rel_int @ A @ B2 @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.46/5.79 => ( Q2 = Q5 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % unique_quotient
% 5.46/5.79 thf(fact_8883_unique__remainder,axiom,
% 5.46/5.79 ! [A: int,B2: int,Q2: int,R2: int,Q5: int,R4: int] :
% 5.46/5.79 ( ( eucl_rel_int @ A @ B2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.79 => ( ( eucl_rel_int @ A @ B2 @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.46/5.79 => ( R2 = R4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % unique_remainder
% 5.46/5.79 thf(fact_8884_eucl__rel__int__by0,axiom,
% 5.46/5.79 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.46/5.79
% 5.46/5.79 % eucl_rel_int_by0
% 5.46/5.79 thf(fact_8885_summable__rabs__comparison__test,axiom,
% 5.46/5.79 ! [F: nat > real,G: nat > real] :
% 5.46/5.79 ( ? [N7: nat] :
% 5.46/5.79 ! [N4: nat] :
% 5.46/5.79 ( ( ord_less_eq_nat @ N7 @ N4 )
% 5.46/5.79 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N4 ) ) @ ( G @ N4 ) ) )
% 5.46/5.79 => ( ( summable_real @ G )
% 5.46/5.79 => ( summable_real
% 5.46/5.79 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % summable_rabs_comparison_test
% 5.46/5.79 thf(fact_8886_div__int__unique,axiom,
% 5.46/5.79 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.46/5.79 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.79 => ( ( divide_divide_int @ K @ L2 )
% 5.46/5.79 = Q2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % div_int_unique
% 5.46/5.79 thf(fact_8887_mod__int__unique,axiom,
% 5.46/5.79 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.46/5.79 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.79 => ( ( modulo_modulo_int @ K @ L2 )
% 5.46/5.79 = R2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % mod_int_unique
% 5.46/5.79 thf(fact_8888_summable__rabs,axiom,
% 5.46/5.79 ! [F: nat > real] :
% 5.46/5.79 ( ( summable_real
% 5.46/5.79 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 5.46/5.79 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.46/5.79 @ ( suminf_real
% 5.46/5.79 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % summable_rabs
% 5.46/5.79 thf(fact_8889_eucl__rel__int__dividesI,axiom,
% 5.46/5.79 ! [L2: int,K: int,Q2: int] :
% 5.46/5.79 ( ( L2 != zero_zero_int )
% 5.46/5.79 => ( ( K
% 5.46/5.79 = ( times_times_int @ Q2 @ L2 ) )
% 5.46/5.79 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % eucl_rel_int_dividesI
% 5.46/5.79 thf(fact_8890_eucl__rel__int,axiom,
% 5.46/5.79 ! [K: int,L2: int] : ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L2 ) @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % eucl_rel_int
% 5.46/5.79 thf(fact_8891_summable__power__series,axiom,
% 5.46/5.79 ! [F: nat > real,Z: real] :
% 5.46/5.79 ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 5.46/5.79 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.46/5.79 => ( ( ord_less_real @ Z @ one_one_real )
% 5.46/5.79 => ( summable_real
% 5.46/5.79 @ ^ [I2: nat] : ( times_times_real @ ( F @ I2 ) @ ( power_power_real @ Z @ I2 ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % summable_power_series
% 5.46/5.79 thf(fact_8892_zminus1__lemma,axiom,
% 5.46/5.79 ! [A: int,B2: int,Q2: int,R2: int] :
% 5.46/5.79 ( ( eucl_rel_int @ A @ B2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.79 => ( ( B2 != zero_zero_int )
% 5.46/5.79 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B2 @ ( 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 @ B2 @ R2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % zminus1_lemma
% 5.46/5.79 thf(fact_8893_eucl__rel__int__iff,axiom,
% 5.46/5.79 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.46/5.79 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.46/5.79 = ( ( K
% 5.46/5.79 = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R2 ) )
% 5.46/5.79 & ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.79 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.46/5.79 & ( ord_less_int @ R2 @ L2 ) ) )
% 5.46/5.79 & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 5.46/5.79 => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.46/5.79 => ( ( ord_less_int @ L2 @ R2 )
% 5.46/5.79 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 5.46/5.79 & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 5.46/5.79 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % eucl_rel_int_iff
% 5.46/5.79 thf(fact_8894_eucl__rel__int__remainderI,axiom,
% 5.46/5.79 ! [R2: int,L2: int,K: int,Q2: int] :
% 5.46/5.79 ( ( ( sgn_sgn_int @ R2 )
% 5.46/5.79 = ( sgn_sgn_int @ L2 ) )
% 5.46/5.79 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L2 ) )
% 5.46/5.79 => ( ( K
% 5.46/5.79 = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R2 ) )
% 5.46/5.79 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % eucl_rel_int_remainderI
% 5.46/5.79 thf(fact_8895_eucl__rel__int_Osimps,axiom,
% 5.46/5.79 ( eucl_rel_int
% 5.46/5.79 = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 5.46/5.79 ( ? [K3: int] :
% 5.46/5.79 ( ( A1 = K3 )
% 5.46/5.79 & ( A22 = zero_zero_int )
% 5.46/5.79 & ( A32
% 5.46/5.79 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.46/5.79 | ? [L: int,K3: int,Q4: int] :
% 5.46/5.79 ( ( A1 = K3 )
% 5.46/5.79 & ( A22 = L )
% 5.46/5.79 & ( A32
% 5.46/5.79 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.46/5.79 & ( L != zero_zero_int )
% 5.46/5.79 & ( K3
% 5.46/5.79 = ( times_times_int @ Q4 @ L ) ) )
% 5.46/5.79 | ? [R5: int,L: int,K3: int,Q4: int] :
% 5.46/5.79 ( ( A1 = K3 )
% 5.46/5.79 & ( A22 = L )
% 5.46/5.79 & ( A32
% 5.46/5.79 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.46/5.79 & ( ( sgn_sgn_int @ R5 )
% 5.46/5.79 = ( sgn_sgn_int @ L ) )
% 5.46/5.79 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 5.46/5.79 & ( K3
% 5.46/5.79 = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R5 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % eucl_rel_int.simps
% 5.46/5.79 thf(fact_8896_eucl__rel__int_Ocases,axiom,
% 5.46/5.79 ! [A12: int,A23: int,A33: product_prod_int_int] :
% 5.46/5.79 ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 5.46/5.79 => ( ( ( A23 = zero_zero_int )
% 5.46/5.79 => ( A33
% 5.46/5.79 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.46/5.79 => ( ! [Q3: int] :
% 5.46/5.79 ( ( A33
% 5.46/5.79 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.46/5.79 => ( ( A23 != zero_zero_int )
% 5.46/5.79 => ( A12
% 5.46/5.79 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 5.46/5.79 => ~ ! [R3: int,Q3: int] :
% 5.46/5.79 ( ( A33
% 5.46/5.79 = ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.46/5.79 => ( ( ( sgn_sgn_int @ R3 )
% 5.46/5.79 = ( sgn_sgn_int @ A23 ) )
% 5.46/5.79 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A23 ) )
% 5.46/5.79 => ( A12
% 5.46/5.79 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % eucl_rel_int.cases
% 5.46/5.79 thf(fact_8897_and__int_Oelims,axiom,
% 5.46/5.79 ! [X4: int,Xa: int,Y3: int] :
% 5.46/5.79 ( ( ( bit_se725231765392027082nd_int @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ( ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.79 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( uminus_uminus_int
% 5.46/5.79 @ ( zero_n2684676970156552555ol_int
% 5.46/5.79 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 5.46/5.79 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.46/5.79 & ( ~ ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.79 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( plus_plus_int
% 5.46/5.79 @ ( zero_n2684676970156552555ol_int
% 5.46/5.79 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 5.46/5.79 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.46/5.79 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % and_int.elims
% 5.46/5.79 thf(fact_8898_and__int_Osimps,axiom,
% 5.46/5.79 ( bit_se725231765392027082nd_int
% 5.46/5.79 = ( ^ [K3: int,L: int] :
% 5.46/5.79 ( if_int
% 5.46/5.79 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.79 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.79 @ ( uminus_uminus_int
% 5.46/5.79 @ ( zero_n2684676970156552555ol_int
% 5.46/5.79 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.46/5.79 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.46/5.79 @ ( plus_plus_int
% 5.46/5.79 @ ( zero_n2684676970156552555ol_int
% 5.46/5.79 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.46/5.79 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.46/5.79 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % and_int.simps
% 5.46/5.79 thf(fact_8899_vebt__buildup_Oelims,axiom,
% 5.46/5.79 ! [X4: nat,Y3: vEBT_VEBT] :
% 5.46/5.79 ( ( ( vEBT_vebt_buildup @ X4 )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ( ( X4 = zero_zero_nat )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.46/5.79 => ( ( ( X4
% 5.46/5.79 = ( suc @ zero_zero_nat ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.46/5.79 => ~ ! [Va: nat] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( suc @ ( suc @ Va ) ) )
% 5.46/5.79 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( 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 ) ) ) ) ) ) )
% 5.46/5.79 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_buildup.elims
% 5.46/5.79 thf(fact_8900_sin__paired,axiom,
% 5.46/5.79 ! [X4: real] :
% 5.46/5.79 ( sums_real
% 5.46/5.79 @ ^ [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 @ X4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.46/5.79 @ ( sin_real @ X4 ) ) ).
% 5.46/5.79
% 5.46/5.79 % sin_paired
% 5.46/5.79 thf(fact_8901_atLeastAtMostPlus1__int__conv,axiom,
% 5.46/5.79 ! [M: int,N: int] :
% 5.46/5.79 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.46/5.79 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.46/5.79 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeastAtMostPlus1_int_conv
% 5.46/5.79 thf(fact_8902_simp__from__to,axiom,
% 5.46/5.79 ( set_or1266510415728281911st_int
% 5.46/5.79 = ( ^ [I2: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I2 ) @ bot_bot_set_int @ ( insert_int @ I2 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % simp_from_to
% 5.46/5.79 thf(fact_8903_power__half__series,axiom,
% 5.46/5.79 ( sums_real
% 5.46/5.79 @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 5.46/5.79 @ one_one_real ) ).
% 5.46/5.79
% 5.46/5.79 % power_half_series
% 5.46/5.79 thf(fact_8904_sums__if_H,axiom,
% 5.46/5.79 ! [G: nat > real,X4: real] :
% 5.46/5.79 ( ( sums_real @ G @ X4 )
% 5.46/5.79 => ( sums_real
% 5.46/5.79 @ ^ [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 ) ) ) ) )
% 5.46/5.79 @ X4 ) ) ).
% 5.46/5.79
% 5.46/5.79 % sums_if'
% 5.46/5.79 thf(fact_8905_sums__if,axiom,
% 5.46/5.79 ! [G: nat > real,X4: real,F: nat > real,Y3: real] :
% 5.46/5.79 ( ( sums_real @ G @ X4 )
% 5.46/5.79 => ( ( sums_real @ F @ Y3 )
% 5.46/5.79 => ( sums_real
% 5.46/5.79 @ ^ [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 ) ) ) ) )
% 5.46/5.79 @ ( plus_plus_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % sums_if
% 5.46/5.79 thf(fact_8906_cos__paired,axiom,
% 5.46/5.79 ! [X4: real] :
% 5.46/5.79 ( sums_real
% 5.46/5.79 @ ^ [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 @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.79 @ ( cos_real @ X4 ) ) ).
% 5.46/5.79
% 5.46/5.79 % cos_paired
% 5.46/5.79 thf(fact_8907_vebt__buildup_Osimps_I3_J,axiom,
% 5.46/5.79 ! [Va2: nat] :
% 5.46/5.79 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.46/5.79 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.46/5.79 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.46/5.79 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_buildup.simps(3)
% 5.46/5.79 thf(fact_8908_and__int_Opelims,axiom,
% 5.46/5.79 ! [X4: int,Xa: int,Y3: int] :
% 5.46/5.79 ( ( ( bit_se725231765392027082nd_int @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X4 @ Xa ) )
% 5.46/5.79 => ~ ( ( ( ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.79 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( uminus_uminus_int
% 5.46/5.79 @ ( zero_n2684676970156552555ol_int
% 5.46/5.79 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 5.46/5.79 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.46/5.79 & ( ~ ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.79 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( plus_plus_int
% 5.46/5.79 @ ( zero_n2684676970156552555ol_int
% 5.46/5.79 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 5.46/5.79 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.46/5.79 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.46/5.79 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X4 @ Xa ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % and_int.pelims
% 5.46/5.79 thf(fact_8909_and__int_Opsimps,axiom,
% 5.46/5.79 ! [K: int,L2: int] :
% 5.46/5.79 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 5.46/5.79 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.79 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.79 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.46/5.79 = ( uminus_uminus_int
% 5.46/5.79 @ ( zero_n2684676970156552555ol_int
% 5.46/5.79 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.46/5.79 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 5.46/5.79 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.79 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.79 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.46/5.79 = ( plus_plus_int
% 5.46/5.79 @ ( zero_n2684676970156552555ol_int
% 5.46/5.79 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.46/5.79 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.46/5.79 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % and_int.psimps
% 5.46/5.79 thf(fact_8910_obtain__set__succ,axiom,
% 5.46/5.79 ! [X4: nat,Z: nat,A3: set_nat,B4: set_nat] :
% 5.46/5.79 ( ( ord_less_nat @ X4 @ Z )
% 5.46/5.79 => ( ( vEBT_VEBT_max_in_set @ A3 @ Z )
% 5.46/5.79 => ( ( finite_finite_nat @ B4 )
% 5.46/5.79 => ( ( A3 = B4 )
% 5.46/5.79 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A3 @ X4 @ X_1 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % obtain_set_succ
% 5.46/5.79 thf(fact_8911_set__vebt__finite,axiom,
% 5.46/5.79 ! [T: vEBT_VEBT,N: nat] :
% 5.46/5.79 ( ( vEBT_invar_vebt @ T @ N )
% 5.46/5.79 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % set_vebt_finite
% 5.46/5.79 thf(fact_8912_succ__none__empty,axiom,
% 5.46/5.79 ! [Xs2: set_nat,A: nat] :
% 5.46/5.79 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_1 )
% 5.46/5.79 => ( ( finite_finite_nat @ Xs2 )
% 5.46/5.79 => ~ ? [X5: nat] :
% 5.46/5.79 ( ( member_nat @ X5 @ Xs2 )
% 5.46/5.79 & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % succ_none_empty
% 5.46/5.79 thf(fact_8913_finite__atLeastAtMost,axiom,
% 5.46/5.79 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_atLeastAtMost
% 5.46/5.79 thf(fact_8914_finite__nat__set__iff__bounded,axiom,
% 5.46/5.79 ( finite_finite_nat
% 5.46/5.79 = ( ^ [N8: set_nat] :
% 5.46/5.79 ? [M6: nat] :
% 5.46/5.79 ! [X: nat] :
% 5.46/5.79 ( ( member_nat @ X @ N8 )
% 5.46/5.79 => ( ord_less_nat @ X @ M6 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_nat_set_iff_bounded
% 5.46/5.79 thf(fact_8915_bounded__nat__set__is__finite,axiom,
% 5.46/5.79 ! [N3: set_nat,N: nat] :
% 5.46/5.79 ( ! [X3: nat] :
% 5.46/5.79 ( ( member_nat @ X3 @ N3 )
% 5.46/5.79 => ( ord_less_nat @ X3 @ N ) )
% 5.46/5.79 => ( finite_finite_nat @ N3 ) ) ).
% 5.46/5.79
% 5.46/5.79 % bounded_nat_set_is_finite
% 5.46/5.79 thf(fact_8916_finite__nat__set__iff__bounded__le,axiom,
% 5.46/5.79 ( finite_finite_nat
% 5.46/5.79 = ( ^ [N8: set_nat] :
% 5.46/5.79 ? [M6: nat] :
% 5.46/5.79 ! [X: nat] :
% 5.46/5.79 ( ( member_nat @ X @ N8 )
% 5.46/5.79 => ( ord_less_eq_nat @ X @ M6 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_nat_set_iff_bounded_le
% 5.46/5.79 thf(fact_8917_finite__M__bounded__by__nat,axiom,
% 5.46/5.79 ! [P: nat > $o,I: nat] :
% 5.46/5.79 ( finite_finite_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [K3: nat] :
% 5.46/5.79 ( ( P @ K3 )
% 5.46/5.79 & ( ord_less_nat @ K3 @ I ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_M_bounded_by_nat
% 5.46/5.79 thf(fact_8918_finite__less__ub,axiom,
% 5.46/5.79 ! [F: nat > nat,U: nat] :
% 5.46/5.79 ( ! [N4: nat] : ( ord_less_eq_nat @ N4 @ ( F @ N4 ) )
% 5.46/5.79 => ( finite_finite_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_less_ub
% 5.46/5.79 thf(fact_8919_atLeast0__atMost__Suc,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.46/5.79 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeast0_atMost_Suc
% 5.46/5.79 thf(fact_8920_Icc__eq__insert__lb__nat,axiom,
% 5.46/5.79 ! [M: nat,N: nat] :
% 5.46/5.79 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.79 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.46/5.79 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Icc_eq_insert_lb_nat
% 5.46/5.79 thf(fact_8921_atLeastAtMostSuc__conv,axiom,
% 5.46/5.79 ! [M: nat,N: nat] :
% 5.46/5.79 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.46/5.79 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.46/5.79 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeastAtMostSuc_conv
% 5.46/5.79 thf(fact_8922_atLeastAtMost__insertL,axiom,
% 5.46/5.79 ! [M: nat,N: nat] :
% 5.46/5.79 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.79 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.46/5.79 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeastAtMost_insertL
% 5.46/5.79 thf(fact_8923_finite__divisors__nat,axiom,
% 5.46/5.79 ! [M: nat] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.79 => ( finite_finite_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_divisors_nat
% 5.46/5.79 thf(fact_8924_subset__eq__atLeast0__atMost__finite,axiom,
% 5.46/5.79 ! [N3: set_nat,N: nat] :
% 5.46/5.79 ( ( ord_less_eq_set_nat @ N3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.79 => ( finite_finite_nat @ N3 ) ) ).
% 5.46/5.79
% 5.46/5.79 % subset_eq_atLeast0_atMost_finite
% 5.46/5.79 thf(fact_8925_set__decode__plus__power__2,axiom,
% 5.46/5.79 ! [N: nat,Z: nat] :
% 5.46/5.79 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 5.46/5.79 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 5.46/5.79 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % set_decode_plus_power_2
% 5.46/5.79 thf(fact_8926_and__int_Opinduct,axiom,
% 5.46/5.79 ! [A0: int,A12: int,P: int > int > $o] :
% 5.46/5.79 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.46/5.79 => ( ! [K2: int,L3: int] :
% 5.46/5.79 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L3 ) )
% 5.46/5.79 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.46/5.79 & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.46/5.79 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.79 => ( P @ K2 @ L3 ) ) )
% 5.46/5.79 => ( P @ A0 @ A12 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % and_int.pinduct
% 5.46/5.79 thf(fact_8927_finite__Collect__le__nat,axiom,
% 5.46/5.79 ! [K: nat] :
% 5.46/5.79 ( finite_finite_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_Collect_le_nat
% 5.46/5.79 thf(fact_8928_finite__Collect__less__nat,axiom,
% 5.46/5.79 ! [K: nat] :
% 5.46/5.79 ( finite_finite_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_Collect_less_nat
% 5.46/5.79 thf(fact_8929_finite__atLeastAtMost__int,axiom,
% 5.46/5.79 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_atLeastAtMost_int
% 5.46/5.79 thf(fact_8930_finite__interval__int4,axiom,
% 5.46/5.79 ! [A: int,B2: int] :
% 5.46/5.79 ( finite_finite_int
% 5.46/5.79 @ ( collect_int
% 5.46/5.79 @ ^ [I2: int] :
% 5.46/5.79 ( ( ord_less_int @ A @ I2 )
% 5.46/5.79 & ( ord_less_int @ I2 @ B2 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_interval_int4
% 5.46/5.79 thf(fact_8931_finite__interval__int3,axiom,
% 5.46/5.79 ! [A: int,B2: int] :
% 5.46/5.79 ( finite_finite_int
% 5.46/5.79 @ ( collect_int
% 5.46/5.79 @ ^ [I2: int] :
% 5.46/5.79 ( ( ord_less_int @ A @ I2 )
% 5.46/5.79 & ( ord_less_eq_int @ I2 @ B2 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_interval_int3
% 5.46/5.79 thf(fact_8932_finite__interval__int2,axiom,
% 5.46/5.79 ! [A: int,B2: int] :
% 5.46/5.79 ( finite_finite_int
% 5.46/5.79 @ ( collect_int
% 5.46/5.79 @ ^ [I2: int] :
% 5.46/5.79 ( ( ord_less_eq_int @ A @ I2 )
% 5.46/5.79 & ( ord_less_int @ I2 @ B2 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_interval_int2
% 5.46/5.79 thf(fact_8933_finite__nth__roots,axiom,
% 5.46/5.79 ! [N: nat,C: complex] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( finite3207457112153483333omplex
% 5.46/5.79 @ ( collect_complex
% 5.46/5.79 @ ^ [Z5: complex] :
% 5.46/5.79 ( ( power_power_complex @ Z5 @ N )
% 5.46/5.79 = C ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_nth_roots
% 5.46/5.79 thf(fact_8934_set__encode__insert,axiom,
% 5.46/5.79 ! [A3: set_nat,N: nat] :
% 5.46/5.79 ( ( finite_finite_nat @ A3 )
% 5.46/5.79 => ( ~ ( member_nat @ N @ A3 )
% 5.46/5.79 => ( ( nat_set_encode @ ( insert_nat @ N @ A3 ) )
% 5.46/5.79 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A3 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % set_encode_insert
% 5.46/5.79 thf(fact_8935_upto_Opinduct,axiom,
% 5.46/5.79 ! [A0: int,A12: int,P: int > int > $o] :
% 5.46/5.79 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.46/5.79 => ( ! [I3: int,J2: int] :
% 5.46/5.79 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 5.46/5.79 => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 5.46/5.79 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 5.46/5.79 => ( P @ I3 @ J2 ) ) )
% 5.46/5.79 => ( P @ A0 @ A12 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % upto.pinduct
% 5.46/5.79 thf(fact_8936_set__encode__def,axiom,
% 5.46/5.79 ( nat_set_encode
% 5.46/5.79 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % set_encode_def
% 5.46/5.79 thf(fact_8937_mask__eq__sum__exp__nat,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.79 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % mask_eq_sum_exp_nat
% 5.46/5.79 thf(fact_8938_gauss__sum__nat,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [X: nat] : X
% 5.46/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.79 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % gauss_sum_nat
% 5.46/5.79 thf(fact_8939_arith__series__nat,axiom,
% 5.46/5.79 ! [A: nat,D: nat,N: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I2 @ D ) )
% 5.46/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.46/5.79 = ( 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 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % arith_series_nat
% 5.46/5.79 thf(fact_8940_Sum__Icc__nat,axiom,
% 5.46/5.79 ! [M: nat,N: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [X: nat] : X
% 5.46/5.79 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.46/5.79 = ( 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 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Sum_Icc_nat
% 5.46/5.79 thf(fact_8941_even__set__encode__iff,axiom,
% 5.46/5.79 ! [A3: set_nat] :
% 5.46/5.79 ( ( finite_finite_nat @ A3 )
% 5.46/5.79 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A3 ) )
% 5.46/5.79 = ( ~ ( member_nat @ zero_zero_nat @ A3 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % even_set_encode_iff
% 5.46/5.79 thf(fact_8942_Maclaurin__minus__cos__expansion,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.46/5.79 => ? [T2: real] :
% 5.46/5.79 ( ( ord_less_real @ X4 @ T2 )
% 5.46/5.79 & ( ord_less_real @ T2 @ zero_zero_real )
% 5.46/5.79 & ( ( cos_real @ X4 )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T2 @ ( 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 @ X4 @ N ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_minus_cos_expansion
% 5.46/5.79 thf(fact_8943_Maclaurin__cos__expansion2,axiom,
% 5.46/5.79 ! [X4: real,N: nat] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ? [T2: real] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ T2 )
% 5.46/5.79 & ( ord_less_real @ T2 @ X4 )
% 5.46/5.79 & ( ( cos_real @ X4 )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T2 @ ( 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 @ X4 @ N ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_cos_expansion2
% 5.46/5.79 thf(fact_8944_Maclaurin__sin__expansion3,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ? [T2: real] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ T2 )
% 5.46/5.79 & ( ord_less_real @ T2 @ X4 )
% 5.46/5.79 & ( ( sin_real @ X4 )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T2 @ ( 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 @ X4 @ N ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_sin_expansion3
% 5.46/5.79 thf(fact_8945_Maclaurin__sin__expansion4,axiom,
% 5.46/5.79 ! [X4: real,N: nat] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ? [T2: real] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ T2 )
% 5.46/5.79 & ( ord_less_eq_real @ T2 @ X4 )
% 5.46/5.79 & ( ( sin_real @ X4 )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T2 @ ( 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 @ X4 @ N ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_sin_expansion4
% 5.46/5.79 thf(fact_8946_finite__lessThan,axiom,
% 5.46/5.79 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_lessThan
% 5.46/5.79 thf(fact_8947_lessThan__0,axiom,
% 5.46/5.79 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.46/5.79 = bot_bot_set_nat ) ).
% 5.46/5.79
% 5.46/5.79 % lessThan_0
% 5.46/5.79 thf(fact_8948_sumr__cos__zero__one,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.46/5.79 = one_one_real ) ).
% 5.46/5.79
% 5.46/5.79 % sumr_cos_zero_one
% 5.46/5.79 thf(fact_8949_lessThan__Suc,axiom,
% 5.46/5.79 ! [K: nat] :
% 5.46/5.79 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.46/5.79 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % lessThan_Suc
% 5.46/5.79 thf(fact_8950_lessThan__empty__iff,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( ( set_ord_lessThan_nat @ N )
% 5.46/5.79 = bot_bot_set_nat )
% 5.46/5.79 = ( N = zero_zero_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % lessThan_empty_iff
% 5.46/5.79 thf(fact_8951_lessThan__nat__numeral,axiom,
% 5.46/5.79 ! [K: num] :
% 5.46/5.79 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.46/5.79 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % lessThan_nat_numeral
% 5.46/5.79 thf(fact_8952_sum__nth__roots,axiom,
% 5.46/5.79 ! [N: nat,C: complex] :
% 5.46/5.79 ( ( ord_less_nat @ one_one_nat @ N )
% 5.46/5.79 => ( ( groups7754918857620584856omplex
% 5.46/5.79 @ ^ [X: complex] : X
% 5.46/5.79 @ ( collect_complex
% 5.46/5.79 @ ^ [Z5: complex] :
% 5.46/5.79 ( ( power_power_complex @ Z5 @ N )
% 5.46/5.79 = C ) ) )
% 5.46/5.79 = zero_zero_complex ) ) ).
% 5.46/5.79
% 5.46/5.79 % sum_nth_roots
% 5.46/5.79 thf(fact_8953_sum__roots__unity,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( ord_less_nat @ one_one_nat @ N )
% 5.46/5.79 => ( ( groups7754918857620584856omplex
% 5.46/5.79 @ ^ [X: complex] : X
% 5.46/5.79 @ ( collect_complex
% 5.46/5.79 @ ^ [Z5: complex] :
% 5.46/5.79 ( ( power_power_complex @ Z5 @ N )
% 5.46/5.79 = one_one_complex ) ) )
% 5.46/5.79 = zero_zero_complex ) ) ).
% 5.46/5.79
% 5.46/5.79 % sum_roots_unity
% 5.46/5.79 thf(fact_8954_Maclaurin__lemma,axiom,
% 5.46/5.79 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.46/5.79 => ? [B8: real] :
% 5.46/5.79 ( ( F @ H2 )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_lemma
% 5.46/5.79 thf(fact_8955_sum__split__even__odd,axiom,
% 5.46/5.79 ! [F: nat > real,G: nat > real,N: nat] :
% 5.46/5.79 ( ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [I2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) @ ( F @ I2 ) @ ( G @ I2 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [I2: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [I2: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) @ one_one_nat ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % sum_split_even_odd
% 5.46/5.79 thf(fact_8956_Maclaurin__exp__le,axiom,
% 5.46/5.79 ! [X4: real,N: nat] :
% 5.46/5.79 ? [T2: real] :
% 5.46/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ T2 ) @ ( abs_abs_real @ X4 ) )
% 5.46/5.79 & ( ( exp_real @ X4 )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X4 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_exp_le
% 5.46/5.79 thf(fact_8957_Maclaurin__sin__bound,axiom,
% 5.46/5.79 ! [X4: real,N: nat] :
% 5.46/5.79 ( ord_less_eq_real
% 5.46/5.79 @ ( abs_abs_real
% 5.46/5.79 @ ( minus_minus_real @ ( sin_real @ X4 )
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.46/5.79 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X4 ) @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_sin_bound
% 5.46/5.79 thf(fact_8958_Sum__Icc__int,axiom,
% 5.46/5.79 ! [M: int,N: int] :
% 5.46/5.79 ( ( ord_less_eq_int @ M @ N )
% 5.46/5.79 => ( ( groups4538972089207619220nt_int
% 5.46/5.79 @ ^ [X: int] : X
% 5.46/5.79 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.46/5.79 = ( 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 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Sum_Icc_int
% 5.46/5.79 thf(fact_8959_sum__pos__lt__pair,axiom,
% 5.46/5.79 ! [F: nat > real,K: nat] :
% 5.46/5.79 ( ( summable_real @ F )
% 5.46/5.79 => ( ! [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 ) ) ) ) )
% 5.46/5.79 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % sum_pos_lt_pair
% 5.46/5.79 thf(fact_8960_Maclaurin__exp__lt,axiom,
% 5.46/5.79 ! [X4: real,N: nat] :
% 5.46/5.79 ( ( X4 != zero_zero_real )
% 5.46/5.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ? [T2: real] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T2 ) )
% 5.46/5.79 & ( ord_less_real @ ( abs_abs_real @ T2 ) @ ( abs_abs_real @ X4 ) )
% 5.46/5.79 & ( ( exp_real @ X4 )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X4 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_exp_lt
% 5.46/5.79 thf(fact_8961_Maclaurin__sin__expansion,axiom,
% 5.46/5.79 ! [X4: real,N: nat] :
% 5.46/5.79 ? [T2: real] :
% 5.46/5.79 ( ( sin_real @ X4 )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T2 @ ( 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 @ X4 @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_sin_expansion
% 5.46/5.79 thf(fact_8962_Maclaurin__sin__expansion2,axiom,
% 5.46/5.79 ! [X4: real,N: nat] :
% 5.46/5.79 ? [T2: real] :
% 5.46/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ T2 ) @ ( abs_abs_real @ X4 ) )
% 5.46/5.79 & ( ( sin_real @ X4 )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T2 @ ( 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 @ X4 @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_sin_expansion2
% 5.46/5.79 thf(fact_8963_Maclaurin__cos__expansion,axiom,
% 5.46/5.79 ! [X4: real,N: nat] :
% 5.46/5.79 ? [T2: real] :
% 5.46/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ T2 ) @ ( abs_abs_real @ X4 ) )
% 5.46/5.79 & ( ( cos_real @ X4 )
% 5.46/5.79 = ( plus_plus_real
% 5.46/5.79 @ ( groups6591440286371151544t_real
% 5.46/5.79 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.79 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T2 @ ( 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 @ X4 @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Maclaurin_cos_expansion
% 5.46/5.79 thf(fact_8964_bij__betw__roots__unity,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( bij_betw_nat_complex
% 5.46/5.79 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.46/5.79 @ ( set_ord_lessThan_nat @ N )
% 5.46/5.79 @ ( collect_complex
% 5.46/5.79 @ ^ [Z5: complex] :
% 5.46/5.79 ( ( power_power_complex @ Z5 @ N )
% 5.46/5.79 = one_one_complex ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % bij_betw_roots_unity
% 5.46/5.79 thf(fact_8965_finite__atMost,axiom,
% 5.46/5.79 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_atMost
% 5.46/5.79 thf(fact_8966_atMost__0,axiom,
% 5.46/5.79 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.46/5.79 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % atMost_0
% 5.46/5.79 thf(fact_8967_atMost__atLeast0,axiom,
% 5.46/5.79 ( set_ord_atMost_nat
% 5.46/5.79 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % atMost_atLeast0
% 5.46/5.79 thf(fact_8968_lessThan__Suc__atMost,axiom,
% 5.46/5.79 ! [K: nat] :
% 5.46/5.79 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.46/5.79 = ( set_ord_atMost_nat @ K ) ) ).
% 5.46/5.79
% 5.46/5.79 % lessThan_Suc_atMost
% 5.46/5.79 thf(fact_8969_atMost__Suc,axiom,
% 5.46/5.79 ! [K: nat] :
% 5.46/5.79 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.46/5.79 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atMost_Suc
% 5.46/5.79 thf(fact_8970_atMost__nat__numeral,axiom,
% 5.46/5.79 ! [K: num] :
% 5.46/5.79 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.46/5.79 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atMost_nat_numeral
% 5.46/5.79 thf(fact_8971_sum__choose__upper,axiom,
% 5.46/5.79 ! [M: nat,N: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.46/5.79 @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.79 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % sum_choose_upper
% 5.46/5.79 thf(fact_8972_sum__choose__lower,axiom,
% 5.46/5.79 ! [R2: nat,N: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 5.46/5.79 @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.79 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N ) ) @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % sum_choose_lower
% 5.46/5.79 thf(fact_8973_choose__rising__sum_I2_J,axiom,
% 5.46/5.79 ! [N: nat,M: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.46/5.79 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.79 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 5.46/5.79
% 5.46/5.79 % choose_rising_sum(2)
% 5.46/5.79 thf(fact_8974_choose__rising__sum_I1_J,axiom,
% 5.46/5.79 ! [N: nat,M: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.46/5.79 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.79 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % choose_rising_sum(1)
% 5.46/5.79 thf(fact_8975_atLeast1__atMost__eq__remove0,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.79 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeast1_atMost_eq_remove0
% 5.46/5.79 thf(fact_8976_sum__choose__diagonal,axiom,
% 5.46/5.79 ! [M: nat,N: nat] :
% 5.46/5.79 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.79 => ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.46/5.79 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.79 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % sum_choose_diagonal
% 5.46/5.79 thf(fact_8977_vandermonde,axiom,
% 5.46/5.79 ! [M: nat,N: nat,R2: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 5.46/5.79 @ ( set_ord_atMost_nat @ R2 ) )
% 5.46/5.79 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % vandermonde
% 5.46/5.79 thf(fact_8978_choose__row__sum,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % choose_row_sum
% 5.46/5.79 thf(fact_8979_binomial,axiom,
% 5.46/5.79 ! [A: nat,B2: nat,N: nat] :
% 5.46/5.79 ( ( power_power_nat @ ( plus_plus_nat @ A @ B2 ) @ N )
% 5.46/5.79 = ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B2 @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.46/5.79 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % binomial
% 5.46/5.79 thf(fact_8980_polynomial__product__nat,axiom,
% 5.46/5.79 ! [M: nat,A: nat > nat,N: nat,B2: nat > nat,X4: nat] :
% 5.46/5.79 ( ! [I3: nat] :
% 5.46/5.79 ( ( ord_less_nat @ M @ I3 )
% 5.46/5.79 => ( ( A @ I3 )
% 5.46/5.79 = zero_zero_nat ) )
% 5.46/5.79 => ( ! [J2: nat] :
% 5.46/5.79 ( ( ord_less_nat @ N @ J2 )
% 5.46/5.79 => ( ( B2 @ J2 )
% 5.46/5.79 = zero_zero_nat ) )
% 5.46/5.79 => ( ( times_times_nat
% 5.46/5.79 @ ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [I2: nat] : ( times_times_nat @ ( A @ I2 ) @ ( power_power_nat @ X4 @ I2 ) )
% 5.46/5.79 @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.79 @ ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [J3: nat] : ( times_times_nat @ ( B2 @ J3 ) @ ( power_power_nat @ X4 @ J3 ) )
% 5.46/5.79 @ ( set_ord_atMost_nat @ N ) ) )
% 5.46/5.79 = ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [R5: nat] :
% 5.46/5.79 ( times_times_nat
% 5.46/5.79 @ ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B2 @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.46/5.79 @ ( set_ord_atMost_nat @ R5 ) )
% 5.46/5.79 @ ( power_power_nat @ X4 @ R5 ) )
% 5.46/5.79 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % polynomial_product_nat
% 5.46/5.79 thf(fact_8981_choose__square__sum,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.79 @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.79 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % choose_square_sum
% 5.46/5.79 thf(fact_8982_binomial__r__part__sum,axiom,
% 5.46/5.79 ! [M: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.46/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % binomial_r_part_sum
% 5.46/5.79 thf(fact_8983_choose__linear__sum,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [I2: nat] : ( times_times_nat @ I2 @ ( binomial @ N @ I2 ) )
% 5.46/5.79 @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.79 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % choose_linear_sum
% 5.46/5.79 thf(fact_8984_of__nat__id,axiom,
% 5.46/5.79 ( semiri1316708129612266289at_nat
% 5.46/5.79 = ( ^ [N2: nat] : N2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % of_nat_id
% 5.46/5.79 thf(fact_8985_real__scaleR__def,axiom,
% 5.46/5.79 real_V1485227260804924795R_real = times_times_real ).
% 5.46/5.79
% 5.46/5.79 % real_scaleR_def
% 5.46/5.79 thf(fact_8986_complex__scaleR,axiom,
% 5.46/5.79 ! [R2: real,A: real,B2: real] :
% 5.46/5.79 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B2 ) )
% 5.46/5.79 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_scaleR
% 5.46/5.79 thf(fact_8987_bij__betw__nth__root__unity,axiom,
% 5.46/5.79 ! [C: complex,N: nat] :
% 5.46/5.79 ( ( C != zero_zero_complex )
% 5.46/5.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.46/5.79 @ ( collect_complex
% 5.46/5.79 @ ^ [Z5: complex] :
% 5.46/5.79 ( ( power_power_complex @ Z5 @ N )
% 5.46/5.79 = one_one_complex ) )
% 5.46/5.79 @ ( collect_complex
% 5.46/5.79 @ ^ [Z5: complex] :
% 5.46/5.79 ( ( power_power_complex @ Z5 @ N )
% 5.46/5.79 = C ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % bij_betw_nth_root_unity
% 5.46/5.79 thf(fact_8988_infinite__int__iff__unbounded,axiom,
% 5.46/5.79 ! [S2: set_int] :
% 5.46/5.79 ( ( ~ ( finite_finite_int @ S2 ) )
% 5.46/5.79 = ( ! [M6: int] :
% 5.46/5.79 ? [N2: int] :
% 5.46/5.79 ( ( ord_less_int @ M6 @ ( abs_abs_int @ N2 ) )
% 5.46/5.79 & ( member_int @ N2 @ S2 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % infinite_int_iff_unbounded
% 5.46/5.79 thf(fact_8989_Arg__def,axiom,
% 5.46/5.79 ( arg
% 5.46/5.79 = ( ^ [Z5: complex] :
% 5.46/5.79 ( if_real @ ( Z5 = zero_zero_complex ) @ zero_zero_real
% 5.46/5.79 @ ( fChoice_real
% 5.46/5.79 @ ^ [A4: real] :
% 5.46/5.79 ( ( ( sgn_sgn_complex @ Z5 )
% 5.46/5.79 = ( cis @ A4 ) )
% 5.46/5.79 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 5.46/5.79 & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Arg_def
% 5.46/5.79 thf(fact_8990_real__root__zero,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( root @ N @ zero_zero_real )
% 5.46/5.79 = zero_zero_real ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_zero
% 5.46/5.79 thf(fact_8991_real__root__Suc__0,axiom,
% 5.46/5.79 ! [X4: real] :
% 5.46/5.79 ( ( root @ ( suc @ zero_zero_nat ) @ X4 )
% 5.46/5.79 = X4 ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_Suc_0
% 5.46/5.79 thf(fact_8992_real__root__eq__iff,axiom,
% 5.46/5.79 ! [N: nat,X4: real,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ( root @ N @ X4 )
% 5.46/5.79 = ( root @ N @ Y3 ) )
% 5.46/5.79 = ( X4 = Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_eq_iff
% 5.46/5.79 thf(fact_8993_root__0,axiom,
% 5.46/5.79 ! [X4: real] :
% 5.46/5.79 ( ( root @ zero_zero_nat @ X4 )
% 5.46/5.79 = zero_zero_real ) ).
% 5.46/5.79
% 5.46/5.79 % root_0
% 5.46/5.79 thf(fact_8994_real__root__eq__0__iff,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ( root @ N @ X4 )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 = ( X4 = zero_zero_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_eq_0_iff
% 5.46/5.79 thf(fact_8995_real__root__less__iff,axiom,
% 5.46/5.79 ! [N: nat,X4: real,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ ( root @ N @ X4 ) @ ( root @ N @ Y3 ) )
% 5.46/5.79 = ( ord_less_real @ X4 @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_less_iff
% 5.46/5.79 thf(fact_8996_real__root__le__iff,axiom,
% 5.46/5.79 ! [N: nat,X4: real,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_real @ ( root @ N @ X4 ) @ ( root @ N @ Y3 ) )
% 5.46/5.79 = ( ord_less_eq_real @ X4 @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_le_iff
% 5.46/5.79 thf(fact_8997_real__root__one,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( root @ N @ one_one_real )
% 5.46/5.79 = one_one_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_one
% 5.46/5.79 thf(fact_8998_real__root__eq__1__iff,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ( root @ N @ X4 )
% 5.46/5.79 = one_one_real )
% 5.46/5.79 = ( X4 = one_one_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_eq_1_iff
% 5.46/5.79 thf(fact_8999_real__root__gt__0__iff,axiom,
% 5.46/5.79 ! [N: nat,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y3 ) )
% 5.46/5.79 = ( ord_less_real @ zero_zero_real @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_gt_0_iff
% 5.46/5.79 thf(fact_9000_real__root__lt__0__iff,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ ( root @ N @ X4 ) @ zero_zero_real )
% 5.46/5.79 = ( ord_less_real @ X4 @ zero_zero_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_lt_0_iff
% 5.46/5.79 thf(fact_9001_real__root__le__0__iff,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_real @ ( root @ N @ X4 ) @ zero_zero_real )
% 5.46/5.79 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_le_0_iff
% 5.46/5.79 thf(fact_9002_real__root__ge__0__iff,axiom,
% 5.46/5.79 ! [N: nat,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y3 ) )
% 5.46/5.79 = ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_ge_0_iff
% 5.46/5.79 thf(fact_9003_real__root__gt__1__iff,axiom,
% 5.46/5.79 ! [N: nat,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y3 ) )
% 5.46/5.79 = ( ord_less_real @ one_one_real @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_gt_1_iff
% 5.46/5.79 thf(fact_9004_real__root__lt__1__iff,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ ( root @ N @ X4 ) @ one_one_real )
% 5.46/5.79 = ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_lt_1_iff
% 5.46/5.79 thf(fact_9005_real__root__ge__1__iff,axiom,
% 5.46/5.79 ! [N: nat,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y3 ) )
% 5.46/5.79 = ( ord_less_eq_real @ one_one_real @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_ge_1_iff
% 5.46/5.79 thf(fact_9006_real__root__le__1__iff,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_real @ ( root @ N @ X4 ) @ one_one_real )
% 5.46/5.79 = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_le_1_iff
% 5.46/5.79 thf(fact_9007_real__root__pow__pos2,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ( power_power_real @ ( root @ N @ X4 ) @ N )
% 5.46/5.79 = X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_pow_pos2
% 5.46/5.79 thf(fact_9008_real__root__minus,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( root @ N @ ( uminus_uminus_real @ X4 ) )
% 5.46/5.79 = ( uminus_uminus_real @ ( root @ N @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_minus
% 5.46/5.79 thf(fact_9009_real__root__inverse,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( root @ N @ ( inverse_inverse_real @ X4 ) )
% 5.46/5.79 = ( inverse_inverse_real @ ( root @ N @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_inverse
% 5.46/5.79 thf(fact_9010_real__root__commute,axiom,
% 5.46/5.79 ! [M: nat,N: nat,X4: real] :
% 5.46/5.79 ( ( root @ M @ ( root @ N @ X4 ) )
% 5.46/5.79 = ( root @ N @ ( root @ M @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_commute
% 5.46/5.79 thf(fact_9011_real__root__mult,axiom,
% 5.46/5.79 ! [N: nat,X4: real,Y3: real] :
% 5.46/5.79 ( ( root @ N @ ( times_times_real @ X4 @ Y3 ) )
% 5.46/5.79 = ( times_times_real @ ( root @ N @ X4 ) @ ( root @ N @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_mult
% 5.46/5.79 thf(fact_9012_real__root__mult__exp,axiom,
% 5.46/5.79 ! [M: nat,N: nat,X4: real] :
% 5.46/5.79 ( ( root @ ( times_times_nat @ M @ N ) @ X4 )
% 5.46/5.79 = ( root @ M @ ( root @ N @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_mult_exp
% 5.46/5.79 thf(fact_9013_real__root__divide,axiom,
% 5.46/5.79 ! [N: nat,X4: real,Y3: real] :
% 5.46/5.79 ( ( root @ N @ ( divide_divide_real @ X4 @ Y3 ) )
% 5.46/5.79 = ( divide_divide_real @ ( root @ N @ X4 ) @ ( root @ N @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_divide
% 5.46/5.79 thf(fact_9014_real__root__pos__pos__le,axiom,
% 5.46/5.79 ! [X4: real,N: nat] :
% 5.46/5.79 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_pos_pos_le
% 5.46/5.79 thf(fact_9015_real__root__less__mono,axiom,
% 5.46/5.79 ! [N: nat,X4: real,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.79 => ( ord_less_real @ ( root @ N @ X4 ) @ ( root @ N @ Y3 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_less_mono
% 5.46/5.79 thf(fact_9016_real__root__le__mono,axiom,
% 5.46/5.79 ! [N: nat,X4: real,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.46/5.79 => ( ord_less_eq_real @ ( root @ N @ X4 ) @ ( root @ N @ Y3 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_le_mono
% 5.46/5.79 thf(fact_9017_real__root__power,axiom,
% 5.46/5.79 ! [N: nat,X4: real,K: nat] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( root @ N @ ( power_power_real @ X4 @ K ) )
% 5.46/5.79 = ( power_power_real @ ( root @ N @ X4 ) @ K ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_power
% 5.46/5.79 thf(fact_9018_real__root__abs,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( root @ N @ ( abs_abs_real @ X4 ) )
% 5.46/5.79 = ( abs_abs_real @ ( root @ N @ X4 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_abs
% 5.46/5.79 thf(fact_9019_sgn__root,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( sgn_sgn_real @ ( root @ N @ X4 ) )
% 5.46/5.79 = ( sgn_sgn_real @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % sgn_root
% 5.46/5.79 thf(fact_9020_real__root__gt__zero,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X4 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_gt_zero
% 5.46/5.79 thf(fact_9021_real__root__strict__decreasing,axiom,
% 5.46/5.79 ! [N: nat,N3: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_nat @ N @ N3 )
% 5.46/5.79 => ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.79 => ( ord_less_real @ ( root @ N3 @ X4 ) @ ( root @ N @ X4 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_strict_decreasing
% 5.46/5.79 thf(fact_9022_sqrt__def,axiom,
% 5.46/5.79 ( sqrt
% 5.46/5.79 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % sqrt_def
% 5.46/5.79 thf(fact_9023_root__abs__power,axiom,
% 5.46/5.79 ! [N: nat,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y3 @ N ) ) )
% 5.46/5.79 = ( abs_abs_real @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % root_abs_power
% 5.46/5.79 thf(fact_9024_real__root__pos__pos,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X4 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_pos_pos
% 5.46/5.79 thf(fact_9025_real__root__strict__increasing,axiom,
% 5.46/5.79 ! [N: nat,N3: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_nat @ N @ N3 )
% 5.46/5.79 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.79 => ( ord_less_real @ ( root @ N @ X4 ) @ ( root @ N3 @ X4 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_strict_increasing
% 5.46/5.79 thf(fact_9026_real__root__decreasing,axiom,
% 5.46/5.79 ! [N: nat,N3: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.46/5.79 => ( ord_less_eq_real @ ( root @ N3 @ X4 ) @ ( root @ N @ X4 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_decreasing
% 5.46/5.79 thf(fact_9027_real__root__pow__pos,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ( power_power_real @ ( root @ N @ X4 ) @ N )
% 5.46/5.79 = X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_pow_pos
% 5.46/5.79 thf(fact_9028_real__root__pos__unique,axiom,
% 5.46/5.79 ! [N: nat,Y3: real,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.46/5.79 => ( ( ( power_power_real @ Y3 @ N )
% 5.46/5.79 = X4 )
% 5.46/5.79 => ( ( root @ N @ X4 )
% 5.46/5.79 = Y3 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_pos_unique
% 5.46/5.79 thf(fact_9029_real__root__power__cancel,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ( root @ N @ ( power_power_real @ X4 @ N ) )
% 5.46/5.79 = X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_power_cancel
% 5.46/5.79 thf(fact_9030_odd__real__root__pow,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.79 => ( ( power_power_real @ ( root @ N @ X4 ) @ N )
% 5.46/5.79 = X4 ) ) ).
% 5.46/5.79
% 5.46/5.79 % odd_real_root_pow
% 5.46/5.79 thf(fact_9031_odd__real__root__unique,axiom,
% 5.46/5.79 ! [N: nat,Y3: real,X4: real] :
% 5.46/5.79 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.79 => ( ( ( power_power_real @ Y3 @ N )
% 5.46/5.79 = X4 )
% 5.46/5.79 => ( ( root @ N @ X4 )
% 5.46/5.79 = Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % odd_real_root_unique
% 5.46/5.79 thf(fact_9032_odd__real__root__power__cancel,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.79 => ( ( root @ N @ ( power_power_real @ X4 @ N ) )
% 5.46/5.79 = X4 ) ) ).
% 5.46/5.79
% 5.46/5.79 % odd_real_root_power_cancel
% 5.46/5.79 thf(fact_9033_real__root__increasing,axiom,
% 5.46/5.79 ! [N: nat,N3: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.79 => ( ord_less_eq_real @ ( root @ N @ X4 ) @ ( root @ N3 @ X4 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_root_increasing
% 5.46/5.79 thf(fact_9034_sgn__power__root,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X4 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X4 ) ) @ N ) )
% 5.46/5.79 = X4 ) ) ).
% 5.46/5.79
% 5.46/5.79 % sgn_power_root
% 5.46/5.79 thf(fact_9035_root__sgn__power,axiom,
% 5.46/5.79 ! [N: nat,Y3: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N ) ) )
% 5.46/5.79 = Y3 ) ) ).
% 5.46/5.79
% 5.46/5.79 % root_sgn_power
% 5.46/5.79 thf(fact_9036_ln__root,axiom,
% 5.46/5.79 ! [N: nat,B2: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.79 => ( ( ln_ln_real @ ( root @ N @ B2 ) )
% 5.46/5.79 = ( divide_divide_real @ ( ln_ln_real @ B2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % ln_root
% 5.46/5.79 thf(fact_9037_log__root,axiom,
% 5.46/5.79 ! [N: nat,A: real,B2: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.46/5.79 => ( ( log @ B2 @ ( root @ N @ A ) )
% 5.46/5.79 = ( divide_divide_real @ ( log @ B2 @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % log_root
% 5.46/5.79 thf(fact_9038_log__base__root,axiom,
% 5.46/5.79 ! [N: nat,B2: real,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ zero_zero_real @ B2 )
% 5.46/5.79 => ( ( log @ ( root @ N @ B2 ) @ X4 )
% 5.46/5.79 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B2 @ X4 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % log_base_root
% 5.46/5.79 thf(fact_9039_split__root,axiom,
% 5.46/5.79 ! [P: real > $o,N: nat,X4: real] :
% 5.46/5.79 ( ( P @ ( root @ N @ X4 ) )
% 5.46/5.79 = ( ( ( N = zero_zero_nat )
% 5.46/5.79 => ( P @ zero_zero_real ) )
% 5.46/5.79 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ! [Y: real] :
% 5.46/5.79 ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.46/5.79 = X4 )
% 5.46/5.79 => ( P @ Y ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % split_root
% 5.46/5.79 thf(fact_9040_infinite__nat__iff__unbounded,axiom,
% 5.46/5.79 ! [S2: set_nat] :
% 5.46/5.79 ( ( ~ ( finite_finite_nat @ S2 ) )
% 5.46/5.79 = ( ! [M6: nat] :
% 5.46/5.79 ? [N2: nat] :
% 5.46/5.79 ( ( ord_less_nat @ M6 @ N2 )
% 5.46/5.79 & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % infinite_nat_iff_unbounded
% 5.46/5.79 thf(fact_9041_unbounded__k__infinite,axiom,
% 5.46/5.79 ! [K: nat,S2: set_nat] :
% 5.46/5.79 ( ! [M4: nat] :
% 5.46/5.79 ( ( ord_less_nat @ K @ M4 )
% 5.46/5.79 => ? [N6: nat] :
% 5.46/5.79 ( ( ord_less_nat @ M4 @ N6 )
% 5.46/5.79 & ( member_nat @ N6 @ S2 ) ) )
% 5.46/5.79 => ~ ( finite_finite_nat @ S2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % unbounded_k_infinite
% 5.46/5.79 thf(fact_9042_infinite__nat__iff__unbounded__le,axiom,
% 5.46/5.79 ! [S2: set_nat] :
% 5.46/5.79 ( ( ~ ( finite_finite_nat @ S2 ) )
% 5.46/5.79 = ( ! [M6: nat] :
% 5.46/5.79 ? [N2: nat] :
% 5.46/5.79 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.46/5.79 & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % infinite_nat_iff_unbounded_le
% 5.46/5.79 thf(fact_9043_root__powr__inverse,axiom,
% 5.46/5.79 ! [N: nat,X4: real] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.79 => ( ( root @ N @ X4 )
% 5.46/5.79 = ( powr_real @ X4 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % root_powr_inverse
% 5.46/5.79 thf(fact_9044_divmod__BitM__2__eq,axiom,
% 5.46/5.79 ! [M: num] :
% 5.46/5.79 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.46/5.79 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_BitM_2_eq
% 5.46/5.79 thf(fact_9045_insert__simp__excp,axiom,
% 5.46/5.79 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X4: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.46/5.79 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.79 => ( ( ord_less_nat @ X4 @ Mi )
% 5.46/5.79 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.46/5.79 => ( ( X4 != Ma )
% 5.46/5.79 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X4 @ ( 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 ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % insert_simp_excp
% 5.46/5.79 thf(fact_9046_insert__simp__norm,axiom,
% 5.46/5.79 ! [X4: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.46/5.79 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.79 => ( ( ord_less_nat @ Mi @ X4 )
% 5.46/5.79 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.46/5.79 => ( ( X4 != Ma )
% 5.46/5.79 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X4 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % insert_simp_norm
% 5.46/5.79 thf(fact_9047_max__Suc__Suc,axiom,
% 5.46/5.79 ! [M: nat,N: nat] :
% 5.46/5.79 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.46/5.79 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % max_Suc_Suc
% 5.46/5.79 thf(fact_9048_max__0R,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.46/5.79 = N ) ).
% 5.46/5.79
% 5.46/5.79 % max_0R
% 5.46/5.79 thf(fact_9049_max__0L,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.46/5.79 = N ) ).
% 5.46/5.79
% 5.46/5.79 % max_0L
% 5.46/5.79 thf(fact_9050_max__nat_Oright__neutral,axiom,
% 5.46/5.79 ! [A: nat] :
% 5.46/5.79 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.46/5.79 = A ) ).
% 5.46/5.79
% 5.46/5.79 % max_nat.right_neutral
% 5.46/5.79 thf(fact_9051_max__nat_Oneutr__eq__iff,axiom,
% 5.46/5.79 ! [A: nat,B2: nat] :
% 5.46/5.79 ( ( zero_zero_nat
% 5.46/5.79 = ( ord_max_nat @ A @ B2 ) )
% 5.46/5.79 = ( ( A = zero_zero_nat )
% 5.46/5.79 & ( B2 = zero_zero_nat ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % max_nat.neutr_eq_iff
% 5.46/5.79 thf(fact_9052_max__nat_Oleft__neutral,axiom,
% 5.46/5.79 ! [A: nat] :
% 5.46/5.79 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.46/5.79 = A ) ).
% 5.46/5.79
% 5.46/5.79 % max_nat.left_neutral
% 5.46/5.79 thf(fact_9053_max__nat_Oeq__neutr__iff,axiom,
% 5.46/5.79 ! [A: nat,B2: nat] :
% 5.46/5.79 ( ( ( ord_max_nat @ A @ B2 )
% 5.46/5.79 = zero_zero_nat )
% 5.46/5.79 = ( ( A = zero_zero_nat )
% 5.46/5.79 & ( B2 = zero_zero_nat ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % max_nat.eq_neutr_iff
% 5.46/5.79 thf(fact_9054_max__numeral__Suc,axiom,
% 5.46/5.79 ! [K: num,N: nat] :
% 5.46/5.79 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.46/5.79 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % max_numeral_Suc
% 5.46/5.79 thf(fact_9055_max__Suc__numeral,axiom,
% 5.46/5.79 ! [N: nat,K: num] :
% 5.46/5.79 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.79 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % max_Suc_numeral
% 5.46/5.79 thf(fact_9056_pred__numeral__simps_I2_J,axiom,
% 5.46/5.79 ! [K: num] :
% 5.46/5.79 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.46/5.79 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % pred_numeral_simps(2)
% 5.46/5.79 thf(fact_9057_nat__add__max__right,axiom,
% 5.46/5.79 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.79 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.46/5.79 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % nat_add_max_right
% 5.46/5.79 thf(fact_9058_nat__add__max__left,axiom,
% 5.46/5.79 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.79 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.46/5.79 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % nat_add_max_left
% 5.46/5.79 thf(fact_9059_nat__mult__max__right,axiom,
% 5.46/5.79 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.79 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.46/5.79 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % nat_mult_max_right
% 5.46/5.79 thf(fact_9060_nat__mult__max__left,axiom,
% 5.46/5.79 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.79 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.46/5.79 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % nat_mult_max_left
% 5.46/5.79 thf(fact_9061_semiring__norm_I26_J,axiom,
% 5.46/5.79 ( ( bitM @ one )
% 5.46/5.79 = one ) ).
% 5.46/5.79
% 5.46/5.79 % semiring_norm(26)
% 5.46/5.79 thf(fact_9062_nat__minus__add__max,axiom,
% 5.46/5.79 ! [N: nat,M: nat] :
% 5.46/5.79 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.46/5.79 = ( ord_max_nat @ N @ M ) ) ).
% 5.46/5.79
% 5.46/5.79 % nat_minus_add_max
% 5.46/5.79 thf(fact_9063_semiring__norm_I27_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bitM @ ( bit0 @ N ) )
% 5.46/5.79 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % semiring_norm(27)
% 5.46/5.79 thf(fact_9064_semiring__norm_I28_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bitM @ ( bit1 @ N ) )
% 5.46/5.79 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % semiring_norm(28)
% 5.46/5.79 thf(fact_9065_inc__BitM__eq,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( inc @ ( bitM @ N ) )
% 5.46/5.79 = ( bit0 @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % inc_BitM_eq
% 5.46/5.79 thf(fact_9066_BitM__inc__eq,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bitM @ ( inc @ N ) )
% 5.46/5.79 = ( bit1 @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % BitM_inc_eq
% 5.46/5.79 thf(fact_9067_eval__nat__numeral_I2_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.46/5.79 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % eval_nat_numeral(2)
% 5.46/5.79 thf(fact_9068_one__plus__BitM,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.46/5.79 = ( bit0 @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % one_plus_BitM
% 5.46/5.79 thf(fact_9069_BitM__plus__one,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.46/5.79 = ( bit0 @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % BitM_plus_one
% 5.46/5.79 thf(fact_9070_vebt__insert_Osimps_I5_J,axiom,
% 5.46/5.79 ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X4: nat] :
% 5.46/5.79 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X4 )
% 5.46/5.79 = ( if_VEBT_VEBT
% 5.46/5.79 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X4 @ Mi ) @ Mi @ X4 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.46/5.79 & ~ ( ( X4 = Mi )
% 5.46/5.79 | ( X4 = Ma ) ) )
% 5.46/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X4 @ Mi ) @ X4 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X4 @ Mi ) @ Mi @ X4 ) @ Ma ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X4 @ Mi ) @ Mi @ X4 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X4 @ Mi ) @ Mi @ X4 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X4 @ Mi ) @ Mi @ X4 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X4 @ Mi ) @ Mi @ X4 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X4 @ Mi ) @ Mi @ X4 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.46/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_insert.simps(5)
% 5.46/5.79 thf(fact_9071_vebt__insert_Oelims,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 5.46/5.79 ( ( ( vEBT_vebt_insert @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ~ ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.46/5.79 & ( ( Xa != one_one_nat )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) ) )
% 5.46/5.79 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) ) )
% 5.46/5.79 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) ) )
% 5.46/5.79 => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa @ Xa ) ) @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.46/5.79 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( if_VEBT_VEBT
% 5.46/5.79 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 & ~ ( ( Xa = Mi2 )
% 5.46/5.79 | ( Xa = Ma2 ) ) )
% 5.46/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Xa @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.46/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_insert.elims
% 5.46/5.79 thf(fact_9072_vebt__insert_Opelims,axiom,
% 5.46/5.79 ! [X4: vEBT_VEBT,Xa: nat,Y3: vEBT_VEBT] :
% 5.46/5.79 ( ( ( vEBT_vebt_insert @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.79 => ( ! [A5: $o,B5: $o] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.79 => ( ( ( ( Xa = zero_zero_nat )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 5.46/5.79 & ( ( Xa != zero_zero_nat )
% 5.46/5.79 => ( ( ( Xa = one_one_nat )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.46/5.79 & ( ( Xa != one_one_nat )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ Xa ) ) ) )
% 5.46/5.79 => ( ! [V3: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa @ Xa ) ) @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) )
% 5.46/5.79 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( if_VEBT_VEBT
% 5.46/5.79 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.46/5.79 & ~ ( ( Xa = Mi2 )
% 5.46/5.79 | ( Xa = Ma2 ) ) )
% 5.46/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Xa @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa @ Mi2 ) @ Mi2 @ Xa ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.46/5.79 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 5.46/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_insert.pelims
% 5.46/5.79 thf(fact_9073_vebt__buildup_Opelims,axiom,
% 5.46/5.79 ! [X4: nat,Y3: vEBT_VEBT] :
% 5.46/5.79 ( ( ( vEBT_vebt_buildup @ X4 )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X4 )
% 5.46/5.79 => ( ( ( X4 = zero_zero_nat )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.79 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.46/5.79 => ( ( ( X4
% 5.46/5.79 = ( suc @ zero_zero_nat ) )
% 5.46/5.79 => ( ( Y3
% 5.46/5.79 = ( vEBT_Leaf @ $false @ $false ) )
% 5.46/5.79 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.46/5.79 => ~ ! [Va: nat] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( suc @ ( suc @ Va ) ) )
% 5.46/5.79 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( 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 ) ) ) ) ) ) )
% 5.46/5.79 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 = ( 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 ) ) ) ) ) ) ) ) )
% 5.46/5.79 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % vebt_buildup.pelims
% 5.46/5.79 thf(fact_9074_max__enat__simps_I2_J,axiom,
% 5.46/5.79 ! [Q2: extended_enat] :
% 5.46/5.79 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.46/5.79 = Q2 ) ).
% 5.46/5.79
% 5.46/5.79 % max_enat_simps(2)
% 5.46/5.79 thf(fact_9075_max__enat__simps_I3_J,axiom,
% 5.46/5.79 ! [Q2: extended_enat] :
% 5.46/5.79 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.46/5.79 = Q2 ) ).
% 5.46/5.79
% 5.46/5.79 % max_enat_simps(3)
% 5.46/5.79 thf(fact_9076_divmod__step__nat__def,axiom,
% 5.46/5.79 ( unique5026877609467782581ep_nat
% 5.46/5.79 = ( ^ [L: num] :
% 5.46/5.79 ( produc2626176000494625587at_nat
% 5.46/5.79 @ ^ [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 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_step_nat_def
% 5.46/5.79 thf(fact_9077_divmod__step__int__def,axiom,
% 5.46/5.79 ( unique5024387138958732305ep_int
% 5.46/5.79 = ( ^ [L: num] :
% 5.46/5.79 ( produc4245557441103728435nt_int
% 5.46/5.79 @ ^ [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 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_step_int_def
% 5.46/5.79 thf(fact_9078_divmod__nat__if,axiom,
% 5.46/5.79 ( divmod_nat
% 5.46/5.79 = ( ^ [M6: nat,N2: nat] :
% 5.46/5.79 ( if_Pro6206227464963214023at_nat
% 5.46/5.79 @ ( ( N2 = zero_zero_nat )
% 5.46/5.79 | ( ord_less_nat @ M6 @ N2 ) )
% 5.46/5.79 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 5.46/5.79 @ ( produc2626176000494625587at_nat
% 5.46/5.79 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.46/5.79 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_nat_if
% 5.46/5.79 thf(fact_9079_arctan__def,axiom,
% 5.46/5.79 ( arctan
% 5.46/5.79 = ( ^ [Y: real] :
% 5.46/5.79 ( the_real
% 5.46/5.79 @ ^ [X: real] :
% 5.46/5.79 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.46/5.79 & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.79 & ( ( tan_real @ X )
% 5.46/5.79 = Y ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % arctan_def
% 5.46/5.79 thf(fact_9080_ln__neg__is__const,axiom,
% 5.46/5.79 ! [X4: real] :
% 5.46/5.79 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.46/5.79 => ( ( ln_ln_real @ X4 )
% 5.46/5.79 = ( the_real
% 5.46/5.79 @ ^ [X: real] : $false ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % ln_neg_is_const
% 5.46/5.79 thf(fact_9081_arccos__def,axiom,
% 5.46/5.79 ( arccos
% 5.46/5.79 = ( ^ [Y: real] :
% 5.46/5.79 ( the_real
% 5.46/5.79 @ ^ [X: real] :
% 5.46/5.79 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.46/5.79 & ( ord_less_eq_real @ X @ pi )
% 5.46/5.79 & ( ( cos_real @ X )
% 5.46/5.79 = Y ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % arccos_def
% 5.46/5.79 thf(fact_9082_divmod__nat__def,axiom,
% 5.46/5.79 ( divmod_nat
% 5.46/5.79 = ( ^ [M6: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N2 ) @ ( modulo_modulo_nat @ M6 @ N2 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_nat_def
% 5.46/5.79 thf(fact_9083_pi__half,axiom,
% 5.46/5.79 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.79 = ( the_real
% 5.46/5.79 @ ^ [X: real] :
% 5.46/5.79 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.46/5.79 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.79 & ( ( cos_real @ X )
% 5.46/5.79 = zero_zero_real ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % pi_half
% 5.46/5.79 thf(fact_9084_pi__def,axiom,
% 5.46/5.79 ( pi
% 5.46/5.79 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.46/5.79 @ ( the_real
% 5.46/5.79 @ ^ [X: real] :
% 5.46/5.79 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.46/5.79 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.46/5.79 & ( ( cos_real @ X )
% 5.46/5.79 = zero_zero_real ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % pi_def
% 5.46/5.79 thf(fact_9085_arcsin__def,axiom,
% 5.46/5.79 ( arcsin
% 5.46/5.79 = ( ^ [Y: real] :
% 5.46/5.79 ( the_real
% 5.46/5.79 @ ^ [X: real] :
% 5.46/5.79 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.46/5.79 & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.79 & ( ( sin_real @ X )
% 5.46/5.79 = Y ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % arcsin_def
% 5.46/5.79 thf(fact_9086_or__int__unfold,axiom,
% 5.46/5.79 ( bit_se1409905431419307370or_int
% 5.46/5.79 = ( ^ [K3: int,L: int] :
% 5.46/5.79 ( if_int
% 5.46/5.79 @ ( ( K3
% 5.46/5.79 = ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.79 | ( L
% 5.46/5.79 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.46/5.79 @ ( uminus_uminus_int @ one_one_int )
% 5.46/5.79 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_int_unfold
% 5.46/5.79 thf(fact_9087_horner__sum__of__bool__2__less,axiom,
% 5.46/5.79 ! [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 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % horner_sum_of_bool_2_less
% 5.46/5.79 thf(fact_9088_or__nonnegative__int__iff,axiom,
% 5.46/5.79 ! [K: int,L2: int] :
% 5.46/5.79 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 5.46/5.79 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.46/5.79 & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_nonnegative_int_iff
% 5.46/5.79 thf(fact_9089_or__negative__int__iff,axiom,
% 5.46/5.79 ! [K: int,L2: int] :
% 5.46/5.79 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 5.46/5.79 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.46/5.79 | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_negative_int_iff
% 5.46/5.79 thf(fact_9090_or__minus__numerals_I2_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_minus_numerals(2)
% 5.46/5.79 thf(fact_9091_or__minus__numerals_I6_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.46/5.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_minus_numerals(6)
% 5.46/5.79 thf(fact_9092_or__minus__minus__numerals,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.79 = ( 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 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_minus_minus_numerals
% 5.46/5.79 thf(fact_9093_and__minus__minus__numerals,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.79 = ( 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 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % and_minus_minus_numerals
% 5.46/5.79 thf(fact_9094_bit__or__int__iff,axiom,
% 5.46/5.79 ! [K: int,L2: int,N: nat] :
% 5.46/5.79 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N )
% 5.46/5.79 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.46/5.79 | ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % bit_or_int_iff
% 5.46/5.79 thf(fact_9095_OR__lower,axiom,
% 5.46/5.79 ! [X4: int,Y3: int] :
% 5.46/5.79 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.79 => ( ( ord_less_eq_int @ zero_zero_int @ Y3 )
% 5.46/5.79 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % OR_lower
% 5.46/5.79 thf(fact_9096_or__greater__eq,axiom,
% 5.46/5.79 ! [L2: int,K: int] :
% 5.46/5.79 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.46/5.79 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_greater_eq
% 5.46/5.79 thf(fact_9097_plus__and__or,axiom,
% 5.46/5.79 ! [X4: int,Y3: int] :
% 5.46/5.79 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X4 @ Y3 ) @ ( bit_se1409905431419307370or_int @ X4 @ Y3 ) )
% 5.46/5.79 = ( plus_plus_int @ X4 @ Y3 ) ) ).
% 5.46/5.79
% 5.46/5.79 % plus_and_or
% 5.46/5.79 thf(fact_9098_or__int__def,axiom,
% 5.46/5.79 ( bit_se1409905431419307370or_int
% 5.46/5.79 = ( ^ [K3: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_int_def
% 5.46/5.79 thf(fact_9099_or__not__numerals_I1_J,axiom,
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.79 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_numerals(1)
% 5.46/5.79 thf(fact_9100_xor__int__def,axiom,
% 5.46/5.79 ( bit_se6526347334894502574or_int
% 5.46/5.79 = ( ^ [K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % xor_int_def
% 5.46/5.79 thf(fact_9101_concat__bit__def,axiom,
% 5.46/5.79 ( bit_concat_bit
% 5.46/5.79 = ( ^ [N2: nat,K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % concat_bit_def
% 5.46/5.79 thf(fact_9102_set__bit__int__def,axiom,
% 5.46/5.79 ( bit_se7879613467334960850it_int
% 5.46/5.79 = ( ^ [N2: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % set_bit_int_def
% 5.46/5.79 thf(fact_9103_or__not__numerals_I4_J,axiom,
% 5.46/5.79 ! [M: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.79 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_numerals(4)
% 5.46/5.79 thf(fact_9104_or__not__numerals_I2_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.79 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_numerals(2)
% 5.46/5.79 thf(fact_9105_or__not__numerals_I3_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.79 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_numerals(3)
% 5.46/5.79 thf(fact_9106_or__not__numerals_I7_J,axiom,
% 5.46/5.79 ! [M: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.46/5.79 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_numerals(7)
% 5.46/5.79 thf(fact_9107_or__not__numerals_I6_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.79 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_numerals(6)
% 5.46/5.79 thf(fact_9108_OR__upper,axiom,
% 5.46/5.79 ! [X4: int,N: nat,Y3: int] :
% 5.46/5.79 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.46/5.79 => ( ( ord_less_int @ X4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.79 => ( ( ord_less_int @ Y3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.46/5.79 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X4 @ Y3 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % OR_upper
% 5.46/5.79 thf(fact_9109_or__not__numerals_I5_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.79 = ( 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 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_numerals(5)
% 5.46/5.79 thf(fact_9110_or__not__numerals_I9_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.79 = ( 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 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_numerals(9)
% 5.46/5.79 thf(fact_9111_or__not__numerals_I8_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.79 = ( 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 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_numerals(8)
% 5.46/5.79 thf(fact_9112_or__int__rec,axiom,
% 5.46/5.79 ( bit_se1409905431419307370or_int
% 5.46/5.79 = ( ^ [K3: int,L: int] :
% 5.46/5.79 ( plus_plus_int
% 5.46/5.79 @ ( zero_n2684676970156552555ol_int
% 5.46/5.79 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.46/5.79 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.46/5.79 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_int_rec
% 5.46/5.79 thf(fact_9113_or__minus__numerals_I5_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.46/5.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_minus_numerals(5)
% 5.46/5.79 thf(fact_9114_or__minus__numerals_I1_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_minus_numerals(1)
% 5.46/5.79 thf(fact_9115_or__nat__numerals_I2_J,axiom,
% 5.46/5.79 ! [Y3: num] :
% 5.46/5.79 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) )
% 5.46/5.79 = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_nat_numerals(2)
% 5.46/5.79 thf(fact_9116_or__nat__numerals_I4_J,axiom,
% 5.46/5.79 ! [X4: num] :
% 5.46/5.79 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.79 = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_nat_numerals(4)
% 5.46/5.79 thf(fact_9117_or__nat__numerals_I1_J,axiom,
% 5.46/5.79 ! [Y3: num] :
% 5.46/5.79 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y3 ) ) )
% 5.46/5.79 = ( numeral_numeral_nat @ ( bit1 @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_nat_numerals(1)
% 5.46/5.79 thf(fact_9118_or__nat__numerals_I3_J,axiom,
% 5.46/5.79 ! [X4: num] :
% 5.46/5.79 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.46/5.79 = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_nat_numerals(3)
% 5.46/5.79 thf(fact_9119_or__minus__numerals_I4_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_minus_numerals(4)
% 5.46/5.79 thf(fact_9120_or__minus__numerals_I8_J,axiom,
% 5.46/5.79 ! [N: num,M: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_minus_numerals(8)
% 5.46/5.79 thf(fact_9121_or__minus__numerals_I7_J,axiom,
% 5.46/5.79 ! [N: num,M: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_minus_numerals(7)
% 5.46/5.79 thf(fact_9122_or__minus__numerals_I3_J,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_minus_numerals(3)
% 5.46/5.79 thf(fact_9123_or__not__num__neg_Osimps_I1_J,axiom,
% 5.46/5.79 ( ( bit_or_not_num_neg @ one @ one )
% 5.46/5.79 = one ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_num_neg.simps(1)
% 5.46/5.79 thf(fact_9124_set__bit__nat__def,axiom,
% 5.46/5.79 ( bit_se7882103937844011126it_nat
% 5.46/5.79 = ( ^ [M6: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % set_bit_nat_def
% 5.46/5.79 thf(fact_9125_or__not__num__neg_Osimps_I4_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.46/5.79 = ( bit0 @ one ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_num_neg.simps(4)
% 5.46/5.79 thf(fact_9126_or__not__num__neg_Osimps_I6_J,axiom,
% 5.46/5.79 ! [N: num,M: num] :
% 5.46/5.79 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.46/5.79 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_num_neg.simps(6)
% 5.46/5.79 thf(fact_9127_or__not__num__neg_Osimps_I3_J,axiom,
% 5.46/5.79 ! [M: num] :
% 5.46/5.79 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.46/5.79 = ( bit1 @ M ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_num_neg.simps(3)
% 5.46/5.79 thf(fact_9128_or__not__num__neg_Osimps_I7_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.46/5.79 = one ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_num_neg.simps(7)
% 5.46/5.79 thf(fact_9129_or__not__num__neg_Osimps_I5_J,axiom,
% 5.46/5.79 ! [N: num,M: num] :
% 5.46/5.79 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.46/5.79 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_num_neg.simps(5)
% 5.46/5.79 thf(fact_9130_or__not__num__neg_Osimps_I9_J,axiom,
% 5.46/5.79 ! [N: num,M: num] :
% 5.46/5.79 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 5.46/5.79 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_num_neg.simps(9)
% 5.46/5.79 thf(fact_9131_or__nat__def,axiom,
% 5.46/5.79 ( bit_se1412395901928357646or_nat
% 5.46/5.79 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_nat_def
% 5.46/5.79 thf(fact_9132_or__not__num__neg_Osimps_I2_J,axiom,
% 5.46/5.79 ! [M: num] :
% 5.46/5.79 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.46/5.79 = ( bit1 @ M ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_num_neg.simps(2)
% 5.46/5.79 thf(fact_9133_or__not__num__neg_Osimps_I8_J,axiom,
% 5.46/5.79 ! [N: num,M: num] :
% 5.46/5.79 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.46/5.79 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_num_neg.simps(8)
% 5.46/5.79 thf(fact_9134_or__not__num__neg_Oelims,axiom,
% 5.46/5.79 ! [X4: num,Xa: num,Y3: num] :
% 5.46/5.79 ( ( ( bit_or_not_num_neg @ X4 @ Xa )
% 5.46/5.79 = Y3 )
% 5.46/5.79 => ( ( ( X4 = one )
% 5.46/5.79 => ( ( Xa = one )
% 5.46/5.79 => ( Y3 != one ) ) )
% 5.46/5.79 => ( ( ( X4 = one )
% 5.46/5.79 => ! [M4: num] :
% 5.46/5.79 ( ( Xa
% 5.46/5.79 = ( bit0 @ M4 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( bit1 @ M4 ) ) ) )
% 5.46/5.79 => ( ( ( X4 = one )
% 5.46/5.79 => ! [M4: num] :
% 5.46/5.79 ( ( Xa
% 5.46/5.79 = ( bit1 @ M4 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( bit1 @ M4 ) ) ) )
% 5.46/5.79 => ( ( ? [N4: num] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( bit0 @ N4 ) )
% 5.46/5.79 => ( ( Xa = one )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( bit0 @ one ) ) ) )
% 5.46/5.79 => ( ! [N4: num] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( bit0 @ N4 ) )
% 5.46/5.79 => ! [M4: num] :
% 5.46/5.79 ( ( Xa
% 5.46/5.79 = ( bit0 @ M4 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( bitM @ ( bit_or_not_num_neg @ N4 @ M4 ) ) ) ) )
% 5.46/5.79 => ( ! [N4: num] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( bit0 @ N4 ) )
% 5.46/5.79 => ! [M4: num] :
% 5.46/5.79 ( ( Xa
% 5.46/5.79 = ( bit1 @ M4 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( bit0 @ ( bit_or_not_num_neg @ N4 @ M4 ) ) ) ) )
% 5.46/5.79 => ( ( ? [N4: num] :
% 5.46/5.79 ( X4
% 5.46/5.79 = ( bit1 @ N4 ) )
% 5.46/5.79 => ( ( Xa = one )
% 5.46/5.79 => ( Y3 != one ) ) )
% 5.46/5.79 => ( ! [N4: num] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( bit1 @ N4 ) )
% 5.46/5.79 => ! [M4: num] :
% 5.46/5.79 ( ( Xa
% 5.46/5.79 = ( bit0 @ M4 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( bitM @ ( bit_or_not_num_neg @ N4 @ M4 ) ) ) ) )
% 5.46/5.79 => ~ ! [N4: num] :
% 5.46/5.79 ( ( X4
% 5.46/5.79 = ( bit1 @ N4 ) )
% 5.46/5.79 => ! [M4: num] :
% 5.46/5.79 ( ( Xa
% 5.46/5.79 = ( bit1 @ M4 ) )
% 5.46/5.79 => ( Y3
% 5.46/5.79 != ( bitM @ ( bit_or_not_num_neg @ N4 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_not_num_neg.elims
% 5.46/5.79 thf(fact_9135_numeral__or__not__num__eq,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % numeral_or_not_num_eq
% 5.46/5.79 thf(fact_9136_int__numeral__not__or__num__neg,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % int_numeral_not_or_num_neg
% 5.46/5.79 thf(fact_9137_int__numeral__or__not__num__neg,axiom,
% 5.46/5.79 ! [M: num,N: num] :
% 5.46/5.79 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % int_numeral_or_not_num_neg
% 5.46/5.79 thf(fact_9138_or__Suc__0__eq,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.79 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_Suc_0_eq
% 5.46/5.79 thf(fact_9139_Suc__0__or__eq,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.79 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Suc_0_or_eq
% 5.46/5.79 thf(fact_9140_or__nat__rec,axiom,
% 5.46/5.79 ( bit_se1412395901928357646or_nat
% 5.46/5.79 = ( ^ [M6: nat,N2: nat] :
% 5.46/5.79 ( plus_plus_nat
% 5.46/5.79 @ ( zero_n2687167440665602831ol_nat
% 5.46/5.79 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.46/5.79 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.79 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_nat_rec
% 5.46/5.79 thf(fact_9141_or__nat__unfold,axiom,
% 5.46/5.79 ( bit_se1412395901928357646or_nat
% 5.46/5.79 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % or_nat_unfold
% 5.46/5.79 thf(fact_9142_Sum__Ico__nat,axiom,
% 5.46/5.79 ! [M: nat,N: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [X: nat] : X
% 5.46/5.79 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.46/5.79 = ( 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 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Sum_Ico_nat
% 5.46/5.79 thf(fact_9143_sum__power2,axiom,
% 5.46/5.79 ! [K: nat] :
% 5.46/5.79 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.46/5.79 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % sum_power2
% 5.46/5.79 thf(fact_9144_finite__atLeastLessThan,axiom,
% 5.46/5.79 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_atLeastLessThan
% 5.46/5.79 thf(fact_9145_atLeastLessThan__singleton,axiom,
% 5.46/5.79 ! [M: nat] :
% 5.46/5.79 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.46/5.79 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeastLessThan_singleton
% 5.46/5.79 thf(fact_9146_all__nat__less__eq,axiom,
% 5.46/5.79 ! [N: nat,P: nat > $o] :
% 5.46/5.79 ( ( ! [M6: nat] :
% 5.46/5.79 ( ( ord_less_nat @ M6 @ N )
% 5.46/5.79 => ( P @ M6 ) ) )
% 5.46/5.79 = ( ! [X: nat] :
% 5.46/5.79 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.46/5.79 => ( P @ X ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % all_nat_less_eq
% 5.46/5.79 thf(fact_9147_ex__nat__less__eq,axiom,
% 5.46/5.79 ! [N: nat,P: nat > $o] :
% 5.46/5.79 ( ( ? [M6: nat] :
% 5.46/5.79 ( ( ord_less_nat @ M6 @ N )
% 5.46/5.79 & ( P @ M6 ) ) )
% 5.46/5.79 = ( ? [X: nat] :
% 5.46/5.79 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.46/5.79 & ( P @ X ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % ex_nat_less_eq
% 5.46/5.79 thf(fact_9148_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.46/5.79 ! [L2: nat,U: nat] :
% 5.46/5.79 ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 5.46/5.79 = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeastLessThanSuc_atLeastAtMost
% 5.46/5.79 thf(fact_9149_lessThan__atLeast0,axiom,
% 5.46/5.79 ( set_ord_lessThan_nat
% 5.46/5.79 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % lessThan_atLeast0
% 5.46/5.79 thf(fact_9150_atLeastLessThan0,axiom,
% 5.46/5.79 ! [M: nat] :
% 5.46/5.79 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 5.46/5.79 = bot_bot_set_nat ) ).
% 5.46/5.79
% 5.46/5.79 % atLeastLessThan0
% 5.46/5.79 thf(fact_9151_atLeast0__lessThan__Suc,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.46/5.79 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeast0_lessThan_Suc
% 5.46/5.79 thf(fact_9152_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.46/5.79 ! [N3: set_nat,N: nat] :
% 5.46/5.79 ( ( ord_less_eq_set_nat @ N3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.46/5.79 => ( finite_finite_nat @ N3 ) ) ).
% 5.46/5.79
% 5.46/5.79 % subset_eq_atLeast0_lessThan_finite
% 5.46/5.79 thf(fact_9153_atLeastLessThanSuc,axiom,
% 5.46/5.79 ! [M: nat,N: nat] :
% 5.46/5.79 ( ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.79 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.46/5.79 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.46/5.79 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.46/5.79 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.46/5.79 = bot_bot_set_nat ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeastLessThanSuc
% 5.46/5.79 thf(fact_9154_prod__Suc__fact,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.46/5.79 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_Suc_fact
% 5.46/5.79 thf(fact_9155_prod__Suc__Suc__fact,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.46/5.79 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % prod_Suc_Suc_fact
% 5.46/5.79 thf(fact_9156_atLeastLessThan__nat__numeral,axiom,
% 5.46/5.79 ! [M: nat,K: num] :
% 5.46/5.79 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.46/5.79 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.46/5.79 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.46/5.79 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.46/5.79 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.46/5.79 = bot_bot_set_nat ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeastLessThan_nat_numeral
% 5.46/5.79 thf(fact_9157_atLeast1__lessThan__eq__remove0,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.46/5.79 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeast1_lessThan_eq_remove0
% 5.46/5.79 thf(fact_9158_Chebyshev__sum__upper__nat,axiom,
% 5.46/5.79 ! [N: nat,A: nat > nat,B2: nat > nat] :
% 5.46/5.79 ( ! [I3: nat,J2: nat] :
% 5.46/5.79 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.46/5.79 => ( ( ord_less_nat @ J2 @ N )
% 5.46/5.79 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 5.46/5.79 => ( ! [I3: nat,J2: nat] :
% 5.46/5.79 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.46/5.79 => ( ( ord_less_nat @ J2 @ N )
% 5.46/5.79 => ( ord_less_eq_nat @ ( B2 @ J2 ) @ ( B2 @ I3 ) ) ) )
% 5.46/5.79 => ( ord_less_eq_nat
% 5.46/5.79 @ ( times_times_nat @ N
% 5.46/5.79 @ ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [I2: nat] : ( times_times_nat @ ( A @ I2 ) @ ( B2 @ I2 ) )
% 5.46/5.79 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.46/5.79 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Chebyshev_sum_upper_nat
% 5.46/5.79 thf(fact_9159_finite__atLeastLessThan__int,axiom,
% 5.46/5.79 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_atLeastLessThan_int
% 5.46/5.79 thf(fact_9160_finite__atLeastZeroLessThan__int,axiom,
% 5.46/5.79 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 5.46/5.79
% 5.46/5.79 % finite_atLeastZeroLessThan_int
% 5.46/5.79 thf(fact_9161_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.46/5.79 ! [L2: int,U: int] :
% 5.46/5.79 ( ( set_or4662586982721622107an_int @ L2 @ ( plus_plus_int @ U @ one_one_int ) )
% 5.46/5.79 = ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 5.46/5.79
% 5.46/5.79 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.46/5.79 thf(fact_9162_valid__eq,axiom,
% 5.46/5.79 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.46/5.79
% 5.46/5.79 % valid_eq
% 5.46/5.79 thf(fact_9163_valid__eq1,axiom,
% 5.46/5.79 ! [T: vEBT_VEBT,D: nat] :
% 5.46/5.79 ( ( vEBT_invar_vebt @ T @ D )
% 5.46/5.79 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.46/5.79
% 5.46/5.79 % valid_eq1
% 5.46/5.79 thf(fact_9164_valid__eq2,axiom,
% 5.46/5.79 ! [T: vEBT_VEBT,D: nat] :
% 5.46/5.79 ( ( vEBT_VEBT_valid @ T @ D )
% 5.46/5.79 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.46/5.79
% 5.46/5.79 % valid_eq2
% 5.46/5.79 thf(fact_9165_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.46/5.79 ! [Uu3: $o,Uv2: $o,D: nat] :
% 5.46/5.79 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu3 @ Uv2 ) @ D )
% 5.46/5.79 = ( D = one_one_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % VEBT_internal.valid'.simps(1)
% 5.46/5.79 thf(fact_9166_divmod__step__integer__def,axiom,
% 5.46/5.79 ( unique4921790084139445826nteger
% 5.46/5.79 = ( ^ [L: num] :
% 5.46/5.79 ( produc6916734918728496179nteger
% 5.46/5.79 @ ^ [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 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_step_integer_def
% 5.46/5.79 thf(fact_9167_csqrt_Osimps_I1_J,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( re @ ( csqrt @ Z ) )
% 5.46/5.79 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % csqrt.simps(1)
% 5.46/5.79 thf(fact_9168_complex__Re__numeral,axiom,
% 5.46/5.79 ! [V: num] :
% 5.46/5.79 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.46/5.79 = ( numeral_numeral_real @ V ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_Re_numeral
% 5.46/5.79 thf(fact_9169_Re__divide__of__nat,axiom,
% 5.46/5.79 ! [Z: complex,N: nat] :
% 5.46/5.79 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.46/5.79 = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_divide_of_nat
% 5.46/5.79 thf(fact_9170_Re__divide__of__real,axiom,
% 5.46/5.79 ! [Z: complex,R2: real] :
% 5.46/5.79 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R2 ) ) )
% 5.46/5.79 = ( divide_divide_real @ ( re @ Z ) @ R2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_divide_of_real
% 5.46/5.79 thf(fact_9171_Re__sgn,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( re @ ( sgn_sgn_complex @ Z ) )
% 5.46/5.79 = ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_sgn
% 5.46/5.79 thf(fact_9172_Re__divide__numeral,axiom,
% 5.46/5.79 ! [Z: complex,W: num] :
% 5.46/5.79 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.79 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_divide_numeral
% 5.46/5.79 thf(fact_9173_plus__integer__code_I1_J,axiom,
% 5.46/5.79 ! [K: code_integer] :
% 5.46/5.79 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 5.46/5.79 = K ) ).
% 5.46/5.79
% 5.46/5.79 % plus_integer_code(1)
% 5.46/5.79 thf(fact_9174_plus__integer__code_I2_J,axiom,
% 5.46/5.79 ! [L2: code_integer] :
% 5.46/5.79 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.46/5.79 = L2 ) ).
% 5.46/5.79
% 5.46/5.79 % plus_integer_code(2)
% 5.46/5.79 thf(fact_9175_times__integer__code_I1_J,axiom,
% 5.46/5.79 ! [K: code_integer] :
% 5.46/5.79 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.46/5.79 = zero_z3403309356797280102nteger ) ).
% 5.46/5.79
% 5.46/5.79 % times_integer_code(1)
% 5.46/5.79 thf(fact_9176_times__integer__code_I2_J,axiom,
% 5.46/5.79 ! [L2: code_integer] :
% 5.46/5.79 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.46/5.79 = zero_z3403309356797280102nteger ) ).
% 5.46/5.79
% 5.46/5.79 % times_integer_code(2)
% 5.46/5.79 thf(fact_9177_divmod__integer_H__def,axiom,
% 5.46/5.79 ( unique3479559517661332726nteger
% 5.46/5.79 = ( ^ [M6: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_integer'_def
% 5.46/5.79 thf(fact_9178_sgn__integer__code,axiom,
% 5.46/5.79 ( sgn_sgn_Code_integer
% 5.46/5.79 = ( ^ [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 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % sgn_integer_code
% 5.46/5.79 thf(fact_9179_minus__integer__code_I2_J,axiom,
% 5.46/5.79 ! [L2: code_integer] :
% 5.46/5.79 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.46/5.79 = ( uminus1351360451143612070nteger @ L2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % minus_integer_code(2)
% 5.46/5.79 thf(fact_9180_minus__integer__code_I1_J,axiom,
% 5.46/5.79 ! [K: code_integer] :
% 5.46/5.79 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 5.46/5.79 = K ) ).
% 5.46/5.79
% 5.46/5.79 % minus_integer_code(1)
% 5.46/5.79 thf(fact_9181_complex__Re__le__cmod,axiom,
% 5.46/5.79 ! [X4: complex] : ( ord_less_eq_real @ ( re @ X4 ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_Re_le_cmod
% 5.46/5.79 thf(fact_9182_one__complex_Osimps_I1_J,axiom,
% 5.46/5.79 ( ( re @ one_one_complex )
% 5.46/5.79 = one_one_real ) ).
% 5.46/5.79
% 5.46/5.79 % one_complex.simps(1)
% 5.46/5.79 thf(fact_9183_plus__complex_Osimps_I1_J,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( re @ ( plus_plus_complex @ X4 @ Y3 ) )
% 5.46/5.79 = ( plus_plus_real @ ( re @ X4 ) @ ( re @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % plus_complex.simps(1)
% 5.46/5.79 thf(fact_9184_scaleR__complex_Osimps_I1_J,axiom,
% 5.46/5.79 ! [R2: real,X4: complex] :
% 5.46/5.79 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X4 ) )
% 5.46/5.79 = ( times_times_real @ R2 @ ( re @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % scaleR_complex.simps(1)
% 5.46/5.79 thf(fact_9185_minus__complex_Osimps_I1_J,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( re @ ( minus_minus_complex @ X4 @ Y3 ) )
% 5.46/5.79 = ( minus_minus_real @ ( re @ X4 ) @ ( re @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % minus_complex.simps(1)
% 5.46/5.79 thf(fact_9186_abs__Re__le__cmod,axiom,
% 5.46/5.79 ! [X4: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 5.46/5.79
% 5.46/5.79 % abs_Re_le_cmod
% 5.46/5.79 thf(fact_9187_Re__csqrt,axiom,
% 5.46/5.79 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_csqrt
% 5.46/5.79 thf(fact_9188_one__natural_Orsp,axiom,
% 5.46/5.79 one_one_nat = one_one_nat ).
% 5.46/5.79
% 5.46/5.79 % one_natural.rsp
% 5.46/5.79 thf(fact_9189_cmod__plus__Re__le__0__iff,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.46/5.79 = ( ( re @ Z )
% 5.46/5.79 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % cmod_plus_Re_le_0_iff
% 5.46/5.79 thf(fact_9190_cos__n__Re__cis__pow__n,axiom,
% 5.46/5.79 ! [N: nat,A: real] :
% 5.46/5.79 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.46/5.79 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % cos_n_Re_cis_pow_n
% 5.46/5.79 thf(fact_9191_csqrt_Ocode,axiom,
% 5.46/5.79 ( csqrt
% 5.46/5.79 = ( ^ [Z5: complex] :
% 5.46/5.79 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.79 @ ( times_times_real
% 5.46/5.79 @ ( if_real
% 5.46/5.79 @ ( ( im @ Z5 )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 @ one_one_real
% 5.46/5.79 @ ( sgn_sgn_real @ ( im @ Z5 ) ) )
% 5.46/5.79 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % csqrt.code
% 5.46/5.79 thf(fact_9192_csqrt_Osimps_I2_J,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( im @ ( csqrt @ Z ) )
% 5.46/5.79 = ( times_times_real
% 5.46/5.79 @ ( if_real
% 5.46/5.79 @ ( ( im @ Z )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 @ one_one_real
% 5.46/5.79 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.46/5.79 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % csqrt.simps(2)
% 5.46/5.79 thf(fact_9193_integer__of__int__code,axiom,
% 5.46/5.79 ( code_integer_of_int
% 5.46/5.79 = ( ^ [K3: int] :
% 5.46/5.79 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.46/5.79 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.46/5.79 @ ( if_Code_integer
% 5.46/5.79 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.46/5.79 = zero_zero_int )
% 5.46/5.79 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.46/5.79 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % integer_of_int_code
% 5.46/5.79 thf(fact_9194_Im__i__times,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.46/5.79 = ( re @ Z ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_i_times
% 5.46/5.79 thf(fact_9195_Im__divide__of__real,axiom,
% 5.46/5.79 ! [Z: complex,R2: real] :
% 5.46/5.79 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R2 ) ) )
% 5.46/5.79 = ( divide_divide_real @ ( im @ Z ) @ R2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_divide_of_real
% 5.46/5.79 thf(fact_9196_Im__sgn,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( im @ ( sgn_sgn_complex @ Z ) )
% 5.46/5.79 = ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_sgn
% 5.46/5.79 thf(fact_9197_Re__power__real,axiom,
% 5.46/5.79 ! [X4: complex,N: nat] :
% 5.46/5.79 ( ( ( im @ X4 )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 => ( ( re @ ( power_power_complex @ X4 @ N ) )
% 5.46/5.79 = ( power_power_real @ ( re @ X4 ) @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_power_real
% 5.46/5.79 thf(fact_9198_Re__i__times,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.46/5.79 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_i_times
% 5.46/5.79 thf(fact_9199_Im__divide__numeral,axiom,
% 5.46/5.79 ! [Z: complex,W: num] :
% 5.46/5.79 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.46/5.79 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_divide_numeral
% 5.46/5.79 thf(fact_9200_Im__divide__of__nat,axiom,
% 5.46/5.79 ! [Z: complex,N: nat] :
% 5.46/5.79 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.46/5.79 = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_divide_of_nat
% 5.46/5.79 thf(fact_9201_csqrt__of__real__nonneg,axiom,
% 5.46/5.79 ! [X4: complex] :
% 5.46/5.79 ( ( ( im @ X4 )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X4 ) )
% 5.46/5.79 => ( ( csqrt @ X4 )
% 5.46/5.79 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X4 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % csqrt_of_real_nonneg
% 5.46/5.79 thf(fact_9202_csqrt__minus,axiom,
% 5.46/5.79 ! [X4: complex] :
% 5.46/5.79 ( ( ( ord_less_real @ ( im @ X4 ) @ zero_zero_real )
% 5.46/5.79 | ( ( ( im @ X4 )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X4 ) ) ) )
% 5.46/5.79 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X4 ) )
% 5.46/5.79 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X4 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % csqrt_minus
% 5.46/5.79 thf(fact_9203_csqrt__of__real__nonpos,axiom,
% 5.46/5.79 ! [X4: complex] :
% 5.46/5.79 ( ( ( im @ X4 )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 => ( ( ord_less_eq_real @ ( re @ X4 ) @ zero_zero_real )
% 5.46/5.79 => ( ( csqrt @ X4 )
% 5.46/5.79 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X4 ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % csqrt_of_real_nonpos
% 5.46/5.79 thf(fact_9204_divide__integer_Oabs__eq,axiom,
% 5.46/5.79 ! [Xa: int,X4: int] :
% 5.46/5.79 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 5.46/5.79 = ( code_integer_of_int @ ( divide_divide_int @ Xa @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divide_integer.abs_eq
% 5.46/5.79 thf(fact_9205_modulo__integer_Oabs__eq,axiom,
% 5.46/5.79 ! [Xa: int,X4: int] :
% 5.46/5.79 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 5.46/5.79 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % modulo_integer.abs_eq
% 5.46/5.79 thf(fact_9206_less__integer__code_I1_J,axiom,
% 5.46/5.79 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.46/5.79
% 5.46/5.79 % less_integer_code(1)
% 5.46/5.79 thf(fact_9207_less__integer_Oabs__eq,axiom,
% 5.46/5.79 ! [Xa: int,X4: int] :
% 5.46/5.79 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 5.46/5.79 = ( ord_less_int @ Xa @ X4 ) ) ).
% 5.46/5.79
% 5.46/5.79 % less_integer.abs_eq
% 5.46/5.79 thf(fact_9208_abs__integer__code,axiom,
% 5.46/5.79 ( abs_abs_Code_integer
% 5.46/5.79 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % abs_integer_code
% 5.46/5.79 thf(fact_9209_imaginary__unit_Osimps_I2_J,axiom,
% 5.46/5.79 ( ( im @ imaginary_unit )
% 5.46/5.79 = one_one_real ) ).
% 5.46/5.79
% 5.46/5.79 % imaginary_unit.simps(2)
% 5.46/5.79 thf(fact_9210_plus__integer_Oabs__eq,axiom,
% 5.46/5.79 ! [Xa: int,X4: int] :
% 5.46/5.79 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 5.46/5.79 = ( code_integer_of_int @ ( plus_plus_int @ Xa @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % plus_integer.abs_eq
% 5.46/5.79 thf(fact_9211_times__integer_Oabs__eq,axiom,
% 5.46/5.79 ! [Xa: int,X4: int] :
% 5.46/5.79 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 5.46/5.79 = ( code_integer_of_int @ ( times_times_int @ Xa @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % times_integer.abs_eq
% 5.46/5.79 thf(fact_9212_minus__integer_Oabs__eq,axiom,
% 5.46/5.79 ! [Xa: int,X4: int] :
% 5.46/5.79 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 5.46/5.79 = ( code_integer_of_int @ ( minus_minus_int @ Xa @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % minus_integer.abs_eq
% 5.46/5.79 thf(fact_9213_plus__complex_Osimps_I2_J,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( im @ ( plus_plus_complex @ X4 @ Y3 ) )
% 5.46/5.79 = ( plus_plus_real @ ( im @ X4 ) @ ( im @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % plus_complex.simps(2)
% 5.46/5.79 thf(fact_9214_scaleR__complex_Osimps_I2_J,axiom,
% 5.46/5.79 ! [R2: real,X4: complex] :
% 5.46/5.79 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X4 ) )
% 5.46/5.79 = ( times_times_real @ R2 @ ( im @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % scaleR_complex.simps(2)
% 5.46/5.79 thf(fact_9215_minus__complex_Osimps_I2_J,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( im @ ( minus_minus_complex @ X4 @ Y3 ) )
% 5.46/5.79 = ( minus_minus_real @ ( im @ X4 ) @ ( im @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % minus_complex.simps(2)
% 5.46/5.79 thf(fact_9216_abs__Im__le__cmod,axiom,
% 5.46/5.79 ! [X4: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 5.46/5.79
% 5.46/5.79 % abs_Im_le_cmod
% 5.46/5.79 thf(fact_9217_times__complex_Osimps_I2_J,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( im @ ( times_times_complex @ X4 @ Y3 ) )
% 5.46/5.79 = ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( im @ Y3 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y3 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % times_complex.simps(2)
% 5.46/5.79 thf(fact_9218_cmod__Im__le__iff,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( ( re @ X4 )
% 5.46/5.79 = ( re @ Y3 ) )
% 5.46/5.79 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y3 ) )
% 5.46/5.79 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X4 ) ) @ ( abs_abs_real @ ( im @ Y3 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % cmod_Im_le_iff
% 5.46/5.79 thf(fact_9219_cmod__Re__le__iff,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( ( im @ X4 )
% 5.46/5.79 = ( im @ Y3 ) )
% 5.46/5.79 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y3 ) )
% 5.46/5.79 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X4 ) ) @ ( abs_abs_real @ ( re @ Y3 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % cmod_Re_le_iff
% 5.46/5.79 thf(fact_9220_times__complex_Osimps_I1_J,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( re @ ( times_times_complex @ X4 @ Y3 ) )
% 5.46/5.79 = ( minus_minus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( im @ Y3 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % times_complex.simps(1)
% 5.46/5.79 thf(fact_9221_plus__complex_Ocode,axiom,
% 5.46/5.79 ( plus_plus_complex
% 5.46/5.79 = ( ^ [X: complex,Y: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X ) @ ( re @ Y ) ) @ ( plus_plus_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % plus_complex.code
% 5.46/5.79 thf(fact_9222_scaleR__complex_Ocode,axiom,
% 5.46/5.79 ( real_V2046097035970521341omplex
% 5.46/5.79 = ( ^ [R5: real,X: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X ) ) @ ( times_times_real @ R5 @ ( im @ X ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % scaleR_complex.code
% 5.46/5.79 thf(fact_9223_minus__complex_Ocode,axiom,
% 5.46/5.79 ( minus_minus_complex
% 5.46/5.79 = ( ^ [X: complex,Y: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X ) @ ( re @ Y ) ) @ ( minus_minus_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % minus_complex.code
% 5.46/5.79 thf(fact_9224_csqrt__principal,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.46/5.79 | ( ( ( re @ ( csqrt @ Z ) )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % csqrt_principal
% 5.46/5.79 thf(fact_9225_cmod__le,axiom,
% 5.46/5.79 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % cmod_le
% 5.46/5.79 thf(fact_9226_sin__n__Im__cis__pow__n,axiom,
% 5.46/5.79 ! [N: nat,A: real] :
% 5.46/5.79 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.46/5.79 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % sin_n_Im_cis_pow_n
% 5.46/5.79 thf(fact_9227_Re__exp,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( re @ ( exp_complex @ Z ) )
% 5.46/5.79 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_exp
% 5.46/5.79 thf(fact_9228_Im__exp,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( im @ ( exp_complex @ Z ) )
% 5.46/5.79 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_exp
% 5.46/5.79 thf(fact_9229_complex__eq,axiom,
% 5.46/5.79 ! [A: complex] :
% 5.46/5.79 ( A
% 5.46/5.79 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_eq
% 5.46/5.79 thf(fact_9230_times__complex_Ocode,axiom,
% 5.46/5.79 ( times_times_complex
% 5.46/5.79 = ( ^ [X: complex,Y: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % times_complex.code
% 5.46/5.79 thf(fact_9231_exp__eq__polar,axiom,
% 5.46/5.79 ( exp_complex
% 5.46/5.79 = ( ^ [Z5: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z5 ) ) ) @ ( cis @ ( im @ Z5 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % exp_eq_polar
% 5.46/5.79 thf(fact_9232_cmod__power2,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.79 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % cmod_power2
% 5.46/5.79 thf(fact_9233_Im__power2,axiom,
% 5.46/5.79 ! [X4: complex] :
% 5.46/5.79 ( ( im @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.79 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X4 ) ) @ ( im @ X4 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_power2
% 5.46/5.79 thf(fact_9234_Re__power2,axiom,
% 5.46/5.79 ! [X4: complex] :
% 5.46/5.79 ( ( re @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.79 = ( minus_minus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_power2
% 5.46/5.79 thf(fact_9235_complex__eq__0,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( Z = zero_zero_complex )
% 5.46/5.79 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.79 = zero_zero_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_eq_0
% 5.46/5.79 thf(fact_9236_norm__complex__def,axiom,
% 5.46/5.79 ( real_V1022390504157884413omplex
% 5.46/5.79 = ( ^ [Z5: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % norm_complex_def
% 5.46/5.79 thf(fact_9237_inverse__complex_Osimps_I1_J,axiom,
% 5.46/5.79 ! [X4: complex] :
% 5.46/5.79 ( ( re @ ( invers8013647133539491842omplex @ X4 ) )
% 5.46/5.79 = ( divide_divide_real @ ( re @ X4 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % inverse_complex.simps(1)
% 5.46/5.79 thf(fact_9238_complex__neq__0,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( Z != zero_zero_complex )
% 5.46/5.79 = ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_neq_0
% 5.46/5.79 thf(fact_9239_Re__divide,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( re @ ( divide1717551699836669952omplex @ X4 @ Y3 ) )
% 5.46/5.79 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_divide
% 5.46/5.79 thf(fact_9240_csqrt__unique,axiom,
% 5.46/5.79 ! [W: complex,Z: complex] :
% 5.46/5.79 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.46/5.79 = Z )
% 5.46/5.79 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.46/5.79 | ( ( ( re @ W )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.46/5.79 => ( ( csqrt @ Z )
% 5.46/5.79 = W ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % csqrt_unique
% 5.46/5.79 thf(fact_9241_csqrt__square,axiom,
% 5.46/5.79 ! [B2: complex] :
% 5.46/5.79 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B2 ) )
% 5.46/5.79 | ( ( ( re @ B2 )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B2 ) ) ) )
% 5.46/5.79 => ( ( csqrt @ ( power_power_complex @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.79 = B2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % csqrt_square
% 5.46/5.79 thf(fact_9242_inverse__complex_Osimps_I2_J,axiom,
% 5.46/5.79 ! [X4: complex] :
% 5.46/5.79 ( ( im @ ( invers8013647133539491842omplex @ X4 ) )
% 5.46/5.79 = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X4 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % inverse_complex.simps(2)
% 5.46/5.79 thf(fact_9243_Im__divide,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( im @ ( divide1717551699836669952omplex @ X4 @ Y3 ) )
% 5.46/5.79 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( re @ X4 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_divide
% 5.46/5.79 thf(fact_9244_complex__abs__le__norm,axiom,
% 5.46/5.79 ! [Z: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_abs_le_norm
% 5.46/5.79 thf(fact_9245_complex__unit__circle,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( Z != zero_zero_complex )
% 5.46/5.79 => ( ( plus_plus_real @ ( power_power_real @ ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.79 = one_one_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_unit_circle
% 5.46/5.79 thf(fact_9246_inverse__complex_Ocode,axiom,
% 5.46/5.79 ( invers8013647133539491842omplex
% 5.46/5.79 = ( ^ [X: complex] : ( complex2 @ ( 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 ) ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % inverse_complex.code
% 5.46/5.79 thf(fact_9247_Complex__divide,axiom,
% 5.46/5.79 ( divide1717551699836669952omplex
% 5.46/5.79 = ( ^ [X: complex,Y: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( 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 @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Complex_divide
% 5.46/5.79 thf(fact_9248_Im__Reals__divide,axiom,
% 5.46/5.79 ! [R2: complex,Z: complex] :
% 5.46/5.79 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.46/5.79 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.46/5.79 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_Reals_divide
% 5.46/5.79 thf(fact_9249_Re__Reals__divide,axiom,
% 5.46/5.79 ! [R2: complex,Z: complex] :
% 5.46/5.79 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.46/5.79 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.46/5.79 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_Reals_divide
% 5.46/5.79 thf(fact_9250_Re__divide__Reals,axiom,
% 5.46/5.79 ! [R2: complex,Z: complex] :
% 5.46/5.79 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.46/5.79 => ( ( re @ ( divide1717551699836669952omplex @ Z @ R2 ) )
% 5.46/5.79 = ( divide_divide_real @ ( re @ Z ) @ ( re @ R2 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_divide_Reals
% 5.46/5.79 thf(fact_9251_real__eq__imaginary__iff,axiom,
% 5.46/5.79 ! [Y3: complex,X4: complex] :
% 5.46/5.79 ( ( member_complex @ Y3 @ real_V2521375963428798218omplex )
% 5.46/5.79 => ( ( member_complex @ X4 @ real_V2521375963428798218omplex )
% 5.46/5.79 => ( ( X4
% 5.46/5.79 = ( times_times_complex @ imaginary_unit @ Y3 ) )
% 5.46/5.79 = ( ( X4 = zero_zero_complex )
% 5.46/5.79 & ( Y3 = zero_zero_complex ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % real_eq_imaginary_iff
% 5.46/5.79 thf(fact_9252_imaginary__eq__real__iff,axiom,
% 5.46/5.79 ! [Y3: complex,X4: complex] :
% 5.46/5.79 ( ( member_complex @ Y3 @ real_V2521375963428798218omplex )
% 5.46/5.79 => ( ( member_complex @ X4 @ real_V2521375963428798218omplex )
% 5.46/5.79 => ( ( ( times_times_complex @ imaginary_unit @ Y3 )
% 5.46/5.79 = X4 )
% 5.46/5.79 = ( ( X4 = zero_zero_complex )
% 5.46/5.79 & ( Y3 = zero_zero_complex ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % imaginary_eq_real_iff
% 5.46/5.79 thf(fact_9253_Im__divide__Reals,axiom,
% 5.46/5.79 ! [R2: complex,Z: complex] :
% 5.46/5.79 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.46/5.79 => ( ( im @ ( divide1717551699836669952omplex @ Z @ R2 ) )
% 5.46/5.79 = ( divide_divide_real @ ( im @ Z ) @ ( re @ R2 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_divide_Reals
% 5.46/5.79 thf(fact_9254_complex__diff__cnj,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.46/5.79 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_diff_cnj
% 5.46/5.79 thf(fact_9255_complex__mult__cnj,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.46/5.79 = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_mult_cnj
% 5.46/5.79 thf(fact_9256_integer__of__num_I3_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 5.46/5.79 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 5.46/5.79
% 5.46/5.79 % integer_of_num(3)
% 5.46/5.79 thf(fact_9257_complex__cnj__mult,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( cnj @ ( times_times_complex @ X4 @ Y3 ) )
% 5.46/5.79 = ( times_times_complex @ ( cnj @ X4 ) @ ( cnj @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_cnj_mult
% 5.46/5.79 thf(fact_9258_complex__cnj__divide,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( cnj @ ( divide1717551699836669952omplex @ X4 @ Y3 ) )
% 5.46/5.79 = ( divide1717551699836669952omplex @ ( cnj @ X4 ) @ ( cnj @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_cnj_divide
% 5.46/5.79 thf(fact_9259_complex__cnj__add,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( cnj @ ( plus_plus_complex @ X4 @ Y3 ) )
% 5.46/5.79 = ( plus_plus_complex @ ( cnj @ X4 ) @ ( cnj @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_cnj_add
% 5.46/5.79 thf(fact_9260_complex__cnj__diff,axiom,
% 5.46/5.79 ! [X4: complex,Y3: complex] :
% 5.46/5.79 ( ( cnj @ ( minus_minus_complex @ X4 @ Y3 ) )
% 5.46/5.79 = ( minus_minus_complex @ ( cnj @ X4 ) @ ( cnj @ Y3 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_cnj_diff
% 5.46/5.79 thf(fact_9261_complex__In__mult__cnj__zero,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.46/5.79 = zero_zero_real ) ).
% 5.46/5.79
% 5.46/5.79 % complex_In_mult_cnj_zero
% 5.46/5.79 thf(fact_9262_Re__complex__div__eq__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B2 ) ) )
% 5.46/5.79 = zero_zero_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_complex_div_eq_0
% 5.46/5.79 thf(fact_9263_Im__complex__div__eq__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B2 ) )
% 5.46/5.79 = zero_zero_real )
% 5.46/5.79 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B2 ) ) )
% 5.46/5.79 = zero_zero_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_complex_div_eq_0
% 5.46/5.79 thf(fact_9264_complex__mod__sqrt__Re__mult__cnj,axiom,
% 5.46/5.79 ( real_V1022390504157884413omplex
% 5.46/5.79 = ( ^ [Z5: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z5 @ ( cnj @ Z5 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_mod_sqrt_Re_mult_cnj
% 5.46/5.79 thf(fact_9265_integer__of__num__triv_I1_J,axiom,
% 5.46/5.79 ( ( code_integer_of_num @ one )
% 5.46/5.79 = one_one_Code_integer ) ).
% 5.46/5.79
% 5.46/5.79 % integer_of_num_triv(1)
% 5.46/5.79 thf(fact_9266_Re__complex__div__lt__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B2 ) ) @ zero_zero_real )
% 5.46/5.79 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B2 ) ) ) @ zero_zero_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_complex_div_lt_0
% 5.46/5.79 thf(fact_9267_Re__complex__div__gt__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B2 ) ) )
% 5.46/5.79 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_complex_div_gt_0
% 5.46/5.79 thf(fact_9268_Re__complex__div__ge__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B2 ) ) )
% 5.46/5.79 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_complex_div_ge_0
% 5.46/5.79 thf(fact_9269_Re__complex__div__le__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B2 ) ) @ zero_zero_real )
% 5.46/5.79 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B2 ) ) ) @ zero_zero_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % Re_complex_div_le_0
% 5.46/5.79 thf(fact_9270_Im__complex__div__lt__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B2 ) ) @ zero_zero_real )
% 5.46/5.79 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B2 ) ) ) @ zero_zero_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_complex_div_lt_0
% 5.46/5.79 thf(fact_9271_Im__complex__div__gt__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B2 ) ) )
% 5.46/5.79 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_complex_div_gt_0
% 5.46/5.79 thf(fact_9272_Im__complex__div__ge__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B2 ) ) )
% 5.46/5.79 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B2 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_complex_div_ge_0
% 5.46/5.79 thf(fact_9273_Im__complex__div__le__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B2 ) ) @ zero_zero_real )
% 5.46/5.79 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B2 ) ) ) @ zero_zero_real ) ) ).
% 5.46/5.79
% 5.46/5.79 % Im_complex_div_le_0
% 5.46/5.79 thf(fact_9274_integer__of__num_I2_J,axiom,
% 5.46/5.79 ! [N: num] :
% 5.46/5.79 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 5.46/5.79 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % integer_of_num(2)
% 5.46/5.79 thf(fact_9275_complex__mod__mult__cnj,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.46/5.79 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_mod_mult_cnj
% 5.46/5.79 thf(fact_9276_complex__div__gt__0,axiom,
% 5.46/5.79 ! [A: complex,B2: complex] :
% 5.46/5.79 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B2 ) ) )
% 5.46/5.79 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B2 ) ) ) ) )
% 5.46/5.79 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B2 ) ) )
% 5.46/5.79 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B2 ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_div_gt_0
% 5.46/5.79 thf(fact_9277_integer__of__num__triv_I2_J,axiom,
% 5.46/5.79 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.46/5.79 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % integer_of_num_triv(2)
% 5.46/5.79 thf(fact_9278_complex__norm__square,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.79 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_norm_square
% 5.46/5.79 thf(fact_9279_complex__add__cnj,axiom,
% 5.46/5.79 ! [Z: complex] :
% 5.46/5.79 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.46/5.79 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_add_cnj
% 5.46/5.79 thf(fact_9280_complex__div__cnj,axiom,
% 5.46/5.79 ( divide1717551699836669952omplex
% 5.46/5.79 = ( ^ [A4: complex,B3: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A4 @ ( cnj @ B3 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % complex_div_cnj
% 5.46/5.79 thf(fact_9281_cnj__add__mult__eq__Re,axiom,
% 5.46/5.79 ! [Z: complex,W: complex] :
% 5.46/5.79 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.46/5.79 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % cnj_add_mult_eq_Re
% 5.46/5.79 thf(fact_9282_bit__cut__integer__def,axiom,
% 5.46/5.79 ( code_bit_cut_integer
% 5.46/5.79 = ( ^ [K3: code_integer] :
% 5.46/5.79 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.46/5.79 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % bit_cut_integer_def
% 5.46/5.79 thf(fact_9283_divmod__integer__def,axiom,
% 5.46/5.79 ( code_divmod_integer
% 5.46/5.79 = ( ^ [K3: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L ) @ ( modulo364778990260209775nteger @ K3 @ L ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_integer_def
% 5.46/5.79 thf(fact_9284_card__lessThan,axiom,
% 5.46/5.79 ! [U: nat] :
% 5.46/5.79 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 5.46/5.79 = U ) ).
% 5.46/5.79
% 5.46/5.79 % card_lessThan
% 5.46/5.79 thf(fact_9285_card__Collect__less__nat,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( finite_card_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [I2: nat] : ( ord_less_nat @ I2 @ N ) ) )
% 5.46/5.79 = N ) ).
% 5.46/5.79
% 5.46/5.79 % card_Collect_less_nat
% 5.46/5.79 thf(fact_9286_card__atMost,axiom,
% 5.46/5.79 ! [U: nat] :
% 5.46/5.79 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.46/5.79 = ( suc @ U ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_atMost
% 5.46/5.79 thf(fact_9287_card__atLeastLessThan,axiom,
% 5.46/5.79 ! [L2: nat,U: nat] :
% 5.46/5.79 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) )
% 5.46/5.79 = ( minus_minus_nat @ U @ L2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_atLeastLessThan
% 5.46/5.79 thf(fact_9288_card__Collect__le__nat,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( finite_card_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [I2: nat] : ( ord_less_eq_nat @ I2 @ N ) ) )
% 5.46/5.79 = ( suc @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_Collect_le_nat
% 5.46/5.79 thf(fact_9289_card__atLeastAtMost,axiom,
% 5.46/5.79 ! [L2: nat,U: nat] :
% 5.46/5.79 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.46/5.79 = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_atLeastAtMost
% 5.46/5.79 thf(fact_9290_card__atLeastLessThan__int,axiom,
% 5.46/5.79 ! [L2: int,U: int] :
% 5.46/5.79 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L2 @ U ) )
% 5.46/5.79 = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_atLeastLessThan_int
% 5.46/5.79 thf(fact_9291_card__atLeastAtMost__int,axiom,
% 5.46/5.79 ! [L2: int,U: int] :
% 5.46/5.79 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.46/5.79 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_atLeastAtMost_int
% 5.46/5.79 thf(fact_9292_card__less__Suc2,axiom,
% 5.46/5.79 ! [M7: set_nat,I: nat] :
% 5.46/5.79 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.46/5.79 => ( ( finite_card_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [K3: nat] :
% 5.46/5.79 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.46/5.79 & ( ord_less_nat @ K3 @ I ) ) ) )
% 5.46/5.79 = ( finite_card_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [K3: nat] :
% 5.46/5.79 ( ( member_nat @ K3 @ M7 )
% 5.46/5.79 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_less_Suc2
% 5.46/5.79 thf(fact_9293_card__less__Suc,axiom,
% 5.46/5.79 ! [M7: set_nat,I: nat] :
% 5.46/5.79 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.46/5.79 => ( ( suc
% 5.46/5.79 @ ( finite_card_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [K3: nat] :
% 5.46/5.79 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.46/5.79 & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 5.46/5.79 = ( finite_card_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [K3: nat] :
% 5.46/5.79 ( ( member_nat @ K3 @ M7 )
% 5.46/5.79 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_less_Suc
% 5.46/5.79 thf(fact_9294_card__less,axiom,
% 5.46/5.79 ! [M7: set_nat,I: nat] :
% 5.46/5.79 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.46/5.79 => ( ( finite_card_nat
% 5.46/5.79 @ ( collect_nat
% 5.46/5.79 @ ^ [K3: nat] :
% 5.46/5.79 ( ( member_nat @ K3 @ M7 )
% 5.46/5.79 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 5.46/5.79 != zero_zero_nat ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_less
% 5.46/5.79 thf(fact_9295_card__atLeastZeroLessThan__int,axiom,
% 5.46/5.79 ! [U: int] :
% 5.46/5.79 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 5.46/5.79 = ( nat2 @ U ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_atLeastZeroLessThan_int
% 5.46/5.79 thf(fact_9296_subset__card__intvl__is__intvl,axiom,
% 5.46/5.79 ! [A3: set_nat,K: nat] :
% 5.46/5.79 ( ( ord_less_eq_set_nat @ A3 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A3 ) ) ) )
% 5.46/5.79 => ( A3
% 5.46/5.79 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A3 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % subset_card_intvl_is_intvl
% 5.46/5.79 thf(fact_9297_subset__eq__atLeast0__lessThan__card,axiom,
% 5.46/5.79 ! [N3: set_nat,N: nat] :
% 5.46/5.79 ( ( ord_less_eq_set_nat @ N3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.46/5.79 => ( ord_less_eq_nat @ ( finite_card_nat @ N3 ) @ N ) ) ).
% 5.46/5.79
% 5.46/5.79 % subset_eq_atLeast0_lessThan_card
% 5.46/5.79 thf(fact_9298_card__sum__le__nat__sum,axiom,
% 5.46/5.79 ! [S2: set_nat] :
% 5.46/5.79 ( ord_less_eq_nat
% 5.46/5.79 @ ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [X: nat] : X
% 5.46/5.79 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 5.46/5.79 @ ( groups3542108847815614940at_nat
% 5.46/5.79 @ ^ [X: nat] : X
% 5.46/5.79 @ S2 ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_sum_le_nat_sum
% 5.46/5.79 thf(fact_9299_card__nth__roots,axiom,
% 5.46/5.79 ! [C: complex,N: nat] :
% 5.46/5.79 ( ( C != zero_zero_complex )
% 5.46/5.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( finite_card_complex
% 5.46/5.79 @ ( collect_complex
% 5.46/5.79 @ ^ [Z5: complex] :
% 5.46/5.79 ( ( power_power_complex @ Z5 @ N )
% 5.46/5.79 = C ) ) )
% 5.46/5.79 = N ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_nth_roots
% 5.46/5.79 thf(fact_9300_card__roots__unity__eq,axiom,
% 5.46/5.79 ! [N: nat] :
% 5.46/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.79 => ( ( finite_card_complex
% 5.46/5.79 @ ( collect_complex
% 5.46/5.79 @ ^ [Z5: complex] :
% 5.46/5.79 ( ( power_power_complex @ Z5 @ N )
% 5.46/5.79 = one_one_complex ) ) )
% 5.46/5.79 = N ) ) ).
% 5.46/5.79
% 5.46/5.79 % card_roots_unity_eq
% 5.46/5.79 thf(fact_9301_bit__cut__integer__code,axiom,
% 5.46/5.79 ( code_bit_cut_integer
% 5.46/5.79 = ( ^ [K3: code_integer] :
% 5.46/5.79 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.46/5.79 @ ( produc9125791028180074456eger_o
% 5.46/5.79 @ ^ [R5: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 5.46/5.79 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % bit_cut_integer_code
% 5.46/5.79 thf(fact_9302_divmod__abs__def,axiom,
% 5.46/5.79 ( code_divmod_abs
% 5.46/5.79 = ( ^ [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 ) ) ) ) ) ).
% 5.46/5.79
% 5.46/5.79 % divmod_abs_def
% 5.46/5.79 thf(fact_9303_divmod__integer__code,axiom,
% 5.46/5.79 ( code_divmod_integer
% 5.46/5.79 = ( ^ [K3: code_integer,L: code_integer] :
% 5.46/5.79 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.46/5.79 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 5.46/5.79 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L )
% 5.46/5.80 @ ( produc6916734918728496179nteger
% 5.46/5.80 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S4 ) ) )
% 5.46/5.80 @ ( code_divmod_abs @ K3 @ L ) ) )
% 5.46/5.80 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.46/5.80 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.46/5.80 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L )
% 5.46/5.80 @ ( produc6916734918728496179nteger
% 5.46/5.80 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S4 ) ) )
% 5.46/5.80 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % divmod_integer_code
% 5.46/5.80 thf(fact_9304_vebt__maxt_Opelims,axiom,
% 5.46/5.80 ! [X4: vEBT_VEBT,Y3: option_nat] :
% 5.46/5.80 ( ( ( vEBT_vebt_maxt @ X4 )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X4 )
% 5.46/5.80 => ( ! [A5: $o,B5: $o] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.80 => ( ( ( B5
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.80 & ( ~ B5
% 5.46/5.80 => ( ( A5
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.80 & ( ~ A5
% 5.46/5.80 => ( Y3 = none_nat ) ) ) ) )
% 5.46/5.80 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.46/5.80 => ( ! [Uu2: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) )
% 5.46/5.80 => ( ( Y3 = none_nat )
% 5.46/5.80 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) ) ) )
% 5.46/5.80 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy2 @ Uz ) )
% 5.46/5.80 => ( ( Y3
% 5.46/5.80 = ( some_nat @ Ma2 ) )
% 5.46/5.80 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy2 @ Uz ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % vebt_maxt.pelims
% 5.46/5.80 thf(fact_9305_vebt__mint_Opelims,axiom,
% 5.46/5.80 ! [X4: vEBT_VEBT,Y3: option_nat] :
% 5.46/5.80 ( ( ( vEBT_vebt_mint @ X4 )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X4 )
% 5.46/5.80 => ( ! [A5: $o,B5: $o] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.80 => ( ( ( A5
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( some_nat @ zero_zero_nat ) ) )
% 5.46/5.80 & ( ~ A5
% 5.46/5.80 => ( ( B5
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( some_nat @ one_one_nat ) ) )
% 5.46/5.80 & ( ~ B5
% 5.46/5.80 => ( Y3 = none_nat ) ) ) ) )
% 5.46/5.80 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.46/5.80 => ( ! [Uu2: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) )
% 5.46/5.80 => ( ( Y3 = none_nat )
% 5.46/5.80 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv @ Uw ) ) ) )
% 5.46/5.80 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy2 @ Uz ) )
% 5.46/5.80 => ( ( Y3
% 5.46/5.80 = ( some_nat @ Mi2 ) )
% 5.46/5.80 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy2 @ Uz ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % vebt_mint.pelims
% 5.46/5.80 thf(fact_9306_prod__decode__aux_Osimps,axiom,
% 5.46/5.80 ( nat_prod_decode_aux
% 5.46/5.80 = ( ^ [K3: nat,M6: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M6 @ K3 ) @ ( product_Pair_nat_nat @ M6 @ ( minus_minus_nat @ K3 @ M6 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M6 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % prod_decode_aux.simps
% 5.46/5.80 thf(fact_9307_nat_Odisc__eq__case_I1_J,axiom,
% 5.46/5.80 ! [Nat: nat] :
% 5.46/5.80 ( ( Nat = zero_zero_nat )
% 5.46/5.80 = ( case_nat_o @ $true
% 5.46/5.80 @ ^ [Uu: nat] : $false
% 5.46/5.80 @ Nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % nat.disc_eq_case(1)
% 5.46/5.80 thf(fact_9308_nat_Odisc__eq__case_I2_J,axiom,
% 5.46/5.80 ! [Nat: nat] :
% 5.46/5.80 ( ( Nat != zero_zero_nat )
% 5.46/5.80 = ( case_nat_o @ $false
% 5.46/5.80 @ ^ [Uu: nat] : $true
% 5.46/5.80 @ Nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % nat.disc_eq_case(2)
% 5.46/5.80 thf(fact_9309_less__eq__nat_Osimps_I2_J,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.46/5.80 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % less_eq_nat.simps(2)
% 5.46/5.80 thf(fact_9310_max__Suc2,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.46/5.80 = ( case_nat_nat @ ( suc @ N )
% 5.46/5.80 @ ^ [M2: nat] : ( suc @ ( ord_max_nat @ M2 @ N ) )
% 5.46/5.80 @ M ) ) ).
% 5.46/5.80
% 5.46/5.80 % max_Suc2
% 5.46/5.80 thf(fact_9311_max__Suc1,axiom,
% 5.46/5.80 ! [N: nat,M: nat] :
% 5.46/5.80 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.46/5.80 = ( case_nat_nat @ ( suc @ N )
% 5.46/5.80 @ ^ [M2: nat] : ( suc @ ( ord_max_nat @ N @ M2 ) )
% 5.46/5.80 @ M ) ) ).
% 5.46/5.80
% 5.46/5.80 % max_Suc1
% 5.46/5.80 thf(fact_9312_diff__Suc,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.46/5.80 = ( case_nat_nat @ zero_zero_nat
% 5.46/5.80 @ ^ [K3: nat] : K3
% 5.46/5.80 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % diff_Suc
% 5.46/5.80 thf(fact_9313_prod__decode__aux_Oelims,axiom,
% 5.46/5.80 ! [X4: nat,Xa: nat,Y3: product_prod_nat_nat] :
% 5.46/5.80 ( ( ( nat_prod_decode_aux @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( ( ord_less_eq_nat @ Xa @ X4 )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X4 @ Xa ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_eq_nat @ Xa @ X4 )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( nat_prod_decode_aux @ ( suc @ X4 ) @ ( minus_minus_nat @ Xa @ ( suc @ X4 ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % prod_decode_aux.elims
% 5.46/5.80 thf(fact_9314_pred__def,axiom,
% 5.46/5.80 ( pred
% 5.46/5.80 = ( case_nat_nat @ zero_zero_nat
% 5.46/5.80 @ ^ [X23: nat] : X23 ) ) ).
% 5.46/5.80
% 5.46/5.80 % pred_def
% 5.46/5.80 thf(fact_9315_floor__real__def,axiom,
% 5.46/5.80 ( archim6058952711729229775r_real
% 5.46/5.80 = ( ^ [X: real] :
% 5.46/5.80 ( the_int
% 5.46/5.80 @ ^ [Z5: int] :
% 5.46/5.80 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X )
% 5.46/5.80 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % floor_real_def
% 5.46/5.80 thf(fact_9316_floor__rat__def,axiom,
% 5.46/5.80 ( archim3151403230148437115or_rat
% 5.46/5.80 = ( ^ [X: rat] :
% 5.46/5.80 ( the_int
% 5.46/5.80 @ ^ [Z5: int] :
% 5.46/5.80 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X )
% 5.46/5.80 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % floor_rat_def
% 5.46/5.80 thf(fact_9317_drop__bit__numeral__minus__bit1,axiom,
% 5.46/5.80 ! [L2: num,K: num] :
% 5.46/5.80 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.80 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_numeral_minus_bit1
% 5.46/5.80 thf(fact_9318_Suc__0__mod__numeral,axiom,
% 5.46/5.80 ! [K: num] :
% 5.46/5.80 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.80 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Suc_0_mod_numeral
% 5.46/5.80 thf(fact_9319_drop__bit__nonnegative__int__iff,axiom,
% 5.46/5.80 ! [N: nat,K: int] :
% 5.46/5.80 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.46/5.80 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_nonnegative_int_iff
% 5.46/5.80 thf(fact_9320_drop__bit__negative__int__iff,axiom,
% 5.46/5.80 ! [N: nat,K: int] :
% 5.46/5.80 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.46/5.80 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_negative_int_iff
% 5.46/5.80 thf(fact_9321_drop__bit__minus__one,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.46/5.80 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_minus_one
% 5.46/5.80 thf(fact_9322_snd__divmod__nat,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.46/5.80 = ( modulo_modulo_nat @ M @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % snd_divmod_nat
% 5.46/5.80 thf(fact_9323_drop__bit__Suc__minus__bit0,axiom,
% 5.46/5.80 ! [N: nat,K: num] :
% 5.46/5.80 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.80 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_Suc_minus_bit0
% 5.46/5.80 thf(fact_9324_drop__bit__numeral__minus__bit0,axiom,
% 5.46/5.80 ! [L2: num,K: num] :
% 5.46/5.80 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.46/5.80 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_numeral_minus_bit0
% 5.46/5.80 thf(fact_9325_drop__bit__Suc__minus__bit1,axiom,
% 5.46/5.80 ! [N: nat,K: num] :
% 5.46/5.80 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.46/5.80 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_Suc_minus_bit1
% 5.46/5.80 thf(fact_9326_abs__rat__def,axiom,
% 5.46/5.80 ( abs_abs_rat
% 5.46/5.80 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % abs_rat_def
% 5.46/5.80 thf(fact_9327_sgn__rat__def,axiom,
% 5.46/5.80 ( sgn_sgn_rat
% 5.46/5.80 = ( ^ [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 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sgn_rat_def
% 5.46/5.80 thf(fact_9328_obtain__pos__sum,axiom,
% 5.46/5.80 ! [R2: rat] :
% 5.46/5.80 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.46/5.80 => ~ ! [S3: rat] :
% 5.46/5.80 ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 5.46/5.80 => ! [T2: rat] :
% 5.46/5.80 ( ( ord_less_rat @ zero_zero_rat @ T2 )
% 5.46/5.80 => ( R2
% 5.46/5.80 != ( plus_plus_rat @ S3 @ T2 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % obtain_pos_sum
% 5.46/5.80 thf(fact_9329_less__eq__rat__def,axiom,
% 5.46/5.80 ( ord_less_eq_rat
% 5.46/5.80 = ( ^ [X: rat,Y: rat] :
% 5.46/5.80 ( ( ord_less_rat @ X @ Y )
% 5.46/5.80 | ( X = Y ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % less_eq_rat_def
% 5.46/5.80 thf(fact_9330_drop__bit__push__bit__int,axiom,
% 5.46/5.80 ! [M: nat,N: nat,K: int] :
% 5.46/5.80 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.46/5.80 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_push_bit_int
% 5.46/5.80 thf(fact_9331_drop__bit__int__def,axiom,
% 5.46/5.80 ( bit_se8568078237143864401it_int
% 5.46/5.80 = ( ^ [N2: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_int_def
% 5.46/5.80 thf(fact_9332_rat__inverse__code,axiom,
% 5.46/5.80 ! [P2: rat] :
% 5.46/5.80 ( ( quotient_of @ ( inverse_inverse_rat @ P2 ) )
% 5.46/5.80 = ( produc4245557441103728435nt_int
% 5.46/5.80 @ ^ [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 ) ) )
% 5.46/5.80 @ ( quotient_of @ P2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % rat_inverse_code
% 5.46/5.80 thf(fact_9333_normalize__negative,axiom,
% 5.46/5.80 ! [Q2: int,P2: int] :
% 5.46/5.80 ( ( ord_less_int @ Q2 @ zero_zero_int )
% 5.46/5.80 => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.46/5.80 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P2 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % normalize_negative
% 5.46/5.80 thf(fact_9334_Suc__0__div__numeral,axiom,
% 5.46/5.80 ! [K: num] :
% 5.46/5.80 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.80 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Suc_0_div_numeral
% 5.46/5.80 thf(fact_9335_snd__divmod__integer,axiom,
% 5.46/5.80 ! [K: code_integer,L2: code_integer] :
% 5.46/5.80 ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L2 ) )
% 5.46/5.80 = ( modulo364778990260209775nteger @ K @ L2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % snd_divmod_integer
% 5.46/5.80 thf(fact_9336_snd__divmod__abs,axiom,
% 5.46/5.80 ! [K: code_integer,L2: code_integer] :
% 5.46/5.80 ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L2 ) )
% 5.46/5.80 = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % snd_divmod_abs
% 5.46/5.80 thf(fact_9337_drop__bit__of__Suc__0,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.46/5.80 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_of_Suc_0
% 5.46/5.80 thf(fact_9338_fst__divmod__nat,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.46/5.80 = ( divide_divide_nat @ M @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % fst_divmod_nat
% 5.46/5.80 thf(fact_9339_quotient__of__denom__pos_H,axiom,
% 5.46/5.80 ! [R2: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % quotient_of_denom_pos'
% 5.46/5.80 thf(fact_9340_diff__rat__def,axiom,
% 5.46/5.80 ( minus_minus_rat
% 5.46/5.80 = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % diff_rat_def
% 5.46/5.80 thf(fact_9341_divide__rat__def,axiom,
% 5.46/5.80 ( divide_divide_rat
% 5.46/5.80 = ( ^ [Q4: rat,R5: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % divide_rat_def
% 5.46/5.80 thf(fact_9342_rat__divide__code,axiom,
% 5.46/5.80 ! [P2: rat,Q2: rat] :
% 5.46/5.80 ( ( quotient_of @ ( divide_divide_rat @ P2 @ Q2 ) )
% 5.46/5.80 = ( produc4245557441103728435nt_int
% 5.46/5.80 @ ^ [A4: int,C2: int] :
% 5.46/5.80 ( produc4245557441103728435nt_int
% 5.46/5.80 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C2 @ B3 ) ) )
% 5.46/5.80 @ ( quotient_of @ Q2 ) )
% 5.46/5.80 @ ( quotient_of @ P2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % rat_divide_code
% 5.46/5.80 thf(fact_9343_rat__times__code,axiom,
% 5.46/5.80 ! [P2: rat,Q2: rat] :
% 5.46/5.80 ( ( quotient_of @ ( times_times_rat @ P2 @ Q2 ) )
% 5.46/5.80 = ( produc4245557441103728435nt_int
% 5.46/5.80 @ ^ [A4: int,C2: int] :
% 5.46/5.80 ( produc4245557441103728435nt_int
% 5.46/5.80 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ B3 ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.46/5.80 @ ( quotient_of @ Q2 ) )
% 5.46/5.80 @ ( quotient_of @ P2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % rat_times_code
% 5.46/5.80 thf(fact_9344_drop__bit__nat__eq,axiom,
% 5.46/5.80 ! [N: nat,K: int] :
% 5.46/5.80 ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 5.46/5.80 = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_nat_eq
% 5.46/5.80 thf(fact_9345_quotient__of__div,axiom,
% 5.46/5.80 ! [R2: rat,N: int,D: int] :
% 5.46/5.80 ( ( ( quotient_of @ R2 )
% 5.46/5.80 = ( product_Pair_int_int @ N @ D ) )
% 5.46/5.80 => ( R2
% 5.46/5.80 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % quotient_of_div
% 5.46/5.80 thf(fact_9346_rat__plus__code,axiom,
% 5.46/5.80 ! [P2: rat,Q2: rat] :
% 5.46/5.80 ( ( quotient_of @ ( plus_plus_rat @ P2 @ Q2 ) )
% 5.46/5.80 = ( produc4245557441103728435nt_int
% 5.46/5.80 @ ^ [A4: int,C2: int] :
% 5.46/5.80 ( produc4245557441103728435nt_int
% 5.46/5.80 @ ^ [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 ) ) )
% 5.46/5.80 @ ( quotient_of @ Q2 ) )
% 5.46/5.80 @ ( quotient_of @ P2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % rat_plus_code
% 5.46/5.80 thf(fact_9347_rat__minus__code,axiom,
% 5.46/5.80 ! [P2: rat,Q2: rat] :
% 5.46/5.80 ( ( quotient_of @ ( minus_minus_rat @ P2 @ Q2 ) )
% 5.46/5.80 = ( produc4245557441103728435nt_int
% 5.46/5.80 @ ^ [A4: int,C2: int] :
% 5.46/5.80 ( produc4245557441103728435nt_int
% 5.46/5.80 @ ^ [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 ) ) )
% 5.46/5.80 @ ( quotient_of @ Q2 ) )
% 5.46/5.80 @ ( quotient_of @ P2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % rat_minus_code
% 5.46/5.80 thf(fact_9348_quotient__of__denom__pos,axiom,
% 5.46/5.80 ! [R2: rat,P2: int,Q2: int] :
% 5.46/5.80 ( ( ( quotient_of @ R2 )
% 5.46/5.80 = ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.46/5.80 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % quotient_of_denom_pos
% 5.46/5.80 thf(fact_9349_normalize__denom__pos,axiom,
% 5.46/5.80 ! [R2: product_prod_int_int,P2: int,Q2: int] :
% 5.46/5.80 ( ( ( normalize @ R2 )
% 5.46/5.80 = ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.46/5.80 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % normalize_denom_pos
% 5.46/5.80 thf(fact_9350_normalize__crossproduct,axiom,
% 5.46/5.80 ! [Q2: int,S: int,P2: int,R2: int] :
% 5.46/5.80 ( ( Q2 != zero_zero_int )
% 5.46/5.80 => ( ( S != zero_zero_int )
% 5.46/5.80 => ( ( ( normalize @ ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.46/5.80 = ( normalize @ ( product_Pair_int_int @ R2 @ S ) ) )
% 5.46/5.80 => ( ( times_times_int @ P2 @ S )
% 5.46/5.80 = ( times_times_int @ R2 @ Q2 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % normalize_crossproduct
% 5.46/5.80 thf(fact_9351_drop__bit__nat__def,axiom,
% 5.46/5.80 ( bit_se8570568707652914677it_nat
% 5.46/5.80 = ( ^ [N2: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_bit_nat_def
% 5.46/5.80 thf(fact_9352_one__mod__minus__numeral,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % one_mod_minus_numeral
% 5.46/5.80 thf(fact_9353_minus__one__mod__numeral,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % minus_one_mod_numeral
% 5.46/5.80 thf(fact_9354_numeral__mod__minus__numeral,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % numeral_mod_minus_numeral
% 5.46/5.80 thf(fact_9355_fst__divmod__integer,axiom,
% 5.46/5.80 ! [K: code_integer,L2: code_integer] :
% 5.46/5.80 ( ( produc8508995932063986495nteger @ ( code_divmod_integer @ K @ L2 ) )
% 5.46/5.80 = ( divide6298287555418463151nteger @ K @ L2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % fst_divmod_integer
% 5.46/5.80 thf(fact_9356_fst__divmod__abs,axiom,
% 5.46/5.80 ! [K: code_integer,L2: code_integer] :
% 5.46/5.80 ( ( produc8508995932063986495nteger @ ( code_divmod_abs @ K @ L2 ) )
% 5.46/5.80 = ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % fst_divmod_abs
% 5.46/5.80 thf(fact_9357_minus__numeral__mod__numeral,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % minus_numeral_mod_numeral
% 5.46/5.80 thf(fact_9358_Divides_Oadjust__mod__def,axiom,
% 5.46/5.80 ( adjust_mod
% 5.46/5.80 = ( ^ [L: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L @ R5 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Divides.adjust_mod_def
% 5.46/5.80 thf(fact_9359_bezw_Osimps,axiom,
% 5.46/5.80 ( bezw
% 5.46/5.80 = ( ^ [X: 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 @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % bezw.simps
% 5.46/5.80 thf(fact_9360_bezw_Oelims,axiom,
% 5.46/5.80 ! [X4: nat,Xa: nat,Y3: product_prod_int_int] :
% 5.46/5.80 ( ( ( bezw @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( ( Xa = zero_zero_nat )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.46/5.80 & ( ( Xa != zero_zero_nat )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Xa ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % bezw.elims
% 5.46/5.80 thf(fact_9361_bezw__non__0,axiom,
% 5.46/5.80 ! [Y3: nat,X4: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ Y3 )
% 5.46/5.80 => ( ( bezw @ X4 @ Y3 )
% 5.46/5.80 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X4 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X4 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X4 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Y3 ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % bezw_non_0
% 5.46/5.80 thf(fact_9362_bezw_Opelims,axiom,
% 5.46/5.80 ! [X4: nat,Xa: nat,Y3: product_prod_int_int] :
% 5.46/5.80 ( ( ( bezw @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 5.46/5.80 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.46/5.80 & ( ( Xa != zero_zero_nat )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Xa ) ) ) ) ) ) ) )
% 5.46/5.80 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % bezw.pelims
% 5.46/5.80 thf(fact_9363_normalize__def,axiom,
% 5.46/5.80 ( normalize
% 5.46/5.80 = ( ^ [P3: product_prod_int_int] :
% 5.46/5.80 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P3 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P3 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P3 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) )
% 5.46/5.80 @ ( if_Pro3027730157355071871nt_int
% 5.46/5.80 @ ( ( product_snd_int_int @ P3 )
% 5.46/5.80 = zero_zero_int )
% 5.46/5.80 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.46/5.80 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P3 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P3 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P3 ) @ ( product_snd_int_int @ P3 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % normalize_def
% 5.46/5.80 thf(fact_9364_Frct__code__post_I5_J,axiom,
% 5.46/5.80 ! [K: num] :
% 5.46/5.80 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.46/5.80 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Frct_code_post(5)
% 5.46/5.80 thf(fact_9365_gcd__pos__int,axiom,
% 5.46/5.80 ! [M: int,N: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 5.46/5.80 = ( ( M != zero_zero_int )
% 5.46/5.80 | ( N != zero_zero_int ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_pos_int
% 5.46/5.80 thf(fact_9366_gcd__red__int,axiom,
% 5.46/5.80 ( gcd_gcd_int
% 5.46/5.80 = ( ^ [X: int,Y: int] : ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X @ Y ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_red_int
% 5.46/5.80 thf(fact_9367_bezout__int,axiom,
% 5.46/5.80 ! [X4: int,Y3: int] :
% 5.46/5.80 ? [U3: int,V3: int] :
% 5.46/5.80 ( ( plus_plus_int @ ( times_times_int @ U3 @ X4 ) @ ( times_times_int @ V3 @ Y3 ) )
% 5.46/5.80 = ( gcd_gcd_int @ X4 @ Y3 ) ) ).
% 5.46/5.80
% 5.46/5.80 % bezout_int
% 5.46/5.80 thf(fact_9368_gcd__mult__distrib__int,axiom,
% 5.46/5.80 ! [K: int,M: int,N: int] :
% 5.46/5.80 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 5.46/5.80 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_mult_distrib_int
% 5.46/5.80 thf(fact_9369_gcd__le1__int,axiom,
% 5.46/5.80 ! [A: int,B2: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ A )
% 5.46/5.80 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B2 ) @ A ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_le1_int
% 5.46/5.80 thf(fact_9370_gcd__le2__int,axiom,
% 5.46/5.80 ! [B2: int,A: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.80 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B2 ) @ B2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_le2_int
% 5.46/5.80 thf(fact_9371_gcd__non__0__int,axiom,
% 5.46/5.80 ! [Y3: int,X4: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ Y3 )
% 5.46/5.80 => ( ( gcd_gcd_int @ X4 @ Y3 )
% 5.46/5.80 = ( gcd_gcd_int @ Y3 @ ( modulo_modulo_int @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_non_0_int
% 5.46/5.80 thf(fact_9372_gcd__code__int,axiom,
% 5.46/5.80 ( gcd_gcd_int
% 5.46/5.80 = ( ^ [K3: int,L: int] : ( abs_abs_int @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( gcd_gcd_int @ L @ ( modulo_modulo_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_code_int
% 5.46/5.80 thf(fact_9373_Frct__code__post_I6_J,axiom,
% 5.46/5.80 ! [K: num,L2: num] :
% 5.46/5.80 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 5.46/5.80 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Frct_code_post(6)
% 5.46/5.80 thf(fact_9374_prod__decode__aux_Opelims,axiom,
% 5.46/5.80 ! [X4: nat,Xa: nat,Y3: product_prod_nat_nat] :
% 5.46/5.80 ( ( ( nat_prod_decode_aux @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 5.46/5.80 => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X4 )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X4 @ Xa ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_eq_nat @ Xa @ X4 )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( nat_prod_decode_aux @ ( suc @ X4 ) @ ( minus_minus_nat @ Xa @ ( suc @ X4 ) ) ) ) ) )
% 5.46/5.80 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % prod_decode_aux.pelims
% 5.46/5.80 thf(fact_9375_finite__enumerate,axiom,
% 5.46/5.80 ! [S2: set_nat] :
% 5.46/5.80 ( ( finite_finite_nat @ S2 )
% 5.46/5.80 => ? [R3: nat > nat] :
% 5.46/5.80 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 5.46/5.80 & ! [N6: nat] :
% 5.46/5.80 ( ( ord_less_nat @ N6 @ ( finite_card_nat @ S2 ) )
% 5.46/5.80 => ( member_nat @ ( R3 @ N6 ) @ S2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % finite_enumerate
% 5.46/5.80 thf(fact_9376_gcd__1__nat,axiom,
% 5.46/5.80 ! [M: nat] :
% 5.46/5.80 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.46/5.80 = one_one_nat ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_1_nat
% 5.46/5.80 thf(fact_9377_gcd__Suc__0,axiom,
% 5.46/5.80 ! [M: nat] :
% 5.46/5.80 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.46/5.80 = ( suc @ zero_zero_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_Suc_0
% 5.46/5.80 thf(fact_9378_gcd__pos__nat,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.46/5.80 = ( ( M != zero_zero_nat )
% 5.46/5.80 | ( N != zero_zero_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_pos_nat
% 5.46/5.80 thf(fact_9379_gcd__red__nat,axiom,
% 5.46/5.80 ( gcd_gcd_nat
% 5.46/5.80 = ( ^ [X: nat,Y: nat] : ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_red_nat
% 5.46/5.80 thf(fact_9380_gcd__mult__distrib__nat,axiom,
% 5.46/5.80 ! [K: nat,M: nat,N: nat] :
% 5.46/5.80 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 5.46/5.80 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_mult_distrib_nat
% 5.46/5.80 thf(fact_9381_gcd__le2__nat,axiom,
% 5.46/5.80 ! [B2: nat,A: nat] :
% 5.46/5.80 ( ( B2 != zero_zero_nat )
% 5.46/5.80 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B2 ) @ B2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_le2_nat
% 5.46/5.80 thf(fact_9382_gcd__le1__nat,axiom,
% 5.46/5.80 ! [A: nat,B2: nat] :
% 5.46/5.80 ( ( A != zero_zero_nat )
% 5.46/5.80 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B2 ) @ A ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_le1_nat
% 5.46/5.80 thf(fact_9383_gcd__diff2__nat,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.80 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.46/5.80 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_diff2_nat
% 5.46/5.80 thf(fact_9384_gcd__diff1__nat,axiom,
% 5.46/5.80 ! [N: nat,M: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ N @ M )
% 5.46/5.80 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.46/5.80 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_diff1_nat
% 5.46/5.80 thf(fact_9385_gcd__non__0__nat,axiom,
% 5.46/5.80 ! [Y3: nat,X4: nat] :
% 5.46/5.80 ( ( Y3 != zero_zero_nat )
% 5.46/5.80 => ( ( gcd_gcd_nat @ X4 @ Y3 )
% 5.46/5.80 = ( gcd_gcd_nat @ Y3 @ ( modulo_modulo_nat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_non_0_nat
% 5.46/5.80 thf(fact_9386_gcd__nat_Osimps,axiom,
% 5.46/5.80 ( gcd_gcd_nat
% 5.46/5.80 = ( ^ [X: nat,Y: nat] : ( if_nat @ ( Y = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_nat.simps
% 5.46/5.80 thf(fact_9387_gcd__nat_Oelims,axiom,
% 5.46/5.80 ! [X4: nat,Xa: nat,Y3: nat] :
% 5.46/5.80 ( ( ( gcd_gcd_nat @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( ( Xa = zero_zero_nat )
% 5.46/5.80 => ( Y3 = X4 ) )
% 5.46/5.80 & ( ( Xa != zero_zero_nat )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_nat.elims
% 5.46/5.80 thf(fact_9388_bezout__nat,axiom,
% 5.46/5.80 ! [A: nat,B2: nat] :
% 5.46/5.80 ( ( A != zero_zero_nat )
% 5.46/5.80 => ? [X3: nat,Y4: nat] :
% 5.46/5.80 ( ( times_times_nat @ A @ X3 )
% 5.46/5.80 = ( plus_plus_nat @ ( times_times_nat @ B2 @ Y4 ) @ ( gcd_gcd_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % bezout_nat
% 5.46/5.80 thf(fact_9389_bezout__gcd__nat_H,axiom,
% 5.46/5.80 ! [B2: nat,A: nat] :
% 5.46/5.80 ? [X3: nat,Y4: nat] :
% 5.46/5.80 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B2 @ Y4 ) @ ( times_times_nat @ A @ X3 ) )
% 5.46/5.80 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B2 @ Y4 ) )
% 5.46/5.80 = ( gcd_gcd_nat @ A @ B2 ) ) )
% 5.46/5.80 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y4 ) @ ( times_times_nat @ B2 @ X3 ) )
% 5.46/5.80 & ( ( minus_minus_nat @ ( times_times_nat @ B2 @ X3 ) @ ( times_times_nat @ A @ Y4 ) )
% 5.46/5.80 = ( gcd_gcd_nat @ A @ B2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % bezout_gcd_nat'
% 5.46/5.80 thf(fact_9390_gcd__code__integer,axiom,
% 5.46/5.80 ( gcd_gcd_Code_integer
% 5.46/5.80 = ( ^ [K3: code_integer,L: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L = zero_z3403309356797280102nteger ) @ K3 @ ( gcd_gcd_Code_integer @ L @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_code_integer
% 5.46/5.80 thf(fact_9391_bezw__aux,axiom,
% 5.46/5.80 ! [X4: nat,Y3: nat] :
% 5.46/5.80 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X4 @ Y3 ) )
% 5.46/5.80 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X4 @ Y3 ) ) @ ( semiri1314217659103216013at_int @ X4 ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X4 @ Y3 ) ) @ ( semiri1314217659103216013at_int @ Y3 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % bezw_aux
% 5.46/5.80 thf(fact_9392_nat__descend__induct,axiom,
% 5.46/5.80 ! [N: nat,P: nat > $o,M: nat] :
% 5.46/5.80 ( ! [K2: nat] :
% 5.46/5.80 ( ( ord_less_nat @ N @ K2 )
% 5.46/5.80 => ( P @ K2 ) )
% 5.46/5.80 => ( ! [K2: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ K2 @ N )
% 5.46/5.80 => ( ! [I4: nat] :
% 5.46/5.80 ( ( ord_less_nat @ K2 @ I4 )
% 5.46/5.80 => ( P @ I4 ) )
% 5.46/5.80 => ( P @ K2 ) ) )
% 5.46/5.80 => ( P @ M ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % nat_descend_induct
% 5.46/5.80 thf(fact_9393_gcd__nat_Opelims,axiom,
% 5.46/5.80 ! [X4: nat,Xa: nat,Y3: nat] :
% 5.46/5.80 ( ( ( gcd_gcd_nat @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 5.46/5.80 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.46/5.80 => ( Y3 = X4 ) )
% 5.46/5.80 & ( ( Xa != zero_zero_nat )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) ) )
% 5.46/5.80 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_nat.pelims
% 5.46/5.80 thf(fact_9394_divmod__integer__eq__cases,axiom,
% 5.46/5.80 ( code_divmod_integer
% 5.46/5.80 = ( ^ [K3: code_integer,L: code_integer] :
% 5.46/5.80 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.46/5.80 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.46/5.80 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 5.46/5.80 @ ( if_Pro6119634080678213985nteger
% 5.46/5.80 @ ( ( sgn_sgn_Code_integer @ K3 )
% 5.46/5.80 = ( sgn_sgn_Code_integer @ L ) )
% 5.46/5.80 @ ( code_divmod_abs @ K3 @ L )
% 5.46/5.80 @ ( produc6916734918728496179nteger
% 5.46/5.80 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S4 ) ) )
% 5.46/5.80 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % divmod_integer_eq_cases
% 5.46/5.80 thf(fact_9395_card__greaterThanLessThan__int,axiom,
% 5.46/5.80 ! [L2: int,U: int] :
% 5.46/5.80 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 5.46/5.80 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % card_greaterThanLessThan_int
% 5.46/5.80 thf(fact_9396_xor__minus__numerals_I2_J,axiom,
% 5.46/5.80 ! [K: int,N: num] :
% 5.46/5.80 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_minus_numerals(2)
% 5.46/5.80 thf(fact_9397_xor__minus__numerals_I1_J,axiom,
% 5.46/5.80 ! [N: num,K: int] :
% 5.46/5.80 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.46/5.80 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_minus_numerals(1)
% 5.46/5.80 thf(fact_9398_finite__greaterThanLessThan__int,axiom,
% 5.46/5.80 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 5.46/5.80
% 5.46/5.80 % finite_greaterThanLessThan_int
% 5.46/5.80 thf(fact_9399_card_Ocomp__fun__commute__on,axiom,
% 5.46/5.80 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.46/5.80 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.46/5.80
% 5.46/5.80 % card.comp_fun_commute_on
% 5.46/5.80 thf(fact_9400_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.46/5.80 ! [L2: int,U: int] :
% 5.46/5.80 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 5.46/5.80 = ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 5.46/5.80
% 5.46/5.80 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.46/5.80 thf(fact_9401_sub__BitM__One__eq,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.46/5.80 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sub_BitM_One_eq
% 5.46/5.80 thf(fact_9402_finite__greaterThanLessThan,axiom,
% 5.46/5.80 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 5.46/5.80
% 5.46/5.80 % finite_greaterThanLessThan
% 5.46/5.80 thf(fact_9403_card__greaterThanLessThan,axiom,
% 5.46/5.80 ! [L2: nat,U: nat] :
% 5.46/5.80 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 5.46/5.80 = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % card_greaterThanLessThan
% 5.46/5.80 thf(fact_9404_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.46/5.80 ! [L2: nat,U: nat] :
% 5.46/5.80 ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 5.46/5.80 = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 5.46/5.80
% 5.46/5.80 % atLeastSucLessThan_greaterThanLessThan
% 5.46/5.80 thf(fact_9405_tanh__real__bounds,axiom,
% 5.46/5.80 ! [X4: real] : ( member_real @ ( tanh_real @ X4 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.46/5.80
% 5.46/5.80 % tanh_real_bounds
% 5.46/5.80 thf(fact_9406_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.46/5.80 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.46/5.80 @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 5.46/5.80 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X ) ) ).
% 5.46/5.80
% 5.46/5.80 % max_nat.semilattice_neutr_order_axioms
% 5.46/5.80 thf(fact_9407_Suc__funpow,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( compow_nat_nat @ N @ suc )
% 5.46/5.80 = ( plus_plus_nat @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % Suc_funpow
% 5.46/5.80 thf(fact_9408_int__of__integer__code,axiom,
% 5.46/5.80 ( code_int_of_integer
% 5.46/5.80 = ( ^ [K3: code_integer] :
% 5.46/5.80 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.46/5.80 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.46/5.80 @ ( produc1553301316500091796er_int
% 5.46/5.80 @ ^ [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 ) )
% 5.46/5.80 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % int_of_integer_code
% 5.46/5.80 thf(fact_9409_plus__integer_Orep__eq,axiom,
% 5.46/5.80 ! [X4: code_integer,Xa: code_integer] :
% 5.46/5.80 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X4 @ Xa ) )
% 5.46/5.80 = ( plus_plus_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % plus_integer.rep_eq
% 5.46/5.80 thf(fact_9410_times__integer_Orep__eq,axiom,
% 5.46/5.80 ! [X4: code_integer,Xa: code_integer] :
% 5.46/5.80 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X4 @ Xa ) )
% 5.46/5.80 = ( times_times_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % times_integer.rep_eq
% 5.46/5.80 thf(fact_9411_minus__integer_Orep__eq,axiom,
% 5.46/5.80 ! [X4: code_integer,Xa: code_integer] :
% 5.46/5.80 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X4 @ Xa ) )
% 5.46/5.80 = ( minus_minus_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % minus_integer.rep_eq
% 5.46/5.80 thf(fact_9412_divide__integer_Orep__eq,axiom,
% 5.46/5.80 ! [X4: code_integer,Xa: code_integer] :
% 5.46/5.80 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X4 @ Xa ) )
% 5.46/5.80 = ( divide_divide_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % divide_integer.rep_eq
% 5.46/5.80 thf(fact_9413_modulo__integer_Orep__eq,axiom,
% 5.46/5.80 ! [X4: code_integer,Xa: code_integer] :
% 5.46/5.80 ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X4 @ Xa ) )
% 5.46/5.80 = ( modulo_modulo_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % modulo_integer.rep_eq
% 5.46/5.80 thf(fact_9414_less__integer_Orep__eq,axiom,
% 5.46/5.80 ( ord_le6747313008572928689nteger
% 5.46/5.80 = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % less_integer.rep_eq
% 5.46/5.80 thf(fact_9415_integer__less__iff,axiom,
% 5.46/5.80 ( ord_le6747313008572928689nteger
% 5.46/5.80 = ( ^ [K3: code_integer,L: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % integer_less_iff
% 5.46/5.80 thf(fact_9416_times__int_Oabs__eq,axiom,
% 5.46/5.80 ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 5.46/5.80 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 5.46/5.80 = ( abs_Integ
% 5.46/5.80 @ ( produc27273713700761075at_nat
% 5.46/5.80 @ ^ [X: nat,Y: nat] :
% 5.46/5.80 ( produc2626176000494625587at_nat
% 5.46/5.80 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U4 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U4 ) ) ) )
% 5.46/5.80 @ Xa
% 5.46/5.80 @ X4 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % times_int.abs_eq
% 5.46/5.80 thf(fact_9417_Gcd__remove0__nat,axiom,
% 5.46/5.80 ! [M7: set_nat] :
% 5.46/5.80 ( ( finite_finite_nat @ M7 )
% 5.46/5.80 => ( ( gcd_Gcd_nat @ M7 )
% 5.46/5.80 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Gcd_remove0_nat
% 5.46/5.80 thf(fact_9418_Gcd__nat__eq__one,axiom,
% 5.46/5.80 ! [N3: set_nat] :
% 5.46/5.80 ( ( member_nat @ one_one_nat @ N3 )
% 5.46/5.80 => ( ( gcd_Gcd_nat @ N3 )
% 5.46/5.80 = one_one_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % Gcd_nat_eq_one
% 5.46/5.80 thf(fact_9419_nat_Oabs__eq,axiom,
% 5.46/5.80 ! [X4: product_prod_nat_nat] :
% 5.46/5.80 ( ( nat2 @ ( abs_Integ @ X4 ) )
% 5.46/5.80 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X4 ) ) ).
% 5.46/5.80
% 5.46/5.80 % nat.abs_eq
% 5.46/5.80 thf(fact_9420_one__int__def,axiom,
% 5.46/5.80 ( one_one_int
% 5.46/5.80 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % one_int_def
% 5.46/5.80 thf(fact_9421_less__int_Oabs__eq,axiom,
% 5.46/5.80 ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 5.46/5.80 ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 5.46/5.80 = ( produc8739625826339149834_nat_o
% 5.46/5.80 @ ^ [X: nat,Y: nat] :
% 5.46/5.80 ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U4 @ Y ) ) )
% 5.46/5.80 @ Xa
% 5.46/5.80 @ X4 ) ) ).
% 5.46/5.80
% 5.46/5.80 % less_int.abs_eq
% 5.46/5.80 thf(fact_9422_less__eq__int_Oabs__eq,axiom,
% 5.46/5.80 ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 5.46/5.80 ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 5.46/5.80 = ( produc8739625826339149834_nat_o
% 5.46/5.80 @ ^ [X: nat,Y: nat] :
% 5.46/5.80 ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [U4: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U4 @ Y ) ) )
% 5.46/5.80 @ Xa
% 5.46/5.80 @ X4 ) ) ).
% 5.46/5.80
% 5.46/5.80 % less_eq_int.abs_eq
% 5.46/5.80 thf(fact_9423_plus__int_Oabs__eq,axiom,
% 5.46/5.80 ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 5.46/5.80 ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 5.46/5.80 = ( abs_Integ
% 5.46/5.80 @ ( produc27273713700761075at_nat
% 5.46/5.80 @ ^ [X: nat,Y: nat] :
% 5.46/5.80 ( produc2626176000494625587at_nat
% 5.46/5.80 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U4 ) @ ( plus_plus_nat @ Y @ V4 ) ) )
% 5.46/5.80 @ Xa
% 5.46/5.80 @ X4 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % plus_int.abs_eq
% 5.46/5.80 thf(fact_9424_minus__int_Oabs__eq,axiom,
% 5.46/5.80 ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 5.46/5.80 ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 5.46/5.80 = ( abs_Integ
% 5.46/5.80 @ ( produc27273713700761075at_nat
% 5.46/5.80 @ ^ [X: nat,Y: nat] :
% 5.46/5.80 ( produc2626176000494625587at_nat
% 5.46/5.80 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U4 ) ) )
% 5.46/5.80 @ Xa
% 5.46/5.80 @ X4 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % minus_int.abs_eq
% 5.46/5.80 thf(fact_9425_num__of__nat_Osimps_I2_J,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( num_of_nat @ ( suc @ N ) )
% 5.46/5.80 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( num_of_nat @ ( suc @ N ) )
% 5.46/5.80 = one ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % num_of_nat.simps(2)
% 5.46/5.80 thf(fact_9426_num__of__nat__numeral__eq,axiom,
% 5.46/5.80 ! [Q2: num] :
% 5.46/5.80 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.46/5.80 = Q2 ) ).
% 5.46/5.80
% 5.46/5.80 % num_of_nat_numeral_eq
% 5.46/5.80 thf(fact_9427_num__of__nat_Osimps_I1_J,axiom,
% 5.46/5.80 ( ( num_of_nat @ zero_zero_nat )
% 5.46/5.80 = one ) ).
% 5.46/5.80
% 5.46/5.80 % num_of_nat.simps(1)
% 5.46/5.80 thf(fact_9428_numeral__num__of__nat,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.46/5.80 = N ) ) ).
% 5.46/5.80
% 5.46/5.80 % numeral_num_of_nat
% 5.46/5.80 thf(fact_9429_num__of__nat__One,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.46/5.80 => ( ( num_of_nat @ N )
% 5.46/5.80 = one ) ) ).
% 5.46/5.80
% 5.46/5.80 % num_of_nat_One
% 5.46/5.80 thf(fact_9430_num__of__nat__double,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.46/5.80 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % num_of_nat_double
% 5.46/5.80 thf(fact_9431_num__of__nat__plus__distrib,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.46/5.80 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % num_of_nat_plus_distrib
% 5.46/5.80 thf(fact_9432_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.46/5.80 ! [N: nat,J: nat,I: nat] :
% 5.46/5.80 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 5.46/5.80 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 5.46/5.80 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % nth_sorted_list_of_set_greaterThanLessThan
% 5.46/5.80 thf(fact_9433_less__eq__int_Orep__eq,axiom,
% 5.46/5.80 ( ord_less_eq_int
% 5.46/5.80 = ( ^ [X: int,Xa4: int] :
% 5.46/5.80 ( produc8739625826339149834_nat_o
% 5.46/5.80 @ ^ [Y: nat,Z5: nat] :
% 5.46/5.80 ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [U4: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U4 @ Z5 ) ) )
% 5.46/5.80 @ ( rep_Integ @ X )
% 5.46/5.80 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % less_eq_int.rep_eq
% 5.46/5.80 thf(fact_9434_less__int_Orep__eq,axiom,
% 5.46/5.80 ( ord_less_int
% 5.46/5.80 = ( ^ [X: int,Xa4: int] :
% 5.46/5.80 ( produc8739625826339149834_nat_o
% 5.46/5.80 @ ^ [Y: nat,Z5: nat] :
% 5.46/5.80 ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U4 @ Z5 ) ) )
% 5.46/5.80 @ ( rep_Integ @ X )
% 5.46/5.80 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % less_int.rep_eq
% 5.46/5.80 thf(fact_9435_nat_Orep__eq,axiom,
% 5.46/5.80 ( nat2
% 5.46/5.80 = ( ^ [X: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % nat.rep_eq
% 5.46/5.80 thf(fact_9436_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.46/5.80 ! [N: nat,J: nat,I: nat] :
% 5.46/5.80 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 5.46/5.80 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 5.46/5.80 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % nth_sorted_list_of_set_greaterThanAtMost
% 5.46/5.80 thf(fact_9437_prod__encode__def,axiom,
% 5.46/5.80 ( nat_prod_encode
% 5.46/5.80 = ( produc6842872674320459806at_nat
% 5.46/5.80 @ ^ [M6: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N2 ) ) @ M6 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % prod_encode_def
% 5.46/5.80 thf(fact_9438_pow_Osimps_I3_J,axiom,
% 5.46/5.80 ! [X4: num,Y3: num] :
% 5.46/5.80 ( ( pow @ X4 @ ( bit1 @ Y3 ) )
% 5.46/5.80 = ( times_times_num @ ( sqr @ ( pow @ X4 @ Y3 ) ) @ X4 ) ) ).
% 5.46/5.80
% 5.46/5.80 % pow.simps(3)
% 5.46/5.80 thf(fact_9439_finite__greaterThanAtMost,axiom,
% 5.46/5.80 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 5.46/5.80
% 5.46/5.80 % finite_greaterThanAtMost
% 5.46/5.80 thf(fact_9440_card__greaterThanAtMost,axiom,
% 5.46/5.80 ! [L2: nat,U: nat] :
% 5.46/5.80 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) )
% 5.46/5.80 = ( minus_minus_nat @ U @ L2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % card_greaterThanAtMost
% 5.46/5.80 thf(fact_9441_sqr_Osimps_I2_J,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( sqr @ ( bit0 @ N ) )
% 5.46/5.80 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sqr.simps(2)
% 5.46/5.80 thf(fact_9442_sqr_Osimps_I1_J,axiom,
% 5.46/5.80 ( ( sqr @ one )
% 5.46/5.80 = one ) ).
% 5.46/5.80
% 5.46/5.80 % sqr.simps(1)
% 5.46/5.80 thf(fact_9443_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.46/5.80 ! [L2: nat,U: nat] :
% 5.46/5.80 ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 5.46/5.80 = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 5.46/5.80
% 5.46/5.80 % atLeastSucAtMost_greaterThanAtMost
% 5.46/5.80 thf(fact_9444_sqr__conv__mult,axiom,
% 5.46/5.80 ( sqr
% 5.46/5.80 = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sqr_conv_mult
% 5.46/5.80 thf(fact_9445_le__prod__encode__1,axiom,
% 5.46/5.80 ! [A: nat,B2: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % le_prod_encode_1
% 5.46/5.80 thf(fact_9446_le__prod__encode__2,axiom,
% 5.46/5.80 ! [B2: nat,A: nat] : ( ord_less_eq_nat @ B2 @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % le_prod_encode_2
% 5.46/5.80 thf(fact_9447_pow_Osimps_I2_J,axiom,
% 5.46/5.80 ! [X4: num,Y3: num] :
% 5.46/5.80 ( ( pow @ X4 @ ( bit0 @ Y3 ) )
% 5.46/5.80 = ( sqr @ ( pow @ X4 @ Y3 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % pow.simps(2)
% 5.46/5.80 thf(fact_9448_sqr_Osimps_I3_J,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( sqr @ ( bit1 @ N ) )
% 5.46/5.80 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sqr.simps(3)
% 5.46/5.80 thf(fact_9449_prod__encode__prod__decode__aux,axiom,
% 5.46/5.80 ! [K: nat,M: nat] :
% 5.46/5.80 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.46/5.80 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.46/5.80
% 5.46/5.80 % prod_encode_prod_decode_aux
% 5.46/5.80 thf(fact_9450_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.46/5.80 ! [X4: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.46/5.80 ( ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( ? [Uu2: $o,Uv: $o] :
% 5.46/5.80 ( X4
% 5.46/5.80 = ( vEBT_Leaf @ Uu2 @ Uv ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( Xa != one_one_nat ) ) )
% 5.46/5.80 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( ~ ( ( Deg2 = Xa )
% 5.46/5.80 & ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.80 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 & ( case_o184042715313410164at_nat
% 5.46/5.80 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.46/5.80 & ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 @ ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.80 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 & ! [I2: nat] :
% 5.46/5.80 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X6 ) )
% 5.46/5.80 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.46/5.80 & ( ( Mi3 = Ma3 )
% 5.46/5.80 => ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 & ( ( Mi3 != Ma3 )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.46/5.80 & ! [X: nat] :
% 5.46/5.80 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.46/5.80 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.80 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.80 @ Mima ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % VEBT_internal.valid'.elims(1)
% 5.46/5.80 thf(fact_9451_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.46/5.80 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.80 ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.46/5.80 => ( ( ? [Uu2: $o,Uv: $o] :
% 5.46/5.80 ( X4
% 5.46/5.80 = ( vEBT_Leaf @ Uu2 @ Uv ) )
% 5.46/5.80 => ( Xa != one_one_nat ) )
% 5.46/5.80 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.80 => ~ ( ( Deg2 = Xa )
% 5.46/5.80 & ! [X5: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.80 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 & ( case_o184042715313410164at_nat
% 5.46/5.80 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.46/5.80 & ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 @ ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.80 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 & ! [I2: nat] :
% 5.46/5.80 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X6 ) )
% 5.46/5.80 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.46/5.80 & ( ( Mi3 = Ma3 )
% 5.46/5.80 => ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 & ( ( Mi3 != Ma3 )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.46/5.80 & ! [X: nat] :
% 5.46/5.80 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.46/5.80 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.80 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.80 @ Mima ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % VEBT_internal.valid'.elims(2)
% 5.46/5.80 thf(fact_9452_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.46/5.80 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.80 ( ~ ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.46/5.80 => ( ( ? [Uu2: $o,Uv: $o] :
% 5.46/5.80 ( X4
% 5.46/5.80 = ( vEBT_Leaf @ Uu2 @ Uv ) )
% 5.46/5.80 => ( Xa = one_one_nat ) )
% 5.46/5.80 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.80 => ( ( Deg2 = Xa )
% 5.46/5.80 & ! [X3: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.80 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 & ( case_o184042715313410164at_nat
% 5.46/5.80 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.46/5.80 & ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 @ ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.80 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 & ! [I2: nat] :
% 5.46/5.80 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X6 ) )
% 5.46/5.80 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.46/5.80 & ( ( Mi3 = Ma3 )
% 5.46/5.80 => ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 & ( ( Mi3 != Ma3 )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.46/5.80 & ! [X: nat] :
% 5.46/5.80 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.46/5.80 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.80 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.80 @ Mima ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % VEBT_internal.valid'.elims(3)
% 5.46/5.80 thf(fact_9453_finite__greaterThanAtMost__int,axiom,
% 5.46/5.80 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 5.46/5.80
% 5.46/5.80 % finite_greaterThanAtMost_int
% 5.46/5.80 thf(fact_9454_card__greaterThanAtMost__int,axiom,
% 5.46/5.80 ! [L2: int,U: int] :
% 5.46/5.80 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L2 @ U ) )
% 5.46/5.80 = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % card_greaterThanAtMost_int
% 5.46/5.80 thf(fact_9455_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.46/5.80 ! [L2: int,U: int] :
% 5.46/5.80 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 5.46/5.80 = ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 5.46/5.80
% 5.46/5.80 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.46/5.80 thf(fact_9456_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.46/5.80 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 5.46/5.80 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg3 )
% 5.46/5.80 = ( ( Deg = Deg3 )
% 5.46/5.80 & ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.80 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.46/5.80 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 & ( case_o184042715313410164at_nat
% 5.46/5.80 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X6 )
% 5.46/5.80 & ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 @ ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.80 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.46/5.80 & ! [I2: nat] :
% 5.46/5.80 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X6 ) )
% 5.46/5.80 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.46/5.80 & ( ( Mi3 = Ma3 )
% 5.46/5.80 => ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 & ( ( Mi3 != Ma3 )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.46/5.80 & ! [X: nat] :
% 5.46/5.80 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.46/5.80 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.80 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.80 @ Mima2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % VEBT_internal.valid'.simps(2)
% 5.46/5.80 thf(fact_9457_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.46/5.80 ! [X4: vEBT_VEBT,Xa: nat,Y3: $o] :
% 5.46/5.80 ( ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.80 => ( ! [Uu2: $o,Uv: $o] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Leaf @ Uu2 @ Uv ) )
% 5.46/5.80 => ( ( Y3
% 5.46/5.80 = ( Xa = one_one_nat ) )
% 5.46/5.80 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv ) @ Xa ) ) ) )
% 5.46/5.80 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.80 => ( ( Y3
% 5.46/5.80 = ( ( Deg2 = Xa )
% 5.46/5.80 & ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.80 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 & ( case_o184042715313410164at_nat
% 5.46/5.80 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.46/5.80 & ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 @ ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.80 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 & ! [I2: nat] :
% 5.46/5.80 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X6 ) )
% 5.46/5.80 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.46/5.80 & ( ( Mi3 = Ma3 )
% 5.46/5.80 => ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 & ( ( Mi3 != Ma3 )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.46/5.80 & ! [X: nat] :
% 5.46/5.80 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.46/5.80 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.80 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.80 @ Mima ) ) )
% 5.46/5.80 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % VEBT_internal.valid'.pelims(1)
% 5.46/5.80 thf(fact_9458_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.46/5.80 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.80 ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.46/5.80 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.80 => ( ! [Uu2: $o,Uv: $o] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Leaf @ Uu2 @ Uv ) )
% 5.46/5.80 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv ) @ Xa ) )
% 5.46/5.80 => ( Xa != one_one_nat ) ) )
% 5.46/5.80 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.80 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) )
% 5.46/5.80 => ~ ( ( Deg2 = Xa )
% 5.46/5.80 & ! [X5: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.80 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 & ( case_o184042715313410164at_nat
% 5.46/5.80 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.46/5.80 & ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 @ ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.80 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 & ! [I2: nat] :
% 5.46/5.80 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X6 ) )
% 5.46/5.80 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.46/5.80 & ( ( Mi3 = Ma3 )
% 5.46/5.80 => ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 & ( ( Mi3 != Ma3 )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.46/5.80 & ! [X: nat] :
% 5.46/5.80 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.46/5.80 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.80 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.80 @ Mima ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % VEBT_internal.valid'.pelims(2)
% 5.46/5.80 thf(fact_9459_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.46/5.80 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.46/5.80 ( ~ ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.46/5.80 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.46/5.80 => ( ! [Uu2: $o,Uv: $o] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Leaf @ Uu2 @ Uv ) )
% 5.46/5.80 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv ) @ Xa ) )
% 5.46/5.80 => ( Xa = one_one_nat ) ) )
% 5.46/5.80 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.80 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa ) )
% 5.46/5.80 => ( ( Deg2 = Xa )
% 5.46/5.80 & ! [X3: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.46/5.80 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 & ( case_o184042715313410164at_nat
% 5.46/5.80 @ ( ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X6 )
% 5.46/5.80 & ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 @ ( produc6081775807080527818_nat_o
% 5.46/5.80 @ ^ [Mi3: nat,Ma3: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.46/5.80 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 & ! [I2: nat] :
% 5.46/5.80 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 => ( ( ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X6 ) )
% 5.46/5.80 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.46/5.80 & ( ( Mi3 = Ma3 )
% 5.46/5.80 => ! [X: vEBT_VEBT] :
% 5.46/5.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.46/5.80 => ~ ? [X6: nat] : ( vEBT_V8194947554948674370ptions @ X @ X6 ) ) )
% 5.46/5.80 & ( ( Mi3 != Ma3 )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.46/5.80 & ! [X: nat] :
% 5.46/5.80 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.46/5.80 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.46/5.80 => ( ( ord_less_nat @ Mi3 @ X )
% 5.46/5.80 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.46/5.80 @ Mima ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % VEBT_internal.valid'.pelims(3)
% 5.46/5.80 thf(fact_9460_GreatestI__nat,axiom,
% 5.46/5.80 ! [P: nat > $o,K: nat,B2: nat] :
% 5.46/5.80 ( ( P @ K )
% 5.46/5.80 => ( ! [Y4: nat] :
% 5.46/5.80 ( ( P @ Y4 )
% 5.46/5.80 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 5.46/5.80 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % GreatestI_nat
% 5.46/5.80 thf(fact_9461_Greatest__le__nat,axiom,
% 5.46/5.80 ! [P: nat > $o,K: nat,B2: nat] :
% 5.46/5.80 ( ( P @ K )
% 5.46/5.80 => ( ! [Y4: nat] :
% 5.46/5.80 ( ( P @ Y4 )
% 5.46/5.80 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 5.46/5.80 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Greatest_le_nat
% 5.46/5.80 thf(fact_9462_GreatestI__ex__nat,axiom,
% 5.46/5.80 ! [P: nat > $o,B2: nat] :
% 5.46/5.80 ( ? [X_12: nat] : ( P @ X_12 )
% 5.46/5.80 => ( ! [Y4: nat] :
% 5.46/5.80 ( ( P @ Y4 )
% 5.46/5.80 => ( ord_less_eq_nat @ Y4 @ B2 ) )
% 5.46/5.80 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % GreatestI_ex_nat
% 5.46/5.80 thf(fact_9463_rat__floor__lemma,axiom,
% 5.46/5.80 ! [A: int,B2: int] :
% 5.46/5.80 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B2 ) ) @ ( fract @ A @ B2 ) )
% 5.46/5.80 & ( ord_less_rat @ ( fract @ A @ B2 ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B2 ) @ one_one_int ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % rat_floor_lemma
% 5.46/5.80 thf(fact_9464_image__minus__const__atLeastLessThan__nat,axiom,
% 5.46/5.80 ! [C: nat,Y3: nat,X4: nat] :
% 5.46/5.80 ( ( ( ord_less_nat @ C @ Y3 )
% 5.46/5.80 => ( ( image_nat_nat
% 5.46/5.80 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 5.46/5.80 @ ( set_or4665077453230672383an_nat @ X4 @ Y3 ) )
% 5.46/5.80 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X4 @ C ) @ ( minus_minus_nat @ Y3 @ C ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_nat @ C @ Y3 )
% 5.46/5.80 => ( ( ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.80 => ( ( image_nat_nat
% 5.46/5.80 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 5.46/5.80 @ ( set_or4665077453230672383an_nat @ X4 @ Y3 ) )
% 5.46/5.80 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.46/5.80 & ( ~ ( ord_less_nat @ X4 @ Y3 )
% 5.46/5.80 => ( ( image_nat_nat
% 5.46/5.80 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 5.46/5.80 @ ( set_or4665077453230672383an_nat @ X4 @ Y3 ) )
% 5.46/5.80 = bot_bot_set_nat ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % image_minus_const_atLeastLessThan_nat
% 5.46/5.80 thf(fact_9465_take__bit__numeral__minus__numeral__int,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = ( case_option_int_num @ zero_zero_int
% 5.46/5.80 @ ^ [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 ) ) )
% 5.46/5.80 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % take_bit_numeral_minus_numeral_int
% 5.46/5.80 thf(fact_9466_take__bit__num__simps_I1_J,axiom,
% 5.46/5.80 ! [M: num] :
% 5.46/5.80 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.46/5.80 = none_num ) ).
% 5.46/5.80
% 5.46/5.80 % take_bit_num_simps(1)
% 5.46/5.80 thf(fact_9467_bij__betw__Suc,axiom,
% 5.46/5.80 ! [M7: set_nat,N3: set_nat] :
% 5.46/5.80 ( ( bij_betw_nat_nat @ suc @ M7 @ N3 )
% 5.46/5.80 = ( ( image_nat_nat @ suc @ M7 )
% 5.46/5.80 = N3 ) ) ).
% 5.46/5.80
% 5.46/5.80 % bij_betw_Suc
% 5.46/5.80 thf(fact_9468_take__bit__num__simps_I2_J,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.46/5.80 = ( some_num @ one ) ) ).
% 5.46/5.80
% 5.46/5.80 % take_bit_num_simps(2)
% 5.46/5.80 thf(fact_9469_take__bit__num__simps_I5_J,axiom,
% 5.46/5.80 ! [R2: num] :
% 5.46/5.80 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 5.46/5.80 = ( some_num @ one ) ) ).
% 5.46/5.80
% 5.46/5.80 % take_bit_num_simps(5)
% 5.46/5.80 thf(fact_9470_image__Suc__atLeastAtMost,axiom,
% 5.46/5.80 ! [I: nat,J: nat] :
% 5.46/5.80 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.46/5.80 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % image_Suc_atLeastAtMost
% 5.46/5.80 thf(fact_9471_image__Suc__atLeastLessThan,axiom,
% 5.46/5.80 ! [I: nat,J: nat] :
% 5.46/5.80 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 5.46/5.80 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % image_Suc_atLeastLessThan
% 5.46/5.80 thf(fact_9472_mult__rat,axiom,
% 5.46/5.80 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.80 ( ( times_times_rat @ ( fract @ A @ B2 ) @ ( fract @ C @ D ) )
% 5.46/5.80 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B2 @ D ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % mult_rat
% 5.46/5.80 thf(fact_9473_divide__rat,axiom,
% 5.46/5.80 ! [A: int,B2: int,C: int,D: int] :
% 5.46/5.80 ( ( divide_divide_rat @ ( fract @ A @ B2 ) @ ( fract @ C @ D ) )
% 5.46/5.80 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B2 @ C ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % divide_rat
% 5.46/5.80 thf(fact_9474_floor__Fract,axiom,
% 5.46/5.80 ! [A: int,B2: int] :
% 5.46/5.80 ( ( archim3151403230148437115or_rat @ ( fract @ A @ B2 ) )
% 5.46/5.80 = ( divide_divide_int @ A @ B2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % floor_Fract
% 5.46/5.80 thf(fact_9475_less__rat,axiom,
% 5.46/5.80 ! [B2: int,D: int,A: int,C: int] :
% 5.46/5.80 ( ( B2 != zero_zero_int )
% 5.46/5.80 => ( ( D != zero_zero_int )
% 5.46/5.80 => ( ( ord_less_rat @ ( fract @ A @ B2 ) @ ( fract @ C @ D ) )
% 5.46/5.80 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B2 @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B2 ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % less_rat
% 5.46/5.80 thf(fact_9476_add__rat,axiom,
% 5.46/5.80 ! [B2: int,D: int,A: int,C: int] :
% 5.46/5.80 ( ( B2 != zero_zero_int )
% 5.46/5.80 => ( ( D != zero_zero_int )
% 5.46/5.80 => ( ( plus_plus_rat @ ( fract @ A @ B2 ) @ ( fract @ C @ D ) )
% 5.46/5.80 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B2 ) ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % add_rat
% 5.46/5.80 thf(fact_9477_le__rat,axiom,
% 5.46/5.80 ! [B2: int,D: int,A: int,C: int] :
% 5.46/5.80 ( ( B2 != zero_zero_int )
% 5.46/5.80 => ( ( D != zero_zero_int )
% 5.46/5.80 => ( ( ord_less_eq_rat @ ( fract @ A @ B2 ) @ ( fract @ C @ D ) )
% 5.46/5.80 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B2 @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B2 ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % le_rat
% 5.46/5.80 thf(fact_9478_diff__rat,axiom,
% 5.46/5.80 ! [B2: int,D: int,A: int,C: int] :
% 5.46/5.80 ( ( B2 != zero_zero_int )
% 5.46/5.80 => ( ( D != zero_zero_int )
% 5.46/5.80 => ( ( minus_minus_rat @ ( fract @ A @ B2 ) @ ( fract @ C @ D ) )
% 5.46/5.80 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B2 ) ) @ ( times_times_int @ B2 @ D ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % diff_rat
% 5.46/5.80 thf(fact_9479_sgn__rat,axiom,
% 5.46/5.80 ! [A: int,B2: int] :
% 5.46/5.80 ( ( sgn_sgn_rat @ ( fract @ A @ B2 ) )
% 5.46/5.80 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sgn_rat
% 5.46/5.80 thf(fact_9480_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( bit_take_bit_num @ N @ one )
% 5.46/5.80 = ( case_nat_option_num @ none_num
% 5.46/5.80 @ ^ [N2: nat] : ( some_num @ one )
% 5.46/5.80 @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.46/5.80 thf(fact_9481_zero__notin__Suc__image,axiom,
% 5.46/5.80 ! [A3: set_nat] :
% 5.46/5.80 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A3 ) ) ).
% 5.46/5.80
% 5.46/5.80 % zero_notin_Suc_image
% 5.46/5.80 thf(fact_9482_Rat__induct__pos,axiom,
% 5.46/5.80 ! [P: rat > $o,Q2: rat] :
% 5.46/5.80 ( ! [A5: int,B5: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.46/5.80 => ( P @ ( fract @ A5 @ B5 ) ) )
% 5.46/5.80 => ( P @ Q2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rat_induct_pos
% 5.46/5.80 thf(fact_9483_eq__rat_I1_J,axiom,
% 5.46/5.80 ! [B2: int,D: int,A: int,C: int] :
% 5.46/5.80 ( ( B2 != zero_zero_int )
% 5.46/5.80 => ( ( D != zero_zero_int )
% 5.46/5.80 => ( ( ( fract @ A @ B2 )
% 5.46/5.80 = ( fract @ C @ D ) )
% 5.46/5.80 = ( ( times_times_int @ A @ D )
% 5.46/5.80 = ( times_times_int @ C @ B2 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % eq_rat(1)
% 5.46/5.80 thf(fact_9484_mult__rat__cancel,axiom,
% 5.46/5.80 ! [C: int,A: int,B2: int] :
% 5.46/5.80 ( ( C != zero_zero_int )
% 5.46/5.80 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B2 ) )
% 5.46/5.80 = ( fract @ A @ B2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % mult_rat_cancel
% 5.46/5.80 thf(fact_9485_Fract__coprime,axiom,
% 5.46/5.80 ! [A: int,B2: int] :
% 5.46/5.80 ( ( fract @ ( divide_divide_int @ A @ ( gcd_gcd_int @ A @ B2 ) ) @ ( divide_divide_int @ B2 @ ( gcd_gcd_int @ A @ B2 ) ) )
% 5.46/5.80 = ( fract @ A @ B2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % Fract_coprime
% 5.46/5.80 thf(fact_9486_Fract__of__int__quotient,axiom,
% 5.46/5.80 ( fract
% 5.46/5.80 = ( ^ [K3: int,L: int] : ( divide_divide_rat @ ( ring_1_of_int_rat @ K3 ) @ ( ring_1_of_int_rat @ L ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Fract_of_int_quotient
% 5.46/5.80 thf(fact_9487_image__Suc__lessThan,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % image_Suc_lessThan
% 5.46/5.80 thf(fact_9488_image__Suc__atMost,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.46/5.80 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % image_Suc_atMost
% 5.46/5.80 thf(fact_9489_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.46/5.80 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % atLeast0_atMost_Suc_eq_insert_0
% 5.46/5.80 thf(fact_9490_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.46/5.80 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % atLeast0_lessThan_Suc_eq_insert_0
% 5.46/5.80 thf(fact_9491_lessThan__Suc__eq__insert__0,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.46/5.80 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lessThan_Suc_eq_insert_0
% 5.46/5.80 thf(fact_9492_atMost__Suc__eq__insert__0,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.46/5.80 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % atMost_Suc_eq_insert_0
% 5.46/5.80 thf(fact_9493_Fract__less__zero__iff,axiom,
% 5.46/5.80 ! [B2: int,A: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.80 => ( ( ord_less_rat @ ( fract @ A @ B2 ) @ zero_zero_rat )
% 5.46/5.80 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Fract_less_zero_iff
% 5.46/5.80 thf(fact_9494_zero__less__Fract__iff,axiom,
% 5.46/5.80 ! [B2: int,A: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.80 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B2 ) )
% 5.46/5.80 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % zero_less_Fract_iff
% 5.46/5.80 thf(fact_9495_Fract__less__one__iff,axiom,
% 5.46/5.80 ! [B2: int,A: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.80 => ( ( ord_less_rat @ ( fract @ A @ B2 ) @ one_one_rat )
% 5.46/5.80 = ( ord_less_int @ A @ B2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Fract_less_one_iff
% 5.46/5.80 thf(fact_9496_one__less__Fract__iff,axiom,
% 5.46/5.80 ! [B2: int,A: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.80 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B2 ) )
% 5.46/5.80 = ( ord_less_int @ B2 @ A ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % one_less_Fract_iff
% 5.46/5.80 thf(fact_9497_Fract__add__one,axiom,
% 5.46/5.80 ! [N: int,M: int] :
% 5.46/5.80 ( ( N != zero_zero_int )
% 5.46/5.80 => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 5.46/5.80 = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Fract_add_one
% 5.46/5.80 thf(fact_9498_Fract__le__zero__iff,axiom,
% 5.46/5.80 ! [B2: int,A: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.80 => ( ( ord_less_eq_rat @ ( fract @ A @ B2 ) @ zero_zero_rat )
% 5.46/5.80 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Fract_le_zero_iff
% 5.46/5.80 thf(fact_9499_zero__le__Fract__iff,axiom,
% 5.46/5.80 ! [B2: int,A: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.80 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B2 ) )
% 5.46/5.80 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % zero_le_Fract_iff
% 5.46/5.80 thf(fact_9500_one__le__Fract__iff,axiom,
% 5.46/5.80 ! [B2: int,A: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.80 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B2 ) )
% 5.46/5.80 = ( ord_less_eq_int @ B2 @ A ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % one_le_Fract_iff
% 5.46/5.80 thf(fact_9501_Fract__le__one__iff,axiom,
% 5.46/5.80 ! [B2: int,A: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.46/5.80 => ( ( ord_less_eq_rat @ ( fract @ A @ B2 ) @ one_one_rat )
% 5.46/5.80 = ( ord_less_eq_int @ A @ B2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Fract_le_one_iff
% 5.46/5.80 thf(fact_9502_take__bit__num__def,axiom,
% 5.46/5.80 ( bit_take_bit_num
% 5.46/5.80 = ( ^ [N2: nat,M6: num] :
% 5.46/5.80 ( if_option_num
% 5.46/5.80 @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) )
% 5.46/5.80 = zero_zero_nat )
% 5.46/5.80 @ none_num
% 5.46/5.80 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % take_bit_num_def
% 5.46/5.80 thf(fact_9503_and__minus__numerals_I3_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.46/5.80 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_minus_numerals(3)
% 5.46/5.80 thf(fact_9504_and__minus__numerals_I7_J,axiom,
% 5.46/5.80 ! [N: num,M: num] :
% 5.46/5.80 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.46/5.80 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_minus_numerals(7)
% 5.46/5.80 thf(fact_9505_and__minus__numerals_I4_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.46/5.80 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_minus_numerals(4)
% 5.46/5.80 thf(fact_9506_take__bit__num__simps_I4_J,axiom,
% 5.46/5.80 ! [N: nat,M: num] :
% 5.46/5.80 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 5.46/5.80 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % take_bit_num_simps(4)
% 5.46/5.80 thf(fact_9507_take__bit__num__simps_I3_J,axiom,
% 5.46/5.80 ! [N: nat,M: num] :
% 5.46/5.80 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 5.46/5.80 = ( case_o6005452278849405969um_num @ none_num
% 5.46/5.80 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.46/5.80 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % take_bit_num_simps(3)
% 5.46/5.80 thf(fact_9508_take__bit__num__simps_I7_J,axiom,
% 5.46/5.80 ! [R2: num,M: num] :
% 5.46/5.80 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 5.46/5.80 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % take_bit_num_simps(7)
% 5.46/5.80 thf(fact_9509_take__bit__num__simps_I6_J,axiom,
% 5.46/5.80 ! [R2: num,M: num] :
% 5.46/5.80 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 5.46/5.80 = ( case_o6005452278849405969um_num @ none_num
% 5.46/5.80 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.46/5.80 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % take_bit_num_simps(6)
% 5.46/5.80 thf(fact_9510_and__minus__numerals_I8_J,axiom,
% 5.46/5.80 ! [N: num,M: num] :
% 5.46/5.80 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.46/5.80 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_minus_numerals(8)
% 5.46/5.80 thf(fact_9511_and__not__num_Osimps_I8_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.80 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.80 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.46/5.80 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num.simps(8)
% 5.46/5.80 thf(fact_9512_and__not__num_Osimps_I1_J,axiom,
% 5.46/5.80 ( ( bit_and_not_num @ one @ one )
% 5.46/5.80 = none_num ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num.simps(1)
% 5.46/5.80 thf(fact_9513_and__not__num_Osimps_I2_J,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 5.46/5.80 = ( some_num @ one ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num.simps(2)
% 5.46/5.80 thf(fact_9514_and__not__num_Osimps_I4_J,axiom,
% 5.46/5.80 ! [M: num] :
% 5.46/5.80 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.46/5.80 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num.simps(4)
% 5.46/5.80 thf(fact_9515_and__not__num_Osimps_I3_J,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.46/5.80 = none_num ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num.simps(3)
% 5.46/5.80 thf(fact_9516_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.46/5.80 ! [N: nat,M: num] :
% 5.46/5.80 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 5.46/5.80 = ( case_nat_option_num @ none_num
% 5.46/5.80 @ ^ [N2: nat] :
% 5.46/5.80 ( case_o6005452278849405969um_num @ none_num
% 5.46/5.80 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.46/5.80 @ ( bit_take_bit_num @ N2 @ M ) )
% 5.46/5.80 @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.46/5.80 thf(fact_9517_image__int__atLeastAtMost,axiom,
% 5.46/5.80 ! [A: nat,B2: nat] :
% 5.46/5.80 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B2 ) )
% 5.46/5.80 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % image_int_atLeastAtMost
% 5.46/5.80 thf(fact_9518_image__int__atLeastLessThan,axiom,
% 5.46/5.80 ! [A: nat,B2: nat] :
% 5.46/5.80 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B2 ) )
% 5.46/5.80 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % image_int_atLeastLessThan
% 5.46/5.80 thf(fact_9519_and__not__num_Osimps_I7_J,axiom,
% 5.46/5.80 ! [M: num] :
% 5.46/5.80 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.46/5.80 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num.simps(7)
% 5.46/5.80 thf(fact_9520_and__not__num__eq__Some__iff,axiom,
% 5.46/5.80 ! [M: num,N: num,Q2: num] :
% 5.46/5.80 ( ( ( bit_and_not_num @ M @ N )
% 5.46/5.80 = ( some_num @ Q2 ) )
% 5.46/5.80 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num_eq_Some_iff
% 5.46/5.80 thf(fact_9521_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.46/5.80 ! [N: nat,M: num] :
% 5.46/5.80 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 5.46/5.80 = ( case_nat_option_num @ none_num
% 5.46/5.80 @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 5.46/5.80 @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.46/5.80 thf(fact_9522_image__add__int__atLeastLessThan,axiom,
% 5.46/5.80 ! [L2: int,U: int] :
% 5.46/5.80 ( ( image_int_int
% 5.46/5.80 @ ^ [X: int] : ( plus_plus_int @ X @ L2 )
% 5.46/5.80 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 5.46/5.80 = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 5.46/5.80
% 5.46/5.80 % image_add_int_atLeastLessThan
% 5.46/5.80 thf(fact_9523_and__not__num__eq__None__iff,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( ( bit_and_not_num @ M @ N )
% 5.46/5.80 = none_num )
% 5.46/5.80 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = zero_zero_int ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num_eq_None_iff
% 5.46/5.80 thf(fact_9524_image__atLeastZeroLessThan__int,axiom,
% 5.46/5.80 ! [U: int] :
% 5.46/5.80 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.46/5.80 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.46/5.80 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % image_atLeastZeroLessThan_int
% 5.46/5.80 thf(fact_9525_int__numeral__and__not__num,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % int_numeral_and_not_num
% 5.46/5.80 thf(fact_9526_int__numeral__not__and__num,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % int_numeral_not_and_num
% 5.46/5.80 thf(fact_9527_positive__rat,axiom,
% 5.46/5.80 ! [A: int,B2: int] :
% 5.46/5.80 ( ( positive @ ( fract @ A @ B2 ) )
% 5.46/5.80 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % positive_rat
% 5.46/5.80 thf(fact_9528_Rat_Opositive__add,axiom,
% 5.46/5.80 ! [X4: rat,Y3: rat] :
% 5.46/5.80 ( ( positive @ X4 )
% 5.46/5.80 => ( ( positive @ Y3 )
% 5.46/5.80 => ( positive @ ( plus_plus_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rat.positive_add
% 5.46/5.80 thf(fact_9529_Rat_Opositive__mult,axiom,
% 5.46/5.80 ! [X4: rat,Y3: rat] :
% 5.46/5.80 ( ( positive @ X4 )
% 5.46/5.80 => ( ( positive @ Y3 )
% 5.46/5.80 => ( positive @ ( times_times_rat @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rat.positive_mult
% 5.46/5.80 thf(fact_9530_less__rat__def,axiom,
% 5.46/5.80 ( ord_less_rat
% 5.46/5.80 = ( ^ [X: rat,Y: rat] : ( positive @ ( minus_minus_rat @ Y @ X ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % less_rat_def
% 5.46/5.80 thf(fact_9531_Rat_Opositive_Orep__eq,axiom,
% 5.46/5.80 ( positive
% 5.46/5.80 = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rat.positive.rep_eq
% 5.46/5.80 thf(fact_9532_and__not__num_Oelims,axiom,
% 5.46/5.80 ! [X4: num,Xa: num,Y3: option_num] :
% 5.46/5.80 ( ( ( bit_and_not_num @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( ( X4 = one )
% 5.46/5.80 => ( ( Xa = one )
% 5.46/5.80 => ( Y3 != none_num ) ) )
% 5.46/5.80 => ( ( ( X4 = one )
% 5.46/5.80 => ( ? [N4: num] :
% 5.46/5.80 ( Xa
% 5.46/5.80 = ( bit0 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ one ) ) ) )
% 5.46/5.80 => ( ( ( X4 = one )
% 5.46/5.80 => ( ? [N4: num] :
% 5.46/5.80 ( Xa
% 5.46/5.80 = ( bit1 @ N4 ) )
% 5.46/5.80 => ( Y3 != none_num ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit0 @ M4 ) )
% 5.46/5.80 => ( ( Xa = one )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit0 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit0 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N4 ) ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit0 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit1 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N4 ) ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit1 @ M4 ) )
% 5.46/5.80 => ( ( Xa = one )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit1 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit0 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.80 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.46/5.80 @ ( bit_and_not_num @ M4 @ N4 ) ) ) ) )
% 5.46/5.80 => ~ ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit1 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit1 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num.elims
% 5.46/5.80 thf(fact_9533_Bit__Operations_Otake__bit__num__code,axiom,
% 5.46/5.80 ( bit_take_bit_num
% 5.46/5.80 = ( ^ [N2: nat,M6: num] :
% 5.46/5.80 ( produc478579273971653890on_num
% 5.46/5.80 @ ^ [A4: nat,X: num] :
% 5.46/5.80 ( case_nat_option_num @ none_num
% 5.46/5.80 @ ^ [O: nat] :
% 5.46/5.80 ( case_num_option_num @ ( some_num @ one )
% 5.46/5.80 @ ^ [P3: num] :
% 5.46/5.80 ( case_o6005452278849405969um_num @ none_num
% 5.46/5.80 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.46/5.80 @ ( bit_take_bit_num @ O @ P3 ) )
% 5.46/5.80 @ ^ [P3: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P3 ) ) )
% 5.46/5.80 @ X )
% 5.46/5.80 @ A4 )
% 5.46/5.80 @ ( product_Pair_nat_num @ N2 @ M6 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Bit_Operations.take_bit_num_code
% 5.46/5.80 thf(fact_9534_and__not__num_Osimps_I5_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.46/5.80 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num.simps(5)
% 5.46/5.80 thf(fact_9535_and__not__num_Osimps_I9_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.80 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num.simps(9)
% 5.46/5.80 thf(fact_9536_and__not__num_Osimps_I6_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.80 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_not_num.simps(6)
% 5.46/5.80 thf(fact_9537_and__num_Oelims,axiom,
% 5.46/5.80 ! [X4: num,Xa: num,Y3: option_num] :
% 5.46/5.80 ( ( ( bit_un7362597486090784418nd_num @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( ( X4 = one )
% 5.46/5.80 => ( ( Xa = one )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ one ) ) ) )
% 5.46/5.80 => ( ( ( X4 = one )
% 5.46/5.80 => ( ? [N4: num] :
% 5.46/5.80 ( Xa
% 5.46/5.80 = ( bit0 @ N4 ) )
% 5.46/5.80 => ( Y3 != none_num ) ) )
% 5.46/5.80 => ( ( ( X4 = one )
% 5.46/5.80 => ( ? [N4: num] :
% 5.46/5.80 ( Xa
% 5.46/5.80 = ( bit1 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ one ) ) ) )
% 5.46/5.80 => ( ( ? [M4: num] :
% 5.46/5.80 ( X4
% 5.46/5.80 = ( bit0 @ M4 ) )
% 5.46/5.80 => ( ( Xa = one )
% 5.46/5.80 => ( Y3 != none_num ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit0 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit0 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N4 ) ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit0 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit1 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N4 ) ) ) ) )
% 5.46/5.80 => ( ( ? [M4: num] :
% 5.46/5.80 ( X4
% 5.46/5.80 = ( bit1 @ M4 ) )
% 5.46/5.80 => ( ( Xa = one )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ one ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit1 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit0 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N4 ) ) ) ) )
% 5.46/5.80 => ~ ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit1 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit1 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.80 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.46/5.80 @ ( bit_un7362597486090784418nd_num @ M4 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_num.elims
% 5.46/5.80 thf(fact_9538_xor__num_Oelims,axiom,
% 5.46/5.80 ! [X4: num,Xa: num,Y3: option_num] :
% 5.46/5.80 ( ( ( bit_un2480387367778600638or_num @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( ( X4 = one )
% 5.46/5.80 => ( ( Xa = one )
% 5.46/5.80 => ( Y3 != none_num ) ) )
% 5.46/5.80 => ( ( ( X4 = one )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit0 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ ( bit1 @ N4 ) ) ) ) )
% 5.46/5.80 => ( ( ( X4 = one )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit1 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ ( bit0 @ N4 ) ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit0 @ M4 ) )
% 5.46/5.80 => ( ( Xa = one )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ ( bit1 @ M4 ) ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit0 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit0 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N4 ) ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit0 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit1 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N4 ) ) ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit1 @ M4 ) )
% 5.46/5.80 => ( ( Xa = one )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.46/5.80 => ( ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit1 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit0 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N4 ) ) ) ) ) )
% 5.46/5.80 => ~ ! [M4: num] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( bit1 @ M4 ) )
% 5.46/5.80 => ! [N4: num] :
% 5.46/5.80 ( ( Xa
% 5.46/5.80 = ( bit1 @ N4 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_num.elims
% 5.46/5.80 thf(fact_9539_xor__num_Osimps_I8_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.80 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_num.simps(8)
% 5.46/5.80 thf(fact_9540_and__num_Osimps_I1_J,axiom,
% 5.46/5.80 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.46/5.80 = ( some_num @ one ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_num.simps(1)
% 5.46/5.80 thf(fact_9541_xor__num_Osimps_I1_J,axiom,
% 5.46/5.80 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.46/5.80 = none_num ) ).
% 5.46/5.80
% 5.46/5.80 % xor_num.simps(1)
% 5.46/5.80 thf(fact_9542_and__num_Osimps_I5_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.46/5.80 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_num.simps(5)
% 5.46/5.80 thf(fact_9543_xor__num_Osimps_I5_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.46/5.80 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_num.simps(5)
% 5.46/5.80 thf(fact_9544_and__num_Osimps_I7_J,axiom,
% 5.46/5.80 ! [M: num] :
% 5.46/5.80 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.46/5.80 = ( some_num @ one ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_num.simps(7)
% 5.46/5.80 thf(fact_9545_and__num_Osimps_I3_J,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 5.46/5.80 = ( some_num @ one ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_num.simps(3)
% 5.46/5.80 thf(fact_9546_and__num_Osimps_I2_J,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 5.46/5.80 = none_num ) ).
% 5.46/5.80
% 5.46/5.80 % and_num.simps(2)
% 5.46/5.80 thf(fact_9547_and__num_Osimps_I4_J,axiom,
% 5.46/5.80 ! [M: num] :
% 5.46/5.80 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.46/5.80 = none_num ) ).
% 5.46/5.80
% 5.46/5.80 % and_num.simps(4)
% 5.46/5.80 thf(fact_9548_xor__num_Osimps_I9_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.80 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_num.simps(9)
% 5.46/5.80 thf(fact_9549_and__num_Osimps_I6_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.80 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_num.simps(6)
% 5.46/5.80 thf(fact_9550_and__num_Osimps_I8_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.46/5.80 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_num.simps(8)
% 5.46/5.80 thf(fact_9551_xor__num_Osimps_I7_J,axiom,
% 5.46/5.80 ! [M: num] :
% 5.46/5.80 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.46/5.80 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_num.simps(7)
% 5.46/5.80 thf(fact_9552_xor__num_Osimps_I4_J,axiom,
% 5.46/5.80 ! [M: num] :
% 5.46/5.80 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.46/5.80 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_num.simps(4)
% 5.46/5.80 thf(fact_9553_xor__num_Osimps_I3_J,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 5.46/5.80 = ( some_num @ ( bit0 @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_num.simps(3)
% 5.46/5.80 thf(fact_9554_xor__num_Osimps_I2_J,axiom,
% 5.46/5.80 ! [N: num] :
% 5.46/5.80 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 5.46/5.80 = ( some_num @ ( bit1 @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_num.simps(2)
% 5.46/5.80 thf(fact_9555_and__num_Osimps_I9_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.46/5.80 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.80 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.46/5.80 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % and_num.simps(9)
% 5.46/5.80 thf(fact_9556_xor__num_Osimps_I6_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.46/5.80 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % xor_num.simps(6)
% 5.46/5.80 thf(fact_9557_and__num__dict,axiom,
% 5.46/5.80 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 5.46/5.80
% 5.46/5.80 % and_num_dict
% 5.46/5.80 thf(fact_9558_xor__num__dict,axiom,
% 5.46/5.80 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 5.46/5.80
% 5.46/5.80 % xor_num_dict
% 5.46/5.80 thf(fact_9559_num__of__integer__code,axiom,
% 5.46/5.80 ( code_num_of_integer
% 5.46/5.80 = ( ^ [K3: code_integer] :
% 5.46/5.80 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.46/5.80 @ ( produc7336495610019696514er_num
% 5.46/5.80 @ ^ [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 ) )
% 5.46/5.80 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % num_of_integer_code
% 5.46/5.80 thf(fact_9560_min__Suc__Suc,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.46/5.80 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % min_Suc_Suc
% 5.46/5.80 thf(fact_9561_min__0R,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.46/5.80 = zero_zero_nat ) ).
% 5.46/5.80
% 5.46/5.80 % min_0R
% 5.46/5.80 thf(fact_9562_min__0L,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.46/5.80 = zero_zero_nat ) ).
% 5.46/5.80
% 5.46/5.80 % min_0L
% 5.46/5.80 thf(fact_9563_min__numeral__Suc,axiom,
% 5.46/5.80 ! [K: num,N: nat] :
% 5.46/5.80 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.46/5.80 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % min_numeral_Suc
% 5.46/5.80 thf(fact_9564_min__Suc__numeral,axiom,
% 5.46/5.80 ! [N: nat,K: num] :
% 5.46/5.80 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.46/5.80 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % min_Suc_numeral
% 5.46/5.80 thf(fact_9565_nat__mult__min__right,axiom,
% 5.46/5.80 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.80 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 5.46/5.80 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % nat_mult_min_right
% 5.46/5.80 thf(fact_9566_nat__mult__min__left,axiom,
% 5.46/5.80 ! [M: nat,N: nat,Q2: nat] :
% 5.46/5.80 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 5.46/5.80 = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % nat_mult_min_left
% 5.46/5.80 thf(fact_9567_min__diff,axiom,
% 5.46/5.80 ! [M: nat,I: nat,N: nat] :
% 5.46/5.80 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 5.46/5.80 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 5.46/5.80
% 5.46/5.80 % min_diff
% 5.46/5.80 thf(fact_9568_concat__bit__assoc__sym,axiom,
% 5.46/5.80 ! [M: nat,N: nat,K: int,L2: int,R2: int] :
% 5.46/5.80 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L2 ) @ R2 )
% 5.46/5.80 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L2 @ R2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % concat_bit_assoc_sym
% 5.46/5.80 thf(fact_9569_take__bit__concat__bit__eq,axiom,
% 5.46/5.80 ! [M: nat,N: nat,K: int,L2: int] :
% 5.46/5.80 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L2 ) )
% 5.46/5.80 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % take_bit_concat_bit_eq
% 5.46/5.80 thf(fact_9570_min__Suc1,axiom,
% 5.46/5.80 ! [N: nat,M: nat] :
% 5.46/5.80 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 5.46/5.80 = ( case_nat_nat @ zero_zero_nat
% 5.46/5.80 @ ^ [M2: nat] : ( suc @ ( ord_min_nat @ N @ M2 ) )
% 5.46/5.80 @ M ) ) ).
% 5.46/5.80
% 5.46/5.80 % min_Suc1
% 5.46/5.80 thf(fact_9571_min__Suc2,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 5.46/5.80 = ( case_nat_nat @ zero_zero_nat
% 5.46/5.80 @ ^ [M2: nat] : ( suc @ ( ord_min_nat @ M2 @ N ) )
% 5.46/5.80 @ M ) ) ).
% 5.46/5.80
% 5.46/5.80 % min_Suc2
% 5.46/5.80 thf(fact_9572_card__le__Suc__Max,axiom,
% 5.46/5.80 ! [S2: set_nat] :
% 5.46/5.80 ( ( finite_finite_nat @ S2 )
% 5.46/5.80 => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % card_le_Suc_Max
% 5.46/5.80 thf(fact_9573_divide__nat__def,axiom,
% 5.46/5.80 ( divide_divide_nat
% 5.46/5.80 = ( ^ [M6: nat,N2: nat] :
% 5.46/5.80 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.46/5.80 @ ( lattic8265883725875713057ax_nat
% 5.46/5.80 @ ( collect_nat
% 5.46/5.80 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N2 ) @ M6 ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % divide_nat_def
% 5.46/5.80 thf(fact_9574_gcd__is__Max__divisors__nat,axiom,
% 5.46/5.80 ! [N: nat,M: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( gcd_gcd_nat @ M @ N )
% 5.46/5.80 = ( lattic8265883725875713057ax_nat
% 5.46/5.80 @ ( collect_nat
% 5.46/5.80 @ ^ [D2: nat] :
% 5.46/5.80 ( ( dvd_dvd_nat @ D2 @ M )
% 5.46/5.80 & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % gcd_is_Max_divisors_nat
% 5.46/5.80 thf(fact_9575_min__enat__simps_I2_J,axiom,
% 5.46/5.80 ! [Q2: extended_enat] :
% 5.46/5.80 ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.46/5.80 = zero_z5237406670263579293d_enat ) ).
% 5.46/5.80
% 5.46/5.80 % min_enat_simps(2)
% 5.46/5.80 thf(fact_9576_min__enat__simps_I3_J,axiom,
% 5.46/5.80 ! [Q2: extended_enat] :
% 5.46/5.80 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.46/5.80 = zero_z5237406670263579293d_enat ) ).
% 5.46/5.80
% 5.46/5.80 % min_enat_simps(3)
% 5.46/5.80 thf(fact_9577_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.46/5.80 ! [I: nat,J: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 5.46/5.80 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 5.46/5.80 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sorted_list_of_set_greaterThanAtMost
% 5.46/5.80 thf(fact_9578_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.46/5.80 ! [I: nat,J: nat] :
% 5.46/5.80 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 5.46/5.80 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 5.46/5.80 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sorted_list_of_set_greaterThanLessThan
% 5.46/5.80 thf(fact_9579_upto__aux__rec,axiom,
% 5.46/5.80 ( upto_aux
% 5.46/5.80 = ( ^ [I2: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I2 ) @ Js @ ( upto_aux @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_aux_rec
% 5.46/5.80 thf(fact_9580_list__encode_Osimps_I2_J,axiom,
% 5.46/5.80 ! [X4: nat,Xs2: list_nat] :
% 5.46/5.80 ( ( nat_list_encode @ ( cons_nat @ X4 @ Xs2 ) )
% 5.46/5.80 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % list_encode.simps(2)
% 5.46/5.80 thf(fact_9581_list__encode_Oelims,axiom,
% 5.46/5.80 ! [X4: list_nat,Y3: nat] :
% 5.46/5.80 ( ( ( nat_list_encode @ X4 )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( ( X4 = nil_nat )
% 5.46/5.80 => ( Y3 != zero_zero_nat ) )
% 5.46/5.80 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( cons_nat @ X3 @ Xs3 ) )
% 5.46/5.80 => ( Y3
% 5.46/5.80 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % list_encode.elims
% 5.46/5.80 thf(fact_9582_quotient__of__def,axiom,
% 5.46/5.80 ( quotient_of
% 5.46/5.80 = ( ^ [X: rat] :
% 5.46/5.80 ( the_Pr4378521158711661632nt_int
% 5.46/5.80 @ ^ [Pair: product_prod_int_int] :
% 5.46/5.80 ( ( X
% 5.46/5.80 = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 5.46/5.80 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 5.46/5.80 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % quotient_of_def
% 5.46/5.80 thf(fact_9583_coprime__abs__right__iff,axiom,
% 5.46/5.80 ! [K: int,L2: int] :
% 5.46/5.80 ( ( algebr932160517623751201me_int @ K @ ( abs_abs_int @ L2 ) )
% 5.46/5.80 = ( algebr932160517623751201me_int @ K @ L2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_abs_right_iff
% 5.46/5.80 thf(fact_9584_coprime__abs__left__iff,axiom,
% 5.46/5.80 ! [K: int,L2: int] :
% 5.46/5.80 ( ( algebr932160517623751201me_int @ ( abs_abs_int @ K ) @ L2 )
% 5.46/5.80 = ( algebr932160517623751201me_int @ K @ L2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_abs_left_iff
% 5.46/5.80 thf(fact_9585_normalize__stable,axiom,
% 5.46/5.80 ! [Q2: int,P2: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ Q2 )
% 5.46/5.80 => ( ( algebr932160517623751201me_int @ P2 @ Q2 )
% 5.46/5.80 => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.46/5.80 = ( product_Pair_int_int @ P2 @ Q2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % normalize_stable
% 5.46/5.80 thf(fact_9586_coprime__crossproduct__int,axiom,
% 5.46/5.80 ! [A: int,D: int,B2: int,C: int] :
% 5.46/5.80 ( ( algebr932160517623751201me_int @ A @ D )
% 5.46/5.80 => ( ( algebr932160517623751201me_int @ B2 @ C )
% 5.46/5.80 => ( ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ C ) )
% 5.46/5.80 = ( times_times_int @ ( abs_abs_int @ B2 ) @ ( abs_abs_int @ D ) ) )
% 5.46/5.80 = ( ( ( abs_abs_int @ A )
% 5.46/5.80 = ( abs_abs_int @ B2 ) )
% 5.46/5.80 & ( ( abs_abs_int @ C )
% 5.46/5.80 = ( abs_abs_int @ D ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_crossproduct_int
% 5.46/5.80 thf(fact_9587_Rat__cases,axiom,
% 5.46/5.80 ! [Q2: rat] :
% 5.46/5.80 ~ ! [A5: int,B5: int] :
% 5.46/5.80 ( ( Q2
% 5.46/5.80 = ( fract @ A5 @ B5 ) )
% 5.46/5.80 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.46/5.80 => ~ ( algebr932160517623751201me_int @ A5 @ B5 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rat_cases
% 5.46/5.80 thf(fact_9588_Rat__induct,axiom,
% 5.46/5.80 ! [P: rat > $o,Q2: rat] :
% 5.46/5.80 ( ! [A5: int,B5: int] :
% 5.46/5.80 ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.46/5.80 => ( ( algebr932160517623751201me_int @ A5 @ B5 )
% 5.46/5.80 => ( P @ ( fract @ A5 @ B5 ) ) ) )
% 5.46/5.80 => ( P @ Q2 ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rat_induct
% 5.46/5.80 thf(fact_9589_coprime__common__divisor__int,axiom,
% 5.46/5.80 ! [A: int,B2: int,X4: int] :
% 5.46/5.80 ( ( algebr932160517623751201me_int @ A @ B2 )
% 5.46/5.80 => ( ( dvd_dvd_int @ X4 @ A )
% 5.46/5.80 => ( ( dvd_dvd_int @ X4 @ B2 )
% 5.46/5.80 => ( ( abs_abs_int @ X4 )
% 5.46/5.80 = one_one_int ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_common_divisor_int
% 5.46/5.80 thf(fact_9590_Rat__cases__nonzero,axiom,
% 5.46/5.80 ! [Q2: rat] :
% 5.46/5.80 ( ! [A5: int,B5: int] :
% 5.46/5.80 ( ( Q2
% 5.46/5.80 = ( fract @ A5 @ B5 ) )
% 5.46/5.80 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.46/5.80 => ( ( A5 != zero_zero_int )
% 5.46/5.80 => ~ ( algebr932160517623751201me_int @ A5 @ B5 ) ) ) )
% 5.46/5.80 => ( Q2 = zero_zero_rat ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rat_cases_nonzero
% 5.46/5.80 thf(fact_9591_card__length__sum__list__rec,axiom,
% 5.46/5.80 ! [M: nat,N3: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.46/5.80 => ( ( finite_card_list_nat
% 5.46/5.80 @ ( collect_list_nat
% 5.46/5.80 @ ^ [L: list_nat] :
% 5.46/5.80 ( ( ( size_size_list_nat @ L )
% 5.46/5.80 = M )
% 5.46/5.80 & ( ( groups4561878855575611511st_nat @ L )
% 5.46/5.80 = N3 ) ) ) )
% 5.46/5.80 = ( plus_plus_nat
% 5.46/5.80 @ ( finite_card_list_nat
% 5.46/5.80 @ ( collect_list_nat
% 5.46/5.80 @ ^ [L: list_nat] :
% 5.46/5.80 ( ( ( size_size_list_nat @ L )
% 5.46/5.80 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.46/5.80 & ( ( groups4561878855575611511st_nat @ L )
% 5.46/5.80 = N3 ) ) ) )
% 5.46/5.80 @ ( finite_card_list_nat
% 5.46/5.80 @ ( collect_list_nat
% 5.46/5.80 @ ^ [L: list_nat] :
% 5.46/5.80 ( ( ( size_size_list_nat @ L )
% 5.46/5.80 = M )
% 5.46/5.80 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L ) @ one_one_nat )
% 5.46/5.80 = N3 ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % card_length_sum_list_rec
% 5.46/5.80 thf(fact_9592_card__length__sum__list,axiom,
% 5.46/5.80 ! [M: nat,N3: nat] :
% 5.46/5.80 ( ( finite_card_list_nat
% 5.46/5.80 @ ( collect_list_nat
% 5.46/5.80 @ ^ [L: list_nat] :
% 5.46/5.80 ( ( ( size_size_list_nat @ L )
% 5.46/5.80 = M )
% 5.46/5.80 & ( ( groups4561878855575611511st_nat @ L )
% 5.46/5.80 = N3 ) ) ) )
% 5.46/5.80 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N3 @ M ) @ one_one_nat ) @ N3 ) ) ).
% 5.46/5.80
% 5.46/5.80 % card_length_sum_list
% 5.46/5.80 thf(fact_9593_quotient__of__unique,axiom,
% 5.46/5.80 ! [R2: rat] :
% 5.46/5.80 ? [X3: product_prod_int_int] :
% 5.46/5.80 ( ( R2
% 5.46/5.80 = ( fract @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 5.46/5.80 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X3 ) )
% 5.46/5.80 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) )
% 5.46/5.80 & ! [Y5: product_prod_int_int] :
% 5.46/5.80 ( ( ( R2
% 5.46/5.80 = ( fract @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 5.46/5.80 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y5 ) )
% 5.46/5.80 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 5.46/5.80 => ( Y5 = X3 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % quotient_of_unique
% 5.46/5.80 thf(fact_9594_sorted__list__of__set__atMost__Suc,axiom,
% 5.46/5.80 ! [K: nat] :
% 5.46/5.80 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.46/5.80 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sorted_list_of_set_atMost_Suc
% 5.46/5.80 thf(fact_9595_sorted__list__of__set__lessThan__Suc,axiom,
% 5.46/5.80 ! [K: nat] :
% 5.46/5.80 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.46/5.80 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sorted_list_of_set_lessThan_Suc
% 5.46/5.80 thf(fact_9596_coprime__int__iff,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.46/5.80 = ( algebr934650988132801477me_nat @ M @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_int_iff
% 5.46/5.80 thf(fact_9597_coprime__nat__abs__right__iff,axiom,
% 5.46/5.80 ! [N: nat,K: int] :
% 5.46/5.80 ( ( algebr934650988132801477me_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.46/5.80 = ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_nat_abs_right_iff
% 5.46/5.80 thf(fact_9598_coprime__nat__abs__left__iff,axiom,
% 5.46/5.80 ! [K: int,N: nat] :
% 5.46/5.80 ( ( algebr934650988132801477me_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.46/5.80 = ( algebr932160517623751201me_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_nat_abs_left_iff
% 5.46/5.80 thf(fact_9599_coprime__common__divisor__nat,axiom,
% 5.46/5.80 ! [A: nat,B2: nat,X4: nat] :
% 5.46/5.80 ( ( algebr934650988132801477me_nat @ A @ B2 )
% 5.46/5.80 => ( ( dvd_dvd_nat @ X4 @ A )
% 5.46/5.80 => ( ( dvd_dvd_nat @ X4 @ B2 )
% 5.46/5.80 => ( X4 = one_one_nat ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_common_divisor_nat
% 5.46/5.80 thf(fact_9600_coprime__Suc__0__right,axiom,
% 5.46/5.80 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_Suc_0_right
% 5.46/5.80 thf(fact_9601_coprime__Suc__0__left,axiom,
% 5.46/5.80 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_Suc_0_left
% 5.46/5.80 thf(fact_9602_coprime__Suc__left__nat,axiom,
% 5.46/5.80 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ N ) @ N ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_Suc_left_nat
% 5.46/5.80 thf(fact_9603_coprime__Suc__right__nat,axiom,
% 5.46/5.80 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_Suc_right_nat
% 5.46/5.80 thf(fact_9604_coprime__crossproduct__nat,axiom,
% 5.46/5.80 ! [A: nat,D: nat,B2: nat,C: nat] :
% 5.46/5.80 ( ( algebr934650988132801477me_nat @ A @ D )
% 5.46/5.80 => ( ( algebr934650988132801477me_nat @ B2 @ C )
% 5.46/5.80 => ( ( ( times_times_nat @ A @ C )
% 5.46/5.80 = ( times_times_nat @ B2 @ D ) )
% 5.46/5.80 = ( ( A = B2 )
% 5.46/5.80 & ( C = D ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_crossproduct_nat
% 5.46/5.80 thf(fact_9605_coprime__diff__one__right__nat,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_diff_one_right_nat
% 5.46/5.80 thf(fact_9606_coprime__diff__one__left__nat,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % coprime_diff_one_left_nat
% 5.46/5.80 thf(fact_9607_upto_Opsimps,axiom,
% 5.46/5.80 ! [I: int,J: int] :
% 5.46/5.80 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 5.46/5.80 => ( ( ( ord_less_eq_int @ I @ J )
% 5.46/5.80 => ( ( upto @ I @ J )
% 5.46/5.80 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_eq_int @ I @ J )
% 5.46/5.80 => ( ( upto @ I @ J )
% 5.46/5.80 = nil_int ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto.psimps
% 5.46/5.80 thf(fact_9608_upto__Nil,axiom,
% 5.46/5.80 ! [I: int,J: int] :
% 5.46/5.80 ( ( ( upto @ I @ J )
% 5.46/5.80 = nil_int )
% 5.46/5.80 = ( ord_less_int @ J @ I ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_Nil
% 5.46/5.80 thf(fact_9609_upto__Nil2,axiom,
% 5.46/5.80 ! [I: int,J: int] :
% 5.46/5.80 ( ( nil_int
% 5.46/5.80 = ( upto @ I @ J ) )
% 5.46/5.80 = ( ord_less_int @ J @ I ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_Nil2
% 5.46/5.80 thf(fact_9610_upto__empty,axiom,
% 5.46/5.80 ! [J: int,I: int] :
% 5.46/5.80 ( ( ord_less_int @ J @ I )
% 5.46/5.80 => ( ( upto @ I @ J )
% 5.46/5.80 = nil_int ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_empty
% 5.46/5.80 thf(fact_9611_nth__upto,axiom,
% 5.46/5.80 ! [I: int,K: nat,J: int] :
% 5.46/5.80 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.46/5.80 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 5.46/5.80 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % nth_upto
% 5.46/5.80 thf(fact_9612_length__upto,axiom,
% 5.46/5.80 ! [I: int,J: int] :
% 5.46/5.80 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 5.46/5.80 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % length_upto
% 5.46/5.80 thf(fact_9613_upto__rec__numeral_I1_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 = nil_int ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_rec_numeral(1)
% 5.46/5.80 thf(fact_9614_upto__rec__numeral_I2_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = nil_int ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_rec_numeral(2)
% 5.46/5.80 thf(fact_9615_upto__rec__numeral_I3_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 = ( 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 ) ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.46/5.80 = nil_int ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_rec_numeral(3)
% 5.46/5.80 thf(fact_9616_upto__rec__numeral_I4_J,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = ( 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 ) ) ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.46/5.80 = nil_int ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_rec_numeral(4)
% 5.46/5.80 thf(fact_9617_upto__split2,axiom,
% 5.46/5.80 ! [I: int,J: int,K: int] :
% 5.46/5.80 ( ( ord_less_eq_int @ I @ J )
% 5.46/5.80 => ( ( ord_less_eq_int @ J @ K )
% 5.46/5.80 => ( ( upto @ I @ K )
% 5.46/5.80 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_split2
% 5.46/5.80 thf(fact_9618_upto__split1,axiom,
% 5.46/5.80 ! [I: int,J: int,K: int] :
% 5.46/5.80 ( ( ord_less_eq_int @ I @ J )
% 5.46/5.80 => ( ( ord_less_eq_int @ J @ K )
% 5.46/5.80 => ( ( upto @ I @ K )
% 5.46/5.80 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_split1
% 5.46/5.80 thf(fact_9619_atLeastLessThan__upto,axiom,
% 5.46/5.80 ( set_or4662586982721622107an_int
% 5.46/5.80 = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % atLeastLessThan_upto
% 5.46/5.80 thf(fact_9620_greaterThanAtMost__upto,axiom,
% 5.46/5.80 ( set_or6656581121297822940st_int
% 5.46/5.80 = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % greaterThanAtMost_upto
% 5.46/5.80 thf(fact_9621_upto__rec1,axiom,
% 5.46/5.80 ! [I: int,J: int] :
% 5.46/5.80 ( ( ord_less_eq_int @ I @ J )
% 5.46/5.80 => ( ( upto @ I @ J )
% 5.46/5.80 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_rec1
% 5.46/5.80 thf(fact_9622_upto_Oelims,axiom,
% 5.46/5.80 ! [X4: int,Xa: int,Y3: list_int] :
% 5.46/5.80 ( ( ( upto @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( ( ord_less_eq_int @ X4 @ Xa )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( cons_int @ X4 @ ( upto @ ( plus_plus_int @ X4 @ one_one_int ) @ Xa ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_eq_int @ X4 @ Xa )
% 5.46/5.80 => ( Y3 = nil_int ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto.elims
% 5.46/5.80 thf(fact_9623_upto_Osimps,axiom,
% 5.46/5.80 ( upto
% 5.46/5.80 = ( ^ [I2: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I2 @ J3 ) @ ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto.simps
% 5.46/5.80 thf(fact_9624_upto__rec2,axiom,
% 5.46/5.80 ! [I: int,J: int] :
% 5.46/5.80 ( ( ord_less_eq_int @ I @ J )
% 5.46/5.80 => ( ( upto @ I @ J )
% 5.46/5.80 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_rec2
% 5.46/5.80 thf(fact_9625_greaterThanLessThan__upto,axiom,
% 5.46/5.80 ( set_or5832277885323065728an_int
% 5.46/5.80 = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % greaterThanLessThan_upto
% 5.46/5.80 thf(fact_9626_upto__split3,axiom,
% 5.46/5.80 ! [I: int,J: int,K: int] :
% 5.46/5.80 ( ( ord_less_eq_int @ I @ J )
% 5.46/5.80 => ( ( ord_less_eq_int @ J @ K )
% 5.46/5.80 => ( ( upto @ I @ K )
% 5.46/5.80 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto_split3
% 5.46/5.80 thf(fact_9627_upto_Opelims,axiom,
% 5.46/5.80 ! [X4: int,Xa: int,Y3: list_int] :
% 5.46/5.80 ( ( ( upto @ X4 @ Xa )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X4 @ Xa ) )
% 5.46/5.80 => ~ ( ( ( ( ord_less_eq_int @ X4 @ Xa )
% 5.46/5.80 => ( Y3
% 5.46/5.80 = ( cons_int @ X4 @ ( upto @ ( plus_plus_int @ X4 @ one_one_int ) @ Xa ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_eq_int @ X4 @ Xa )
% 5.46/5.80 => ( Y3 = nil_int ) ) )
% 5.46/5.80 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X4 @ Xa ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upto.pelims
% 5.46/5.80 thf(fact_9628_list__encode_Opelims,axiom,
% 5.46/5.80 ! [X4: list_nat,Y3: nat] :
% 5.46/5.80 ( ( ( nat_list_encode @ X4 )
% 5.46/5.80 = Y3 )
% 5.46/5.80 => ( ( accp_list_nat @ nat_list_encode_rel @ X4 )
% 5.46/5.80 => ( ( ( X4 = nil_nat )
% 5.46/5.80 => ( ( Y3 = zero_zero_nat )
% 5.46/5.80 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.46/5.80 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.46/5.80 ( ( X4
% 5.46/5.80 = ( cons_nat @ X3 @ Xs3 ) )
% 5.46/5.80 => ( ( Y3
% 5.46/5.80 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.46/5.80 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs3 ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % list_encode.pelims
% 5.46/5.80 thf(fact_9629_Rats__abs__iff,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( member_real @ ( abs_abs_real @ X4 ) @ field_5140801741446780682s_real )
% 5.46/5.80 = ( member_real @ X4 @ field_5140801741446780682s_real ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rats_abs_iff
% 5.46/5.80 thf(fact_9630_Rats__no__top__le,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ? [X3: real] :
% 5.46/5.80 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.46/5.80 & ( ord_less_eq_real @ X4 @ X3 ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rats_no_top_le
% 5.46/5.80 thf(fact_9631_Rats__no__bot__less,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ? [X3: real] :
% 5.46/5.80 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.46/5.80 & ( ord_less_real @ X3 @ X4 ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rats_no_bot_less
% 5.46/5.80 thf(fact_9632_Rats__dense__in__real,axiom,
% 5.46/5.80 ! [X4: real,Y3: real] :
% 5.46/5.80 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.80 => ? [X3: real] :
% 5.46/5.80 ( ( member_real @ X3 @ field_5140801741446780682s_real )
% 5.46/5.80 & ( ord_less_real @ X4 @ X3 )
% 5.46/5.80 & ( ord_less_real @ X3 @ Y3 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rats_dense_in_real
% 5.46/5.80 thf(fact_9633_Rats__abs__nat__div__natE,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 5.46/5.80 => ~ ! [M4: nat,N4: nat] :
% 5.46/5.80 ( ( N4 != zero_zero_nat )
% 5.46/5.80 => ( ( ( abs_abs_real @ X4 )
% 5.46/5.80 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M4 ) @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 5.46/5.80 => ~ ( algebr934650988132801477me_nat @ M4 @ N4 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rats_abs_nat_div_natE
% 5.46/5.80 thf(fact_9634_upt__rec__numeral,axiom,
% 5.46/5.80 ! [M: num,N: num] :
% 5.46/5.80 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.80 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.80 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.80 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.46/5.80 = nil_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upt_rec_numeral
% 5.46/5.80 thf(fact_9635_hd__upt,axiom,
% 5.46/5.80 ! [I: nat,J: nat] :
% 5.46/5.80 ( ( ord_less_nat @ I @ J )
% 5.46/5.80 => ( ( hd_nat @ ( upt @ I @ J ) )
% 5.46/5.80 = I ) ) ).
% 5.46/5.80
% 5.46/5.80 % hd_upt
% 5.46/5.80 thf(fact_9636_drop__upt,axiom,
% 5.46/5.80 ! [M: nat,I: nat,J: nat] :
% 5.46/5.80 ( ( drop_nat @ M @ ( upt @ I @ J ) )
% 5.46/5.80 = ( upt @ ( plus_plus_nat @ I @ M ) @ J ) ) ).
% 5.46/5.80
% 5.46/5.80 % drop_upt
% 5.46/5.80 thf(fact_9637_take__upt,axiom,
% 5.46/5.80 ! [I: nat,M: nat,N: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 5.46/5.80 => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 5.46/5.80 = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % take_upt
% 5.46/5.80 thf(fact_9638_upt__conv__Nil,axiom,
% 5.46/5.80 ! [J: nat,I: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ J @ I )
% 5.46/5.80 => ( ( upt @ I @ J )
% 5.46/5.80 = nil_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % upt_conv_Nil
% 5.46/5.80 thf(fact_9639_length__upt,axiom,
% 5.46/5.80 ! [I: nat,J: nat] :
% 5.46/5.80 ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 5.46/5.80 = ( minus_minus_nat @ J @ I ) ) ).
% 5.46/5.80
% 5.46/5.80 % length_upt
% 5.46/5.80 thf(fact_9640_upt__eq__Nil__conv,axiom,
% 5.46/5.80 ! [I: nat,J: nat] :
% 5.46/5.80 ( ( ( upt @ I @ J )
% 5.46/5.80 = nil_nat )
% 5.46/5.80 = ( ( J = zero_zero_nat )
% 5.46/5.80 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upt_eq_Nil_conv
% 5.46/5.80 thf(fact_9641_nth__upt,axiom,
% 5.46/5.80 ! [I: nat,K: nat,J: nat] :
% 5.46/5.80 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 5.46/5.80 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 5.46/5.80 = ( plus_plus_nat @ I @ K ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % nth_upt
% 5.46/5.80 thf(fact_9642_sum__list__upt,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ M @ N )
% 5.46/5.80 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.46/5.80 = ( groups3542108847815614940at_nat
% 5.46/5.80 @ ^ [X: nat] : X
% 5.46/5.80 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sum_list_upt
% 5.46/5.80 thf(fact_9643_atLeastAtMost__upt,axiom,
% 5.46/5.80 ( set_or1269000886237332187st_nat
% 5.46/5.80 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M6 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % atLeastAtMost_upt
% 5.46/5.80 thf(fact_9644_upt__conv__Cons__Cons,axiom,
% 5.46/5.80 ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 5.46/5.80 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 5.46/5.80 = ( upt @ M @ Q2 ) )
% 5.46/5.80 = ( ( cons_nat @ N @ Ns )
% 5.46/5.80 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upt_conv_Cons_Cons
% 5.46/5.80 thf(fact_9645_greaterThanAtMost__upt,axiom,
% 5.46/5.80 ( set_or6659071591806873216st_nat
% 5.46/5.80 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M6 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % greaterThanAtMost_upt
% 5.46/5.80 thf(fact_9646_greaterThanLessThan__upt,axiom,
% 5.46/5.80 ( set_or5834768355832116004an_nat
% 5.46/5.80 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M6 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % greaterThanLessThan_upt
% 5.46/5.80 thf(fact_9647_atMost__upto,axiom,
% 5.46/5.80 ( set_ord_atMost_nat
% 5.46/5.80 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % atMost_upto
% 5.46/5.80 thf(fact_9648_upt__conv__Cons,axiom,
% 5.46/5.80 ! [I: nat,J: nat] :
% 5.46/5.80 ( ( ord_less_nat @ I @ J )
% 5.46/5.80 => ( ( upt @ I @ J )
% 5.46/5.80 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upt_conv_Cons
% 5.46/5.80 thf(fact_9649_upt__add__eq__append,axiom,
% 5.46/5.80 ! [I: nat,J: nat,K: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.80 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 5.46/5.80 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upt_add_eq_append
% 5.46/5.80 thf(fact_9650_upt__eq__Cons__conv,axiom,
% 5.46/5.80 ! [I: nat,J: nat,X4: nat,Xs2: list_nat] :
% 5.46/5.80 ( ( ( upt @ I @ J )
% 5.46/5.80 = ( cons_nat @ X4 @ Xs2 ) )
% 5.46/5.80 = ( ( ord_less_nat @ I @ J )
% 5.46/5.80 & ( I = X4 )
% 5.46/5.80 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 5.46/5.80 = Xs2 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upt_eq_Cons_conv
% 5.46/5.80 thf(fact_9651_upt__rec,axiom,
% 5.46/5.80 ( upt
% 5.46/5.80 = ( ^ [I2: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I2 @ J3 ) @ ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upt_rec
% 5.46/5.80 thf(fact_9652_upt__Suc__append,axiom,
% 5.46/5.80 ! [I: nat,J: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.80 => ( ( upt @ I @ ( suc @ J ) )
% 5.46/5.80 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upt_Suc_append
% 5.46/5.80 thf(fact_9653_upt__Suc,axiom,
% 5.46/5.80 ! [I: nat,J: nat] :
% 5.46/5.80 ( ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.80 => ( ( upt @ I @ ( suc @ J ) )
% 5.46/5.80 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.46/5.80 & ( ~ ( ord_less_eq_nat @ I @ J )
% 5.46/5.80 => ( ( upt @ I @ ( suc @ J ) )
% 5.46/5.80 = nil_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % upt_Suc
% 5.46/5.80 thf(fact_9654_mono__Suc,axiom,
% 5.46/5.80 order_mono_nat_nat @ suc ).
% 5.46/5.80
% 5.46/5.80 % mono_Suc
% 5.46/5.80 thf(fact_9655_mono__times__nat,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % mono_times_nat
% 5.46/5.80 thf(fact_9656_mono__ge2__power__minus__self,axiom,
% 5.46/5.80 ! [K: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.46/5.80 => ( order_mono_nat_nat
% 5.46/5.80 @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % mono_ge2_power_minus_self
% 5.46/5.80 thf(fact_9657_map__Suc__upt,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 5.46/5.80 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % map_Suc_upt
% 5.46/5.80 thf(fact_9658_sorted__upt,axiom,
% 5.46/5.80 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % sorted_upt
% 5.46/5.80 thf(fact_9659_sorted__wrt__upt,axiom,
% 5.46/5.80 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % sorted_wrt_upt
% 5.46/5.80 thf(fact_9660_map__add__upt,axiom,
% 5.46/5.80 ! [N: nat,M: nat] :
% 5.46/5.80 ( ( map_nat_nat
% 5.46/5.80 @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ N )
% 5.46/5.80 @ ( upt @ zero_zero_nat @ M ) )
% 5.46/5.80 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % map_add_upt
% 5.46/5.80 thf(fact_9661_map__decr__upt,axiom,
% 5.46/5.80 ! [M: nat,N: nat] :
% 5.46/5.80 ( ( map_nat_nat
% 5.46/5.80 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.46/5.80 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.46/5.80 = ( upt @ M @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % map_decr_upt
% 5.46/5.80 thf(fact_9662_sorted__wrt__less__idx,axiom,
% 5.46/5.80 ! [Ns: list_nat,I: nat] :
% 5.46/5.80 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.46/5.80 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 5.46/5.80 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sorted_wrt_less_idx
% 5.46/5.80 thf(fact_9663_sorted__wrt__upto,axiom,
% 5.46/5.80 ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 5.46/5.80
% 5.46/5.80 % sorted_wrt_upto
% 5.46/5.80 thf(fact_9664_Rats__eq__int__div__int,axiom,
% 5.46/5.80 ( field_5140801741446780682s_real
% 5.46/5.80 = ( collect_real
% 5.46/5.80 @ ^ [Uu: real] :
% 5.46/5.80 ? [I2: int,J3: int] :
% 5.46/5.80 ( ( Uu
% 5.46/5.80 = ( divide_divide_real @ ( ring_1_of_int_real @ I2 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.46/5.80 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rats_eq_int_div_int
% 5.46/5.80 thf(fact_9665_Rats__eq__int__div__nat,axiom,
% 5.46/5.80 ( field_5140801741446780682s_real
% 5.46/5.80 = ( collect_real
% 5.46/5.80 @ ^ [Uu: real] :
% 5.46/5.80 ? [I2: int,N2: nat] :
% 5.46/5.80 ( ( Uu
% 5.46/5.80 = ( divide_divide_real @ ( ring_1_of_int_real @ I2 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.46/5.80 & ( N2 != zero_zero_nat ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Rats_eq_int_div_nat
% 5.46/5.80 thf(fact_9666_range__mod,axiom,
% 5.46/5.80 ! [N: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( image_nat_nat
% 5.46/5.80 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N )
% 5.46/5.80 @ top_top_set_nat )
% 5.46/5.80 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % range_mod
% 5.46/5.80 thf(fact_9667_UNIV__nat__eq,axiom,
% 5.46/5.80 ( top_top_set_nat
% 5.46/5.80 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % UNIV_nat_eq
% 5.46/5.80 thf(fact_9668_card__UNIV__unit,axiom,
% 5.46/5.80 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.46/5.80 = one_one_nat ) ).
% 5.46/5.80
% 5.46/5.80 % card_UNIV_unit
% 5.46/5.80 thf(fact_9669_range__mult,axiom,
% 5.46/5.80 ! [A: real] :
% 5.46/5.80 ( ( ( A = zero_zero_real )
% 5.46/5.80 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.46/5.80 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.46/5.80 & ( ( A != zero_zero_real )
% 5.46/5.80 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.46/5.80 = top_top_set_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % range_mult
% 5.46/5.80 thf(fact_9670_card__UNIV__bool,axiom,
% 5.46/5.80 ( ( finite_card_o @ top_top_set_o )
% 5.46/5.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % card_UNIV_bool
% 5.46/5.80 thf(fact_9671_root__def,axiom,
% 5.46/5.80 ( root
% 5.46/5.80 = ( ^ [N2: nat,X: real] :
% 5.46/5.80 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.46/5.80 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.46/5.80 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) )
% 5.46/5.80 @ X ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % root_def
% 5.46/5.80 thf(fact_9672_card__UNIV__char,axiom,
% 5.46/5.80 ( ( finite_card_char @ top_top_set_char )
% 5.46/5.80 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % card_UNIV_char
% 5.46/5.80 thf(fact_9673_UNIV__char__of__nat,axiom,
% 5.46/5.80 ( top_top_set_char
% 5.46/5.80 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % UNIV_char_of_nat
% 5.46/5.80 thf(fact_9674_nat__of__char__less__256,axiom,
% 5.46/5.80 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % nat_of_char_less_256
% 5.46/5.80 thf(fact_9675_range__nat__of__char,axiom,
% 5.46/5.80 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.46/5.80 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % range_nat_of_char
% 5.46/5.80 thf(fact_9676_integer__of__char__code,axiom,
% 5.46/5.80 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.46/5.80 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.46/5.80 = ( 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 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % integer_of_char_code
% 5.46/5.80 thf(fact_9677_String_Ochar__of__ascii__of,axiom,
% 5.46/5.80 ! [C: char] :
% 5.46/5.80 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.46/5.80 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % String.char_of_ascii_of
% 5.46/5.80 thf(fact_9678_DERIV__even__real__root,axiom,
% 5.46/5.80 ! [N: nat,X4: real] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X4 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_even_real_root
% 5.46/5.80 thf(fact_9679_DERIV__real__root__generic,axiom,
% 5.46/5.80 ! [N: nat,X4: real,D4: real] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( X4 != zero_zero_real )
% 5.46/5.80 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.80 => ( D4
% 5.46/5.80 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X4 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.46/5.80 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.46/5.80 => ( D4
% 5.46/5.80 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X4 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.46/5.80 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.80 => ( D4
% 5.46/5.80 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X4 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_real_root_generic
% 5.46/5.80 thf(fact_9680_DERIV__neg__dec__right,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.46/5.80 => ? [D3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.80 & ! [H4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.80 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.80 => ( ord_less_real @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_neg_dec_right
% 5.46/5.80 thf(fact_9681_DERIV__pos__inc__right,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.46/5.80 => ? [D3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.80 & ! [H4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.80 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.80 => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_pos_inc_right
% 5.46/5.80 thf(fact_9682_DERIV__pos__imp__increasing,axiom,
% 5.46/5.80 ! [A: real,B2: real,F: real > real] :
% 5.46/5.80 ( ( ord_less_real @ A @ B2 )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.80 => ( ( ord_less_eq_real @ X3 @ B2 )
% 5.46/5.80 => ? [Y5: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 & ( ord_less_real @ zero_zero_real @ Y5 ) ) ) )
% 5.46/5.80 => ( ord_less_real @ ( F @ A ) @ ( F @ B2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_pos_imp_increasing
% 5.46/5.80 thf(fact_9683_DERIV__neg__imp__decreasing,axiom,
% 5.46/5.80 ! [A: real,B2: real,F: real > real] :
% 5.46/5.80 ( ( ord_less_real @ A @ B2 )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.80 => ( ( ord_less_eq_real @ X3 @ B2 )
% 5.46/5.80 => ? [Y5: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 & ( ord_less_real @ Y5 @ zero_zero_real ) ) ) )
% 5.46/5.80 => ( ord_less_real @ ( F @ B2 ) @ ( F @ A ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_neg_imp_decreasing
% 5.46/5.80 thf(fact_9684_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.46/5.80 ! [A: real,B2: real,F: real > real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.80 => ( ( ord_less_eq_real @ X3 @ B2 )
% 5.46/5.80 => ? [Y5: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 & ( ord_less_eq_real @ Y5 @ zero_zero_real ) ) ) )
% 5.46/5.80 => ( ord_less_eq_real @ ( F @ B2 ) @ ( F @ A ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_nonpos_imp_nonincreasing
% 5.46/5.80 thf(fact_9685_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.46/5.80 ! [A: real,B2: real,F: real > real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.80 => ( ( ord_less_eq_real @ X3 @ B2 )
% 5.46/5.80 => ? [Y5: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 & ( ord_less_eq_real @ zero_zero_real @ Y5 ) ) ) )
% 5.46/5.80 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_nonneg_imp_nondecreasing
% 5.46/5.80 thf(fact_9686_deriv__nonneg__imp__mono,axiom,
% 5.46/5.80 ! [A: real,B2: real,G: real > real,G2: real > real] :
% 5.46/5.80 ( ! [X3: real] :
% 5.46/5.80 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B2 ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B2 ) )
% 5.46/5.80 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 5.46/5.80 => ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.80 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B2 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % deriv_nonneg_imp_mono
% 5.46/5.80 thf(fact_9687_DERIV__isconst__all,axiom,
% 5.46/5.80 ! [F: real > real,X4: real,Y3: real] :
% 5.46/5.80 ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 => ( ( F @ X4 )
% 5.46/5.80 = ( F @ Y3 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_isconst_all
% 5.46/5.80 thf(fact_9688_DERIV__mirror,axiom,
% 5.46/5.80 ! [F: real > real,Y3: real,X4: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ X4 ) @ top_top_set_real ) )
% 5.46/5.80 = ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [X: real] : ( F @ ( uminus_uminus_real @ X ) )
% 5.46/5.80 @ ( uminus_uminus_real @ Y3 )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_mirror
% 5.46/5.80 thf(fact_9689_DERIV__const__ratio__const2,axiom,
% 5.46/5.80 ! [A: real,B2: real,F: real > real,K: real] :
% 5.46/5.80 ( ( A != B2 )
% 5.46/5.80 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B2 ) @ ( F @ A ) ) @ ( minus_minus_real @ B2 @ A ) )
% 5.46/5.80 = K ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_const_ratio_const2
% 5.46/5.80 thf(fact_9690_DERIV__const__ratio__const,axiom,
% 5.46/5.80 ! [A: real,B2: real,F: real > real,K: real] :
% 5.46/5.80 ( ( A != B2 )
% 5.46/5.80 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 => ( ( minus_minus_real @ ( F @ B2 ) @ ( F @ A ) )
% 5.46/5.80 = ( times_times_real @ ( minus_minus_real @ B2 @ A ) @ K ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_const_ratio_const
% 5.46/5.80 thf(fact_9691_DERIV__pos__inc__left,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.46/5.80 => ? [D3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.80 & ! [H4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.80 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.80 => ( ord_less_real @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_pos_inc_left
% 5.46/5.80 thf(fact_9692_DERIV__neg__dec__left,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.46/5.80 => ? [D3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.80 & ! [H4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.80 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.80 => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_neg_dec_left
% 5.46/5.80 thf(fact_9693_DERIV__isconst3,axiom,
% 5.46/5.80 ! [A: real,B2: real,X4: real,Y3: real,F: real > real] :
% 5.46/5.80 ( ( ord_less_real @ A @ B2 )
% 5.46/5.80 => ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B2 ) )
% 5.46/5.80 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B2 ) )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B2 ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.46/5.80 => ( ( F @ X4 )
% 5.46/5.80 = ( F @ Y3 ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_isconst3
% 5.46/5.80 thf(fact_9694_has__real__derivative__pos__inc__left,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real,S2: set_real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.46/5.80 => ? [D3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.80 & ! [H4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.80 => ( ( member_real @ ( minus_minus_real @ X4 @ H4 ) @ S2 )
% 5.46/5.80 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.80 => ( ord_less_real @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % has_real_derivative_pos_inc_left
% 5.46/5.80 thf(fact_9695_has__real__derivative__neg__dec__left,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real,S2: set_real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 5.46/5.80 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.46/5.80 => ? [D3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.80 & ! [H4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.80 => ( ( member_real @ ( minus_minus_real @ X4 @ H4 ) @ S2 )
% 5.46/5.80 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.80 => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % has_real_derivative_neg_dec_left
% 5.46/5.80 thf(fact_9696_has__real__derivative__pos__inc__right,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real,S2: set_real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.46/5.80 => ? [D3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.80 & ! [H4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.80 => ( ( member_real @ ( plus_plus_real @ X4 @ H4 ) @ S2 )
% 5.46/5.80 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.80 => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % has_real_derivative_pos_inc_right
% 5.46/5.80 thf(fact_9697_has__real__derivative__neg__dec__right,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real,S2: set_real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 5.46/5.80 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.46/5.80 => ? [D3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.46/5.80 & ! [H4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.46/5.80 => ( ( member_real @ ( plus_plus_real @ X4 @ H4 ) @ S2 )
% 5.46/5.80 => ( ( ord_less_real @ H4 @ D3 )
% 5.46/5.80 => ( ord_less_real @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % has_real_derivative_neg_dec_right
% 5.46/5.80 thf(fact_9698_MVT2,axiom,
% 5.46/5.80 ! [A: real,B2: real,F: real > real,F4: real > real] :
% 5.46/5.80 ( ( ord_less_real @ A @ B2 )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.80 => ( ( ord_less_eq_real @ X3 @ B2 )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.80 => ? [Z2: real] :
% 5.46/5.80 ( ( ord_less_real @ A @ Z2 )
% 5.46/5.80 & ( ord_less_real @ Z2 @ B2 )
% 5.46/5.80 & ( ( minus_minus_real @ ( F @ B2 ) @ ( F @ A ) )
% 5.46/5.80 = ( times_times_real @ ( minus_minus_real @ B2 @ A ) @ ( F4 @ Z2 ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % MVT2
% 5.46/5.80 thf(fact_9699_DERIV__local__const,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real,D: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.46/5.80 => ( ! [Y4: real] :
% 5.46/5.80 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) @ D )
% 5.46/5.80 => ( ( F @ X4 )
% 5.46/5.80 = ( F @ Y4 ) ) )
% 5.46/5.80 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_local_const
% 5.46/5.80 thf(fact_9700_DERIV__ln,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_ln
% 5.46/5.80 thf(fact_9701_DERIV__const__average,axiom,
% 5.46/5.80 ! [A: real,B2: real,V: real > real,K: real] :
% 5.46/5.80 ( ( A != B2 )
% 5.46/5.80 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.46/5.80 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_const_average
% 5.46/5.80 thf(fact_9702_DERIV__local__max,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real,D: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.46/5.80 => ( ! [Y4: real] :
% 5.46/5.80 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) @ D )
% 5.46/5.80 => ( ord_less_eq_real @ ( F @ Y4 ) @ ( F @ X4 ) ) )
% 5.46/5.80 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_local_max
% 5.46/5.80 thf(fact_9703_DERIV__local__min,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,X4: real,D: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.46/5.80 => ( ! [Y4: real] :
% 5.46/5.80 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) @ D )
% 5.46/5.80 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 5.46/5.80 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_local_min
% 5.46/5.80 thf(fact_9704_DERIV__ln__divide,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_ln_divide
% 5.46/5.80 thf(fact_9705_DERIV__pow,axiom,
% 5.46/5.80 ! [N: nat,X4: real,S: set_real] :
% 5.46/5.80 ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [X: real] : ( power_power_real @ X @ N )
% 5.46/5.80 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X4 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ S ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_pow
% 5.46/5.80 thf(fact_9706_DERIV__fun__pow,axiom,
% 5.46/5.80 ! [G: real > real,M: real,X4: real,N: nat] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [X: real] : ( power_power_real @ ( G @ X ) @ N )
% 5.46/5.80 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X4 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_fun_pow
% 5.46/5.80 thf(fact_9707_has__real__derivative__powr,axiom,
% 5.46/5.80 ! [Z: real,R2: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.46/5.80 => ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [Z5: real] : ( powr_real @ Z5 @ R2 )
% 5.46/5.80 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % has_real_derivative_powr
% 5.46/5.80 thf(fact_9708_DERIV__log,axiom,
% 5.46/5.80 ! [X4: real,B2: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( log @ B2 ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B2 ) @ X4 ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_log
% 5.46/5.80 thf(fact_9709_DERIV__fun__powr,axiom,
% 5.46/5.80 ! [G: real > real,M: real,X4: real,R2: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ ( G @ X4 ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ R2 )
% 5.46/5.80 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X4 ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_fun_powr
% 5.46/5.80 thf(fact_9710_DERIV__powr,axiom,
% 5.46/5.80 ! [G: real > real,M: real,X4: real,F: real > real,R2: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ ( G @ X4 ) )
% 5.46/5.80 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ ( F @ X ) )
% 5.46/5.80 @ ( times_times_real @ ( powr_real @ ( G @ X4 ) @ ( F @ X4 ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G @ X4 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X4 ) ) @ ( G @ X4 ) ) ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_powr
% 5.46/5.80 thf(fact_9711_DERIV__real__sqrt,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_real_sqrt
% 5.46/5.80 thf(fact_9712_DERIV__series_H,axiom,
% 5.46/5.80 ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B2: real,L5: nat > real] :
% 5.46/5.80 ( ! [N4: nat] :
% 5.46/5.80 ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [X: real] : ( F @ X @ N4 )
% 5.46/5.80 @ ( F4 @ X0 @ N4 )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B2 ) )
% 5.46/5.80 => ( summable_real @ ( F @ X3 ) ) )
% 5.46/5.80 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B2 ) )
% 5.46/5.80 => ( ( summable_real @ ( F4 @ X0 ) )
% 5.46/5.80 => ( ( summable_real @ L5 )
% 5.46/5.80 => ( ! [N4: nat,X3: real,Y4: real] :
% 5.46/5.80 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B2 ) )
% 5.46/5.80 => ( ( member_real @ Y4 @ ( set_or1633881224788618240n_real @ A @ B2 ) )
% 5.46/5.80 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N4 ) @ ( F @ Y4 @ N4 ) ) ) @ ( times_times_real @ ( L5 @ N4 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y4 ) ) ) ) ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [X: real] : ( suminf_real @ ( F @ X ) )
% 5.46/5.80 @ ( suminf_real @ ( F4 @ X0 ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_series'
% 5.46/5.80 thf(fact_9713_DERIV__arctan,axiom,
% 5.46/5.80 ! [X4: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_arctan
% 5.46/5.80 thf(fact_9714_arsinh__real__has__field__derivative,axiom,
% 5.46/5.80 ! [X4: real,A3: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A3 ) ) ).
% 5.46/5.80
% 5.46/5.80 % arsinh_real_has_field_derivative
% 5.46/5.80 thf(fact_9715_DERIV__real__sqrt__generic,axiom,
% 5.46/5.80 ! [X4: real,D4: real] :
% 5.46/5.80 ( ( X4 != zero_zero_real )
% 5.46/5.80 => ( ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.80 => ( D4
% 5.46/5.80 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 => ( ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.46/5.80 => ( D4
% 5.46/5.80 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_real_sqrt_generic
% 5.46/5.80 thf(fact_9716_arcosh__real__has__field__derivative,axiom,
% 5.46/5.80 ! [X4: real,A3: set_real] :
% 5.46/5.80 ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A3 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % arcosh_real_has_field_derivative
% 5.46/5.80 thf(fact_9717_artanh__real__has__field__derivative,axiom,
% 5.46/5.80 ! [X4: real,A3: set_real] :
% 5.46/5.80 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A3 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % artanh_real_has_field_derivative
% 5.46/5.80 thf(fact_9718_DERIV__power__series_H,axiom,
% 5.46/5.80 ! [R: real,F: nat > real,X0: real] :
% 5.46/5.80 ( ! [X3: real] :
% 5.46/5.80 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.46/5.80 => ( summable_real
% 5.46/5.80 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X3 @ N2 ) ) ) )
% 5.46/5.80 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.46/5.80 => ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( suminf_real
% 5.46/5.80 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) )
% 5.46/5.80 @ ( suminf_real
% 5.46/5.80 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_power_series'
% 5.46/5.80 thf(fact_9719_DERIV__real__root,axiom,
% 5.46/5.80 ! [N: nat,X4: real] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X4 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_real_root
% 5.46/5.80 thf(fact_9720_DERIV__arccos,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_arccos
% 5.46/5.80 thf(fact_9721_DERIV__arcsin,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_arcsin
% 5.46/5.80 thf(fact_9722_Maclaurin__all__le__objl,axiom,
% 5.46/5.80 ! [Diff: nat > real > real,F: real > real,X4: real,N: nat] :
% 5.46/5.80 ( ( ( ( Diff @ zero_zero_nat )
% 5.46/5.80 = F )
% 5.46/5.80 & ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.46/5.80 => ? [T2: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ ( abs_abs_real @ T2 ) @ ( abs_abs_real @ X4 ) )
% 5.46/5.80 & ( ( F @ X4 )
% 5.46/5.80 = ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Maclaurin_all_le_objl
% 5.46/5.80 thf(fact_9723_Maclaurin__all__le,axiom,
% 5.46/5.80 ! [Diff: nat > real > real,F: real > real,X4: real,N: nat] :
% 5.46/5.80 ( ( ( Diff @ zero_zero_nat )
% 5.46/5.80 = F )
% 5.46/5.80 => ( ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 => ? [T2: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ ( abs_abs_real @ T2 ) @ ( abs_abs_real @ X4 ) )
% 5.46/5.80 & ( ( F @ X4 )
% 5.46/5.80 = ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Maclaurin_all_le
% 5.46/5.80 thf(fact_9724_DERIV__odd__real__root,axiom,
% 5.46/5.80 ! [N: nat,X4: real] :
% 5.46/5.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.80 => ( ( X4 != zero_zero_real )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X4 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_odd_real_root
% 5.46/5.80 thf(fact_9725_Maclaurin,axiom,
% 5.46/5.80 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.46/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.80 = F )
% 5.46/5.80 => ( ! [M4: nat,T2: real] :
% 5.46/5.80 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.80 & ( ord_less_eq_real @ zero_zero_real @ T2 )
% 5.46/5.80 & ( ord_less_eq_real @ T2 @ H2 ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T2 ) @ ( topolo2177554685111907308n_real @ T2 @ top_top_set_real ) ) )
% 5.46/5.80 => ? [T2: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ T2 )
% 5.46/5.80 & ( ord_less_real @ T2 @ H2 )
% 5.46/5.80 & ( ( F @ H2 )
% 5.46/5.80 = ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Maclaurin
% 5.46/5.80 thf(fact_9726_Maclaurin2,axiom,
% 5.46/5.80 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.46/5.80 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.80 = F )
% 5.46/5.80 => ( ! [M4: nat,T2: real] :
% 5.46/5.80 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.80 & ( ord_less_eq_real @ zero_zero_real @ T2 )
% 5.46/5.80 & ( ord_less_eq_real @ T2 @ H2 ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T2 ) @ ( topolo2177554685111907308n_real @ T2 @ top_top_set_real ) ) )
% 5.46/5.80 => ? [T2: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ T2 )
% 5.46/5.80 & ( ord_less_eq_real @ T2 @ H2 )
% 5.46/5.80 & ( ( F @ H2 )
% 5.46/5.80 = ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Maclaurin2
% 5.46/5.80 thf(fact_9727_Maclaurin__minus,axiom,
% 5.46/5.80 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.46/5.80 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.46/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.80 = F )
% 5.46/5.80 => ( ! [M4: nat,T2: real] :
% 5.46/5.80 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.80 & ( ord_less_eq_real @ H2 @ T2 )
% 5.46/5.80 & ( ord_less_eq_real @ T2 @ zero_zero_real ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T2 ) @ ( topolo2177554685111907308n_real @ T2 @ top_top_set_real ) ) )
% 5.46/5.80 => ? [T2: real] :
% 5.46/5.80 ( ( ord_less_real @ H2 @ T2 )
% 5.46/5.80 & ( ord_less_real @ T2 @ zero_zero_real )
% 5.46/5.80 & ( ( F @ H2 )
% 5.46/5.80 = ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Maclaurin_minus
% 5.46/5.80 thf(fact_9728_Maclaurin__all__lt,axiom,
% 5.46/5.80 ! [Diff: nat > real > real,F: real > real,N: nat,X4: real] :
% 5.46/5.80 ( ( ( Diff @ zero_zero_nat )
% 5.46/5.80 = F )
% 5.46/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( X4 != zero_zero_real )
% 5.46/5.80 => ( ! [M4: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 => ? [T2: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T2 ) )
% 5.46/5.80 & ( ord_less_real @ ( abs_abs_real @ T2 ) @ ( abs_abs_real @ X4 ) )
% 5.46/5.80 & ( ( F @ X4 )
% 5.46/5.80 = ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Maclaurin_all_lt
% 5.46/5.80 thf(fact_9729_Maclaurin__bi__le,axiom,
% 5.46/5.80 ! [Diff: nat > real > real,F: real > real,N: nat,X4: real] :
% 5.46/5.80 ( ( ( Diff @ zero_zero_nat )
% 5.46/5.80 = F )
% 5.46/5.80 => ( ! [M4: nat,T2: real] :
% 5.46/5.80 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.80 & ( ord_less_eq_real @ ( abs_abs_real @ T2 ) @ ( abs_abs_real @ X4 ) ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T2 ) @ ( topolo2177554685111907308n_real @ T2 @ top_top_set_real ) ) )
% 5.46/5.80 => ? [T2: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ ( abs_abs_real @ T2 ) @ ( abs_abs_real @ X4 ) )
% 5.46/5.80 & ( ( F @ X4 )
% 5.46/5.80 = ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Maclaurin_bi_le
% 5.46/5.80 thf(fact_9730_Taylor,axiom,
% 5.46/5.80 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B2: real,C: real,X4: real] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.80 = F )
% 5.46/5.80 => ( ! [M4: nat,T2: real] :
% 5.46/5.80 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.80 & ( ord_less_eq_real @ A @ T2 )
% 5.46/5.80 & ( ord_less_eq_real @ T2 @ B2 ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T2 ) @ ( topolo2177554685111907308n_real @ T2 @ top_top_set_real ) ) )
% 5.46/5.80 => ( ( ord_less_eq_real @ A @ C )
% 5.46/5.80 => ( ( ord_less_eq_real @ C @ B2 )
% 5.46/5.80 => ( ( ord_less_eq_real @ A @ X4 )
% 5.46/5.80 => ( ( ord_less_eq_real @ X4 @ B2 )
% 5.46/5.80 => ( ( X4 != C )
% 5.46/5.80 => ? [T2: real] :
% 5.46/5.80 ( ( ( ord_less_real @ X4 @ C )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ T2 )
% 5.46/5.80 & ( ord_less_real @ T2 @ C ) ) )
% 5.46/5.80 & ( ~ ( ord_less_real @ X4 @ C )
% 5.46/5.80 => ( ( ord_less_real @ C @ T2 )
% 5.46/5.80 & ( ord_less_real @ T2 @ X4 ) ) )
% 5.46/5.80 & ( ( F @ X4 )
% 5.46/5.80 = ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ C ) @ M6 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Taylor
% 5.46/5.80 thf(fact_9731_Taylor__up,axiom,
% 5.46/5.80 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B2: real,C: real] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.80 = F )
% 5.46/5.80 => ( ! [M4: nat,T2: real] :
% 5.46/5.80 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.80 & ( ord_less_eq_real @ A @ T2 )
% 5.46/5.80 & ( ord_less_eq_real @ T2 @ B2 ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T2 ) @ ( topolo2177554685111907308n_real @ T2 @ top_top_set_real ) ) )
% 5.46/5.80 => ( ( ord_less_eq_real @ A @ C )
% 5.46/5.80 => ( ( ord_less_real @ C @ B2 )
% 5.46/5.80 => ? [T2: real] :
% 5.46/5.80 ( ( ord_less_real @ C @ T2 )
% 5.46/5.80 & ( ord_less_real @ T2 @ B2 )
% 5.46/5.80 & ( ( F @ B2 )
% 5.46/5.80 = ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B2 @ C ) @ M6 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B2 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Taylor_up
% 5.46/5.80 thf(fact_9732_Taylor__down,axiom,
% 5.46/5.80 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B2: real,C: real] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( ( Diff @ zero_zero_nat )
% 5.46/5.80 = F )
% 5.46/5.80 => ( ! [M4: nat,T2: real] :
% 5.46/5.80 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.80 & ( ord_less_eq_real @ A @ T2 )
% 5.46/5.80 & ( ord_less_eq_real @ T2 @ B2 ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T2 ) @ ( topolo2177554685111907308n_real @ T2 @ top_top_set_real ) ) )
% 5.46/5.80 => ( ( ord_less_real @ A @ C )
% 5.46/5.80 => ( ( ord_less_eq_real @ C @ B2 )
% 5.46/5.80 => ? [T2: real] :
% 5.46/5.80 ( ( ord_less_real @ A @ T2 )
% 5.46/5.80 & ( ord_less_real @ T2 @ C )
% 5.46/5.80 & ( ( F @ A )
% 5.46/5.80 = ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ N ) )
% 5.46/5.80 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Taylor_down
% 5.46/5.80 thf(fact_9733_Maclaurin__lemma2,axiom,
% 5.46/5.80 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B4: real] :
% 5.46/5.80 ( ! [M4: nat,T2: real] :
% 5.46/5.80 ( ( ( ord_less_nat @ M4 @ N )
% 5.46/5.80 & ( ord_less_eq_real @ zero_zero_real @ T2 )
% 5.46/5.80 & ( ord_less_eq_real @ T2 @ H2 ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T2 ) @ ( topolo2177554685111907308n_real @ T2 @ top_top_set_real ) ) )
% 5.46/5.80 => ( ( N
% 5.46/5.80 = ( suc @ K ) )
% 5.46/5.80 => ! [M5: nat,T4: real] :
% 5.46/5.80 ( ( ( ord_less_nat @ M5 @ N )
% 5.46/5.80 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.46/5.80 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.46/5.80 => ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [U4: real] :
% 5.46/5.80 ( minus_minus_real @ ( Diff @ M5 @ U4 )
% 5.46/5.80 @ ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [P3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M5 @ P3 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P3 ) ) @ ( power_power_real @ U4 @ P3 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M5 ) ) )
% 5.46/5.80 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ U4 @ ( minus_minus_nat @ N @ M5 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M5 ) ) ) ) ) )
% 5.46/5.80 @ ( minus_minus_real @ ( Diff @ ( suc @ M5 ) @ T4 )
% 5.46/5.80 @ ( plus_plus_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [P3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M5 ) @ P3 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P3 ) ) @ ( power_power_real @ T4 @ P3 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) )
% 5.46/5.80 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ T4 @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) ) ) ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Maclaurin_lemma2
% 5.46/5.80 thf(fact_9734_DERIV__arctan__series,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.80 => ( has_fi5821293074295781190e_real
% 5.46/5.80 @ ^ [X9: real] :
% 5.46/5.80 ( suminf_real
% 5.46/5.80 @ ^ [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 ) ) ) ) )
% 5.46/5.80 @ ( suminf_real
% 5.46/5.80 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X4 @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_arctan_series
% 5.46/5.80 thf(fact_9735_isCont__Lb__Ub,axiom,
% 5.46/5.80 ! [A: real,B2: real,F: real > real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.80 & ( ord_less_eq_real @ X3 @ B2 ) )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.46/5.80 => ? [L6: real,M9: real] :
% 5.46/5.80 ( ! [X5: real] :
% 5.46/5.80 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.46/5.80 & ( ord_less_eq_real @ X5 @ B2 ) )
% 5.46/5.80 => ( ( ord_less_eq_real @ L6 @ ( F @ X5 ) )
% 5.46/5.80 & ( ord_less_eq_real @ ( F @ X5 ) @ M9 ) ) )
% 5.46/5.80 & ! [Y5: real] :
% 5.46/5.80 ( ( ( ord_less_eq_real @ L6 @ Y5 )
% 5.46/5.80 & ( ord_less_eq_real @ Y5 @ M9 ) )
% 5.46/5.80 => ? [X3: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.80 & ( ord_less_eq_real @ X3 @ B2 )
% 5.46/5.80 & ( ( F @ X3 )
% 5.46/5.80 = Y5 ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % isCont_Lb_Ub
% 5.46/5.80 thf(fact_9736_LIM__fun__less__zero,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,C: real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.46/5.80 => ? [R3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.46/5.80 & ! [X5: real] :
% 5.46/5.80 ( ( ( X5 != C )
% 5.46/5.80 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.46/5.80 => ( ord_less_real @ ( F @ X5 ) @ zero_zero_real ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIM_fun_less_zero
% 5.46/5.80 thf(fact_9737_LIM__fun__not__zero,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,C: real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.46/5.80 => ( ( L2 != zero_zero_real )
% 5.46/5.80 => ? [R3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.46/5.80 & ! [X5: real] :
% 5.46/5.80 ( ( ( X5 != C )
% 5.46/5.80 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.46/5.80 => ( ( F @ X5 )
% 5.46/5.80 != zero_zero_real ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIM_fun_not_zero
% 5.46/5.80 thf(fact_9738_LIM__fun__gt__zero,axiom,
% 5.46/5.80 ! [F: real > real,L2: real,C: real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.46/5.80 => ? [R3: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.46/5.80 & ! [X5: real] :
% 5.46/5.80 ( ( ( X5 != C )
% 5.46/5.80 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.46/5.80 => ( ord_less_real @ zero_zero_real @ ( F @ X5 ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIM_fun_gt_zero
% 5.46/5.80 thf(fact_9739_isCont__real__sqrt,axiom,
% 5.46/5.80 ! [X4: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ sqrt ) ).
% 5.46/5.80
% 5.46/5.80 % isCont_real_sqrt
% 5.46/5.80 thf(fact_9740_isCont__real__root,axiom,
% 5.46/5.80 ! [X4: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ ( root @ N ) ) ).
% 5.46/5.80
% 5.46/5.80 % isCont_real_root
% 5.46/5.80 thf(fact_9741_continuous__frac,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ~ ( member_real @ X4 @ ring_1_Ints_real )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ archim2898591450579166408c_real ) ) ).
% 5.46/5.80
% 5.46/5.80 % continuous_frac
% 5.46/5.80 thf(fact_9742_isCont__inverse__function2,axiom,
% 5.46/5.80 ! [A: real,X4: real,B2: real,G: real > real,F: real > real] :
% 5.46/5.80 ( ( ord_less_real @ A @ X4 )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ B2 )
% 5.46/5.80 => ( ! [Z2: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ Z2 )
% 5.46/5.80 => ( ( ord_less_eq_real @ Z2 @ B2 )
% 5.46/5.80 => ( ( G @ ( F @ Z2 ) )
% 5.46/5.80 = Z2 ) ) )
% 5.46/5.80 => ( ! [Z2: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ Z2 )
% 5.46/5.80 => ( ( ord_less_eq_real @ Z2 @ B2 )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X4 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % isCont_inverse_function2
% 5.46/5.80 thf(fact_9743_isCont__arcosh,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.46/5.80
% 5.46/5.80 % isCont_arcosh
% 5.46/5.80 thf(fact_9744_LIM__cos__div__sin,axiom,
% 5.46/5.80 ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIM_cos_div_sin
% 5.46/5.80 thf(fact_9745_continuous__floor,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ~ ( member_real @ X4 @ ring_1_Ints_real )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ ( comp_int_real_real @ ring_1_of_int_real @ archim6058952711729229775r_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % continuous_floor
% 5.46/5.80 thf(fact_9746_DERIV__inverse__function,axiom,
% 5.46/5.80 ! [F: real > real,D4: real,G: real > real,X4: real,A: real,B2: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X4 ) @ top_top_set_real ) )
% 5.46/5.80 => ( ( D4 != zero_zero_real )
% 5.46/5.80 => ( ( ord_less_real @ A @ X4 )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ B2 )
% 5.46/5.80 => ( ! [Y4: real] :
% 5.46/5.80 ( ( ord_less_real @ A @ Y4 )
% 5.46/5.80 => ( ( ord_less_real @ Y4 @ B2 )
% 5.46/5.80 => ( ( F @ ( G @ Y4 ) )
% 5.46/5.80 = Y4 ) ) )
% 5.46/5.80 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_inverse_function
% 5.46/5.80 thf(fact_9747_isCont__arccos,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arccos ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % isCont_arccos
% 5.46/5.80 thf(fact_9748_isCont__arcsin,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % isCont_arcsin
% 5.46/5.80 thf(fact_9749_LIM__less__bound,axiom,
% 5.46/5.80 ! [B2: real,X4: real,F: real > real] :
% 5.46/5.80 ( ( ord_less_real @ B2 @ X4 )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ B2 @ X4 ) )
% 5.46/5.80 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.46/5.80 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F )
% 5.46/5.80 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIM_less_bound
% 5.46/5.80 thf(fact_9750_isCont__artanh,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % isCont_artanh
% 5.46/5.80 thf(fact_9751_isCont__inverse__function,axiom,
% 5.46/5.80 ! [D: real,X4: real,G: real > real,F: real > real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ D )
% 5.46/5.80 => ( ! [Z2: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X4 ) ) @ D )
% 5.46/5.80 => ( ( G @ ( F @ Z2 ) )
% 5.46/5.80 = Z2 ) )
% 5.46/5.80 => ( ! [Z2: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X4 ) ) @ D )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X4 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % isCont_inverse_function
% 5.46/5.80 thf(fact_9752_GMVT_H,axiom,
% 5.46/5.80 ! [A: real,B2: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 5.46/5.80 ( ( ord_less_real @ A @ B2 )
% 5.46/5.80 => ( ! [Z2: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ Z2 )
% 5.46/5.80 => ( ( ord_less_eq_real @ Z2 @ B2 )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.46/5.80 => ( ! [Z2: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ A @ Z2 )
% 5.46/5.80 => ( ( ord_less_eq_real @ Z2 @ B2 )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ G ) ) )
% 5.46/5.80 => ( ! [Z2: real] :
% 5.46/5.80 ( ( ord_less_real @ A @ Z2 )
% 5.46/5.80 => ( ( ord_less_real @ Z2 @ B2 )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.46/5.80 => ( ! [Z2: real] :
% 5.46/5.80 ( ( ord_less_real @ A @ Z2 )
% 5.46/5.80 => ( ( ord_less_real @ Z2 @ B2 )
% 5.46/5.80 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.46/5.80 => ? [C3: real] :
% 5.46/5.80 ( ( ord_less_real @ A @ C3 )
% 5.46/5.80 & ( ord_less_real @ C3 @ B2 )
% 5.46/5.80 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B2 ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 5.46/5.80 = ( times_times_real @ ( minus_minus_real @ ( G @ B2 ) @ ( G @ A ) ) @ ( F4 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % GMVT'
% 5.46/5.80 thf(fact_9753_summable__Leibniz_I2_J,axiom,
% 5.46/5.80 ! [A: nat > real] :
% 5.46/5.80 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ( ( topolo6980174941875973593q_real @ A )
% 5.46/5.80 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.46/5.80 => ! [N6: nat] :
% 5.46/5.80 ( member_real
% 5.46/5.80 @ ( suminf_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 5.46/5.80 @ ( set_or1222579329274155063t_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % summable_Leibniz(2)
% 5.46/5.80 thf(fact_9754_summable__Leibniz_I3_J,axiom,
% 5.46/5.80 ! [A: nat > real] :
% 5.46/5.80 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ( ( topolo6980174941875973593q_real @ A )
% 5.46/5.80 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.46/5.80 => ! [N6: nat] :
% 5.46/5.80 ( member_real
% 5.46/5.80 @ ( suminf_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 5.46/5.80 @ ( set_or1222579329274155063t_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % summable_Leibniz(3)
% 5.46/5.80 thf(fact_9755_incseq__convergent,axiom,
% 5.46/5.80 ! [X8: nat > real,B4: real] :
% 5.46/5.80 ( ( order_mono_nat_real @ X8 )
% 5.46/5.80 => ( ! [I3: nat] : ( ord_less_eq_real @ ( X8 @ I3 ) @ B4 )
% 5.46/5.80 => ~ ! [L6: real] :
% 5.46/5.80 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.46/5.80 => ~ ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ L6 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % incseq_convergent
% 5.46/5.80 thf(fact_9756_mult__nat__left__at__top,axiom,
% 5.46/5.80 ! [C: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.80 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % mult_nat_left_at_top
% 5.46/5.80 thf(fact_9757_mult__nat__right__at__top,axiom,
% 5.46/5.80 ! [C: nat] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.46/5.80 => ( filterlim_nat_nat
% 5.46/5.80 @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 5.46/5.80 @ at_top_nat
% 5.46/5.80 @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % mult_nat_right_at_top
% 5.46/5.80 thf(fact_9758_monoseq__convergent,axiom,
% 5.46/5.80 ! [X8: nat > real,B4: real] :
% 5.46/5.80 ( ( topolo6980174941875973593q_real @ X8 )
% 5.46/5.80 => ( ! [I3: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I3 ) ) @ B4 )
% 5.46/5.80 => ~ ! [L6: real] :
% 5.46/5.80 ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % monoseq_convergent
% 5.46/5.80 thf(fact_9759_LIMSEQ__root,axiom,
% 5.46/5.80 ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.46/5.80 @ at_top_nat ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_root
% 5.46/5.80 thf(fact_9760_nested__sequence__unique,axiom,
% 5.46/5.80 ! [F: nat > real,G: nat > real] :
% 5.46/5.80 ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N4 ) ) @ ( G @ N4 ) )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.46/5.80 => ( ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ at_top_nat )
% 5.46/5.80 => ? [L3: real] :
% 5.46/5.80 ( ! [N6: nat] : ( ord_less_eq_real @ ( F @ N6 ) @ L3 )
% 5.46/5.80 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L3 ) @ at_top_nat )
% 5.46/5.80 & ! [N6: nat] : ( ord_less_eq_real @ L3 @ ( G @ N6 ) )
% 5.46/5.80 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L3 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % nested_sequence_unique
% 5.46/5.80 thf(fact_9761_LIMSEQ__inverse__zero,axiom,
% 5.46/5.80 ! [X8: nat > real] :
% 5.46/5.80 ( ! [R3: real] :
% 5.46/5.80 ? [N7: nat] :
% 5.46/5.80 ! [N4: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ N7 @ N4 )
% 5.46/5.80 => ( ord_less_real @ R3 @ ( X8 @ N4 ) ) )
% 5.46/5.80 => ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( inverse_inverse_real @ ( X8 @ N2 ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_inverse_zero
% 5.46/5.80 thf(fact_9762_lim__inverse__n_H,axiom,
% 5.46/5.80 ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ at_top_nat ) ).
% 5.46/5.80
% 5.46/5.80 % lim_inverse_n'
% 5.46/5.80 thf(fact_9763_LIMSEQ__root__const,axiom,
% 5.46/5.80 ! [C: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ C )
% 5.46/5.80 => ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( root @ N2 @ C )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.46/5.80 @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_root_const
% 5.46/5.80 thf(fact_9764_LIMSEQ__inverse__real__of__nat,axiom,
% 5.46/5.80 ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ at_top_nat ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_inverse_real_of_nat
% 5.46/5.80 thf(fact_9765_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.46/5.80 ! [R2: real] :
% 5.46/5.80 ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ R2 )
% 5.46/5.80 @ at_top_nat ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_inverse_real_of_nat_add
% 5.46/5.80 thf(fact_9766_increasing__LIMSEQ,axiom,
% 5.46/5.80 ! [F: nat > real,L2: real] :
% 5.46/5.80 ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ L2 )
% 5.46/5.80 => ( ! [E2: real] :
% 5.46/5.80 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.46/5.80 => ? [N6: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N6 ) @ E2 ) ) )
% 5.46/5.80 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % increasing_LIMSEQ
% 5.46/5.80 thf(fact_9767_LIMSEQ__realpow__zero,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.80 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.46/5.80 => ( filterlim_nat_real @ ( power_power_real @ X4 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_realpow_zero
% 5.46/5.80 thf(fact_9768_LIMSEQ__divide__realpow__zero,axiom,
% 5.46/5.80 ! [X4: real,A: real] :
% 5.46/5.80 ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.80 => ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X4 @ N2 ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_divide_realpow_zero
% 5.46/5.80 thf(fact_9769_LIMSEQ__abs__realpow__zero,axiom,
% 5.46/5.80 ! [C: real] :
% 5.46/5.80 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.46/5.80 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_abs_realpow_zero
% 5.46/5.80 thf(fact_9770_LIMSEQ__abs__realpow__zero2,axiom,
% 5.46/5.80 ! [C: real] :
% 5.46/5.80 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.46/5.80 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_abs_realpow_zero2
% 5.46/5.80 thf(fact_9771_LIMSEQ__inverse__realpow__zero,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_real @ one_one_real @ X4 )
% 5.46/5.80 => ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X4 @ N2 ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_inverse_realpow_zero
% 5.46/5.80 thf(fact_9772_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.46/5.80 ! [R2: real] :
% 5.46/5.80 ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ R2 )
% 5.46/5.80 @ at_top_nat ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.46/5.80 thf(fact_9773_tendsto__exp__limit__sequentially,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 5.46/5.80 @ at_top_nat ) ).
% 5.46/5.80
% 5.46/5.80 % tendsto_exp_limit_sequentially
% 5.46/5.80 thf(fact_9774_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.46/5.80 ! [R2: real] :
% 5.46/5.80 ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ R2 )
% 5.46/5.80 @ at_top_nat ) ).
% 5.46/5.80
% 5.46/5.80 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.46/5.80 thf(fact_9775_summable__Leibniz_I1_J,axiom,
% 5.46/5.80 ! [A: nat > real] :
% 5.46/5.80 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ( ( topolo6980174941875973593q_real @ A )
% 5.46/5.80 => ( summable_real
% 5.46/5.80 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % summable_Leibniz(1)
% 5.46/5.80 thf(fact_9776_summable,axiom,
% 5.46/5.80 ! [A: nat > real] :
% 5.46/5.80 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.46/5.80 => ( summable_real
% 5.46/5.80 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % summable
% 5.46/5.80 thf(fact_9777_cos__diff__limit__1,axiom,
% 5.46/5.80 ! [Theta: nat > real,Theta2: real] :
% 5.46/5.80 ( ( filterlim_nat_real
% 5.46/5.80 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.46/5.80 @ at_top_nat )
% 5.46/5.80 => ~ ! [K2: nat > int] :
% 5.46/5.80 ~ ( filterlim_nat_real
% 5.46/5.80 @ ^ [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 ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.46/5.80 @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % cos_diff_limit_1
% 5.46/5.80 thf(fact_9778_cos__limit__1,axiom,
% 5.46/5.80 ! [Theta: nat > real] :
% 5.46/5.80 ( ( filterlim_nat_real
% 5.46/5.80 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.46/5.80 @ at_top_nat )
% 5.46/5.80 => ? [K2: nat > int] :
% 5.46/5.80 ( filterlim_nat_real
% 5.46/5.80 @ ^ [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 ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % cos_limit_1
% 5.46/5.80 thf(fact_9779_summable__Leibniz_I4_J,axiom,
% 5.46/5.80 ! [A: nat > real] :
% 5.46/5.80 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ( ( topolo6980174941875973593q_real @ A )
% 5.46/5.80 => ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] :
% 5.46/5.80 ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real
% 5.46/5.80 @ ( suminf_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.46/5.80 @ at_top_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % summable_Leibniz(4)
% 5.46/5.80 thf(fact_9780_zeroseq__arctan__series,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.46/5.80 => ( filterlim_nat_real
% 5.46/5.80 @ ^ [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 @ X4 @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % zeroseq_arctan_series
% 5.46/5.80 thf(fact_9781_summable__Leibniz_H_I2_J,axiom,
% 5.46/5.80 ! [A: nat > real,N: nat] :
% 5.46/5.80 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.46/5.80 => ( ord_less_eq_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.80 @ ( suminf_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % summable_Leibniz'(2)
% 5.46/5.80 thf(fact_9782_summable__Leibniz_H_I3_J,axiom,
% 5.46/5.80 ! [A: nat > real] :
% 5.46/5.80 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.46/5.80 => ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] :
% 5.46/5.80 ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real
% 5.46/5.80 @ ( suminf_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.46/5.80 @ at_top_nat ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % summable_Leibniz'(3)
% 5.46/5.80 thf(fact_9783_sums__alternating__upper__lower,axiom,
% 5.46/5.80 ! [A: nat > real] :
% 5.46/5.80 ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.46/5.80 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ? [L3: real] :
% 5.46/5.80 ( ! [N6: nat] :
% 5.46/5.80 ( ord_less_eq_real
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 5.46/5.80 @ L3 )
% 5.46/5.80 & ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] :
% 5.46/5.80 ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ L3 )
% 5.46/5.80 @ at_top_nat )
% 5.46/5.80 & ! [N6: nat] :
% 5.46/5.80 ( ord_less_eq_real @ L3
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) )
% 5.46/5.80 & ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] :
% 5.46/5.80 ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ L3 )
% 5.46/5.80 @ at_top_nat ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % sums_alternating_upper_lower
% 5.46/5.80 thf(fact_9784_summable__Leibniz_I5_J,axiom,
% 5.46/5.80 ! [A: nat > real] :
% 5.46/5.80 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ( ( topolo6980174941875973593q_real @ A )
% 5.46/5.80 => ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] :
% 5.46/5.80 ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real
% 5.46/5.80 @ ( suminf_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.46/5.80 @ at_top_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % summable_Leibniz(5)
% 5.46/5.80 thf(fact_9785_summable__Leibniz_H_I5_J,axiom,
% 5.46/5.80 ! [A: nat > real] :
% 5.46/5.80 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.46/5.80 => ( filterlim_nat_real
% 5.46/5.80 @ ^ [N2: nat] :
% 5.46/5.80 ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real
% 5.46/5.80 @ ( suminf_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.46/5.80 @ at_top_nat ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % summable_Leibniz'(5)
% 5.46/5.80 thf(fact_9786_summable__Leibniz_H_I4_J,axiom,
% 5.46/5.80 ! [A: nat > real,N: nat] :
% 5.46/5.80 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 5.46/5.80 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 5.46/5.80 => ( ord_less_eq_real
% 5.46/5.80 @ ( suminf_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 5.46/5.80 @ ( groups6591440286371151544t_real
% 5.46/5.80 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.46/5.80 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % summable_Leibniz'(4)
% 5.46/5.80 thf(fact_9787_eventually__sequentially__Suc,axiom,
% 5.46/5.80 ! [P: nat > $o] :
% 5.46/5.80 ( ( eventually_nat
% 5.46/5.80 @ ^ [I2: nat] : ( P @ ( suc @ I2 ) )
% 5.46/5.80 @ at_top_nat )
% 5.46/5.80 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % eventually_sequentially_Suc
% 5.46/5.80 thf(fact_9788_eventually__sequentially__seg,axiom,
% 5.46/5.80 ! [P: nat > $o,K: nat] :
% 5.46/5.80 ( ( eventually_nat
% 5.46/5.80 @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 5.46/5.80 @ at_top_nat )
% 5.46/5.80 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % eventually_sequentially_seg
% 5.46/5.80 thf(fact_9789_sequentially__offset,axiom,
% 5.46/5.80 ! [P: nat > $o,K: nat] :
% 5.46/5.80 ( ( eventually_nat @ P @ at_top_nat )
% 5.46/5.80 => ( eventually_nat
% 5.46/5.80 @ ^ [I2: nat] : ( P @ ( plus_plus_nat @ I2 @ K ) )
% 5.46/5.80 @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % sequentially_offset
% 5.46/5.80 thf(fact_9790_eventually__sequentially,axiom,
% 5.46/5.80 ! [P: nat > $o] :
% 5.46/5.80 ( ( eventually_nat @ P @ at_top_nat )
% 5.46/5.80 = ( ? [N8: nat] :
% 5.46/5.80 ! [N2: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ N8 @ N2 )
% 5.46/5.80 => ( P @ N2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % eventually_sequentially
% 5.46/5.80 thf(fact_9791_eventually__sequentiallyI,axiom,
% 5.46/5.80 ! [C: nat,P: nat > $o] :
% 5.46/5.80 ( ! [X3: nat] :
% 5.46/5.80 ( ( ord_less_eq_nat @ C @ X3 )
% 5.46/5.80 => ( P @ X3 ) )
% 5.46/5.80 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % eventually_sequentiallyI
% 5.46/5.80 thf(fact_9792_le__sequentially,axiom,
% 5.46/5.80 ! [F5: filter_nat] :
% 5.46/5.80 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.46/5.80 = ( ! [N8: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N8 ) @ F5 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % le_sequentially
% 5.46/5.80 thf(fact_9793_filterlim__Suc,axiom,
% 5.46/5.80 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.46/5.80
% 5.46/5.80 % filterlim_Suc
% 5.46/5.80 thf(fact_9794_real__bounded__linear,axiom,
% 5.46/5.80 ( real_V5970128139526366754l_real
% 5.46/5.80 = ( ^ [F2: real > real] :
% 5.46/5.80 ? [C2: real] :
% 5.46/5.80 ( F2
% 5.46/5.80 = ( ^ [X: real] : ( times_times_real @ X @ C2 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % real_bounded_linear
% 5.46/5.80 thf(fact_9795_sqrt__at__top,axiom,
% 5.46/5.80 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.46/5.80
% 5.46/5.80 % sqrt_at_top
% 5.46/5.80 thf(fact_9796_lhopital__left__at__top__at__top,axiom,
% 5.46/5.80 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.80 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ at_top_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ at_top_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_left_at_top_at_top
% 5.46/5.80 thf(fact_9797_lhopital__at__top__at__top,axiom,
% 5.46/5.80 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.80 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ at_top_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ at_top_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_at_top_at_top
% 5.46/5.80 thf(fact_9798_eventually__at__left__real,axiom,
% 5.46/5.80 ! [B2: real,A: real] :
% 5.46/5.80 ( ( ord_less_real @ B2 @ A )
% 5.46/5.80 => ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ B2 @ A ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % eventually_at_left_real
% 5.46/5.80 thf(fact_9799_lhopital__left__at__top,axiom,
% 5.46/5.80 ! [G: real > real,X4: real,G2: real > real,F: real > real,F4: real > real,Y3: real] :
% 5.46/5.80 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G2 @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_left_at_top
% 5.46/5.80 thf(fact_9800_lhospital__at__top__at__top,axiom,
% 5.46/5.80 ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X4: real] :
% 5.46/5.80 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G2 @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ at_top_real )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ at_top_real )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ at_top_real )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ X4 )
% 5.46/5.80 @ at_top_real )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ X4 )
% 5.46/5.80 @ at_top_real ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhospital_at_top_at_top
% 5.46/5.80 thf(fact_9801_lhopital__at__top,axiom,
% 5.46/5.80 ! [G: real > real,X4: real,G2: real > real,F: real > real,F4: real > real,Y3: real] :
% 5.46/5.80 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G2 @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_at_top
% 5.46/5.80 thf(fact_9802_tanh__real__at__top,axiom,
% 5.46/5.80 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.46/5.80
% 5.46/5.80 % tanh_real_at_top
% 5.46/5.80 thf(fact_9803_artanh__real__at__left__1,axiom,
% 5.46/5.80 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.46/5.80
% 5.46/5.80 % artanh_real_at_left_1
% 5.46/5.80 thf(fact_9804_ln__x__over__x__tendsto__0,axiom,
% 5.46/5.80 ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ X ) @ X )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ at_top_real ) ).
% 5.46/5.80
% 5.46/5.80 % ln_x_over_x_tendsto_0
% 5.46/5.80 thf(fact_9805_tendsto__power__div__exp__0,axiom,
% 5.46/5.80 ! [K: nat] :
% 5.46/5.80 ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( power_power_real @ X @ K ) @ ( exp_real @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.46/5.80 @ at_top_real ) ).
% 5.46/5.80
% 5.46/5.80 % tendsto_power_div_exp_0
% 5.46/5.80 thf(fact_9806_lhopital__left,axiom,
% 5.46/5.80 ! [F: real > real,X4: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G2 @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ F5
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ F5
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5984915006950818249n_real @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_left
% 5.46/5.80 thf(fact_9807_lhopital,axiom,
% 5.46/5.80 ! [F: real > real,X4: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G2 @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ F5
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ F5
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital
% 5.46/5.80 thf(fact_9808_tendsto__exp__limit__at__top,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( filterlim_real_real
% 5.46/5.80 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ Y ) ) @ Y )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 5.46/5.80 @ at_top_real ) ).
% 5.46/5.80
% 5.46/5.80 % tendsto_exp_limit_at_top
% 5.46/5.80 thf(fact_9809_filterlim__tan__at__left,axiom,
% 5.46/5.80 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 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % filterlim_tan_at_left
% 5.46/5.80 thf(fact_9810_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.46/5.80 ! [B2: real,F: real > real,Flim: real] :
% 5.46/5.80 ( ! [X3: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ B2 @ X3 )
% 5.46/5.80 => ? [Y5: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 & ( ord_less_real @ Y5 @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.46/5.80 => ( ord_less_real @ Flim @ ( F @ B2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_neg_imp_decreasing_at_top
% 5.46/5.80 thf(fact_9811_tendsto__arctan__at__top,axiom,
% 5.46/5.80 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.46/5.80
% 5.46/5.80 % tendsto_arctan_at_top
% 5.46/5.80 thf(fact_9812_filterlim__pow__at__bot__even,axiom,
% 5.46/5.80 ! [N: nat,F: real > real,F5: filter_real] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.46/5.80 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 5.46/5.80 @ at_top_real
% 5.46/5.80 @ F5 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % filterlim_pow_at_bot_even
% 5.46/5.80 thf(fact_9813_dist__real__def,axiom,
% 5.46/5.80 ( real_V975177566351809787t_real
% 5.46/5.80 = ( ^ [X: real,Y: real] : ( abs_abs_real @ ( minus_minus_real @ X @ Y ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % dist_real_def
% 5.46/5.80 thf(fact_9814_dist__complex__def,axiom,
% 5.46/5.80 ( real_V3694042436643373181omplex
% 5.46/5.80 = ( ^ [X: complex,Y: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % dist_complex_def
% 5.46/5.80 thf(fact_9815_tanh__real__at__bot,axiom,
% 5.46/5.80 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.46/5.80
% 5.46/5.80 % tanh_real_at_bot
% 5.46/5.80 thf(fact_9816_lhopital__at__top__at__bot,axiom,
% 5.46/5.80 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.80 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ at_bot_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ at_bot_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_at_top_at_bot
% 5.46/5.80 thf(fact_9817_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.46/5.80 ! [B2: real,F: real > real,Flim: real] :
% 5.46/5.80 ( ! [X3: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ X3 @ B2 )
% 5.46/5.80 => ? [Y5: real] :
% 5.46/5.80 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.80 & ( ord_less_real @ zero_zero_real @ Y5 ) ) )
% 5.46/5.80 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.46/5.80 => ( ord_less_real @ Flim @ ( F @ B2 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % DERIV_pos_imp_increasing_at_bot
% 5.46/5.80 thf(fact_9818_filterlim__pow__at__bot__odd,axiom,
% 5.46/5.80 ! [N: nat,F: real > real,F5: filter_real] :
% 5.46/5.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.80 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.46/5.80 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 5.46/5.80 @ at_bot_real
% 5.46/5.80 @ F5 ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % filterlim_pow_at_bot_odd
% 5.46/5.80 thf(fact_9819_lhopital__left__at__top__at__bot,axiom,
% 5.46/5.80 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.80 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ at_bot_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ at_bot_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_left_at_top_at_bot
% 5.46/5.80 thf(fact_9820_tendsto__arctan__at__bot,axiom,
% 5.46/5.80 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.46/5.80
% 5.46/5.80 % tendsto_arctan_at_bot
% 5.46/5.80 thf(fact_9821_incseq__bounded,axiom,
% 5.46/5.80 ! [X8: nat > real,B4: real] :
% 5.46/5.80 ( ( order_mono_nat_real @ X8 )
% 5.46/5.80 => ( ! [I3: nat] : ( ord_less_eq_real @ ( X8 @ I3 ) @ B4 )
% 5.46/5.80 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % incseq_bounded
% 5.46/5.80 thf(fact_9822_Bseq__realpow,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.80 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.80 => ( bfun_nat_real @ ( power_power_real @ X4 ) @ at_top_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % Bseq_realpow
% 5.46/5.80 thf(fact_9823_tendsto__exp__limit__at__right,axiom,
% 5.46/5.80 ! [X4: real] :
% 5.46/5.80 ( filterlim_real_real
% 5.46/5.80 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X4 @ Y ) ) @ ( divide_divide_real @ one_one_real @ Y ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % tendsto_exp_limit_at_right
% 5.46/5.80 thf(fact_9824_filterlim__tan__at__right,axiom,
% 5.46/5.80 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 ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % filterlim_tan_at_right
% 5.46/5.80 thf(fact_9825_eventually__at__right__to__0,axiom,
% 5.46/5.80 ! [P: real > $o,A: real] :
% 5.46/5.80 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 = ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( P @ ( plus_plus_real @ X @ A ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % eventually_at_right_to_0
% 5.46/5.80 thf(fact_9826_eventually__at__right__real,axiom,
% 5.46/5.80 ! [A: real,B2: real] :
% 5.46/5.80 ( ( ord_less_real @ A @ B2 )
% 5.46/5.80 => ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B2 ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % eventually_at_right_real
% 5.46/5.80 thf(fact_9827_tendsto__arcosh__at__left__1,axiom,
% 5.46/5.80 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.46/5.80
% 5.46/5.80 % tendsto_arcosh_at_left_1
% 5.46/5.80 thf(fact_9828_artanh__real__at__right__1,axiom,
% 5.46/5.80 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 ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % artanh_real_at_right_1
% 5.46/5.80 thf(fact_9829_lhopital__right__at__top__at__top,axiom,
% 5.46/5.80 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ at_top_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ at_top_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_right_at_top_at_top
% 5.46/5.80 thf(fact_9830_lhopital__right__0,axiom,
% 5.46/5.80 ! [F0: real > real,G0: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.46/5.80 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G0 @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G2 @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ F5
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F0 @ X ) @ ( G0 @ X ) )
% 5.46/5.80 @ F5
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_right_0
% 5.46/5.80 thf(fact_9831_lhopital__right,axiom,
% 5.46/5.80 ! [F: real > real,X4: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G2 @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ F5
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ F5
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_right
% 5.46/5.80 thf(fact_9832_lhopital__right__at__top__at__bot,axiom,
% 5.46/5.80 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.46/5.80 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ at_bot_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ at_bot_real
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_right_at_top_at_bot
% 5.46/5.80 thf(fact_9833_lhopital__right__at__top,axiom,
% 5.46/5.80 ! [G: real > real,X4: real,G2: real > real,F: real > real,F4: real > real,Y3: real] :
% 5.46/5.80 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G2 @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ Y3 )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ X4 @ ( set_or5849166863359141190n_real @ X4 ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_right_at_top
% 5.46/5.80 thf(fact_9834_lhopital__right__0__at__top,axiom,
% 5.46/5.80 ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X4: real] :
% 5.46/5.80 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] :
% 5.46/5.80 ( ( G2 @ X )
% 5.46/5.80 != zero_zero_real )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( eventually_real
% 5.46/5.80 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F4 @ X ) @ ( G2 @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ X4 )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.46/5.80 => ( filterlim_real_real
% 5.46/5.80 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.46/5.80 @ ( topolo2815343760600316023s_real @ X4 )
% 5.46/5.80 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % lhopital_right_0_at_top
% 5.46/5.80 thf(fact_9835_atLeast__0,axiom,
% 5.46/5.80 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 5.46/5.80 = top_top_set_nat ) ).
% 5.46/5.80
% 5.46/5.80 % atLeast_0
% 5.46/5.80 thf(fact_9836_atLeast__Suc__greaterThan,axiom,
% 5.46/5.80 ! [K: nat] :
% 5.46/5.80 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.46/5.80 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.46/5.80
% 5.46/5.80 % atLeast_Suc_greaterThan
% 5.46/5.80 thf(fact_9837_decseq__bounded,axiom,
% 5.46/5.80 ! [X8: nat > real,B4: real] :
% 5.46/5.80 ( ( order_9091379641038594480t_real @ X8 )
% 5.46/5.80 => ( ! [I3: nat] : ( ord_less_eq_real @ B4 @ ( X8 @ I3 ) )
% 5.46/5.80 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % decseq_bounded
% 5.46/5.80 thf(fact_9838_greaterThan__0,axiom,
% 5.46/5.80 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.46/5.80 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.46/5.80
% 5.46/5.80 % greaterThan_0
% 5.46/5.80 thf(fact_9839_greaterThan__Suc,axiom,
% 5.46/5.80 ! [K: nat] :
% 5.46/5.80 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.46/5.80 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % greaterThan_Suc
% 5.46/5.80 thf(fact_9840_decseq__convergent,axiom,
% 5.46/5.80 ! [X8: nat > real,B4: real] :
% 5.46/5.80 ( ( order_9091379641038594480t_real @ X8 )
% 5.46/5.80 => ( ! [I3: nat] : ( ord_less_eq_real @ B4 @ ( X8 @ I3 ) )
% 5.46/5.80 => ~ ! [L6: real] :
% 5.46/5.80 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.46/5.80 => ~ ! [I4: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I4 ) ) ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % decseq_convergent
% 5.46/5.80 thf(fact_9841_atLeast__Suc,axiom,
% 5.46/5.80 ! [K: nat] :
% 5.46/5.80 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.46/5.80 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.46/5.80
% 5.46/5.80 % atLeast_Suc
% 5.46/5.80 thf(fact_9842_GMVT,axiom,
% 5.46/5.80 ! [A: real,B2: real,F: real > real,G: real > real] :
% 5.46/5.80 ( ( ord_less_real @ A @ B2 )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.80 & ( ord_less_eq_real @ X3 @ B2 ) )
% 5.46/5.80 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.46/5.80 => ( ! [X3: real] :
% 5.46/5.80 ( ( ( ord_less_real @ A @ X3 )
% 5.46/5.80 & ( ord_less_real @ X3 @ B2 ) )
% 5.46/5.80 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.46/5.81 & ( ord_less_eq_real @ X3 @ B2 ) )
% 5.46/5.81 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G ) )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( ( ord_less_real @ A @ X3 )
% 5.46/5.81 & ( ord_less_real @ X3 @ B2 ) )
% 5.46/5.81 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.46/5.81 => ? [G_c: real,F_c: real,C3: real] :
% 5.46/5.81 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.46/5.81 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.46/5.81 & ( ord_less_real @ A @ C3 )
% 5.46/5.81 & ( ord_less_real @ C3 @ B2 )
% 5.46/5.81 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B2 ) @ ( F @ A ) ) @ G_c )
% 5.46/5.81 = ( times_times_real @ ( minus_minus_real @ ( G @ B2 ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % GMVT
% 5.46/5.81 thf(fact_9843_real__differentiableE,axiom,
% 5.46/5.81 ! [F: real > real,X4: real,S: set_real] :
% 5.46/5.81 ( ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ S ) )
% 5.46/5.81 => ~ ! [Df: real] :
% 5.46/5.81 ~ ( has_fi5821293074295781190e_real @ F @ Df @ ( topolo2177554685111907308n_real @ X4 @ S ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % real_differentiableE
% 5.46/5.81 thf(fact_9844_real__differentiable__def,axiom,
% 5.46/5.81 ! [F: real > real,X4: real,S: set_real] :
% 5.46/5.81 ( ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ S ) )
% 5.46/5.81 = ( ? [D6: real] : ( has_fi5821293074295781190e_real @ F @ D6 @ ( topolo2177554685111907308n_real @ X4 @ S ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % real_differentiable_def
% 5.46/5.81 thf(fact_9845_MVT,axiom,
% 5.46/5.81 ! [A: real,B2: real,F: real > real] :
% 5.46/5.81 ( ( ord_less_real @ A @ B2 )
% 5.46/5.81 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ F )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ X3 )
% 5.46/5.81 => ( ( ord_less_real @ X3 @ B2 )
% 5.46/5.81 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.81 => ? [L3: real,Z2: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ Z2 )
% 5.46/5.81 & ( ord_less_real @ Z2 @ B2 )
% 5.46/5.81 & ( has_fi5821293074295781190e_real @ F @ L3 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) )
% 5.46/5.81 & ( ( minus_minus_real @ ( F @ B2 ) @ ( F @ A ) )
% 5.46/5.81 = ( times_times_real @ ( minus_minus_real @ B2 @ A ) @ L3 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % MVT
% 5.46/5.81 thf(fact_9846_suminf__eq__SUP__real,axiom,
% 5.46/5.81 ! [X8: nat > real] :
% 5.46/5.81 ( ( summable_real @ X8 )
% 5.46/5.81 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I3 ) )
% 5.46/5.81 => ( ( suminf_real @ X8 )
% 5.46/5.81 = ( comple1385675409528146559p_real
% 5.46/5.81 @ ( image_nat_real
% 5.46/5.81 @ ^ [I2: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I2 ) )
% 5.46/5.81 @ top_top_set_nat ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % suminf_eq_SUP_real
% 5.46/5.81 thf(fact_9847_continuous__on__arcosh,axiom,
% 5.46/5.81 ! [A3: set_real] :
% 5.46/5.81 ( ( ord_less_eq_set_real @ A3 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.46/5.81 => ( topolo5044208981011980120l_real @ A3 @ arcosh_real ) ) ).
% 5.46/5.81
% 5.46/5.81 % continuous_on_arcosh
% 5.46/5.81 thf(fact_9848_continuous__on__arcosh_H,axiom,
% 5.46/5.81 ! [A3: set_real,F: real > real] :
% 5.46/5.81 ( ( topolo5044208981011980120l_real @ A3 @ F )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( member_real @ X3 @ A3 )
% 5.46/5.81 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.46/5.81 => ( topolo5044208981011980120l_real @ A3
% 5.46/5.81 @ ^ [X: real] : ( arcosh_real @ ( F @ X ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % continuous_on_arcosh'
% 5.46/5.81 thf(fact_9849_continuous__image__closed__interval,axiom,
% 5.46/5.81 ! [A: real,B2: real,F: real > real] :
% 5.46/5.81 ( ( ord_less_eq_real @ A @ B2 )
% 5.46/5.81 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ F )
% 5.46/5.81 => ? [C3: real,D3: real] :
% 5.46/5.81 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B2 ) )
% 5.46/5.81 = ( set_or1222579329274155063t_real @ C3 @ D3 ) )
% 5.46/5.81 & ( ord_less_eq_real @ C3 @ D3 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % continuous_image_closed_interval
% 5.46/5.81 thf(fact_9850_continuous__on__arccos_H,axiom,
% 5.46/5.81 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.46/5.81
% 5.46/5.81 % continuous_on_arccos'
% 5.46/5.81 thf(fact_9851_continuous__on__arcsin_H,axiom,
% 5.46/5.81 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.46/5.81
% 5.46/5.81 % continuous_on_arcsin'
% 5.46/5.81 thf(fact_9852_continuous__on__artanh,axiom,
% 5.46/5.81 ! [A3: set_real] :
% 5.46/5.81 ( ( ord_less_eq_set_real @ A3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.46/5.81 => ( topolo5044208981011980120l_real @ A3 @ artanh_real ) ) ).
% 5.46/5.81
% 5.46/5.81 % continuous_on_artanh
% 5.46/5.81 thf(fact_9853_continuous__on__artanh_H,axiom,
% 5.46/5.81 ! [A3: set_real,F: real > real] :
% 5.46/5.81 ( ( topolo5044208981011980120l_real @ A3 @ F )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( member_real @ X3 @ A3 )
% 5.46/5.81 => ( member_real @ ( F @ X3 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.46/5.81 => ( topolo5044208981011980120l_real @ A3
% 5.46/5.81 @ ^ [X: real] : ( artanh_real @ ( F @ X ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % continuous_on_artanh'
% 5.46/5.81 thf(fact_9854_Rolle__deriv,axiom,
% 5.46/5.81 ! [A: real,B2: real,F: real > real,F4: real > real > real] :
% 5.46/5.81 ( ( ord_less_real @ A @ B2 )
% 5.46/5.81 => ( ( ( F @ A )
% 5.46/5.81 = ( F @ B2 ) )
% 5.46/5.81 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ F )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ X3 )
% 5.46/5.81 => ( ( ord_less_real @ X3 @ B2 )
% 5.46/5.81 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.81 => ? [Z2: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ Z2 )
% 5.46/5.81 & ( ord_less_real @ Z2 @ B2 )
% 5.46/5.81 & ( ( F4 @ Z2 )
% 5.46/5.81 = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Rolle_deriv
% 5.46/5.81 thf(fact_9855_mvt,axiom,
% 5.46/5.81 ! [A: real,B2: real,F: real > real,F4: real > real > real] :
% 5.46/5.81 ( ( ord_less_real @ A @ B2 )
% 5.46/5.81 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ F )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ X3 )
% 5.46/5.81 => ( ( ord_less_real @ X3 @ B2 )
% 5.46/5.81 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.81 => ~ ! [Xi: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ Xi )
% 5.46/5.81 => ( ( ord_less_real @ Xi @ B2 )
% 5.46/5.81 => ( ( minus_minus_real @ ( F @ B2 ) @ ( F @ A ) )
% 5.46/5.81 != ( F4 @ Xi @ ( minus_minus_real @ B2 @ A ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % mvt
% 5.46/5.81 thf(fact_9856_DERIV__pos__imp__increasing__open,axiom,
% 5.46/5.81 ! [A: real,B2: real,F: real > real] :
% 5.46/5.81 ( ( ord_less_real @ A @ B2 )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ X3 )
% 5.46/5.81 => ( ( ord_less_real @ X3 @ B2 )
% 5.46/5.81 => ? [Y5: real] :
% 5.46/5.81 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.81 & ( ord_less_real @ zero_zero_real @ Y5 ) ) ) )
% 5.46/5.81 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ F )
% 5.46/5.81 => ( ord_less_real @ ( F @ A ) @ ( F @ B2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % DERIV_pos_imp_increasing_open
% 5.46/5.81 thf(fact_9857_DERIV__neg__imp__decreasing__open,axiom,
% 5.46/5.81 ! [A: real,B2: real,F: real > real] :
% 5.46/5.81 ( ( ord_less_real @ A @ B2 )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ X3 )
% 5.46/5.81 => ( ( ord_less_real @ X3 @ B2 )
% 5.46/5.81 => ? [Y5: real] :
% 5.46/5.81 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.81 & ( ord_less_real @ Y5 @ zero_zero_real ) ) ) )
% 5.46/5.81 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ F )
% 5.46/5.81 => ( ord_less_real @ ( F @ B2 ) @ ( F @ A ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % DERIV_neg_imp_decreasing_open
% 5.46/5.81 thf(fact_9858_DERIV__isconst__end,axiom,
% 5.46/5.81 ! [A: real,B2: real,F: real > real] :
% 5.46/5.81 ( ( ord_less_real @ A @ B2 )
% 5.46/5.81 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ F )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ X3 )
% 5.46/5.81 => ( ( ord_less_real @ X3 @ B2 )
% 5.46/5.81 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.81 => ( ( F @ B2 )
% 5.46/5.81 = ( F @ A ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % DERIV_isconst_end
% 5.46/5.81 thf(fact_9859_DERIV__isconst2,axiom,
% 5.46/5.81 ! [A: real,B2: real,F: real > real,X4: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ B2 )
% 5.46/5.81 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ F )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ X3 )
% 5.46/5.81 => ( ( ord_less_real @ X3 @ B2 )
% 5.46/5.81 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.81 => ( ( ord_less_eq_real @ A @ X4 )
% 5.46/5.81 => ( ( ord_less_eq_real @ X4 @ B2 )
% 5.46/5.81 => ( ( F @ X4 )
% 5.46/5.81 = ( F @ A ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % DERIV_isconst2
% 5.46/5.81 thf(fact_9860_Rolle,axiom,
% 5.46/5.81 ! [A: real,B2: real,F: real > real] :
% 5.46/5.81 ( ( ord_less_real @ A @ B2 )
% 5.46/5.81 => ( ( ( F @ A )
% 5.46/5.81 = ( F @ B2 ) )
% 5.46/5.81 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B2 ) @ F )
% 5.46/5.81 => ( ! [X3: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ X3 )
% 5.46/5.81 => ( ( ord_less_real @ X3 @ B2 )
% 5.46/5.81 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.46/5.81 => ? [Z2: real] :
% 5.46/5.81 ( ( ord_less_real @ A @ Z2 )
% 5.46/5.81 & ( ord_less_real @ Z2 @ B2 )
% 5.46/5.81 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Rolle
% 5.46/5.81 thf(fact_9861_UN__lessThan__UNIV,axiom,
% 5.46/5.81 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.46/5.81 = top_top_set_nat ) ).
% 5.46/5.81
% 5.46/5.81 % UN_lessThan_UNIV
% 5.46/5.81 thf(fact_9862_UN__atMost__UNIV,axiom,
% 5.46/5.81 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.46/5.81 = top_top_set_nat ) ).
% 5.46/5.81
% 5.46/5.81 % UN_atMost_UNIV
% 5.46/5.81 thf(fact_9863_UN__atLeast__UNIV,axiom,
% 5.46/5.81 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.46/5.81 = top_top_set_nat ) ).
% 5.46/5.81
% 5.46/5.81 % UN_atLeast_UNIV
% 5.46/5.81 thf(fact_9864_INT__greaterThan__UNIV,axiom,
% 5.46/5.81 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.46/5.81 = bot_bot_set_nat ) ).
% 5.46/5.81
% 5.46/5.81 % INT_greaterThan_UNIV
% 5.46/5.81 thf(fact_9865_Inf__real__def,axiom,
% 5.46/5.81 ( comple4887499456419720421f_real
% 5.46/5.81 = ( ^ [X6: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X6 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Inf_real_def
% 5.46/5.81 thf(fact_9866_inf__enat__def,axiom,
% 5.46/5.81 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 5.46/5.81
% 5.46/5.81 % inf_enat_def
% 5.46/5.81 thf(fact_9867_inf__nat__def,axiom,
% 5.46/5.81 inf_inf_nat = ord_min_nat ).
% 5.46/5.81
% 5.46/5.81 % inf_nat_def
% 5.46/5.81 thf(fact_9868_rat__less__code,axiom,
% 5.46/5.81 ( ord_less_rat
% 5.46/5.81 = ( ^ [P3: rat,Q4: rat] :
% 5.46/5.81 ( produc4947309494688390418_int_o
% 5.46/5.81 @ ^ [A4: int,C2: int] :
% 5.46/5.81 ( produc4947309494688390418_int_o
% 5.46/5.81 @ ^ [B3: int,D2: int] : ( ord_less_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C2 @ B3 ) )
% 5.46/5.81 @ ( quotient_of @ Q4 ) )
% 5.46/5.81 @ ( quotient_of @ P3 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % rat_less_code
% 5.46/5.81 thf(fact_9869_rat__less__eq__code,axiom,
% 5.46/5.81 ( ord_less_eq_rat
% 5.46/5.81 = ( ^ [P3: rat,Q4: rat] :
% 5.46/5.81 ( produc4947309494688390418_int_o
% 5.46/5.81 @ ^ [A4: int,C2: int] :
% 5.46/5.81 ( produc4947309494688390418_int_o
% 5.46/5.81 @ ^ [B3: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C2 @ B3 ) )
% 5.46/5.81 @ ( quotient_of @ Q4 ) )
% 5.46/5.81 @ ( quotient_of @ P3 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % rat_less_eq_code
% 5.46/5.81 thf(fact_9870_int__ge__less__than2__def,axiom,
% 5.46/5.81 ( int_ge_less_than2
% 5.46/5.81 = ( ^ [D2: int] :
% 5.46/5.81 ( collec213857154873943460nt_int
% 5.46/5.81 @ ( produc4947309494688390418_int_o
% 5.46/5.81 @ ^ [Z7: int,Z5: int] :
% 5.46/5.81 ( ( ord_less_eq_int @ D2 @ Z5 )
% 5.46/5.81 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % int_ge_less_than2_def
% 5.46/5.81 thf(fact_9871_int__ge__less__than__def,axiom,
% 5.46/5.81 ( int_ge_less_than
% 5.46/5.81 = ( ^ [D2: int] :
% 5.46/5.81 ( collec213857154873943460nt_int
% 5.46/5.81 @ ( produc4947309494688390418_int_o
% 5.46/5.81 @ ^ [Z7: int,Z5: int] :
% 5.46/5.81 ( ( ord_less_eq_int @ D2 @ Z7 )
% 5.46/5.81 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % int_ge_less_than_def
% 5.46/5.81 thf(fact_9872_uniformity__real__def,axiom,
% 5.46/5.81 ( topolo1511823702728130853y_real
% 5.46/5.81 = ( comple2936214249959783750l_real
% 5.46/5.81 @ ( image_2178119161166701260l_real
% 5.46/5.81 @ ^ [E3: real] :
% 5.46/5.81 ( princi6114159922880469582l_real
% 5.46/5.81 @ ( collec3799799289383736868l_real
% 5.46/5.81 @ ( produc5414030515140494994real_o
% 5.46/5.81 @ ^ [X: real,Y: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X @ Y ) @ E3 ) ) ) )
% 5.46/5.81 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % uniformity_real_def
% 5.46/5.81 thf(fact_9873_uniformity__complex__def,axiom,
% 5.46/5.81 ( topolo896644834953643431omplex
% 5.46/5.81 = ( comple8358262395181532106omplex
% 5.46/5.81 @ ( image_5971271580939081552omplex
% 5.46/5.81 @ ^ [E3: real] :
% 5.46/5.81 ( princi3496590319149328850omplex
% 5.46/5.81 @ ( collec8663557070575231912omplex
% 5.46/5.81 @ ( produc6771430404735790350plex_o
% 5.46/5.81 @ ^ [X: complex,Y: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X @ Y ) @ E3 ) ) ) )
% 5.46/5.81 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % uniformity_complex_def
% 5.46/5.81 thf(fact_9874_nonneg__incseq__Bseq__subseq__iff,axiom,
% 5.46/5.81 ! [F: nat > real,G: nat > nat] :
% 5.46/5.81 ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.81 => ( ( order_mono_nat_real @ F )
% 5.46/5.81 => ( ( order_5726023648592871131at_nat @ G )
% 5.46/5.81 => ( ( bfun_nat_real
% 5.46/5.81 @ ^ [X: nat] : ( F @ ( G @ X ) )
% 5.46/5.81 @ at_top_nat )
% 5.46/5.81 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % nonneg_incseq_Bseq_subseq_iff
% 5.46/5.81 thf(fact_9875_inj__sgn__power,axiom,
% 5.46/5.81 ! [N: nat] :
% 5.46/5.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.81 => ( inj_on_real_real
% 5.46/5.81 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.46/5.81 @ top_top_set_real ) ) ).
% 5.46/5.81
% 5.46/5.81 % inj_sgn_power
% 5.46/5.81 thf(fact_9876_strict__mono__imp__increasing,axiom,
% 5.46/5.81 ! [F: nat > nat,N: nat] :
% 5.46/5.81 ( ( order_5726023648592871131at_nat @ F )
% 5.46/5.81 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % strict_mono_imp_increasing
% 5.46/5.81 thf(fact_9877_log__inj,axiom,
% 5.46/5.81 ! [B2: real] :
% 5.46/5.81 ( ( ord_less_real @ one_one_real @ B2 )
% 5.46/5.81 => ( inj_on_real_real @ ( log @ B2 ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % log_inj
% 5.46/5.81 thf(fact_9878_inj__Suc,axiom,
% 5.46/5.81 ! [N3: set_nat] : ( inj_on_nat_nat @ suc @ N3 ) ).
% 5.46/5.81
% 5.46/5.81 % inj_Suc
% 5.46/5.81 thf(fact_9879_inj__on__diff__nat,axiom,
% 5.46/5.81 ! [N3: set_nat,K: nat] :
% 5.46/5.81 ( ! [N4: nat] :
% 5.46/5.81 ( ( member_nat @ N4 @ N3 )
% 5.46/5.81 => ( ord_less_eq_nat @ K @ N4 ) )
% 5.46/5.81 => ( inj_on_nat_nat
% 5.46/5.81 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 5.46/5.81 @ N3 ) ) ).
% 5.46/5.81
% 5.46/5.81 % inj_on_diff_nat
% 5.46/5.81 thf(fact_9880_summable__reindex,axiom,
% 5.46/5.81 ! [F: nat > real,G: nat > nat] :
% 5.46/5.81 ( ( summable_real @ F )
% 5.46/5.81 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.46/5.81 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.81 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % summable_reindex
% 5.46/5.81 thf(fact_9881_suminf__reindex__mono,axiom,
% 5.46/5.81 ! [F: nat > real,G: nat > nat] :
% 5.46/5.81 ( ( summable_real @ F )
% 5.46/5.81 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.46/5.81 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.81 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % suminf_reindex_mono
% 5.46/5.81 thf(fact_9882_powr__real__of__int_H,axiom,
% 5.46/5.81 ! [X4: real,N: int] :
% 5.46/5.81 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.81 => ( ( ( X4 != zero_zero_real )
% 5.46/5.81 | ( ord_less_int @ zero_zero_int @ N ) )
% 5.46/5.81 => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ N ) )
% 5.46/5.81 = ( power_int_real @ X4 @ N ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % powr_real_of_int'
% 5.46/5.81 thf(fact_9883_inj__on__char__of__nat,axiom,
% 5.46/5.81 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % inj_on_char_of_nat
% 5.46/5.81 thf(fact_9884_suminf__reindex,axiom,
% 5.46/5.81 ! [F: nat > real,G: nat > nat] :
% 5.46/5.81 ( ( summable_real @ F )
% 5.46/5.81 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.46/5.81 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 5.46/5.81 => ( ! [X3: nat] :
% 5.46/5.81 ( ~ ( member_nat @ X3 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 5.46/5.81 => ( ( F @ X3 )
% 5.46/5.81 = zero_zero_real ) )
% 5.46/5.81 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 5.46/5.81 = ( suminf_real @ F ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % suminf_reindex
% 5.46/5.81 thf(fact_9885_pos__deriv__imp__strict__mono,axiom,
% 5.46/5.81 ! [F: real > real,F4: real > real] :
% 5.46/5.81 ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.46/5.81 => ( ! [X3: real] : ( ord_less_real @ zero_zero_real @ ( F4 @ X3 ) )
% 5.46/5.81 => ( order_7092887310737990675l_real @ F ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % pos_deriv_imp_strict_mono
% 5.46/5.81 thf(fact_9886_pred__nat__def,axiom,
% 5.46/5.81 ( pred_nat
% 5.46/5.81 = ( collec3392354462482085612at_nat
% 5.46/5.81 @ ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [M6: nat,N2: nat] :
% 5.46/5.81 ( N2
% 5.46/5.81 = ( suc @ M6 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % pred_nat_def
% 5.46/5.81 thf(fact_9887_atLeastLessThan__add__Un,axiom,
% 5.46/5.81 ! [I: nat,J: nat,K: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ I @ J )
% 5.46/5.81 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 5.46/5.81 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % atLeastLessThan_add_Un
% 5.46/5.81 thf(fact_9888_sup__enat__def,axiom,
% 5.46/5.81 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.46/5.81
% 5.46/5.81 % sup_enat_def
% 5.46/5.81 thf(fact_9889_sup__nat__def,axiom,
% 5.46/5.81 sup_sup_nat = ord_max_nat ).
% 5.46/5.81
% 5.46/5.81 % sup_nat_def
% 5.46/5.81 thf(fact_9890_VEBT_Osize_I3_J,axiom,
% 5.46/5.81 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.46/5.81 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.46/5.81 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % VEBT.size(3)
% 5.46/5.81 thf(fact_9891_VEBT_Osize__gen_I1_J,axiom,
% 5.46/5.81 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.46/5.81 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.46/5.81 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % VEBT.size_gen(1)
% 5.46/5.81 thf(fact_9892_tl__upt,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( tl_nat @ ( upt @ M @ N ) )
% 5.46/5.81 = ( upt @ ( suc @ M ) @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % tl_upt
% 5.46/5.81 thf(fact_9893_vanishes__mult__bounded,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ? [A7: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ A7 )
% 5.46/5.81 & ! [N4: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N4 ) ) @ A7 ) )
% 5.46/5.81 => ( ( vanishes @ Y7 )
% 5.46/5.81 => ( vanishes
% 5.46/5.81 @ ^ [N2: nat] : ( times_times_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % vanishes_mult_bounded
% 5.46/5.81 thf(fact_9894_vanishes__const,axiom,
% 5.46/5.81 ! [C: rat] :
% 5.46/5.81 ( ( vanishes
% 5.46/5.81 @ ^ [N2: nat] : C )
% 5.46/5.81 = ( C = zero_zero_rat ) ) ).
% 5.46/5.81
% 5.46/5.81 % vanishes_const
% 5.46/5.81 thf(fact_9895_vanishes__minus,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( vanishes @ X8 )
% 5.46/5.81 => ( vanishes
% 5.46/5.81 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X8 @ N2 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % vanishes_minus
% 5.46/5.81 thf(fact_9896_vanishes__add,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( vanishes @ X8 )
% 5.46/5.81 => ( ( vanishes @ Y7 )
% 5.46/5.81 => ( vanishes
% 5.46/5.81 @ ^ [N2: nat] : ( plus_plus_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % vanishes_add
% 5.46/5.81 thf(fact_9897_vanishes__diff,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( vanishes @ X8 )
% 5.46/5.81 => ( ( vanishes @ Y7 )
% 5.46/5.81 => ( vanishes
% 5.46/5.81 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % vanishes_diff
% 5.46/5.81 thf(fact_9898_vanishesD,axiom,
% 5.46/5.81 ! [X8: nat > rat,R2: rat] :
% 5.46/5.81 ( ( vanishes @ X8 )
% 5.46/5.81 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.46/5.81 => ? [K2: nat] :
% 5.46/5.81 ! [N6: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.46/5.81 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N6 ) ) @ R2 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % vanishesD
% 5.46/5.81 thf(fact_9899_vanishesI,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ! [R3: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.46/5.81 => ? [K4: nat] :
% 5.46/5.81 ! [N4: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K4 @ N4 )
% 5.46/5.81 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N4 ) ) @ R3 ) ) )
% 5.46/5.81 => ( vanishes @ X8 ) ) ).
% 5.46/5.81
% 5.46/5.81 % vanishesI
% 5.46/5.81 thf(fact_9900_vanishes__def,axiom,
% 5.46/5.81 ( vanishes
% 5.46/5.81 = ( ^ [X6: nat > rat] :
% 5.46/5.81 ! [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 => ? [K3: nat] :
% 5.46/5.81 ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_rat @ ( abs_abs_rat @ ( X6 @ N2 ) ) @ R5 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % vanishes_def
% 5.46/5.81 thf(fact_9901_and__not__num_Opelims,axiom,
% 5.46/5.81 ! [X4: num,Xa: num,Y3: option_num] :
% 5.46/5.81 ( ( ( bit_and_not_num @ X4 @ Xa )
% 5.46/5.81 = Y3 )
% 5.46/5.81 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3 = none_num )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ one ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ( ( Y3 = none_num )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.81 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.46/5.81 @ ( bit_and_not_num @ M4 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ~ ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % and_not_num.pelims
% 5.46/5.81 thf(fact_9902_and__num_Opelims,axiom,
% 5.46/5.81 ! [X4: num,Xa: num,Y3: option_num] :
% 5.46/5.81 ( ( ( bit_un7362597486090784418nd_num @ X4 @ Xa )
% 5.46/5.81 = Y3 )
% 5.46/5.81 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ one ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ( ( Y3 = none_num )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ one ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3 = none_num )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ one ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ~ ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.46/5.81 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.46/5.81 @ ( bit_un7362597486090784418nd_num @ M4 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % and_num.pelims
% 5.46/5.81 thf(fact_9903_xor__num_Opelims,axiom,
% 5.46/5.81 ! [X4: num,Xa: num,Y3: option_num] :
% 5.46/5.81 ( ( ( bit_un2480387367778600638or_num @ X4 @ Xa )
% 5.46/5.81 = Y3 )
% 5.46/5.81 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3 = none_num )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ ( bit1 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ ( bit0 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ ( bit1 @ M4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N4 ) ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.46/5.81 => ( ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N4 ) ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 5.46/5.81 => ~ ! [M4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ! [N4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % xor_num.pelims
% 5.46/5.81 thf(fact_9904_or__not__num__neg_Opelims,axiom,
% 5.46/5.81 ! [X4: num,Xa: num,Y3: num] :
% 5.46/5.81 ( ( ( bit_or_not_num_neg @ X4 @ Xa )
% 5.46/5.81 = Y3 )
% 5.46/5.81 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3 = one )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ! [M4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 5.46/5.81 => ( ( ( X4 = one )
% 5.46/5.81 => ! [M4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [N4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( bit0 @ one ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N4 ) @ one ) ) ) ) )
% 5.46/5.81 => ( ! [N4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ! [M4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( bitM @ ( bit_or_not_num_neg @ N4 @ M4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N4 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [N4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit0 @ N4 ) )
% 5.46/5.81 => ! [M4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( bit0 @ ( bit_or_not_num_neg @ N4 @ M4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N4 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 5.46/5.81 => ( ! [N4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ( ( Xa = one )
% 5.46/5.81 => ( ( Y3 = one )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N4 ) @ one ) ) ) ) )
% 5.46/5.81 => ( ! [N4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ! [M4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit0 @ M4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( bitM @ ( bit_or_not_num_neg @ N4 @ M4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N4 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.46/5.81 => ~ ! [N4: num] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( bit1 @ N4 ) )
% 5.46/5.81 => ! [M4: num] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( bit1 @ M4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( bitM @ ( bit_or_not_num_neg @ N4 @ M4 ) ) )
% 5.46/5.81 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N4 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % or_not_num_neg.pelims
% 5.46/5.81 thf(fact_9905_xor__num__rel__dict,axiom,
% 5.46/5.81 bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 5.46/5.81
% 5.46/5.81 % xor_num_rel_dict
% 5.46/5.81 thf(fact_9906_and__num__rel__dict,axiom,
% 5.46/5.81 bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 5.46/5.81
% 5.46/5.81 % and_num_rel_dict
% 5.46/5.81 thf(fact_9907_rcis__inverse,axiom,
% 5.46/5.81 ! [R2: real,A: real] :
% 5.46/5.81 ( ( invers8013647133539491842omplex @ ( rcis @ R2 @ A ) )
% 5.46/5.81 = ( rcis @ ( divide_divide_real @ one_one_real @ R2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % rcis_inverse
% 5.46/5.81 thf(fact_9908_Re__rcis,axiom,
% 5.46/5.81 ! [R2: real,A: real] :
% 5.46/5.81 ( ( re @ ( rcis @ R2 @ A ) )
% 5.46/5.81 = ( times_times_real @ R2 @ ( cos_real @ A ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Re_rcis
% 5.46/5.81 thf(fact_9909_Im__rcis,axiom,
% 5.46/5.81 ! [R2: real,A: real] :
% 5.46/5.81 ( ( im @ ( rcis @ R2 @ A ) )
% 5.46/5.81 = ( times_times_real @ R2 @ ( sin_real @ A ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Im_rcis
% 5.46/5.81 thf(fact_9910_cis__rcis__eq,axiom,
% 5.46/5.81 ( cis
% 5.46/5.81 = ( rcis @ one_one_real ) ) ).
% 5.46/5.81
% 5.46/5.81 % cis_rcis_eq
% 5.46/5.81 thf(fact_9911_rcis__mult,axiom,
% 5.46/5.81 ! [R1: real,A: real,R22: real,B2: real] :
% 5.46/5.81 ( ( times_times_complex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B2 ) )
% 5.46/5.81 = ( rcis @ ( times_times_real @ R1 @ R22 ) @ ( plus_plus_real @ A @ B2 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % rcis_mult
% 5.46/5.81 thf(fact_9912_rcis__divide,axiom,
% 5.46/5.81 ! [R1: real,A: real,R22: real,B2: real] :
% 5.46/5.81 ( ( divide1717551699836669952omplex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B2 ) )
% 5.46/5.81 = ( rcis @ ( divide_divide_real @ R1 @ R22 ) @ ( minus_minus_real @ A @ B2 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % rcis_divide
% 5.46/5.81 thf(fact_9913_rcis__def,axiom,
% 5.46/5.81 ( rcis
% 5.46/5.81 = ( ^ [R5: real,A4: real] : ( times_times_complex @ ( real_V4546457046886955230omplex @ R5 ) @ ( cis @ A4 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % rcis_def
% 5.46/5.81 thf(fact_9914_DeMoivre2,axiom,
% 5.46/5.81 ! [R2: real,A: real,N: nat] :
% 5.46/5.81 ( ( power_power_complex @ ( rcis @ R2 @ A ) @ N )
% 5.46/5.81 = ( rcis @ ( power_power_real @ R2 @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % DeMoivre2
% 5.46/5.81 thf(fact_9915_nat__of__integer__code,axiom,
% 5.46/5.81 ( code_nat_of_integer
% 5.46/5.81 = ( ^ [K3: code_integer] :
% 5.46/5.81 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.46/5.81 @ ( produc1555791787009142072er_nat
% 5.46/5.81 @ ^ [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 ) )
% 5.46/5.81 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % nat_of_integer_code
% 5.46/5.81 thf(fact_9916_nat__of__integer__code__post_I3_J,axiom,
% 5.46/5.81 ! [K: num] :
% 5.46/5.81 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.46/5.81 = ( numeral_numeral_nat @ K ) ) ).
% 5.46/5.81
% 5.46/5.81 % nat_of_integer_code_post(3)
% 5.46/5.81 thf(fact_9917_nat__of__integer__code__post_I2_J,axiom,
% 5.46/5.81 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.46/5.81 = one_one_nat ) ).
% 5.46/5.81
% 5.46/5.81 % nat_of_integer_code_post(2)
% 5.46/5.81 thf(fact_9918_cauchy__def,axiom,
% 5.46/5.81 ( cauchy
% 5.46/5.81 = ( ^ [X6: nat > rat] :
% 5.46/5.81 ! [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 => ? [K3: nat] :
% 5.46/5.81 ! [M6: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ M6 )
% 5.46/5.81 => ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X6 @ M6 ) @ ( X6 @ N2 ) ) ) @ R5 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchy_def
% 5.46/5.81 thf(fact_9919_cauchyI,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ! [R3: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.46/5.81 => ? [K4: nat] :
% 5.46/5.81 ! [M4: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K4 @ M4 )
% 5.46/5.81 => ! [N4: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K4 @ N4 )
% 5.46/5.81 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M4 ) @ ( X8 @ N4 ) ) ) @ R3 ) ) ) )
% 5.46/5.81 => ( cauchy @ X8 ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchyI
% 5.46/5.81 thf(fact_9920_cauchy__inverse,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ~ ( vanishes @ X8 )
% 5.46/5.81 => ( cauchy
% 5.46/5.81 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X8 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchy_inverse
% 5.46/5.81 thf(fact_9921_cauchy__diff,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( cauchy @ Y7 )
% 5.46/5.81 => ( cauchy
% 5.46/5.81 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchy_diff
% 5.46/5.81 thf(fact_9922_cauchy__mult,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( cauchy @ Y7 )
% 5.46/5.81 => ( cauchy
% 5.46/5.81 @ ^ [N2: nat] : ( times_times_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchy_mult
% 5.46/5.81 thf(fact_9923_cauchy__const,axiom,
% 5.46/5.81 ! [X4: rat] :
% 5.46/5.81 ( cauchy
% 5.46/5.81 @ ^ [N2: nat] : X4 ) ).
% 5.46/5.81
% 5.46/5.81 % cauchy_const
% 5.46/5.81 thf(fact_9924_cauchy__minus,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( cauchy
% 5.46/5.81 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X8 @ N2 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchy_minus
% 5.46/5.81 thf(fact_9925_cauchy__add,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( cauchy @ Y7 )
% 5.46/5.81 => ( cauchy
% 5.46/5.81 @ ^ [N2: nat] : ( plus_plus_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchy_add
% 5.46/5.81 thf(fact_9926_cauchy__imp__bounded,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ? [B5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ B5 )
% 5.46/5.81 & ! [N6: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N6 ) ) @ B5 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchy_imp_bounded
% 5.46/5.81 thf(fact_9927_vanishes__diff__inverse,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ~ ( vanishes @ X8 )
% 5.46/5.81 => ( ( cauchy @ Y7 )
% 5.46/5.81 => ( ~ ( vanishes @ Y7 )
% 5.46/5.81 => ( ( vanishes
% 5.46/5.81 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) )
% 5.46/5.81 => ( vanishes
% 5.46/5.81 @ ^ [N2: nat] : ( minus_minus_rat @ ( inverse_inverse_rat @ ( X8 @ N2 ) ) @ ( inverse_inverse_rat @ ( Y7 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % vanishes_diff_inverse
% 5.46/5.81 thf(fact_9928_cauchy__not__vanishes__cases,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ~ ( vanishes @ X8 )
% 5.46/5.81 => ? [B5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ B5 )
% 5.46/5.81 & ? [K2: nat] :
% 5.46/5.81 ( ! [N6: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.46/5.81 => ( ord_less_rat @ B5 @ ( uminus_uminus_rat @ ( X8 @ N6 ) ) ) )
% 5.46/5.81 | ! [N6: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.46/5.81 => ( ord_less_rat @ B5 @ ( X8 @ N6 ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchy_not_vanishes_cases
% 5.46/5.81 thf(fact_9929_cauchy__not__vanishes,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ~ ( vanishes @ X8 )
% 5.46/5.81 => ? [B5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ B5 )
% 5.46/5.81 & ? [K2: nat] :
% 5.46/5.81 ! [N6: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.46/5.81 => ( ord_less_rat @ B5 @ ( abs_abs_rat @ ( X8 @ N6 ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchy_not_vanishes
% 5.46/5.81 thf(fact_9930_cauchyD,axiom,
% 5.46/5.81 ! [X8: nat > rat,R2: rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.46/5.81 => ? [K2: nat] :
% 5.46/5.81 ! [M5: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K2 @ M5 )
% 5.46/5.81 => ! [N6: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.46/5.81 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M5 ) @ ( X8 @ N6 ) ) ) @ R2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cauchyD
% 5.46/5.81 thf(fact_9931_le__Real,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( cauchy @ Y7 )
% 5.46/5.81 => ( ( ord_less_eq_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 5.46/5.81 = ( ! [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 => ? [K3: nat] :
% 5.46/5.81 ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_eq_rat @ ( X8 @ N2 ) @ ( plus_plus_rat @ ( Y7 @ N2 ) @ R5 ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % le_Real
% 5.46/5.81 thf(fact_9932_inverse__Real,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( ( vanishes @ X8 )
% 5.46/5.81 => ( ( inverse_inverse_real @ ( real2 @ X8 ) )
% 5.46/5.81 = zero_zero_real ) )
% 5.46/5.81 & ( ~ ( vanishes @ X8 )
% 5.46/5.81 => ( ( inverse_inverse_real @ ( real2 @ X8 ) )
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X8 @ N2 ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % inverse_Real
% 5.46/5.81 thf(fact_9933_Real__induct,axiom,
% 5.46/5.81 ! [P: real > $o,X4: real] :
% 5.46/5.81 ( ! [X10: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X10 )
% 5.46/5.81 => ( P @ ( real2 @ X10 ) ) )
% 5.46/5.81 => ( P @ X4 ) ) ).
% 5.46/5.81
% 5.46/5.81 % Real_induct
% 5.46/5.81 thf(fact_9934_one__real__def,axiom,
% 5.46/5.81 ( one_one_real
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ^ [N2: nat] : one_one_rat ) ) ).
% 5.46/5.81
% 5.46/5.81 % one_real_def
% 5.46/5.81 thf(fact_9935_of__nat__Real,axiom,
% 5.46/5.81 ( semiri5074537144036343181t_real
% 5.46/5.81 = ( ^ [X: nat] :
% 5.46/5.81 ( real2
% 5.46/5.81 @ ^ [N2: nat] : ( semiri681578069525770553at_rat @ X ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % of_nat_Real
% 5.46/5.81 thf(fact_9936_zero__real__def,axiom,
% 5.46/5.81 ( zero_zero_real
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ^ [N2: nat] : zero_zero_rat ) ) ).
% 5.46/5.81
% 5.46/5.81 % zero_real_def
% 5.46/5.81 thf(fact_9937_of__int__Real,axiom,
% 5.46/5.81 ( ring_1_of_int_real
% 5.46/5.81 = ( ^ [X: int] :
% 5.46/5.81 ( real2
% 5.46/5.81 @ ^ [N2: nat] : ( ring_1_of_int_rat @ X ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % of_int_Real
% 5.46/5.81 thf(fact_9938_minus__Real,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( uminus_uminus_real @ ( real2 @ X8 ) )
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X8 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % minus_Real
% 5.46/5.81 thf(fact_9939_add__Real,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( cauchy @ Y7 )
% 5.46/5.81 => ( ( plus_plus_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ^ [N2: nat] : ( plus_plus_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % add_Real
% 5.46/5.81 thf(fact_9940_mult__Real,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( cauchy @ Y7 )
% 5.46/5.81 => ( ( times_times_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ^ [N2: nat] : ( times_times_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % mult_Real
% 5.46/5.81 thf(fact_9941_diff__Real,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( cauchy @ Y7 )
% 5.46/5.81 => ( ( minus_minus_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % diff_Real
% 5.46/5.81 thf(fact_9942_eq__Real,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( cauchy @ Y7 )
% 5.46/5.81 => ( ( ( real2 @ X8 )
% 5.46/5.81 = ( real2 @ Y7 ) )
% 5.46/5.81 = ( vanishes
% 5.46/5.81 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % eq_Real
% 5.46/5.81 thf(fact_9943_not__positive__Real,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( ~ ( positive2 @ ( real2 @ X8 ) ) )
% 5.46/5.81 = ( ! [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 => ? [K3: nat] :
% 5.46/5.81 ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_eq_rat @ ( X8 @ N2 ) @ R5 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % not_positive_Real
% 5.46/5.81 thf(fact_9944_positive__Real,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( positive2 @ ( real2 @ X8 ) )
% 5.46/5.81 = ( ? [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 & ? [K3: nat] :
% 5.46/5.81 ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_rat @ R5 @ ( X8 @ N2 ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % positive_Real
% 5.46/5.81 thf(fact_9945_Real_Opositive__mult,axiom,
% 5.46/5.81 ! [X4: real,Y3: real] :
% 5.46/5.81 ( ( positive2 @ X4 )
% 5.46/5.81 => ( ( positive2 @ Y3 )
% 5.46/5.81 => ( positive2 @ ( times_times_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Real.positive_mult
% 5.46/5.81 thf(fact_9946_Real_Opositive__add,axiom,
% 5.46/5.81 ! [X4: real,Y3: real] :
% 5.46/5.81 ( ( positive2 @ X4 )
% 5.46/5.81 => ( ( positive2 @ Y3 )
% 5.46/5.81 => ( positive2 @ ( plus_plus_real @ X4 @ Y3 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Real.positive_add
% 5.46/5.81 thf(fact_9947_Real_Opositive__zero,axiom,
% 5.46/5.81 ~ ( positive2 @ zero_zero_real ) ).
% 5.46/5.81
% 5.46/5.81 % Real.positive_zero
% 5.46/5.81 thf(fact_9948_Real_Opositive__minus,axiom,
% 5.46/5.81 ! [X4: real] :
% 5.46/5.81 ( ~ ( positive2 @ X4 )
% 5.46/5.81 => ( ( X4 != zero_zero_real )
% 5.46/5.81 => ( positive2 @ ( uminus_uminus_real @ X4 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Real.positive_minus
% 5.46/5.81 thf(fact_9949_less__real__def,axiom,
% 5.46/5.81 ( ord_less_real
% 5.46/5.81 = ( ^ [X: real,Y: real] : ( positive2 @ ( minus_minus_real @ Y @ X ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_real_def
% 5.46/5.81 thf(fact_9950_Real_Opositive_Orep__eq,axiom,
% 5.46/5.81 ( positive2
% 5.46/5.81 = ( ^ [X: real] :
% 5.46/5.81 ? [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 & ? [K3: nat] :
% 5.46/5.81 ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_rat @ R5 @ ( rep_real @ X @ N2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Real.positive.rep_eq
% 5.46/5.81 thf(fact_9951_inverse__real_Oabs__eq,axiom,
% 5.46/5.81 ! [X4: nat > rat] :
% 5.46/5.81 ( ( realrel @ X4 @ X4 )
% 5.46/5.81 => ( ( inverse_inverse_real @ ( real2 @ X4 ) )
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ( if_nat_rat @ ( vanishes @ X4 )
% 5.46/5.81 @ ^ [N2: nat] : zero_zero_rat
% 5.46/5.81 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X4 @ N2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % inverse_real.abs_eq
% 5.46/5.81 thf(fact_9952_realrel__refl,axiom,
% 5.46/5.81 ! [X8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( realrel @ X8 @ X8 ) ) ).
% 5.46/5.81
% 5.46/5.81 % realrel_refl
% 5.46/5.81 thf(fact_9953_one__real_Orsp,axiom,
% 5.46/5.81 ( realrel
% 5.46/5.81 @ ^ [N2: nat] : one_one_rat
% 5.46/5.81 @ ^ [N2: nat] : one_one_rat ) ).
% 5.46/5.81
% 5.46/5.81 % one_real.rsp
% 5.46/5.81 thf(fact_9954_zero__real_Orsp,axiom,
% 5.46/5.81 ( realrel
% 5.46/5.81 @ ^ [N2: nat] : zero_zero_rat
% 5.46/5.81 @ ^ [N2: nat] : zero_zero_rat ) ).
% 5.46/5.81
% 5.46/5.81 % zero_real.rsp
% 5.46/5.81 thf(fact_9955_real_Oabs__induct,axiom,
% 5.46/5.81 ! [P: real > $o,X4: real] :
% 5.46/5.81 ( ! [Y4: nat > rat] :
% 5.46/5.81 ( ( realrel @ Y4 @ Y4 )
% 5.46/5.81 => ( P @ ( real2 @ Y4 ) ) )
% 5.46/5.81 => ( P @ X4 ) ) ).
% 5.46/5.81
% 5.46/5.81 % real.abs_induct
% 5.46/5.81 thf(fact_9956_uminus__real_Oabs__eq,axiom,
% 5.46/5.81 ! [X4: nat > rat] :
% 5.46/5.81 ( ( realrel @ X4 @ X4 )
% 5.46/5.81 => ( ( uminus_uminus_real @ ( real2 @ X4 ) )
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ^ [N2: nat] : ( uminus_uminus_rat @ ( X4 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % uminus_real.abs_eq
% 5.46/5.81 thf(fact_9957_plus__real_Oabs__eq,axiom,
% 5.46/5.81 ! [Xa: nat > rat,X4: nat > rat] :
% 5.46/5.81 ( ( realrel @ Xa @ Xa )
% 5.46/5.81 => ( ( realrel @ X4 @ X4 )
% 5.46/5.81 => ( ( plus_plus_real @ ( real2 @ Xa ) @ ( real2 @ X4 ) )
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ^ [N2: nat] : ( plus_plus_rat @ ( Xa @ N2 ) @ ( X4 @ N2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_real.abs_eq
% 5.46/5.81 thf(fact_9958_times__real_Oabs__eq,axiom,
% 5.46/5.81 ! [Xa: nat > rat,X4: nat > rat] :
% 5.46/5.81 ( ( realrel @ Xa @ Xa )
% 5.46/5.81 => ( ( realrel @ X4 @ X4 )
% 5.46/5.81 => ( ( times_times_real @ ( real2 @ Xa ) @ ( real2 @ X4 ) )
% 5.46/5.81 = ( real2
% 5.46/5.81 @ ^ [N2: nat] : ( times_times_rat @ ( Xa @ N2 ) @ ( X4 @ N2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_real.abs_eq
% 5.46/5.81 thf(fact_9959_realrelI,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y7: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ( cauchy @ Y7 )
% 5.46/5.81 => ( ( vanishes
% 5.46/5.81 @ ^ [N2: nat] : ( minus_minus_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) )
% 5.46/5.81 => ( realrel @ X8 @ Y7 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % realrelI
% 5.46/5.81 thf(fact_9960_realrel__def,axiom,
% 5.46/5.81 ( realrel
% 5.46/5.81 = ( ^ [X6: nat > rat,Y8: nat > rat] :
% 5.46/5.81 ( ( cauchy @ X6 )
% 5.46/5.81 & ( cauchy @ Y8 )
% 5.46/5.81 & ( vanishes
% 5.46/5.81 @ ^ [N2: nat] : ( minus_minus_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % realrel_def
% 5.46/5.81 thf(fact_9961_Real_Opositive_Oabs__eq,axiom,
% 5.46/5.81 ! [X4: nat > rat] :
% 5.46/5.81 ( ( realrel @ X4 @ X4 )
% 5.46/5.81 => ( ( positive2 @ ( real2 @ X4 ) )
% 5.46/5.81 = ( ? [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 & ? [K3: nat] :
% 5.46/5.81 ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_rat @ R5 @ ( X4 @ N2 ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Real.positive.abs_eq
% 5.46/5.81 thf(fact_9962_inverse__real__def,axiom,
% 5.46/5.81 ( inverse_inverse_real
% 5.46/5.81 = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 5.46/5.81 @ ^ [X6: nat > rat] :
% 5.46/5.81 ( if_nat_rat @ ( vanishes @ X6 )
% 5.46/5.81 @ ^ [N2: nat] : zero_zero_rat
% 5.46/5.81 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X6 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % inverse_real_def
% 5.46/5.81 thf(fact_9963_cr__real__def,axiom,
% 5.46/5.81 ( cr_real
% 5.46/5.81 = ( ^ [X: nat > rat,Y: real] :
% 5.46/5.81 ( ( realrel @ X @ X )
% 5.46/5.81 & ( ( real2 @ X )
% 5.46/5.81 = Y ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cr_real_def
% 5.46/5.81 thf(fact_9964_uminus__real__def,axiom,
% 5.46/5.81 ( uminus_uminus_real
% 5.46/5.81 = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 5.46/5.81 @ ^ [X6: nat > rat,N2: nat] : ( uminus_uminus_rat @ ( X6 @ N2 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % uminus_real_def
% 5.46/5.81 thf(fact_9965_times__real__def,axiom,
% 5.46/5.81 ( times_times_real
% 5.46/5.81 = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 5.46/5.81 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_real_def
% 5.46/5.81 thf(fact_9966_plus__real__def,axiom,
% 5.46/5.81 ( plus_plus_real
% 5.46/5.81 = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 5.46/5.81 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_real_def
% 5.46/5.81 thf(fact_9967_Real_Opositive_Orsp,axiom,
% 5.46/5.81 ( bNF_re728719798268516973at_o_o @ realrel
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [X6: nat > rat] :
% 5.46/5.81 ? [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 & ? [K3: nat] :
% 5.46/5.81 ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) )
% 5.46/5.81 @ ^ [X6: nat > rat] :
% 5.46/5.81 ? [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 & ? [K3: nat] :
% 5.46/5.81 ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Real.positive.rsp
% 5.46/5.81 thf(fact_9968_plus__real_Orsp,axiom,
% 5.46/5.81 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.46/5.81 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) )
% 5.46/5.81 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_real.rsp
% 5.46/5.81 thf(fact_9969_uminus__real_Orsp,axiom,
% 5.46/5.81 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 5.46/5.81 @ ^ [X6: nat > rat,N2: nat] : ( uminus_uminus_rat @ ( X6 @ N2 ) )
% 5.46/5.81 @ ^ [X6: nat > rat,N2: nat] : ( uminus_uminus_rat @ ( X6 @ N2 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % uminus_real.rsp
% 5.46/5.81 thf(fact_9970_times__real_Orsp,axiom,
% 5.46/5.81 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.46/5.81 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) )
% 5.46/5.81 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_real.rsp
% 5.46/5.81 thf(fact_9971_sub_Orsp,axiom,
% 5.46/5.81 ( bNF_re8402795839162346335um_int
% 5.46/5.81 @ ^ [Y6: num,Z4: num] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re1822329894187522285nt_int
% 5.46/5.81 @ ^ [Y6: num,Z4: num] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.81 @ ^ [M6: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) )
% 5.46/5.81 @ ^ [M6: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % sub.rsp
% 5.46/5.81 thf(fact_9972_times__natural_Orsp,axiom,
% 5.46/5.81 ( bNF_re1345281282404953727at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re5653821019739307937at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.46/5.81 @ times_times_nat
% 5.46/5.81 @ times_times_nat ) ).
% 5.46/5.81
% 5.46/5.81 % times_natural.rsp
% 5.46/5.81 thf(fact_9973_times__integer_Orsp,axiom,
% 5.46/5.81 ( bNF_re711492959462206631nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re4712519889275205905nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.81 @ times_times_int
% 5.46/5.81 @ times_times_int ) ).
% 5.46/5.81
% 5.46/5.81 % times_integer.rsp
% 5.46/5.81 thf(fact_9974_minus__integer_Orsp,axiom,
% 5.46/5.81 ( bNF_re711492959462206631nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re4712519889275205905nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.81 @ minus_minus_int
% 5.46/5.81 @ minus_minus_int ) ).
% 5.46/5.81
% 5.46/5.81 % minus_integer.rsp
% 5.46/5.81 thf(fact_9975_minus__natural_Orsp,axiom,
% 5.46/5.81 ( bNF_re1345281282404953727at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re5653821019739307937at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.46/5.81 @ minus_minus_nat
% 5.46/5.81 @ minus_minus_nat ) ).
% 5.46/5.81
% 5.46/5.81 % minus_natural.rsp
% 5.46/5.81 thf(fact_9976_divide__natural_Orsp,axiom,
% 5.46/5.81 ( bNF_re1345281282404953727at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re5653821019739307937at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.46/5.81 @ divide_divide_nat
% 5.46/5.81 @ divide_divide_nat ) ).
% 5.46/5.81
% 5.46/5.81 % divide_natural.rsp
% 5.46/5.81 thf(fact_9977_divide__integer_Orsp,axiom,
% 5.46/5.81 ( bNF_re711492959462206631nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re4712519889275205905nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.81 @ divide_divide_int
% 5.46/5.81 @ divide_divide_int ) ).
% 5.46/5.81
% 5.46/5.81 % divide_integer.rsp
% 5.46/5.81 thf(fact_9978_modulo__natural_Orsp,axiom,
% 5.46/5.81 ( bNF_re1345281282404953727at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re5653821019739307937at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.46/5.81 @ modulo_modulo_nat
% 5.46/5.81 @ modulo_modulo_nat ) ).
% 5.46/5.81
% 5.46/5.81 % modulo_natural.rsp
% 5.46/5.81 thf(fact_9979_modulo__integer_Orsp,axiom,
% 5.46/5.81 ( bNF_re711492959462206631nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re4712519889275205905nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.81 @ modulo_modulo_int
% 5.46/5.81 @ modulo_modulo_int ) ).
% 5.46/5.81
% 5.46/5.81 % modulo_integer.rsp
% 5.46/5.81 thf(fact_9980_Suc_Orsp,axiom,
% 5.46/5.81 ( bNF_re5653821019739307937at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ suc
% 5.46/5.81 @ suc ) ).
% 5.46/5.81
% 5.46/5.81 % Suc.rsp
% 5.46/5.81 thf(fact_9981_dup_Orsp,axiom,
% 5.46/5.81 ( bNF_re4712519889275205905nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 )
% 5.46/5.81 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ).
% 5.46/5.81
% 5.46/5.81 % dup.rsp
% 5.46/5.81 thf(fact_9982_plus__natural_Orsp,axiom,
% 5.46/5.81 ( bNF_re1345281282404953727at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re5653821019739307937at_nat
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.46/5.81 @ plus_plus_nat
% 5.46/5.81 @ plus_plus_nat ) ).
% 5.46/5.81
% 5.46/5.81 % plus_natural.rsp
% 5.46/5.81 thf(fact_9983_plus__integer_Orsp,axiom,
% 5.46/5.81 ( bNF_re711492959462206631nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re4712519889275205905nt_int
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.46/5.81 @ plus_plus_int
% 5.46/5.81 @ plus_plus_int ) ).
% 5.46/5.81
% 5.46/5.81 % plus_integer.rsp
% 5.46/5.81 thf(fact_9984_less__integer_Orsp,axiom,
% 5.46/5.81 ( bNF_re3403563459893282935_int_o
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re5089333283451836215nt_o_o
% 5.46/5.81 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 5.46/5.81 @ ord_less_int
% 5.46/5.81 @ ord_less_int ) ).
% 5.46/5.81
% 5.46/5.81 % less_integer.rsp
% 5.46/5.81 thf(fact_9985_less__natural_Orsp,axiom,
% 5.46/5.81 ( bNF_re578469030762574527_nat_o
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re4705727531993890431at_o_o
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 5.46/5.81 @ ord_less_nat
% 5.46/5.81 @ ord_less_nat ) ).
% 5.46/5.81
% 5.46/5.81 % less_natural.rsp
% 5.46/5.81 thf(fact_9986_less__eq__natural_Orsp,axiom,
% 5.46/5.81 ( bNF_re578469030762574527_nat_o
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ( bNF_re4705727531993890431at_o_o
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 5.46/5.81 @ ord_less_eq_nat
% 5.46/5.81 @ ord_less_eq_nat ) ).
% 5.46/5.81
% 5.46/5.81 % less_eq_natural.rsp
% 5.46/5.81 thf(fact_9987_le__enumerate,axiom,
% 5.46/5.81 ! [S2: set_nat,N: nat] :
% 5.46/5.81 ( ~ ( finite_finite_nat @ S2 )
% 5.46/5.81 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % le_enumerate
% 5.46/5.81 thf(fact_9988_inverse__real_Orsp,axiom,
% 5.46/5.81 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 5.46/5.81 @ ^ [X6: nat > rat] :
% 5.46/5.81 ( if_nat_rat @ ( vanishes @ X6 )
% 5.46/5.81 @ ^ [N2: nat] : zero_zero_rat
% 5.46/5.81 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X6 @ N2 ) ) )
% 5.46/5.81 @ ^ [X6: nat > rat] :
% 5.46/5.81 ( if_nat_rat @ ( vanishes @ X6 )
% 5.46/5.81 @ ^ [N2: nat] : zero_zero_rat
% 5.46/5.81 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X6 @ N2 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % inverse_real.rsp
% 5.46/5.81 thf(fact_9989_finite__le__enumerate,axiom,
% 5.46/5.81 ! [S2: set_nat,N: nat] :
% 5.46/5.81 ( ( finite_finite_nat @ S2 )
% 5.46/5.81 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S2 ) )
% 5.46/5.81 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S2 @ N ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % finite_le_enumerate
% 5.46/5.81 thf(fact_9990_Real_Opositive_Otransfer,axiom,
% 5.46/5.81 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [X6: nat > rat] :
% 5.46/5.81 ? [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 & ? [K3: nat] :
% 5.46/5.81 ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) )
% 5.46/5.81 @ positive2 ) ).
% 5.46/5.81
% 5.46/5.81 % Real.positive.transfer
% 5.46/5.81 thf(fact_9991_plus__rat_Otransfer,axiom,
% 5.46/5.81 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.46/5.81 @ ^ [X: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) ) @ ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y ) ) )
% 5.46/5.81 @ plus_plus_rat ) ).
% 5.46/5.81
% 5.46/5.81 % plus_rat.transfer
% 5.46/5.81 thf(fact_9992_real_Orel__eq__transfer,axiom,
% 5.46/5.81 ( bNF_re4521903465945308077real_o @ pcr_real
% 5.46/5.81 @ ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 5.46/5.81 @ realrel
% 5.46/5.81 @ ^ [Y6: real,Z4: real] : ( Y6 = Z4 ) ) ).
% 5.46/5.81
% 5.46/5.81 % real.rel_eq_transfer
% 5.46/5.81 thf(fact_9993_real_Opcr__cr__eq,axiom,
% 5.46/5.81 pcr_real = cr_real ).
% 5.46/5.81
% 5.46/5.81 % real.pcr_cr_eq
% 5.46/5.81 thf(fact_9994_zero__real_Otransfer,axiom,
% 5.46/5.81 ( pcr_real
% 5.46/5.81 @ ^ [N2: nat] : zero_zero_rat
% 5.46/5.81 @ zero_zero_real ) ).
% 5.46/5.81
% 5.46/5.81 % zero_real.transfer
% 5.46/5.81 thf(fact_9995_one__real_Otransfer,axiom,
% 5.46/5.81 ( pcr_real
% 5.46/5.81 @ ^ [N2: nat] : one_one_rat
% 5.46/5.81 @ one_one_real ) ).
% 5.46/5.81
% 5.46/5.81 % one_real.transfer
% 5.46/5.81 thf(fact_9996_cr__real__eq,axiom,
% 5.46/5.81 ( pcr_real
% 5.46/5.81 = ( ^ [X: nat > rat,Y: real] :
% 5.46/5.81 ( ( cauchy @ X )
% 5.46/5.81 & ( ( real2 @ X )
% 5.46/5.81 = Y ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % cr_real_eq
% 5.46/5.81 thf(fact_9997_uminus__real_Otransfer,axiom,
% 5.46/5.81 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 5.46/5.81 @ ^ [X6: nat > rat,N2: nat] : ( uminus_uminus_rat @ ( X6 @ N2 ) )
% 5.46/5.81 @ uminus_uminus_real ) ).
% 5.46/5.81
% 5.46/5.81 % uminus_real.transfer
% 5.46/5.81 thf(fact_9998_plus__real_Otransfer,axiom,
% 5.46/5.81 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.46/5.81 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( plus_plus_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) )
% 5.46/5.81 @ plus_plus_real ) ).
% 5.46/5.81
% 5.46/5.81 % plus_real.transfer
% 5.46/5.81 thf(fact_9999_times__real_Otransfer,axiom,
% 5.46/5.81 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.46/5.81 @ ^ [X6: nat > rat,Y8: nat > rat,N2: nat] : ( times_times_rat @ ( X6 @ N2 ) @ ( Y8 @ N2 ) )
% 5.46/5.81 @ times_times_real ) ).
% 5.46/5.81
% 5.46/5.81 % times_real.transfer
% 5.46/5.81 thf(fact_10000_inverse__real_Otransfer,axiom,
% 5.46/5.81 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 5.46/5.81 @ ^ [X6: nat > rat] :
% 5.46/5.81 ( if_nat_rat @ ( vanishes @ X6 )
% 5.46/5.81 @ ^ [N2: nat] : zero_zero_rat
% 5.46/5.81 @ ^ [N2: nat] : ( inverse_inverse_rat @ ( X6 @ N2 ) ) )
% 5.46/5.81 @ inverse_inverse_real ) ).
% 5.46/5.81
% 5.46/5.81 % inverse_real.transfer
% 5.46/5.81 thf(fact_10001_times__rat_Otransfer,axiom,
% 5.46/5.81 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.46/5.81 @ ^ [X: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y ) ) )
% 5.46/5.81 @ times_times_rat ) ).
% 5.46/5.81
% 5.46/5.81 % times_rat.transfer
% 5.46/5.81 thf(fact_10002_Rat_Opositive_Otransfer,axiom,
% 5.46/5.81 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 5.46/5.81 @ positive ) ).
% 5.46/5.81
% 5.46/5.81 % Rat.positive.transfer
% 5.46/5.81 thf(fact_10003_times__int_Otransfer,axiom,
% 5.46/5.81 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U4 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U4 ) ) ) ) )
% 5.46/5.81 @ times_times_int ) ).
% 5.46/5.81
% 5.46/5.81 % times_int.transfer
% 5.46/5.81 thf(fact_10004_Least__eq__0,axiom,
% 5.46/5.81 ! [P: nat > $o] :
% 5.46/5.81 ( ( P @ zero_zero_nat )
% 5.46/5.81 => ( ( ord_Least_nat @ P )
% 5.46/5.81 = zero_zero_nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % Least_eq_0
% 5.46/5.81 thf(fact_10005_Least__Suc,axiom,
% 5.46/5.81 ! [P: nat > $o,N: nat] :
% 5.46/5.81 ( ( P @ N )
% 5.46/5.81 => ( ~ ( P @ zero_zero_nat )
% 5.46/5.81 => ( ( ord_Least_nat @ P )
% 5.46/5.81 = ( suc
% 5.46/5.81 @ ( ord_Least_nat
% 5.46/5.81 @ ^ [M6: nat] : ( P @ ( suc @ M6 ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Least_Suc
% 5.46/5.81 thf(fact_10006_Least__Suc2,axiom,
% 5.46/5.81 ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 5.46/5.81 ( ( P @ N )
% 5.46/5.81 => ( ( Q @ M )
% 5.46/5.81 => ( ~ ( P @ zero_zero_nat )
% 5.46/5.81 => ( ! [K2: nat] :
% 5.46/5.81 ( ( P @ ( suc @ K2 ) )
% 5.46/5.81 = ( Q @ K2 ) )
% 5.46/5.81 => ( ( ord_Least_nat @ P )
% 5.46/5.81 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Least_Suc2
% 5.46/5.81 thf(fact_10007_Sup__real__def,axiom,
% 5.46/5.81 ( comple1385675409528146559p_real
% 5.46/5.81 = ( ^ [X6: set_real] :
% 5.46/5.81 ( ord_Least_real
% 5.46/5.81 @ ^ [Z5: real] :
% 5.46/5.81 ! [X: real] :
% 5.46/5.81 ( ( member_real @ X @ X6 )
% 5.46/5.81 => ( ord_less_eq_real @ X @ Z5 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Sup_real_def
% 5.46/5.81 thf(fact_10008_nat_Otransfer,axiom,
% 5.46/5.81 ( bNF_re4555766996558763186at_nat @ pcr_int
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 5.46/5.81 @ nat2 ) ).
% 5.46/5.81
% 5.46/5.81 % nat.transfer
% 5.46/5.81 thf(fact_10009_one__int_Otransfer,axiom,
% 5.46/5.81 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 5.46/5.81
% 5.46/5.81 % one_int.transfer
% 5.46/5.81 thf(fact_10010_less__int_Otransfer,axiom,
% 5.46/5.81 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.46/5.81 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 5.46/5.81 @ ( produc8739625826339149834_nat_o
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U4 @ Y ) ) ) )
% 5.46/5.81 @ ord_less_int ) ).
% 5.46/5.81
% 5.46/5.81 % less_int.transfer
% 5.46/5.81 thf(fact_10011_less__eq__int_Otransfer,axiom,
% 5.46/5.81 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.46/5.81 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 5.46/5.81 @ ( produc8739625826339149834_nat_o
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U4 @ Y ) ) ) )
% 5.46/5.81 @ ord_less_eq_int ) ).
% 5.46/5.81
% 5.46/5.81 % less_eq_int.transfer
% 5.46/5.81 thf(fact_10012_plus__int_Otransfer,axiom,
% 5.46/5.81 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U4 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 5.46/5.81 @ plus_plus_int ) ).
% 5.46/5.81
% 5.46/5.81 % plus_int.transfer
% 5.46/5.81 thf(fact_10013_minus__int_Otransfer,axiom,
% 5.46/5.81 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U4 ) ) ) )
% 5.46/5.81 @ minus_minus_int ) ).
% 5.46/5.81
% 5.46/5.81 % minus_int.transfer
% 5.46/5.81 thf(fact_10014_of__rat__Real,axiom,
% 5.46/5.81 ( field_7254667332652039916t_real
% 5.46/5.81 = ( ^ [X: rat] :
% 5.46/5.81 ( real2
% 5.46/5.81 @ ^ [N2: nat] : X ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % of_rat_Real
% 5.46/5.81 thf(fact_10015_of__rat__dense,axiom,
% 5.46/5.81 ! [X4: real,Y3: real] :
% 5.46/5.81 ( ( ord_less_real @ X4 @ Y3 )
% 5.46/5.81 => ? [Q3: rat] :
% 5.46/5.81 ( ( ord_less_real @ X4 @ ( field_7254667332652039916t_real @ Q3 ) )
% 5.46/5.81 & ( ord_less_real @ ( field_7254667332652039916t_real @ Q3 ) @ Y3 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % of_rat_dense
% 5.46/5.81 thf(fact_10016_less__RealD,axiom,
% 5.46/5.81 ! [Y7: nat > rat,X4: real] :
% 5.46/5.81 ( ( cauchy @ Y7 )
% 5.46/5.81 => ( ( ord_less_real @ X4 @ ( real2 @ Y7 ) )
% 5.46/5.81 => ? [N4: nat] : ( ord_less_real @ X4 @ ( field_7254667332652039916t_real @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_RealD
% 5.46/5.81 thf(fact_10017_le__RealI,axiom,
% 5.46/5.81 ! [Y7: nat > rat,X4: real] :
% 5.46/5.81 ( ( cauchy @ Y7 )
% 5.46/5.81 => ( ! [N4: nat] : ( ord_less_eq_real @ X4 @ ( field_7254667332652039916t_real @ ( Y7 @ N4 ) ) )
% 5.46/5.81 => ( ord_less_eq_real @ X4 @ ( real2 @ Y7 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % le_RealI
% 5.46/5.81 thf(fact_10018_Real__leI,axiom,
% 5.46/5.81 ! [X8: nat > rat,Y3: real] :
% 5.46/5.81 ( ( cauchy @ X8 )
% 5.46/5.81 => ( ! [N4: nat] : ( ord_less_eq_real @ ( field_7254667332652039916t_real @ ( X8 @ N4 ) ) @ Y3 )
% 5.46/5.81 => ( ord_less_eq_real @ ( real2 @ X8 ) @ Y3 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Real_leI
% 5.46/5.81 thf(fact_10019_times__int_Orsp,axiom,
% 5.46/5.81 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U4 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U4 ) ) ) ) )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U4 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U4 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_int.rsp
% 5.46/5.81 thf(fact_10020_intrel__iff,axiom,
% 5.46/5.81 ! [X4: nat,Y3: nat,U: nat,V: nat] :
% 5.46/5.81 ( ( intrel @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ ( product_Pair_nat_nat @ U @ V ) )
% 5.46/5.81 = ( ( plus_plus_nat @ X4 @ V )
% 5.46/5.81 = ( plus_plus_nat @ U @ Y3 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % intrel_iff
% 5.46/5.81 thf(fact_10021_nat_Orsp,axiom,
% 5.46/5.81 ( bNF_re8246922863344978751at_nat @ intrel
% 5.46/5.81 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 5.46/5.81 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 5.46/5.81 @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % nat.rsp
% 5.46/5.81 thf(fact_10022_one__int_Orsp,axiom,
% 5.46/5.81 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.46/5.81
% 5.46/5.81 % one_int.rsp
% 5.46/5.81 thf(fact_10023_intrel__def,axiom,
% 5.46/5.81 ( intrel
% 5.46/5.81 = ( produc8739625826339149834_nat_o
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [U4: nat,V4: nat] :
% 5.46/5.81 ( ( plus_plus_nat @ X @ V4 )
% 5.46/5.81 = ( plus_plus_nat @ U4 @ Y ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % intrel_def
% 5.46/5.81 thf(fact_10024_less__int_Orsp,axiom,
% 5.46/5.81 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.46/5.81 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 5.46/5.81 @ ( produc8739625826339149834_nat_o
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U4 @ Y ) ) ) )
% 5.46/5.81 @ ( produc8739625826339149834_nat_o
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U4 @ Y ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_int.rsp
% 5.46/5.81 thf(fact_10025_less__eq__int_Orsp,axiom,
% 5.46/5.81 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.46/5.81 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 5.46/5.81 @ ( produc8739625826339149834_nat_o
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U4 @ Y ) ) ) )
% 5.46/5.81 @ ( produc8739625826339149834_nat_o
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U4 @ Y ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_eq_int.rsp
% 5.46/5.81 thf(fact_10026_plus__int_Orsp,axiom,
% 5.46/5.81 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U4 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U4 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_int.rsp
% 5.46/5.81 thf(fact_10027_minus__int_Orsp,axiom,
% 5.46/5.81 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U4 ) ) ) )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U4 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % minus_int.rsp
% 5.46/5.81 thf(fact_10028_has__vector__derivative__id,axiom,
% 5.46/5.81 ! [Net: filter_real] :
% 5.46/5.81 ( has_ve631408500373753343e_real
% 5.46/5.81 @ ^ [X: real] : X
% 5.46/5.81 @ one_one_real
% 5.46/5.81 @ Net ) ).
% 5.46/5.81
% 5.46/5.81 % has_vector_derivative_id
% 5.46/5.81 thf(fact_10029_has__field__derivative__iff__has__vector__derivative,axiom,
% 5.46/5.81 has_fi5821293074295781190e_real = has_ve631408500373753343e_real ).
% 5.46/5.81
% 5.46/5.81 % has_field_derivative_iff_has_vector_derivative
% 5.46/5.81 thf(fact_10030_plus__rat_Orsp,axiom,
% 5.46/5.81 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.46/5.81 @ ^ [X: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) ) @ ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y ) ) )
% 5.46/5.81 @ ^ [X: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) ) @ ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_rat.rsp
% 5.46/5.81 thf(fact_10031_ratrel__iff,axiom,
% 5.46/5.81 ( ratrel
% 5.46/5.81 = ( ^ [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.46/5.81 ( ( ( product_snd_int_int @ X )
% 5.46/5.81 != zero_zero_int )
% 5.46/5.81 & ( ( product_snd_int_int @ Y )
% 5.46/5.81 != zero_zero_int )
% 5.46/5.81 & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) )
% 5.46/5.81 = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % ratrel_iff
% 5.46/5.81 thf(fact_10032_ratrel__def,axiom,
% 5.46/5.81 ( ratrel
% 5.46/5.81 = ( ^ [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.46/5.81 ( ( ( product_snd_int_int @ X )
% 5.46/5.81 != zero_zero_int )
% 5.46/5.81 & ( ( product_snd_int_int @ Y )
% 5.46/5.81 != zero_zero_int )
% 5.46/5.81 & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) )
% 5.46/5.81 = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % ratrel_def
% 5.46/5.81 thf(fact_10033_times__rat_Orsp,axiom,
% 5.46/5.81 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.46/5.81 @ ^ [X: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y ) ) )
% 5.46/5.81 @ ^ [X: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_rat.rsp
% 5.46/5.81 thf(fact_10034_Rat_Opositive_Orsp,axiom,
% 5.46/5.81 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 5.46/5.81 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 5.46/5.81 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 5.46/5.81 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Rat.positive.rsp
% 5.46/5.81 thf(fact_10035_plus__rat_Oabs__eq,axiom,
% 5.46/5.81 ! [Xa: product_prod_int_int,X4: product_prod_int_int] :
% 5.46/5.81 ( ( ratrel @ Xa @ Xa )
% 5.46/5.81 => ( ( ratrel @ X4 @ X4 )
% 5.46/5.81 => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X4 ) )
% 5.46/5.81 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_snd_int_int @ X4 ) ) @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_rat.abs_eq
% 5.46/5.81 thf(fact_10036_Rat_Opositive_Oabs__eq,axiom,
% 5.46/5.81 ! [X4: product_prod_int_int] :
% 5.46/5.81 ( ( ratrel @ X4 @ X4 )
% 5.46/5.81 => ( ( positive @ ( abs_Rat @ X4 ) )
% 5.46/5.81 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Rat.positive.abs_eq
% 5.46/5.81 thf(fact_10037_times__rat_Oabs__eq,axiom,
% 5.46/5.81 ! [Xa: product_prod_int_int,X4: product_prod_int_int] :
% 5.46/5.81 ( ( ratrel @ Xa @ Xa )
% 5.46/5.81 => ( ( ratrel @ X4 @ X4 )
% 5.46/5.81 => ( ( times_times_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X4 ) )
% 5.46/5.81 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_fst_int_int @ X4 ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_rat.abs_eq
% 5.46/5.81 thf(fact_10038_last__upt,axiom,
% 5.46/5.81 ! [I: nat,J: nat] :
% 5.46/5.81 ( ( ord_less_nat @ I @ J )
% 5.46/5.81 => ( ( last_nat @ ( upt @ I @ J ) )
% 5.46/5.81 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % last_upt
% 5.46/5.81 thf(fact_10039_Bseq__monoseq__convergent_H__dec,axiom,
% 5.46/5.81 ! [F: nat > real,M7: nat] :
% 5.46/5.81 ( ( bfun_nat_real
% 5.46/5.81 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ M7 ) )
% 5.46/5.81 @ at_top_nat )
% 5.46/5.81 => ( ! [M4: nat,N4: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ M7 @ M4 )
% 5.46/5.81 => ( ( ord_less_eq_nat @ M4 @ N4 )
% 5.46/5.81 => ( ord_less_eq_real @ ( F @ N4 ) @ ( F @ M4 ) ) ) )
% 5.46/5.81 => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Bseq_monoseq_convergent'_dec
% 5.46/5.81 thf(fact_10040_Bseq__monoseq__convergent_H__inc,axiom,
% 5.46/5.81 ! [F: nat > real,M7: nat] :
% 5.46/5.81 ( ( bfun_nat_real
% 5.46/5.81 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ M7 ) )
% 5.46/5.81 @ at_top_nat )
% 5.46/5.81 => ( ! [M4: nat,N4: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ M7 @ M4 )
% 5.46/5.81 => ( ( ord_less_eq_nat @ M4 @ N4 )
% 5.46/5.81 => ( ord_less_eq_real @ ( F @ M4 ) @ ( F @ N4 ) ) ) )
% 5.46/5.81 => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Bseq_monoseq_convergent'_inc
% 5.46/5.81 thf(fact_10041_Bseq__mono__convergent,axiom,
% 5.46/5.81 ! [X8: nat > real] :
% 5.46/5.81 ( ( bfun_nat_real @ X8 @ at_top_nat )
% 5.46/5.81 => ( ! [M4: nat,N4: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ M4 @ N4 )
% 5.46/5.81 => ( ord_less_eq_real @ ( X8 @ M4 ) @ ( X8 @ N4 ) ) )
% 5.46/5.81 => ( topolo7531315842566124627t_real @ X8 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Bseq_mono_convergent
% 5.46/5.81 thf(fact_10042_convergent__realpow,axiom,
% 5.46/5.81 ! [X4: real] :
% 5.46/5.81 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.46/5.81 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.46/5.81 => ( topolo7531315842566124627t_real @ ( power_power_real @ X4 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % convergent_realpow
% 5.46/5.81 thf(fact_10043_filtermap__at__right__shift,axiom,
% 5.46/5.81 ! [D: real,A: real] :
% 5.46/5.81 ( ( filtermap_real_real
% 5.46/5.81 @ ^ [X: real] : ( minus_minus_real @ X @ D )
% 5.46/5.81 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.46/5.81 = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % filtermap_at_right_shift
% 5.46/5.81 thf(fact_10044_at__right__to__0,axiom,
% 5.46/5.81 ! [A: real] :
% 5.46/5.81 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.46/5.81 = ( filtermap_real_real
% 5.46/5.81 @ ^ [X: real] : ( plus_plus_real @ X @ A )
% 5.46/5.81 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % at_right_to_0
% 5.46/5.81 thf(fact_10045_pair__lessI2,axiom,
% 5.46/5.81 ! [A: nat,B2: nat,S: nat,T: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.81 => ( ( ord_less_nat @ S @ T )
% 5.46/5.81 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_less ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % pair_lessI2
% 5.46/5.81 thf(fact_10046_pair__less__iff1,axiom,
% 5.46/5.81 ! [X4: nat,Y3: nat,Z: nat] :
% 5.46/5.81 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ ( product_Pair_nat_nat @ X4 @ Z ) ) @ fun_pair_less )
% 5.46/5.81 = ( ord_less_nat @ Y3 @ Z ) ) ).
% 5.46/5.81
% 5.46/5.81 % pair_less_iff1
% 5.46/5.81 thf(fact_10047_pair__lessI1,axiom,
% 5.46/5.81 ! [A: nat,B2: nat,S: nat,T: nat] :
% 5.46/5.81 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.81 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_less ) ) ).
% 5.46/5.81
% 5.46/5.81 % pair_lessI1
% 5.46/5.81 thf(fact_10048_pair__leqI2,axiom,
% 5.46/5.81 ! [A: nat,B2: nat,S: nat,T: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ A @ B2 )
% 5.46/5.81 => ( ( ord_less_eq_nat @ S @ T )
% 5.46/5.81 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_leq ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % pair_leqI2
% 5.46/5.81 thf(fact_10049_pair__leqI1,axiom,
% 5.46/5.81 ! [A: nat,B2: nat,S: nat,T: nat] :
% 5.46/5.81 ( ( ord_less_nat @ A @ B2 )
% 5.46/5.81 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S ) @ ( product_Pair_nat_nat @ B2 @ T ) ) @ fun_pair_leq ) ) ).
% 5.46/5.81
% 5.46/5.81 % pair_leqI1
% 5.46/5.81 thf(fact_10050_bot__nat__0_Oordering__top__axioms,axiom,
% 5.46/5.81 ( ordering_top_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 5.46/5.81 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X )
% 5.46/5.81 @ zero_zero_nat ) ).
% 5.46/5.81
% 5.46/5.81 % bot_nat_0.ordering_top_axioms
% 5.46/5.81 thf(fact_10051_set__encode__vimage__Suc,axiom,
% 5.46/5.81 ! [A3: set_nat] :
% 5.46/5.81 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A3 ) )
% 5.46/5.81 = ( divide_divide_nat @ ( nat_set_encode @ A3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % set_encode_vimage_Suc
% 5.46/5.81 thf(fact_10052_euclidean__size__int__def,axiom,
% 5.46/5.81 ( euclid4774559944035922753ze_int
% 5.46/5.81 = ( comp_int_nat_int @ nat2 @ abs_abs_int ) ) ).
% 5.46/5.81
% 5.46/5.81 % euclidean_size_int_def
% 5.46/5.81 thf(fact_10053_finite__vimage__Suc__iff,axiom,
% 5.46/5.81 ! [F5: set_nat] :
% 5.46/5.81 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F5 ) )
% 5.46/5.81 = ( finite_finite_nat @ F5 ) ) ).
% 5.46/5.81
% 5.46/5.81 % finite_vimage_Suc_iff
% 5.46/5.81 thf(fact_10054_vimage__Suc__insert__Suc,axiom,
% 5.46/5.81 ! [N: nat,A3: set_nat] :
% 5.46/5.81 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A3 ) )
% 5.46/5.81 = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A3 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % vimage_Suc_insert_Suc
% 5.46/5.81 thf(fact_10055_vimage__Suc__insert__0,axiom,
% 5.46/5.81 ! [A3: set_nat] :
% 5.46/5.81 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A3 ) )
% 5.46/5.81 = ( vimage_nat_nat @ suc @ A3 ) ) ).
% 5.46/5.81
% 5.46/5.81 % vimage_Suc_insert_0
% 5.46/5.81 thf(fact_10056_set__decode__div__2,axiom,
% 5.46/5.81 ! [X4: nat] :
% 5.46/5.81 ( ( nat_set_decode @ ( divide_divide_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.46/5.81 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X4 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % set_decode_div_2
% 5.46/5.81 thf(fact_10057_abs__division__segment,axiom,
% 5.46/5.81 ! [K: int] :
% 5.46/5.81 ( ( abs_abs_int @ ( euclid3395696857347342551nt_int @ K ) )
% 5.46/5.81 = one_one_int ) ).
% 5.46/5.81
% 5.46/5.81 % abs_division_segment
% 5.46/5.81 thf(fact_10058_division__segment__nat__def,axiom,
% 5.46/5.81 ( euclid3398187327856392827nt_nat
% 5.46/5.81 = ( ^ [N2: nat] : one_one_nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % division_segment_nat_def
% 5.46/5.81 thf(fact_10059_division__segment__eq__sgn,axiom,
% 5.46/5.81 ! [K: int] :
% 5.46/5.81 ( ( K != zero_zero_int )
% 5.46/5.81 => ( ( euclid3395696857347342551nt_int @ K )
% 5.46/5.81 = ( sgn_sgn_int @ K ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % division_segment_eq_sgn
% 5.46/5.81 thf(fact_10060_division__segment__int__def,axiom,
% 5.46/5.81 ( euclid3395696857347342551nt_int
% 5.46/5.81 = ( ^ [K3: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % division_segment_int_def
% 5.46/5.81 thf(fact_10061_less__eq__enat__def,axiom,
% 5.46/5.81 ( ord_le2932123472753598470d_enat
% 5.46/5.81 = ( ^ [M6: extended_enat] :
% 5.46/5.81 ( extended_case_enat_o
% 5.46/5.81 @ ^ [N1: nat] :
% 5.46/5.81 ( extended_case_enat_o
% 5.46/5.81 @ ^ [M1: nat] : ( ord_less_eq_nat @ M1 @ N1 )
% 5.46/5.81 @ $false
% 5.46/5.81 @ M6 )
% 5.46/5.81 @ $true ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_eq_enat_def
% 5.46/5.81 thf(fact_10062_transp__realrel,axiom,
% 5.46/5.81 transp_nat_rat @ realrel ).
% 5.46/5.81
% 5.46/5.81 % transp_realrel
% 5.46/5.81 thf(fact_10063_less__enat__def,axiom,
% 5.46/5.81 ( ord_le72135733267957522d_enat
% 5.46/5.81 = ( ^ [M6: extended_enat,N2: extended_enat] :
% 5.46/5.81 ( extended_case_enat_o
% 5.46/5.81 @ ^ [M1: nat] : ( extended_case_enat_o @ ( ord_less_nat @ M1 ) @ $true @ N2 )
% 5.46/5.81 @ $false
% 5.46/5.81 @ M6 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_enat_def
% 5.46/5.81 thf(fact_10064_Divides_Oadjust__div__def,axiom,
% 5.46/5.81 ( adjust_div
% 5.46/5.81 = ( produc8211389475949308722nt_int
% 5.46/5.81 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Divides.adjust_div_def
% 5.46/5.81 thf(fact_10065_rat__floor__code,axiom,
% 5.46/5.81 ( archim3151403230148437115or_rat
% 5.46/5.81 = ( ^ [P3: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P3 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % rat_floor_code
% 5.46/5.81 thf(fact_10066_prod__decode__triangle__add,axiom,
% 5.46/5.81 ! [K: nat,M: nat] :
% 5.46/5.81 ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) )
% 5.46/5.81 = ( nat_prod_decode_aux @ K @ M ) ) ).
% 5.46/5.81
% 5.46/5.81 % prod_decode_triangle_add
% 5.46/5.81 thf(fact_10067_list__decode_Opinduct,axiom,
% 5.46/5.81 ! [A0: nat,P: nat > $o] :
% 5.46/5.81 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 5.46/5.81 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 5.46/5.81 => ( P @ zero_zero_nat ) )
% 5.46/5.81 => ( ! [N4: nat] :
% 5.46/5.81 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N4 ) )
% 5.46/5.81 => ( ! [X5: nat,Y5: nat] :
% 5.46/5.81 ( ( ( product_Pair_nat_nat @ X5 @ Y5 )
% 5.46/5.81 = ( nat_prod_decode @ N4 ) )
% 5.46/5.81 => ( P @ Y5 ) )
% 5.46/5.81 => ( P @ ( suc @ N4 ) ) ) )
% 5.46/5.81 => ( P @ A0 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % list_decode.pinduct
% 5.46/5.81 thf(fact_10068_list__decode_Oelims,axiom,
% 5.46/5.81 ! [X4: nat,Y3: list_nat] :
% 5.46/5.81 ( ( ( nat_list_decode @ X4 )
% 5.46/5.81 = Y3 )
% 5.46/5.81 => ( ( ( X4 = zero_zero_nat )
% 5.46/5.81 => ( Y3 != nil_nat ) )
% 5.46/5.81 => ~ ! [N4: nat] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( suc @ N4 ) )
% 5.46/5.81 => ( Y3
% 5.46/5.81 != ( produc2761476792215241774st_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y ) )
% 5.46/5.81 @ ( nat_prod_decode @ N4 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % list_decode.elims
% 5.46/5.81 thf(fact_10069_list__decode_Opsimps_I2_J,axiom,
% 5.46/5.81 ! [N: nat] :
% 5.46/5.81 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 5.46/5.81 => ( ( nat_list_decode @ ( suc @ N ) )
% 5.46/5.81 = ( produc2761476792215241774st_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y ) )
% 5.46/5.81 @ ( nat_prod_decode @ N ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % list_decode.psimps(2)
% 5.46/5.81 thf(fact_10070_list__decode_Osimps_I2_J,axiom,
% 5.46/5.81 ! [N: nat] :
% 5.46/5.81 ( ( nat_list_decode @ ( suc @ N ) )
% 5.46/5.81 = ( produc2761476792215241774st_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y ) )
% 5.46/5.81 @ ( nat_prod_decode @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % list_decode.simps(2)
% 5.46/5.81 thf(fact_10071_list__decode_Opelims,axiom,
% 5.46/5.81 ! [X4: nat,Y3: list_nat] :
% 5.46/5.81 ( ( ( nat_list_decode @ X4 )
% 5.46/5.81 = Y3 )
% 5.46/5.81 => ( ( accp_nat @ nat_list_decode_rel @ X4 )
% 5.46/5.81 => ( ( ( X4 = zero_zero_nat )
% 5.46/5.81 => ( ( Y3 = nil_nat )
% 5.46/5.81 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 5.46/5.81 => ~ ! [N4: nat] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( suc @ N4 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( produc2761476792215241774st_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] : ( cons_nat @ X @ ( nat_list_decode @ Y ) )
% 5.46/5.81 @ ( nat_prod_decode @ N4 ) ) )
% 5.46/5.81 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N4 ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % list_decode.pelims
% 5.46/5.81 thf(fact_10072_compute__powr__real,axiom,
% 5.46/5.81 ( powr_real2
% 5.46/5.81 = ( ^ [B3: real,I2: real] :
% 5.46/5.81 ( if_real @ ( ord_less_eq_real @ B3 @ zero_zero_real )
% 5.46/5.81 @ ( abort_real @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.81 @ ^ [Uu: product_unit] : ( powr_real2 @ B3 @ I2 ) )
% 5.46/5.81 @ ( if_real
% 5.46/5.81 @ ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ I2 ) )
% 5.46/5.81 = I2 )
% 5.46/5.81 @ ( if_real @ ( ord_less_eq_real @ zero_zero_real @ I2 ) @ ( power_power_real @ B3 @ ( nat2 @ ( archim6058952711729229775r_real @ I2 ) ) ) @ ( divide_divide_real @ one_one_real @ ( power_power_real @ B3 @ ( nat2 @ ( archim6058952711729229775r_real @ ( uminus_uminus_real @ I2 ) ) ) ) ) )
% 5.46/5.81 @ ( abort_real @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $true @ $false @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $true @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $true @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $false @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $false @ $true @ $false @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $true @ $true @ $true @ $true @ ( literal2 @ $false @ $false @ $false @ $false @ $true @ $true @ $true @ ( literal2 @ $true @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $true @ $false @ $true @ $false @ $false @ $true @ $true @ ( literal2 @ $false @ $true @ $true @ $true @ $false @ $true @ $true @ ( literal2 @ $false @ $false @ $true @ $false @ $true @ $true @ $true @ zero_zero_literal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.46/5.81 @ ^ [Uu: product_unit] : ( powr_real2 @ B3 @ I2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % compute_powr_real
% 5.46/5.81 thf(fact_10073_pairs__le__eq__Sigma,axiom,
% 5.46/5.81 ! [M: nat] :
% 5.46/5.81 ( ( collec3392354462482085612at_nat
% 5.46/5.81 @ ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [I2: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ J3 ) @ M ) ) )
% 5.46/5.81 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.46/5.81 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % pairs_le_eq_Sigma
% 5.46/5.81 thf(fact_10074_product__atMost__eq__Un,axiom,
% 5.46/5.81 ! [A3: set_nat,M: nat] :
% 5.46/5.81 ( ( produc457027306803732586at_nat @ A3
% 5.46/5.81 @ ^ [Uu: nat] : ( set_ord_atMost_nat @ M ) )
% 5.46/5.81 = ( sup_su6327502436637775413at_nat
% 5.46/5.81 @ ( produc457027306803732586at_nat @ A3
% 5.46/5.81 @ ^ [I2: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ I2 ) ) )
% 5.46/5.81 @ ( produc457027306803732586at_nat @ A3
% 5.46/5.81 @ ^ [I2: nat] : ( set_or6659071591806873216st_nat @ ( minus_minus_nat @ M @ I2 ) @ M ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % product_atMost_eq_Un
% 5.46/5.81 thf(fact_10075_of__nat__eq__id,axiom,
% 5.46/5.81 semiri1316708129612266289at_nat = id_nat ).
% 5.46/5.81
% 5.46/5.81 % of_nat_eq_id
% 5.46/5.81 thf(fact_10076_Real_Opositive__def,axiom,
% 5.46/5.81 ( positive2
% 5.46/5.81 = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 5.46/5.81 @ ^ [X6: nat > rat] :
% 5.46/5.81 ? [R5: rat] :
% 5.46/5.81 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.46/5.81 & ? [K3: nat] :
% 5.46/5.81 ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ K3 @ N2 )
% 5.46/5.81 => ( ord_less_rat @ R5 @ ( X6 @ N2 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Real.positive_def
% 5.46/5.81 thf(fact_10077_euclidean__size__nat__def,axiom,
% 5.46/5.81 euclid4777050414544973029ze_nat = id_nat ).
% 5.46/5.81
% 5.46/5.81 % euclidean_size_nat_def
% 5.46/5.81 thf(fact_10078_times__rat__def,axiom,
% 5.46/5.81 ( times_times_rat
% 5.46/5.81 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.46/5.81 @ ^ [X: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_fst_int_int @ Y ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_rat_def
% 5.46/5.81 thf(fact_10079_plus__rat__def,axiom,
% 5.46/5.81 ( plus_plus_rat
% 5.46/5.81 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.46/5.81 @ ^ [X: product_prod_int_int,Y: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) ) @ ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X ) @ ( product_snd_int_int @ Y ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_rat_def
% 5.46/5.81 thf(fact_10080_Rat_Opositive__def,axiom,
% 5.46/5.81 ( positive
% 5.46/5.81 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.46/5.81 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Rat.positive_def
% 5.46/5.81 thf(fact_10081_nat__def,axiom,
% 5.46/5.81 ( nat2
% 5.46/5.81 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % nat_def
% 5.46/5.81 thf(fact_10082_less__int__def,axiom,
% 5.46/5.81 ( ord_less_int
% 5.46/5.81 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.46/5.81 @ ( produc8739625826339149834_nat_o
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U4 @ Y ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_int_def
% 5.46/5.81 thf(fact_10083_less__eq__int__def,axiom,
% 5.46/5.81 ( ord_less_eq_int
% 5.46/5.81 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.46/5.81 @ ( produc8739625826339149834_nat_o
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc6081775807080527818_nat_o
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U4 @ Y ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_eq_int_def
% 5.46/5.81 thf(fact_10084_plus__int__def,axiom,
% 5.46/5.81 ( plus_plus_int
% 5.46/5.81 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U4 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_int_def
% 5.46/5.81 thf(fact_10085_minus__int__def,axiom,
% 5.46/5.81 ( minus_minus_int
% 5.46/5.81 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U4 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % minus_int_def
% 5.46/5.81 thf(fact_10086_times__int__def,axiom,
% 5.46/5.81 ( times_times_int
% 5.46/5.81 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.46/5.81 @ ( produc27273713700761075at_nat
% 5.46/5.81 @ ^ [X: nat,Y: nat] :
% 5.46/5.81 ( produc2626176000494625587at_nat
% 5.46/5.81 @ ^ [U4: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U4 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U4 ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_int_def
% 5.46/5.81 thf(fact_10087_eventually__prod__sequentially,axiom,
% 5.46/5.81 ! [P: product_prod_nat_nat > $o] :
% 5.46/5.81 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.46/5.81 = ( ? [N8: nat] :
% 5.46/5.81 ! [M6: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ N8 @ M6 )
% 5.46/5.81 => ! [N2: nat] :
% 5.46/5.81 ( ( ord_less_eq_nat @ N8 @ N2 )
% 5.46/5.81 => ( P @ ( product_Pair_nat_nat @ N2 @ M6 ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % eventually_prod_sequentially
% 5.46/5.81 thf(fact_10088_less__eq,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.46/5.81 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_eq
% 5.46/5.81 thf(fact_10089_numeral__le__enat__iff,axiom,
% 5.46/5.81 ! [M: num,N: nat] :
% 5.46/5.81 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( extended_enat2 @ N ) )
% 5.46/5.81 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % numeral_le_enat_iff
% 5.46/5.81 thf(fact_10090_enat_Oinject,axiom,
% 5.46/5.81 ! [Nat: nat,Nat2: nat] :
% 5.46/5.81 ( ( ( extended_enat2 @ Nat )
% 5.46/5.81 = ( extended_enat2 @ Nat2 ) )
% 5.46/5.81 = ( Nat = Nat2 ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat.inject
% 5.46/5.81 thf(fact_10091_enat__ord__simps_I2_J,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.46/5.81 = ( ord_less_nat @ M @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ord_simps(2)
% 5.46/5.81 thf(fact_10092_enat__ord__simps_I1_J,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.46/5.81 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ord_simps(1)
% 5.46/5.81 thf(fact_10093_plus__enat__simps_I1_J,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( plus_p3455044024723400733d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.46/5.81 = ( extended_enat2 @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_enat_simps(1)
% 5.46/5.81 thf(fact_10094_idiff__enat__0__right,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ( ( minus_3235023915231533773d_enat @ N @ ( extended_enat2 @ zero_zero_nat ) )
% 5.46/5.81 = N ) ).
% 5.46/5.81
% 5.46/5.81 % idiff_enat_0_right
% 5.46/5.81 thf(fact_10095_idiff__enat__0,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N )
% 5.46/5.81 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % idiff_enat_0
% 5.46/5.81 thf(fact_10096_idiff__enat__enat,axiom,
% 5.46/5.81 ! [A: nat,B2: nat] :
% 5.46/5.81 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B2 ) )
% 5.46/5.81 = ( extended_enat2 @ ( minus_minus_nat @ A @ B2 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % idiff_enat_enat
% 5.46/5.81 thf(fact_10097_times__enat__simps_I1_J,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.46/5.81 = ( extended_enat2 @ ( times_times_nat @ M @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_enat_simps(1)
% 5.46/5.81 thf(fact_10098_max__enat__simps_I1_J,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( ord_ma741700101516333627d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.46/5.81 = ( extended_enat2 @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % max_enat_simps(1)
% 5.46/5.81 thf(fact_10099_min__enat__simps_I1_J,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( ord_mi8085742599997312461d_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 5.46/5.81 = ( extended_enat2 @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % min_enat_simps(1)
% 5.46/5.81 thf(fact_10100_numeral__less__enat__iff,axiom,
% 5.46/5.81 ! [M: num,N: nat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( extended_enat2 @ N ) )
% 5.46/5.81 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % numeral_less_enat_iff
% 5.46/5.81 thf(fact_10101_zero__enat__def,axiom,
% 5.46/5.81 ( zero_z5237406670263579293d_enat
% 5.46/5.81 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % zero_enat_def
% 5.46/5.81 thf(fact_10102_enat__0__iff_I1_J,axiom,
% 5.46/5.81 ! [X4: nat] :
% 5.46/5.81 ( ( ( extended_enat2 @ X4 )
% 5.46/5.81 = zero_z5237406670263579293d_enat )
% 5.46/5.81 = ( X4 = zero_zero_nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_0_iff(1)
% 5.46/5.81 thf(fact_10103_enat__0__iff_I2_J,axiom,
% 5.46/5.81 ! [X4: nat] :
% 5.46/5.81 ( ( zero_z5237406670263579293d_enat
% 5.46/5.81 = ( extended_enat2 @ X4 ) )
% 5.46/5.81 = ( X4 = zero_zero_nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_0_iff(2)
% 5.46/5.81 thf(fact_10104_of__nat__eq__enat,axiom,
% 5.46/5.81 semiri4216267220026989637d_enat = extended_enat2 ).
% 5.46/5.81
% 5.46/5.81 % of_nat_eq_enat
% 5.46/5.81 thf(fact_10105_enat__iless,axiom,
% 5.46/5.81 ! [N: extended_enat,M: nat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M ) )
% 5.46/5.81 => ? [K2: nat] :
% 5.46/5.81 ( N
% 5.46/5.81 = ( extended_enat2 @ K2 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_iless
% 5.46/5.81 thf(fact_10106_less__enatE,axiom,
% 5.46/5.81 ! [N: extended_enat,M: nat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ N @ ( extended_enat2 @ M ) )
% 5.46/5.81 => ~ ! [K2: nat] :
% 5.46/5.81 ( ( N
% 5.46/5.81 = ( extended_enat2 @ K2 ) )
% 5.46/5.81 => ~ ( ord_less_nat @ K2 @ M ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_enatE
% 5.46/5.81 thf(fact_10107_one__enat__def,axiom,
% 5.46/5.81 ( one_on7984719198319812577d_enat
% 5.46/5.81 = ( extended_enat2 @ one_one_nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % one_enat_def
% 5.46/5.81 thf(fact_10108_enat__1__iff_I1_J,axiom,
% 5.46/5.81 ! [X4: nat] :
% 5.46/5.81 ( ( ( extended_enat2 @ X4 )
% 5.46/5.81 = one_on7984719198319812577d_enat )
% 5.46/5.81 = ( X4 = one_one_nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_1_iff(1)
% 5.46/5.81 thf(fact_10109_enat__1__iff_I2_J,axiom,
% 5.46/5.81 ! [X4: nat] :
% 5.46/5.81 ( ( one_on7984719198319812577d_enat
% 5.46/5.81 = ( extended_enat2 @ X4 ) )
% 5.46/5.81 = ( X4 = one_one_nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_1_iff(2)
% 5.46/5.81 thf(fact_10110_numeral__eq__enat,axiom,
% 5.46/5.81 ( numera1916890842035813515d_enat
% 5.46/5.81 = ( ^ [K3: num] : ( extended_enat2 @ ( numeral_numeral_nat @ K3 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % numeral_eq_enat
% 5.46/5.81 thf(fact_10111_Suc__ile__eq,axiom,
% 5.46/5.81 ! [M: nat,N: extended_enat] :
% 5.46/5.81 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M ) ) @ N )
% 5.46/5.81 = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % Suc_ile_eq
% 5.46/5.81 thf(fact_10112_finite__enat__bounded,axiom,
% 5.46/5.81 ! [A3: set_Extended_enat,N: nat] :
% 5.46/5.81 ( ! [Y4: extended_enat] :
% 5.46/5.81 ( ( member_Extended_enat @ Y4 @ A3 )
% 5.46/5.81 => ( ord_le2932123472753598470d_enat @ Y4 @ ( extended_enat2 @ N ) ) )
% 5.46/5.81 => ( finite4001608067531595151d_enat @ A3 ) ) ).
% 5.46/5.81
% 5.46/5.81 % finite_enat_bounded
% 5.46/5.81 thf(fact_10113_enat__ile,axiom,
% 5.46/5.81 ! [N: extended_enat,M: nat] :
% 5.46/5.81 ( ( ord_le2932123472753598470d_enat @ N @ ( extended_enat2 @ M ) )
% 5.46/5.81 => ? [K2: nat] :
% 5.46/5.81 ( N
% 5.46/5.81 = ( extended_enat2 @ K2 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ile
% 5.46/5.81 thf(fact_10114_pred__nat__trancl__eq__le,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.46/5.81 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % pred_nat_trancl_eq_le
% 5.46/5.81 thf(fact_10115_iadd__le__enat__iff,axiom,
% 5.46/5.81 ! [X4: extended_enat,Y3: extended_enat,N: nat] :
% 5.46/5.81 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ X4 @ Y3 ) @ ( extended_enat2 @ N ) )
% 5.46/5.81 = ( ? [Y9: nat,X9: nat] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( extended_enat2 @ X9 ) )
% 5.46/5.81 & ( Y3
% 5.46/5.81 = ( extended_enat2 @ Y9 ) )
% 5.46/5.81 & ( ord_less_eq_nat @ ( plus_plus_nat @ X9 @ Y9 ) @ N ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % iadd_le_enat_iff
% 5.46/5.81 thf(fact_10116_elimnum,axiom,
% 5.46/5.81 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.46/5.81 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 5.46/5.81 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.46/5.81 = ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % elimnum
% 5.46/5.81 thf(fact_10117_VEBT__internal_Oelim__dead_Osimps_I3_J,axiom,
% 5.46/5.81 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,L2: nat] :
% 5.46/5.81 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ L2 ) )
% 5.46/5.81 = ( vEBT_Node @ Info @ Deg
% 5.46/5.81 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.81 @ ( map_VE8901447254227204932T_VEBT
% 5.46/5.81 @ ^ [T3: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T3 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.81 @ TreeList2 ) )
% 5.46/5.81 @ ( vEBT_VEBT_elim_dead @ Summary @ ( extended_enat2 @ ( divide_divide_nat @ L2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % VEBT_internal.elim_dead.simps(3)
% 5.46/5.81 thf(fact_10118_VEBT__internal_Oelim__dead_Oelims,axiom,
% 5.46/5.81 ! [X4: vEBT_VEBT,Xa: extended_enat,Y3: vEBT_VEBT] :
% 5.46/5.81 ( ( ( vEBT_VEBT_elim_dead @ X4 @ Xa )
% 5.46/5.81 = Y3 )
% 5.46/5.81 => ( ! [A5: $o,B5: $o] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.81 => ( Y3
% 5.46/5.81 != ( vEBT_Leaf @ A5 @ B5 ) ) )
% 5.46/5.81 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.81 => ( ( Xa = extend5688581933313929465d_enat )
% 5.46/5.81 => ( Y3
% 5.46/5.81 != ( vEBT_Node @ Info2 @ Deg2
% 5.46/5.81 @ ( map_VE8901447254227204932T_VEBT
% 5.46/5.81 @ ^ [T3: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T3 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.81 @ TreeList3 )
% 5.46/5.81 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) ) ) )
% 5.46/5.81 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.81 => ! [L3: nat] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( extended_enat2 @ L3 ) )
% 5.46/5.81 => ( Y3
% 5.46/5.81 != ( vEBT_Node @ Info2 @ Deg2
% 5.46/5.81 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.81 @ ( map_VE8901447254227204932T_VEBT
% 5.46/5.81 @ ^ [T3: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T3 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.81 @ TreeList3 ) )
% 5.46/5.81 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % VEBT_internal.elim_dead.elims
% 5.46/5.81 thf(fact_10119_VEBT__internal_Oelim__dead_Osimps_I2_J,axiom,
% 5.46/5.81 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.46/5.81 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 5.46/5.81 = ( vEBT_Node @ Info @ Deg
% 5.46/5.81 @ ( map_VE8901447254227204932T_VEBT
% 5.46/5.81 @ ^ [T3: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T3 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.81 @ TreeList2 )
% 5.46/5.81 @ ( vEBT_VEBT_elim_dead @ Summary @ extend5688581933313929465d_enat ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % VEBT_internal.elim_dead.simps(2)
% 5.46/5.81 thf(fact_10120_elimcomplete,axiom,
% 5.46/5.81 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.46/5.81 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 5.46/5.81 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 5.46/5.81 = ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % elimcomplete
% 5.46/5.81 thf(fact_10121_not__infinity__eq,axiom,
% 5.46/5.81 ! [X4: extended_enat] :
% 5.46/5.81 ( ( X4 != extend5688581933313929465d_enat )
% 5.46/5.81 = ( ? [I2: nat] :
% 5.46/5.81 ( X4
% 5.46/5.81 = ( extended_enat2 @ I2 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % not_infinity_eq
% 5.46/5.81 thf(fact_10122_not__enat__eq,axiom,
% 5.46/5.81 ! [X4: extended_enat] :
% 5.46/5.81 ( ( ! [Y: nat] :
% 5.46/5.81 ( X4
% 5.46/5.81 != ( extended_enat2 @ Y ) ) )
% 5.46/5.81 = ( X4 = extend5688581933313929465d_enat ) ) ).
% 5.46/5.81
% 5.46/5.81 % not_enat_eq
% 5.46/5.81 thf(fact_10123_enat__ord__simps_I4_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ Q2 @ extend5688581933313929465d_enat )
% 5.46/5.81 = ( Q2 != extend5688581933313929465d_enat ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ord_simps(4)
% 5.46/5.81 thf(fact_10124_enat__ord__simps_I6_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ~ ( ord_le72135733267957522d_enat @ extend5688581933313929465d_enat @ Q2 ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ord_simps(6)
% 5.46/5.81 thf(fact_10125_plus__enat__simps_I2_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ( ( plus_p3455044024723400733d_enat @ extend5688581933313929465d_enat @ Q2 )
% 5.46/5.81 = extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % plus_enat_simps(2)
% 5.46/5.81 thf(fact_10126_plus__enat__simps_I3_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ( ( plus_p3455044024723400733d_enat @ Q2 @ extend5688581933313929465d_enat )
% 5.46/5.81 = extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % plus_enat_simps(3)
% 5.46/5.81 thf(fact_10127_enat__ord__code_I3_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] : ( ord_le2932123472753598470d_enat @ Q2 @ extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ord_code(3)
% 5.46/5.81 thf(fact_10128_enat__ord__simps_I5_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ( ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ Q2 )
% 5.46/5.81 = ( Q2 = extend5688581933313929465d_enat ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ord_simps(5)
% 5.46/5.81 thf(fact_10129_idiff__infinity,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ( ( minus_3235023915231533773d_enat @ extend5688581933313929465d_enat @ N )
% 5.46/5.81 = extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % idiff_infinity
% 5.46/5.81 thf(fact_10130_times__enat__simps_I2_J,axiom,
% 5.46/5.81 ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ extend5688581933313929465d_enat )
% 5.46/5.81 = extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % times_enat_simps(2)
% 5.46/5.81 thf(fact_10131_max__enat__simps_I4_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ( ( ord_ma741700101516333627d_enat @ Q2 @ extend5688581933313929465d_enat )
% 5.46/5.81 = extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % max_enat_simps(4)
% 5.46/5.81 thf(fact_10132_max__enat__simps_I5_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ( ( ord_ma741700101516333627d_enat @ extend5688581933313929465d_enat @ Q2 )
% 5.46/5.81 = extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % max_enat_simps(5)
% 5.46/5.81 thf(fact_10133_min__enat__simps_I4_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ( ( ord_mi8085742599997312461d_enat @ Q2 @ extend5688581933313929465d_enat )
% 5.46/5.81 = Q2 ) ).
% 5.46/5.81
% 5.46/5.81 % min_enat_simps(4)
% 5.46/5.81 thf(fact_10134_min__enat__simps_I5_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ( ( ord_mi8085742599997312461d_enat @ extend5688581933313929465d_enat @ Q2 )
% 5.46/5.81 = Q2 ) ).
% 5.46/5.81
% 5.46/5.81 % min_enat_simps(5)
% 5.46/5.81 thf(fact_10135_idiff__self,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ( ( N != extend5688581933313929465d_enat )
% 5.46/5.81 => ( ( minus_3235023915231533773d_enat @ N @ N )
% 5.46/5.81 = zero_z5237406670263579293d_enat ) ) ).
% 5.46/5.81
% 5.46/5.81 % idiff_self
% 5.46/5.81 thf(fact_10136_add__diff__cancel__enat,axiom,
% 5.46/5.81 ! [X4: extended_enat,Y3: extended_enat] :
% 5.46/5.81 ( ( X4 != extend5688581933313929465d_enat )
% 5.46/5.81 => ( ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X4 @ Y3 ) @ X4 )
% 5.46/5.81 = Y3 ) ) ).
% 5.46/5.81
% 5.46/5.81 % add_diff_cancel_enat
% 5.46/5.81 thf(fact_10137_idiff__infinity__right,axiom,
% 5.46/5.81 ! [A: nat] :
% 5.46/5.81 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ A ) @ extend5688581933313929465d_enat )
% 5.46/5.81 = zero_z5237406670263579293d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % idiff_infinity_right
% 5.46/5.81 thf(fact_10138_times__enat__simps_I3_J,axiom,
% 5.46/5.81 ! [N: nat] :
% 5.46/5.81 ( ( ( N = zero_zero_nat )
% 5.46/5.81 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 5.46/5.81 = zero_z5237406670263579293d_enat ) )
% 5.46/5.81 & ( ( N != zero_zero_nat )
% 5.46/5.81 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 5.46/5.81 = extend5688581933313929465d_enat ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_enat_simps(3)
% 5.46/5.81 thf(fact_10139_times__enat__simps_I4_J,axiom,
% 5.46/5.81 ! [M: nat] :
% 5.46/5.81 ( ( ( M = zero_zero_nat )
% 5.46/5.81 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat )
% 5.46/5.81 = zero_z5237406670263579293d_enat ) )
% 5.46/5.81 & ( ( M != zero_zero_nat )
% 5.46/5.81 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat )
% 5.46/5.81 = extend5688581933313929465d_enat ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_enat_simps(4)
% 5.46/5.81 thf(fact_10140_Sup__enat__def,axiom,
% 5.46/5.81 ( comple4398354569131411667d_enat
% 5.46/5.81 = ( ^ [A6: set_Extended_enat] : ( if_Extended_enat @ ( A6 = bot_bo7653980558646680370d_enat ) @ zero_z5237406670263579293d_enat @ ( if_Extended_enat @ ( finite4001608067531595151d_enat @ A6 ) @ ( lattic921264341876707157d_enat @ A6 ) @ extend5688581933313929465d_enat ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Sup_enat_def
% 5.46/5.81 thf(fact_10141_Inf__enat__def,axiom,
% 5.46/5.81 ( comple2295165028678016749d_enat
% 5.46/5.81 = ( ^ [A6: set_Extended_enat] :
% 5.46/5.81 ( if_Extended_enat @ ( A6 = bot_bo7653980558646680370d_enat ) @ extend5688581933313929465d_enat
% 5.46/5.81 @ ( ord_Le1955565732374568822d_enat
% 5.46/5.81 @ ^ [X: extended_enat] : ( member_Extended_enat @ X @ A6 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % Inf_enat_def
% 5.46/5.81 thf(fact_10142_imult__is__infinity,axiom,
% 5.46/5.81 ! [A: extended_enat,B2: extended_enat] :
% 5.46/5.81 ( ( ( times_7803423173614009249d_enat @ A @ B2 )
% 5.46/5.81 = extend5688581933313929465d_enat )
% 5.46/5.81 = ( ( ( A = extend5688581933313929465d_enat )
% 5.46/5.81 & ( B2 != zero_z5237406670263579293d_enat ) )
% 5.46/5.81 | ( ( B2 = extend5688581933313929465d_enat )
% 5.46/5.81 & ( A != zero_z5237406670263579293d_enat ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % imult_is_infinity
% 5.46/5.81 thf(fact_10143_infinity__ne__i0,axiom,
% 5.46/5.81 extend5688581933313929465d_enat != zero_z5237406670263579293d_enat ).
% 5.46/5.81
% 5.46/5.81 % infinity_ne_i0
% 5.46/5.81 thf(fact_10144_enat__add__left__cancel__less,axiom,
% 5.46/5.81 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ ( plus_p3455044024723400733d_enat @ A @ C ) )
% 5.46/5.81 = ( ( A != extend5688581933313929465d_enat )
% 5.46/5.81 & ( ord_le72135733267957522d_enat @ B2 @ C ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_add_left_cancel_less
% 5.46/5.81 thf(fact_10145_infinity__ne__i1,axiom,
% 5.46/5.81 extend5688581933313929465d_enat != one_on7984719198319812577d_enat ).
% 5.46/5.81
% 5.46/5.81 % infinity_ne_i1
% 5.46/5.81 thf(fact_10146_plus__eq__infty__iff__enat,axiom,
% 5.46/5.81 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.81 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.46/5.81 = extend5688581933313929465d_enat )
% 5.46/5.81 = ( ( M = extend5688581933313929465d_enat )
% 5.46/5.81 | ( N = extend5688581933313929465d_enat ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_eq_infty_iff_enat
% 5.46/5.81 thf(fact_10147_enat__add__left__cancel,axiom,
% 5.46/5.81 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 5.46/5.81 ( ( ( plus_p3455044024723400733d_enat @ A @ B2 )
% 5.46/5.81 = ( plus_p3455044024723400733d_enat @ A @ C ) )
% 5.46/5.81 = ( ( A = extend5688581933313929465d_enat )
% 5.46/5.81 | ( B2 = C ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_add_left_cancel
% 5.46/5.81 thf(fact_10148_numeral__ne__infinity,axiom,
% 5.46/5.81 ! [K: num] :
% 5.46/5.81 ( ( numera1916890842035813515d_enat @ K )
% 5.46/5.81 != extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % numeral_ne_infinity
% 5.46/5.81 thf(fact_10149_top__enat__def,axiom,
% 5.46/5.81 top_to3028658606643905974d_enat = extend5688581933313929465d_enat ).
% 5.46/5.81
% 5.46/5.81 % top_enat_def
% 5.46/5.81 thf(fact_10150_enat__ord__simps_I3_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] : ( ord_le2932123472753598470d_enat @ Q2 @ extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ord_simps(3)
% 5.46/5.81 thf(fact_10151_enat__add__left__cancel__le,axiom,
% 5.46/5.81 ! [A: extended_enat,B2: extended_enat,C: extended_enat] :
% 5.46/5.81 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ A @ B2 ) @ ( plus_p3455044024723400733d_enat @ A @ C ) )
% 5.46/5.81 = ( ( A = extend5688581933313929465d_enat )
% 5.46/5.81 | ( ord_le2932123472753598470d_enat @ B2 @ C ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_add_left_cancel_le
% 5.46/5.81 thf(fact_10152_enat__ord__code_I5_J,axiom,
% 5.46/5.81 ! [N: nat] :
% 5.46/5.81 ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ord_code(5)
% 5.46/5.81 thf(fact_10153_infinity__ileE,axiom,
% 5.46/5.81 ! [M: nat] :
% 5.46/5.81 ~ ( ord_le2932123472753598470d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M ) ) ).
% 5.46/5.81
% 5.46/5.81 % infinity_ileE
% 5.46/5.81 thf(fact_10154_enat__ex__split,axiom,
% 5.46/5.81 ( ( ^ [P5: extended_enat > $o] :
% 5.46/5.81 ? [X7: extended_enat] : ( P5 @ X7 ) )
% 5.46/5.81 = ( ^ [P6: extended_enat > $o] :
% 5.46/5.81 ( ( P6 @ extend5688581933313929465d_enat )
% 5.46/5.81 | ? [X: nat] : ( P6 @ ( extended_enat2 @ X ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ex_split
% 5.46/5.81 thf(fact_10155_enat3__cases,axiom,
% 5.46/5.81 ! [Y3: extended_enat,Ya: extended_enat,Yb: extended_enat] :
% 5.46/5.81 ( ( ? [Nat3: nat] :
% 5.46/5.81 ( Y3
% 5.46/5.81 = ( extended_enat2 @ Nat3 ) )
% 5.46/5.81 => ( ? [Nata: nat] :
% 5.46/5.81 ( Ya
% 5.46/5.81 = ( extended_enat2 @ Nata ) )
% 5.46/5.81 => ! [Natb: nat] :
% 5.46/5.81 ( Yb
% 5.46/5.81 != ( extended_enat2 @ Natb ) ) ) )
% 5.46/5.81 => ( ( ? [Nat3: nat] :
% 5.46/5.81 ( Y3
% 5.46/5.81 = ( extended_enat2 @ Nat3 ) )
% 5.46/5.81 => ( ? [Nata: nat] :
% 5.46/5.81 ( Ya
% 5.46/5.81 = ( extended_enat2 @ Nata ) )
% 5.46/5.81 => ( Yb != extend5688581933313929465d_enat ) ) )
% 5.46/5.81 => ( ( ? [Nat3: nat] :
% 5.46/5.81 ( Y3
% 5.46/5.81 = ( extended_enat2 @ Nat3 ) )
% 5.46/5.81 => ( ( Ya = extend5688581933313929465d_enat )
% 5.46/5.81 => ! [Nata: nat] :
% 5.46/5.81 ( Yb
% 5.46/5.81 != ( extended_enat2 @ Nata ) ) ) )
% 5.46/5.81 => ( ( ? [Nat3: nat] :
% 5.46/5.81 ( Y3
% 5.46/5.81 = ( extended_enat2 @ Nat3 ) )
% 5.46/5.81 => ( ( Ya = extend5688581933313929465d_enat )
% 5.46/5.81 => ( Yb != extend5688581933313929465d_enat ) ) )
% 5.46/5.81 => ( ( ( Y3 = extend5688581933313929465d_enat )
% 5.46/5.81 => ( ? [Nat3: nat] :
% 5.46/5.81 ( Ya
% 5.46/5.81 = ( extended_enat2 @ Nat3 ) )
% 5.46/5.81 => ! [Nata: nat] :
% 5.46/5.81 ( Yb
% 5.46/5.81 != ( extended_enat2 @ Nata ) ) ) )
% 5.46/5.81 => ( ( ( Y3 = extend5688581933313929465d_enat )
% 5.46/5.81 => ( ? [Nat3: nat] :
% 5.46/5.81 ( Ya
% 5.46/5.81 = ( extended_enat2 @ Nat3 ) )
% 5.46/5.81 => ( Yb != extend5688581933313929465d_enat ) ) )
% 5.46/5.81 => ( ( ( Y3 = extend5688581933313929465d_enat )
% 5.46/5.81 => ( ( Ya = extend5688581933313929465d_enat )
% 5.46/5.81 => ! [Nat3: nat] :
% 5.46/5.81 ( Yb
% 5.46/5.81 != ( extended_enat2 @ Nat3 ) ) ) )
% 5.46/5.81 => ~ ( ( Y3 = extend5688581933313929465d_enat )
% 5.46/5.81 => ( ( Ya = extend5688581933313929465d_enat )
% 5.46/5.81 => ( Yb != extend5688581933313929465d_enat ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat3_cases
% 5.46/5.81 thf(fact_10156_enat2__cases,axiom,
% 5.46/5.81 ! [Y3: extended_enat,Ya: extended_enat] :
% 5.46/5.81 ( ( ? [Nat3: nat] :
% 5.46/5.81 ( Y3
% 5.46/5.81 = ( extended_enat2 @ Nat3 ) )
% 5.46/5.81 => ! [Nata: nat] :
% 5.46/5.81 ( Ya
% 5.46/5.81 != ( extended_enat2 @ Nata ) ) )
% 5.46/5.81 => ( ( ? [Nat3: nat] :
% 5.46/5.81 ( Y3
% 5.46/5.81 = ( extended_enat2 @ Nat3 ) )
% 5.46/5.81 => ( Ya != extend5688581933313929465d_enat ) )
% 5.46/5.81 => ( ( ( Y3 = extend5688581933313929465d_enat )
% 5.46/5.81 => ! [Nat3: nat] :
% 5.46/5.81 ( Ya
% 5.46/5.81 != ( extended_enat2 @ Nat3 ) ) )
% 5.46/5.81 => ~ ( ( Y3 = extend5688581933313929465d_enat )
% 5.46/5.81 => ( Ya != extend5688581933313929465d_enat ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat2_cases
% 5.46/5.81 thf(fact_10157_enat_Oexhaust,axiom,
% 5.46/5.81 ! [Y3: extended_enat] :
% 5.46/5.81 ( ! [Nat3: nat] :
% 5.46/5.81 ( Y3
% 5.46/5.81 != ( extended_enat2 @ Nat3 ) )
% 5.46/5.81 => ( Y3 = extend5688581933313929465d_enat ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat.exhaust
% 5.46/5.81 thf(fact_10158_enat_Odistinct_I1_J,axiom,
% 5.46/5.81 ! [Nat: nat] :
% 5.46/5.81 ( ( extended_enat2 @ Nat )
% 5.46/5.81 != extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % enat.distinct(1)
% 5.46/5.81 thf(fact_10159_enat_Odistinct_I2_J,axiom,
% 5.46/5.81 ! [Nat: nat] :
% 5.46/5.81 ( extend5688581933313929465d_enat
% 5.46/5.81 != ( extended_enat2 @ Nat ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat.distinct(2)
% 5.46/5.81 thf(fact_10160_infinity__ilessE,axiom,
% 5.46/5.81 ! [M: nat] :
% 5.46/5.81 ~ ( ord_le72135733267957522d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ M ) ) ).
% 5.46/5.81
% 5.46/5.81 % infinity_ilessE
% 5.46/5.81 thf(fact_10161_less__infinityE,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ N @ extend5688581933313929465d_enat )
% 5.46/5.81 => ~ ! [K2: nat] :
% 5.46/5.81 ( N
% 5.46/5.81 != ( extended_enat2 @ K2 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_infinityE
% 5.46/5.81 thf(fact_10162_enat__ord__code_I4_J,axiom,
% 5.46/5.81 ! [M: nat] : ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % enat_ord_code(4)
% 5.46/5.81 thf(fact_10163_imult__infinity,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.46/5.81 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ N )
% 5.46/5.81 = extend5688581933313929465d_enat ) ) ).
% 5.46/5.81
% 5.46/5.81 % imult_infinity
% 5.46/5.81 thf(fact_10164_imult__infinity__right,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.46/5.81 => ( ( times_7803423173614009249d_enat @ N @ extend5688581933313929465d_enat )
% 5.46/5.81 = extend5688581933313929465d_enat ) ) ).
% 5.46/5.81
% 5.46/5.81 % imult_infinity_right
% 5.46/5.81 thf(fact_10165_plus__enat__def,axiom,
% 5.46/5.81 ( plus_p3455044024723400733d_enat
% 5.46/5.81 = ( ^ [M6: extended_enat,N2: extended_enat] :
% 5.46/5.81 ( extend3600170679010898289d_enat
% 5.46/5.81 @ ^ [O: nat] :
% 5.46/5.81 ( extend3600170679010898289d_enat
% 5.46/5.81 @ ^ [P3: nat] : ( extended_enat2 @ ( plus_plus_nat @ O @ P3 ) )
% 5.46/5.81 @ extend5688581933313929465d_enat
% 5.46/5.81 @ N2 )
% 5.46/5.81 @ extend5688581933313929465d_enat
% 5.46/5.81 @ M6 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_enat_def
% 5.46/5.81 thf(fact_10166_diff__enat__def,axiom,
% 5.46/5.81 ( minus_3235023915231533773d_enat
% 5.46/5.81 = ( ^ [A4: extended_enat,B3: extended_enat] :
% 5.46/5.81 ( extend3600170679010898289d_enat
% 5.46/5.81 @ ^ [X: nat] :
% 5.46/5.81 ( extend3600170679010898289d_enat
% 5.46/5.81 @ ^ [Y: nat] : ( extended_enat2 @ ( minus_minus_nat @ X @ Y ) )
% 5.46/5.81 @ zero_z5237406670263579293d_enat
% 5.46/5.81 @ B3 )
% 5.46/5.81 @ extend5688581933313929465d_enat
% 5.46/5.81 @ A4 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % diff_enat_def
% 5.46/5.81 thf(fact_10167_times__enat__def,axiom,
% 5.46/5.81 ( times_7803423173614009249d_enat
% 5.46/5.81 = ( ^ [M6: extended_enat,N2: extended_enat] :
% 5.46/5.81 ( extend3600170679010898289d_enat
% 5.46/5.81 @ ^ [O: nat] :
% 5.46/5.81 ( extend3600170679010898289d_enat
% 5.46/5.81 @ ^ [P3: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P3 ) )
% 5.46/5.81 @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 5.46/5.81 @ N2 )
% 5.46/5.81 @ ( if_Extended_enat @ ( N2 = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 5.46/5.81 @ M6 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % times_enat_def
% 5.46/5.81 thf(fact_10168_VEBT__internal_Oelim__dead_Opelims,axiom,
% 5.46/5.81 ! [X4: vEBT_VEBT,Xa: extended_enat,Y3: vEBT_VEBT] :
% 5.46/5.81 ( ( ( vEBT_VEBT_elim_dead @ X4 @ Xa )
% 5.46/5.81 = Y3 )
% 5.46/5.81 => ( ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ X4 @ Xa ) )
% 5.46/5.81 => ( ! [A5: $o,B5: $o] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.46/5.81 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) ) ) )
% 5.46/5.81 => ( ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.81 => ( ( Xa = extend5688581933313929465d_enat )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( vEBT_Node @ Info2 @ Deg2
% 5.46/5.81 @ ( map_VE8901447254227204932T_VEBT
% 5.46/5.81 @ ^ [T3: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T3 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.81 @ TreeList3 )
% 5.46/5.81 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) )
% 5.46/5.81 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) @ extend5688581933313929465d_enat ) ) ) ) )
% 5.46/5.81 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.46/5.81 ( ( X4
% 5.46/5.81 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.46/5.81 => ! [L3: nat] :
% 5.46/5.81 ( ( Xa
% 5.46/5.81 = ( extended_enat2 @ L3 ) )
% 5.46/5.81 => ( ( Y3
% 5.46/5.81 = ( vEBT_Node @ Info2 @ Deg2
% 5.46/5.81 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.46/5.81 @ ( map_VE8901447254227204932T_VEBT
% 5.46/5.81 @ ^ [T3: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T3 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.46/5.81 @ TreeList3 ) )
% 5.46/5.81 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.46/5.81 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary2 ) @ ( extended_enat2 @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % VEBT_internal.elim_dead.pelims
% 5.46/5.81 thf(fact_10169_the__enat_Osimps,axiom,
% 5.46/5.81 ! [N: nat] :
% 5.46/5.81 ( ( extended_the_enat @ ( extended_enat2 @ N ) )
% 5.46/5.81 = N ) ).
% 5.46/5.81
% 5.46/5.81 % the_enat.simps
% 5.46/5.81 thf(fact_10170_eSuc__Max,axiom,
% 5.46/5.81 ! [A3: set_Extended_enat] :
% 5.46/5.81 ( ( finite4001608067531595151d_enat @ A3 )
% 5.46/5.81 => ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.46/5.81 => ( ( extended_eSuc @ ( lattic921264341876707157d_enat @ A3 ) )
% 5.46/5.81 = ( lattic921264341876707157d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A3 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_Max
% 5.46/5.81 thf(fact_10171_eSuc__inject,axiom,
% 5.46/5.81 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.81 ( ( ( extended_eSuc @ M )
% 5.46/5.81 = ( extended_eSuc @ N ) )
% 5.46/5.81 = ( M = N ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_inject
% 5.46/5.81 thf(fact_10172_eSuc__infinity,axiom,
% 5.46/5.81 ( ( extended_eSuc @ extend5688581933313929465d_enat )
% 5.46/5.81 = extend5688581933313929465d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_infinity
% 5.46/5.81 thf(fact_10173_eSuc__mono,axiom,
% 5.46/5.81 ! [N: extended_enat,M: extended_enat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 5.46/5.81 = ( ord_le72135733267957522d_enat @ N @ M ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_mono
% 5.46/5.81 thf(fact_10174_eSuc__ile__mono,axiom,
% 5.46/5.81 ! [N: extended_enat,M: extended_enat] :
% 5.46/5.81 ( ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 5.46/5.81 = ( ord_le2932123472753598470d_enat @ N @ M ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_ile_mono
% 5.46/5.81 thf(fact_10175_eSuc__minus__eSuc,axiom,
% 5.46/5.81 ! [N: extended_enat,M: extended_enat] :
% 5.46/5.81 ( ( minus_3235023915231533773d_enat @ ( extended_eSuc @ N ) @ ( extended_eSuc @ M ) )
% 5.46/5.81 = ( minus_3235023915231533773d_enat @ N @ M ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_minus_eSuc
% 5.46/5.81 thf(fact_10176_iless__eSuc0,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ N @ ( extended_eSuc @ zero_z5237406670263579293d_enat ) )
% 5.46/5.81 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.46/5.81
% 5.46/5.81 % iless_eSuc0
% 5.46/5.81 thf(fact_10177_eSuc__minus__1,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ( ( minus_3235023915231533773d_enat @ ( extended_eSuc @ N ) @ one_on7984719198319812577d_enat )
% 5.46/5.81 = N ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_minus_1
% 5.46/5.81 thf(fact_10178_eSuc__numeral,axiom,
% 5.46/5.81 ! [K: num] :
% 5.46/5.81 ( ( extended_eSuc @ ( numera1916890842035813515d_enat @ K ) )
% 5.46/5.81 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ K @ one ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_numeral
% 5.46/5.81 thf(fact_10179_iless__Suc__eq,axiom,
% 5.46/5.81 ! [M: nat,N: extended_enat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M ) @ ( extended_eSuc @ N ) )
% 5.46/5.81 = ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M ) @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % iless_Suc_eq
% 5.46/5.81 thf(fact_10180_one__eSuc,axiom,
% 5.46/5.81 ( one_on7984719198319812577d_enat
% 5.46/5.81 = ( extended_eSuc @ zero_z5237406670263579293d_enat ) ) ).
% 5.46/5.81
% 5.46/5.81 % one_eSuc
% 5.46/5.81 thf(fact_10181_i0__iless__eSuc,axiom,
% 5.46/5.81 ! [N: extended_enat] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( extended_eSuc @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % i0_iless_eSuc
% 5.46/5.81 thf(fact_10182_zero__ne__eSuc,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ( zero_z5237406670263579293d_enat
% 5.46/5.81 != ( extended_eSuc @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % zero_ne_eSuc
% 5.46/5.81 thf(fact_10183_eSuc__plus__1,axiom,
% 5.46/5.81 ( extended_eSuc
% 5.46/5.81 = ( ^ [N2: extended_enat] : ( plus_p3455044024723400733d_enat @ N2 @ one_on7984719198319812577d_enat ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_plus_1
% 5.46/5.81 thf(fact_10184_plus__1__eSuc_I1_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ Q2 )
% 5.46/5.81 = ( extended_eSuc @ Q2 ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_1_eSuc(1)
% 5.46/5.81 thf(fact_10185_plus__1__eSuc_I2_J,axiom,
% 5.46/5.81 ! [Q2: extended_enat] :
% 5.46/5.81 ( ( plus_p3455044024723400733d_enat @ Q2 @ one_on7984719198319812577d_enat )
% 5.46/5.81 = ( extended_eSuc @ Q2 ) ) ).
% 5.46/5.81
% 5.46/5.81 % plus_1_eSuc(2)
% 5.46/5.81 thf(fact_10186_mono__eSuc,axiom,
% 5.46/5.81 order_4130057895858720880d_enat @ extended_eSuc ).
% 5.46/5.81
% 5.46/5.81 % mono_eSuc
% 5.46/5.81 thf(fact_10187_iadd__Suc__right,axiom,
% 5.46/5.81 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.81 ( ( plus_p3455044024723400733d_enat @ M @ ( extended_eSuc @ N ) )
% 5.46/5.81 = ( extended_eSuc @ ( plus_p3455044024723400733d_enat @ M @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % iadd_Suc_right
% 5.46/5.81 thf(fact_10188_iadd__Suc,axiom,
% 5.46/5.81 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.81 ( ( plus_p3455044024723400733d_enat @ ( extended_eSuc @ M ) @ N )
% 5.46/5.81 = ( extended_eSuc @ ( plus_p3455044024723400733d_enat @ M @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % iadd_Suc
% 5.46/5.81 thf(fact_10189_eSuc__max,axiom,
% 5.46/5.81 ! [X4: extended_enat,Y3: extended_enat] :
% 5.46/5.81 ( ( extended_eSuc @ ( ord_ma741700101516333627d_enat @ X4 @ Y3 ) )
% 5.46/5.81 = ( ord_ma741700101516333627d_enat @ ( extended_eSuc @ X4 ) @ ( extended_eSuc @ Y3 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_max
% 5.46/5.81 thf(fact_10190_mult__eSuc__right,axiom,
% 5.46/5.81 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.81 ( ( times_7803423173614009249d_enat @ M @ ( extended_eSuc @ N ) )
% 5.46/5.81 = ( plus_p3455044024723400733d_enat @ M @ ( times_7803423173614009249d_enat @ M @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % mult_eSuc_right
% 5.46/5.81 thf(fact_10191_mult__eSuc,axiom,
% 5.46/5.81 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.81 ( ( times_7803423173614009249d_enat @ ( extended_eSuc @ M ) @ N )
% 5.46/5.81 = ( plus_p3455044024723400733d_enat @ N @ ( times_7803423173614009249d_enat @ M @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % mult_eSuc
% 5.46/5.81 thf(fact_10192_ileI1,axiom,
% 5.46/5.81 ! [M: extended_enat,N: extended_enat] :
% 5.46/5.81 ( ( ord_le72135733267957522d_enat @ M @ N )
% 5.46/5.81 => ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ M ) @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % ileI1
% 5.46/5.81 thf(fact_10193_ile__eSuc,axiom,
% 5.46/5.81 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ N @ ( extended_eSuc @ N ) ) ).
% 5.46/5.81
% 5.46/5.81 % ile_eSuc
% 5.46/5.81 thf(fact_10194_not__eSuc__ilei0,axiom,
% 5.46/5.81 ! [N: extended_enat] :
% 5.46/5.81 ~ ( ord_le2932123472753598470d_enat @ ( extended_eSuc @ N ) @ zero_z5237406670263579293d_enat ) ).
% 5.46/5.81
% 5.46/5.81 % not_eSuc_ilei0
% 5.46/5.81 thf(fact_10195_eSuc__enat,axiom,
% 5.46/5.81 ! [N: nat] :
% 5.46/5.81 ( ( extended_eSuc @ ( extended_enat2 @ N ) )
% 5.46/5.81 = ( extended_enat2 @ ( suc @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_enat
% 5.46/5.81 thf(fact_10196_eSuc__enat__iff,axiom,
% 5.46/5.81 ! [X4: extended_enat,Y3: nat] :
% 5.46/5.81 ( ( ( extended_eSuc @ X4 )
% 5.46/5.81 = ( extended_enat2 @ Y3 ) )
% 5.46/5.81 = ( ? [N2: nat] :
% 5.46/5.81 ( ( Y3
% 5.46/5.81 = ( suc @ N2 ) )
% 5.46/5.81 & ( X4
% 5.46/5.81 = ( extended_enat2 @ N2 ) ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_enat_iff
% 5.46/5.81 thf(fact_10197_enat__eSuc__iff,axiom,
% 5.46/5.81 ! [Y3: nat,X4: extended_enat] :
% 5.46/5.81 ( ( ( extended_enat2 @ Y3 )
% 5.46/5.81 = ( extended_eSuc @ X4 ) )
% 5.46/5.81 = ( ? [N2: nat] :
% 5.46/5.81 ( ( Y3
% 5.46/5.81 = ( suc @ N2 ) )
% 5.46/5.81 & ( ( extended_enat2 @ N2 )
% 5.46/5.81 = X4 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % enat_eSuc_iff
% 5.46/5.81 thf(fact_10198_eSuc__Sup,axiom,
% 5.46/5.81 ! [A3: set_Extended_enat] :
% 5.46/5.81 ( ( A3 != bot_bo7653980558646680370d_enat )
% 5.46/5.81 => ( ( extended_eSuc @ ( comple4398354569131411667d_enat @ A3 ) )
% 5.46/5.81 = ( comple4398354569131411667d_enat @ ( image_80655429650038917d_enat @ extended_eSuc @ A3 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_Sup
% 5.46/5.81 thf(fact_10199_eSuc__def,axiom,
% 5.46/5.81 ( extended_eSuc
% 5.46/5.81 = ( extend3600170679010898289d_enat
% 5.46/5.81 @ ^ [N2: nat] : ( extended_enat2 @ ( suc @ N2 ) )
% 5.46/5.81 @ extend5688581933313929465d_enat ) ) ).
% 5.46/5.81
% 5.46/5.81 % eSuc_def
% 5.46/5.81 thf(fact_10200_less__than__iff,axiom,
% 5.46/5.81 ! [X4: nat,Y3: nat] :
% 5.46/5.81 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ less_than )
% 5.46/5.81 = ( ord_less_nat @ X4 @ Y3 ) ) ).
% 5.46/5.81
% 5.46/5.81 % less_than_iff
% 5.46/5.81 thf(fact_10201_Quotient__real,axiom,
% 5.46/5.81 quotie3684837364556693515t_real @ realrel @ real2 @ rep_real @ cr_real ).
% 5.46/5.81
% 5.46/5.81 % Quotient_real
% 5.46/5.81 thf(fact_10202_lcm__code__integer,axiom,
% 5.46/5.81 ( gcd_lcm_Code_integer
% 5.46/5.81 = ( ^ [A4: code_integer,B3: code_integer] : ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A4 ) @ ( abs_abs_Code_integer @ B3 ) ) @ ( gcd_gcd_Code_integer @ A4 @ B3 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % lcm_code_integer
% 5.46/5.81 thf(fact_10203_lcm__1__iff__nat,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( ( gcd_lcm_nat @ M @ N )
% 5.46/5.81 = ( suc @ zero_zero_nat ) )
% 5.46/5.81 = ( ( M
% 5.46/5.81 = ( suc @ zero_zero_nat ) )
% 5.46/5.81 & ( N
% 5.46/5.81 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % lcm_1_iff_nat
% 5.46/5.81 thf(fact_10204_prod__gcd__lcm__int,axiom,
% 5.46/5.81 ! [M: int,N: int] :
% 5.46/5.81 ( ( times_times_int @ ( abs_abs_int @ M ) @ ( abs_abs_int @ N ) )
% 5.46/5.81 = ( times_times_int @ ( gcd_gcd_int @ M @ N ) @ ( gcd_lcm_int @ M @ N ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % prod_gcd_lcm_int
% 5.46/5.81 thf(fact_10205_prod__gcd__lcm__nat,axiom,
% 5.46/5.81 ( times_times_nat
% 5.46/5.81 = ( ^ [M6: nat,N2: nat] : ( times_times_nat @ ( gcd_gcd_nat @ M6 @ N2 ) @ ( gcd_lcm_nat @ M6 @ N2 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % prod_gcd_lcm_nat
% 5.46/5.81 thf(fact_10206_lcm__nat__def,axiom,
% 5.46/5.81 ( gcd_lcm_nat
% 5.46/5.81 = ( ^ [X: nat,Y: nat] : ( divide_divide_nat @ ( times_times_nat @ X @ Y ) @ ( gcd_gcd_nat @ X @ Y ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % lcm_nat_def
% 5.46/5.81 thf(fact_10207_lcm__pos__nat,axiom,
% 5.46/5.81 ! [M: nat,N: nat] :
% 5.46/5.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.46/5.81 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.46/5.81 => ( ord_less_nat @ zero_zero_nat @ ( gcd_lcm_nat @ M @ N ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % lcm_pos_nat
% 5.46/5.81 thf(fact_10208_lcm__pos__int,axiom,
% 5.46/5.81 ! [M: int,N: int] :
% 5.46/5.81 ( ( M != zero_zero_int )
% 5.46/5.81 => ( ( N != zero_zero_int )
% 5.46/5.81 => ( ord_less_int @ zero_zero_int @ ( gcd_lcm_int @ M @ N ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % lcm_pos_int
% 5.46/5.81 thf(fact_10209_lcm__altdef__int,axiom,
% 5.46/5.81 ( gcd_lcm_int
% 5.46/5.81 = ( ^ [A4: int,B3: int] : ( divide_divide_int @ ( times_times_int @ ( abs_abs_int @ A4 ) @ ( abs_abs_int @ B3 ) ) @ ( gcd_gcd_int @ A4 @ B3 ) ) ) ) ).
% 5.46/5.81
% 5.46/5.81 % lcm_altdef_int
% 5.46/5.81
% 5.46/5.81 % Helper facts (46)
% 5.46/5.81 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.46/5.81 ! [X4: int,Y3: int] :
% 5.46/5.81 ( ( if_int @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.46/5.81 ! [X4: int,Y3: int] :
% 5.46/5.81 ( ( if_int @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.46/5.81 ! [X4: nat,Y3: nat] :
% 5.46/5.81 ( ( if_nat @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.46/5.81 ! [X4: nat,Y3: nat] :
% 5.46/5.81 ( ( if_nat @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.46/5.81 ! [X4: num,Y3: num] :
% 5.46/5.81 ( ( if_num @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.46/5.81 ! [X4: num,Y3: num] :
% 5.46/5.81 ( ( if_num @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.46/5.81 ! [X4: rat,Y3: rat] :
% 5.46/5.81 ( ( if_rat @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.46/5.81 ! [X4: rat,Y3: rat] :
% 5.46/5.81 ( ( if_rat @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.46/5.81 ! [X4: real,Y3: real] :
% 5.46/5.81 ( ( if_real @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.46/5.81 ! [X4: real,Y3: real] :
% 5.46/5.81 ( ( if_real @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.46/5.81 ! [P: real > $o] :
% 5.46/5.81 ( ( P @ ( fChoice_real @ P ) )
% 5.46/5.81 = ( ? [X6: real] : ( P @ X6 ) ) ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.46/5.81 ! [X4: complex,Y3: complex] :
% 5.46/5.81 ( ( if_complex @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.46/5.81 ! [X4: complex,Y3: complex] :
% 5.46/5.81 ( ( if_complex @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.46/5.81 ! [X4: extended_enat,Y3: extended_enat] :
% 5.46/5.81 ( ( if_Extended_enat @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.46/5.81 ! [X4: extended_enat,Y3: extended_enat] :
% 5.46/5.81 ( ( if_Extended_enat @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.46/5.81 ! [X4: code_integer,Y3: code_integer] :
% 5.46/5.81 ( ( if_Code_integer @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.46/5.81 ! [X4: code_integer,Y3: code_integer] :
% 5.46/5.81 ( ( if_Code_integer @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.46/5.81 ! [X4: set_int,Y3: set_int] :
% 5.46/5.81 ( ( if_set_int @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.46/5.81 ! [X4: set_int,Y3: set_int] :
% 5.46/5.81 ( ( if_set_int @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.46/5.81 ! [X4: vEBT_VEBT,Y3: vEBT_VEBT] :
% 5.46/5.81 ( ( if_VEBT_VEBT @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.46/5.81 ! [X4: vEBT_VEBT,Y3: vEBT_VEBT] :
% 5.46/5.81 ( ( if_VEBT_VEBT @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.46/5.81 ! [X4: list_int,Y3: list_int] :
% 5.46/5.81 ( ( if_list_int @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.46/5.81 ! [X4: list_int,Y3: list_int] :
% 5.46/5.81 ( ( if_list_int @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.46/5.81 ! [X4: list_nat,Y3: list_nat] :
% 5.46/5.81 ( ( if_list_nat @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.46/5.81 ! [X4: list_nat,Y3: list_nat] :
% 5.46/5.81 ( ( if_list_nat @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.46/5.81 ! [X4: int > int,Y3: int > int] :
% 5.46/5.81 ( ( if_int_int @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.46/5.81 ! [X4: int > int,Y3: int > int] :
% 5.46/5.81 ( ( if_int_int @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.46/5.81 ! [X4: nat > rat,Y3: nat > rat] :
% 5.46/5.81 ( ( if_nat_rat @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.46/5.81 ! [X4: nat > rat,Y3: nat > rat] :
% 5.46/5.81 ( ( if_nat_rat @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.46/5.81 ! [X4: option_nat,Y3: option_nat] :
% 5.46/5.81 ( ( if_option_nat @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.46/5.81 ! [X4: option_nat,Y3: option_nat] :
% 5.46/5.81 ( ( if_option_nat @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.46/5.81 ! [X4: option_num,Y3: option_num] :
% 5.46/5.81 ( ( if_option_num @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.46/5.81 ! [X4: option_num,Y3: option_num] :
% 5.46/5.81 ( ( if_option_num @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.46/5.81 ! [X4: product_prod_int_int,Y3: product_prod_int_int] :
% 5.46/5.81 ( ( if_Pro3027730157355071871nt_int @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.46/5.81 ! [X4: product_prod_int_int,Y3: product_prod_int_int] :
% 5.46/5.81 ( ( if_Pro3027730157355071871nt_int @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.46/5.81 ! [X4: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.46/5.81 ( ( if_Pro6206227464963214023at_nat @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.46/5.81 ! [X4: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.46/5.81 ( ( if_Pro6206227464963214023at_nat @ $true @ X4 @ Y3 )
% 5.46/5.81 = X4 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.46/5.81 ! [X4: nat > int > int,Y3: nat > int > int] :
% 5.46/5.81 ( ( if_nat_int_int @ $false @ X4 @ Y3 )
% 5.46/5.81 = Y3 ) ).
% 5.46/5.81
% 5.46/5.81 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 6.83/7.10 ! [X4: nat > int > int,Y3: nat > int > int] :
% 6.83/7.10 ( ( if_nat_int_int @ $true @ X4 @ Y3 )
% 6.83/7.10 = X4 ) ).
% 6.83/7.10
% 6.83/7.10 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 6.83/7.10 ! [X4: nat > nat > nat,Y3: nat > nat > nat] :
% 6.83/7.10 ( ( if_nat_nat_nat @ $false @ X4 @ Y3 )
% 6.83/7.10 = Y3 ) ).
% 6.83/7.10
% 6.83/7.10 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 6.83/7.10 ! [X4: nat > nat > nat,Y3: nat > nat > nat] :
% 6.83/7.10 ( ( if_nat_nat_nat @ $true @ X4 @ Y3 )
% 6.83/7.10 = X4 ) ).
% 6.83/7.10
% 6.83/7.10 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.83/7.10 ! [X4: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 6.83/7.10 ( ( if_Pro5737122678794959658eger_o @ $false @ X4 @ Y3 )
% 6.83/7.10 = Y3 ) ).
% 6.83/7.10
% 6.83/7.10 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.83/7.10 ! [X4: produc6271795597528267376eger_o,Y3: produc6271795597528267376eger_o] :
% 6.83/7.10 ( ( if_Pro5737122678794959658eger_o @ $true @ X4 @ Y3 )
% 6.83/7.10 = X4 ) ).
% 6.83/7.10
% 6.83/7.10 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.83/7.10 ! [P: $o] :
% 6.83/7.10 ( ( P = $true )
% 6.83/7.10 | ( P = $false ) ) ).
% 6.83/7.10
% 6.83/7.10 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.83/7.10 ! [X4: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 6.83/7.10 ( ( if_Pro6119634080678213985nteger @ $false @ X4 @ Y3 )
% 6.83/7.10 = Y3 ) ).
% 6.83/7.10
% 6.83/7.10 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.83/7.10 ! [X4: produc8923325533196201883nteger,Y3: produc8923325533196201883nteger] :
% 6.83/7.10 ( ( if_Pro6119634080678213985nteger @ $true @ X4 @ Y3 )
% 6.83/7.10 = X4 ) ).
% 6.83/7.10
% 6.83/7.10 % Conjectures (1)
% 6.83/7.10 thf(conj_0,conjecture,
% 6.83/7.10 ( ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 6.83/7.10 = ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 6.83/7.10
% 6.83/7.10 %------------------------------------------------------------------------------
% 6.83/7.10 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.sftGVEtDjr/cvc5---1.0.5_30919.p...
% 6.83/7.10 (declare-sort $$unsorted 0)
% 6.83/7.10 (declare-sort tptp.produc3368934014287244435at_num 0)
% 6.83/7.10 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.83/7.10 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 6.83/7.10 (declare-sort tptp.produc859450856879609959at_nat 0)
% 6.83/7.10 (declare-sort tptp.set_fi4554929511873752355omplex 0)
% 6.83/7.10 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.83/7.10 (declare-sort tptp.produc2963631642982155120at_num 0)
% 6.83/7.10 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.83/7.10 (declare-sort tptp.set_fi7789364187291644575l_real 0)
% 6.83/7.10 (declare-sort tptp.filter6041513312241820739omplex 0)
% 6.83/7.10 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.83/7.10 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.83/7.10 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.83/7.10 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.83/7.10 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 6.83/7.10 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.83/7.10 (declare-sort tptp.produc7272778201969148633d_enat 0)
% 6.83/7.10 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.83/7.10 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.83/7.10 (declare-sort tptp.filter2146258269922977983l_real 0)
% 6.83/7.10 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.83/7.10 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 6.83/7.10 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 6.83/7.10 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 6.83/7.10 (declare-sort tptp.list_P1726324292696863441at_num 0)
% 6.83/7.10 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.83/7.10 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.83/7.10 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.83/7.10 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.83/7.10 (declare-sort tptp.produc4411394909380815293omplex 0)
% 6.83/7.10 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.83/7.10 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.83/7.10 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.83/7.10 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.83/7.10 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.83/7.10 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.83/7.10 (declare-sort tptp.produc2422161461964618553l_real 0)
% 6.83/7.10 (declare-sort tptp.product_prod_num_num 0)
% 6.83/7.10 (declare-sort tptp.product_prod_nat_num 0)
% 6.83/7.10 (declare-sort tptp.product_prod_nat_nat 0)
% 6.83/7.10 (declare-sort tptp.product_prod_int_int 0)
% 6.83/7.10 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.83/7.10 (declare-sort tptp.list_list_nat 0)
% 6.83/7.10 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.83/7.10 (declare-sort tptp.set_list_nat 0)
% 6.83/7.10 (declare-sort tptp.product_prod_o_nat 0)
% 6.83/7.10 (declare-sort tptp.product_prod_o_int 0)
% 6.83/7.10 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.83/7.10 (declare-sort tptp.set_set_nat 0)
% 6.83/7.10 (declare-sort tptp.set_Code_integer 0)
% 6.83/7.10 (declare-sort tptp.list_Extended_enat 0)
% 6.83/7.10 (declare-sort tptp.set_Product_unit 0)
% 6.83/7.10 (declare-sort tptp.set_Extended_enat 0)
% 6.83/7.10 (declare-sort tptp.list_complex 0)
% 6.83/7.10 (declare-sort tptp.product_prod_o_o 0)
% 6.83/7.10 (declare-sort tptp.set_complex 0)
% 6.83/7.10 (declare-sort tptp.filter_real 0)
% 6.83/7.10 (declare-sort tptp.option_num 0)
% 6.83/7.10 (declare-sort tptp.option_nat 0)
% 6.83/7.10 (declare-sort tptp.filter_nat 0)
% 6.83/7.10 (declare-sort tptp.set_char 0)
% 6.83/7.10 (declare-sort tptp.list_real 0)
% 6.83/7.10 (declare-sort tptp.set_real 0)
% 6.83/7.10 (declare-sort tptp.list_num 0)
% 6.83/7.10 (declare-sort tptp.list_nat 0)
% 6.83/7.10 (declare-sort tptp.list_int 0)
% 6.83/7.10 (declare-sort tptp.vEBT_VEBT 0)
% 6.83/7.10 (declare-sort tptp.set_rat 0)
% 6.83/7.10 (declare-sort tptp.set_num 0)
% 6.83/7.10 (declare-sort tptp.set_nat 0)
% 6.83/7.10 (declare-sort tptp.set_int 0)
% 6.83/7.10 (declare-sort tptp.code_integer 0)
% 6.83/7.10 (declare-sort tptp.product_unit 0)
% 6.83/7.10 (declare-sort tptp.extended_enat 0)
% 6.83/7.10 (declare-sort tptp.list_o 0)
% 6.83/7.10 (declare-sort tptp.complex 0)
% 6.83/7.10 (declare-sort tptp.literal 0)
% 6.83/7.10 (declare-sort tptp.set_o 0)
% 6.83/7.10 (declare-sort tptp.char 0)
% 6.83/7.10 (declare-sort tptp.real 0)
% 6.83/7.10 (declare-sort tptp.rat 0)
% 6.83/7.10 (declare-sort tptp.num 0)
% 6.83/7.10 (declare-sort tptp.nat 0)
% 6.83/7.10 (declare-sort tptp.int 0)
% 6.83/7.10 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 6.83/7.10 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.83/7.10 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.83/7.10 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.83/7.10 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.83/7.10 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.bNF_re4521903465945308077real_o ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> (-> tptp.nat tptp.rat) Bool) (-> tptp.real Bool) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> tptp.real tptp.real Bool)) Bool)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.bNF_re3403563459893282935_int_o ((-> tptp.int tptp.int Bool) (-> (-> tptp.int Bool) (-> tptp.int Bool) Bool) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.bNF_re5089333283451836215nt_o_o ((-> tptp.int tptp.int Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.bNF_re8402795839162346335um_int ((-> tptp.num tptp.num Bool) (-> (-> tptp.num tptp.int) (-> tptp.num tptp.int) Bool) (-> tptp.num tptp.num tptp.int) (-> tptp.num tptp.num tptp.int)) Bool)
% 6.83/7.10 (declare-fun tptp.bNF_re1822329894187522285nt_int ((-> tptp.num tptp.num Bool) (-> tptp.int tptp.int Bool) (-> tptp.num tptp.int) (-> tptp.num tptp.int)) Bool)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.bNF_re4555766996558763186at_nat ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.int tptp.nat)) Bool)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.bNF_re8246922863344978751at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat)) Bool)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.83/7.10 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.83/7.10 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.83/7.10 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.83/7.10 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.83/7.10 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.83/7.10 (declare-fun tptp.bit_ri7632146776885996613nteger (tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bit_se7788150548672797655nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bit_se3222712562003087583nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.bit_un5425074673868309765um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.83/7.10 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.bit_un3595099601533988841um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.83/7.10 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.83/7.10 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.83/7.10 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.83/7.10 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.83/7.10 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.83/7.10 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.83/7.10 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.83/7.10 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.83/7.10 (declare-fun tptp.comple2295165028678016749d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.comple8358262395181532106omplex (tptp.set_fi4554929511873752355omplex) tptp.filter6041513312241820739omplex)
% 6.83/7.10 (declare-fun tptp.comple2936214249959783750l_real (tptp.set_fi7789364187291644575l_real) tptp.filter2146258269922977983l_real)
% 6.83/7.10 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.83/7.10 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.comple4398354569131411667d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.83/7.10 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.83/7.10 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.83/7.10 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.83/7.10 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.83/7.10 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.83/7.10 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.83/7.10 (declare-fun tptp.rcis (tptp.real tptp.real) tptp.complex)
% 6.83/7.10 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.83/7.10 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.83/7.10 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.83/7.10 (declare-fun tptp.has_ve631408500373753343e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.83/7.10 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.83/7.10 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.83/7.10 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.83/7.10 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.83/7.10 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.83/7.10 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.83/7.10 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.83/7.10 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.83/7.10 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.83/7.10 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.83/7.10 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.83/7.10 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.83/7.10 (declare-fun tptp.euclid4774559944035922753ze_int (tptp.int) tptp.nat)
% 6.83/7.10 (declare-fun tptp.euclid4777050414544973029ze_nat (tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.euclid3395696857347342551nt_int (tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.euclid3398187327856392827nt_nat (tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.extended_eSuc (tptp.extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.extended_enat2 (tptp.nat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.extended_case_enat_o ((-> tptp.nat Bool) Bool tptp.extended_enat) Bool)
% 6.83/7.10 (declare-fun tptp.extend3600170679010898289d_enat ((-> tptp.nat tptp.extended_enat) tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.extend5688581933313929465d_enat () tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.extended_the_enat (tptp.extended_enat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.83/7.10 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.83/7.10 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.83/7.10 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.83/7.10 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.83/7.10 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.83/7.10 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.83/7.10 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.83/7.10 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 6.83/7.10 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.83/7.10 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.83/7.10 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.83/7.10 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.83/7.10 (declare-fun tptp.filtermap_real_real ((-> tptp.real tptp.real) tptp.filter_real) tptp.filter_real)
% 6.83/7.10 (declare-fun tptp.princi3496590319149328850omplex (tptp.set_Pr5085853215250843933omplex) tptp.filter6041513312241820739omplex)
% 6.83/7.10 (declare-fun tptp.princi6114159922880469582l_real (tptp.set_Pr6218003697084177305l_real) tptp.filter2146258269922977983l_real)
% 6.83/7.10 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 6.83/7.10 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.83/7.10 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.83/7.10 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.83/7.10 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.83/7.10 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.83/7.10 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.83/7.10 (declare-fun tptp.finite4001608067531595151d_enat (tptp.set_Extended_enat) Bool)
% 6.83/7.10 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.83/7.10 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.83/7.10 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.83/7.10 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.83/7.10 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 6.83/7.10 (declare-fun tptp.comp_int_real_real ((-> tptp.int tptp.real) (-> tptp.real tptp.int) tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.id_o (Bool) Bool)
% 6.83/7.10 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.83/7.10 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.83/7.10 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.83/7.10 (declare-fun tptp.map_fu434086159418415080_int_o ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat Bool) tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.int tptp.int) Bool)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.map_fu4826362097070443709at_o_o ((-> tptp.int tptp.product_prod_nat_nat) (-> Bool Bool) (-> tptp.product_prod_nat_nat Bool) tptp.int) Bool)
% 6.83/7.10 (declare-fun tptp.map_fu2345160673673942751at_nat ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat) tptp.int) tptp.nat)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.map_fu1532550112467129777l_real ((-> tptp.real tptp.nat tptp.rat) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real tptp.real) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.map_fu7146612038024189824t_real ((-> tptp.real tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.real) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.map_fu1856342031159181835at_o_o ((-> tptp.real tptp.nat tptp.rat) (-> Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) tptp.real) Bool)
% 6.83/7.10 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.83/7.10 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 6.83/7.10 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 6.83/7.10 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.83/7.10 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.83/7.10 (declare-fun tptp.gcd_gcd_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.gcd_lcm_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.gcd_lcm_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.gcd_lcm_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.83/7.10 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.minus_8727706125548526216plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool) tptp.complex) Bool)
% 6.83/7.10 (declare-fun tptp.minus_2020553357622893040enat_o ((-> tptp.extended_enat Bool) (-> tptp.extended_enat Bool) tptp.extended_enat) Bool)
% 6.83/7.10 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 6.83/7.10 (declare-fun tptp.minus_1139252259498527702_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.83/7.10 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.minus_minus_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 6.83/7.10 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.83/7.10 (declare-fun tptp.minus_925952699566721837d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) tptp.set_Extended_enat)
% 6.83/7.10 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.minus_7954133019191499631st_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 6.83/7.10 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.83/7.10 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.one_one_int () tptp.int)
% 6.83/7.10 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.83/7.10 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.83/7.10 (declare-fun tptp.one_one_real () tptp.real)
% 6.83/7.10 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.83/7.10 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.plus_plus_literal (tptp.literal tptp.literal) tptp.literal)
% 6.83/7.10 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.83/7.10 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.83/7.10 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.83/7.10 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.83/7.10 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.83/7.10 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.83/7.10 (declare-fun tptp.zero_zero_literal () tptp.literal)
% 6.83/7.10 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.83/7.10 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.83/7.10 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.83/7.10 (declare-fun tptp.groups4622424608036095791omplex ((-> tptp.extended_enat tptp.complex) tptp.set_Extended_enat) tptp.complex)
% 6.83/7.10 (declare-fun tptp.groups2878480467620962989at_int ((-> tptp.extended_enat tptp.int) tptp.set_Extended_enat) tptp.int)
% 6.83/7.10 (declare-fun tptp.groups2880970938130013265at_nat ((-> tptp.extended_enat tptp.nat) tptp.set_Extended_enat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.groups2245840878043517529at_rat ((-> tptp.extended_enat tptp.rat) tptp.set_Extended_enat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.groups97031904164794029t_real ((-> tptp.extended_enat tptp.real) tptp.set_Extended_enat) tptp.real)
% 6.83/7.10 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.83/7.10 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.83/7.10 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.83/7.10 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.83/7.10 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.83/7.10 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.83/7.10 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.83/7.10 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.83/7.10 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.83/7.10 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.83/7.10 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.83/7.10 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.83/7.10 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.83/7.10 (declare-fun tptp.the_Pr4378521158711661632nt_int ((-> tptp.product_prod_int_int Bool)) tptp.product_prod_int_int)
% 6.83/7.10 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.83/7.10 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.if_nat_int_int (Bool (-> tptp.nat tptp.int tptp.int) (-> tptp.nat tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.if_nat_nat_nat (Bool (-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.if_nat_rat (Bool (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.83/7.10 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.83/7.10 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.83/7.10 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.83/7.10 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.83/7.10 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.83/7.10 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.83/7.10 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.83/7.10 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.83/7.10 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.83/7.10 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.83/7.10 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.83/7.10 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.83/7.10 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 6.83/7.10 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 6.83/7.10 (declare-fun tptp.ring_11222124179247155820nteger () tptp.set_Code_integer)
% 6.83/7.10 (declare-fun tptp.ring_1_Ints_complex () tptp.set_complex)
% 6.83/7.10 (declare-fun tptp.ring_1_Ints_int () tptp.set_int)
% 6.83/7.10 (declare-fun tptp.ring_1_Ints_rat () tptp.set_rat)
% 6.83/7.10 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.83/7.10 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.83/7.10 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.83/7.10 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.83/7.10 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.83/7.10 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.83/7.10 (declare-fun tptp.lattic921264341876707157d_enat (tptp.set_Extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.quotie3684837364556693515t_real ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) tptp.real) (-> tptp.real tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.real Bool)) Bool)
% 6.83/7.10 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.83/7.10 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.83/7.10 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.83/7.10 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.nil_int () tptp.list_int)
% 6.83/7.10 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.map_VE8901447254227204932T_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.83/7.10 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.83/7.10 (declare-fun tptp.set_Extended_enat2 (tptp.list_Extended_enat) tptp.set_Extended_enat)
% 6.83/7.10 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.set_list_nat2 (tptp.list_list_nat) tptp.set_list_nat)
% 6.83/7.10 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.83/7.10 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.83/7.10 (declare-fun tptp.nth_Extended_enat (tptp.list_Extended_enat tptp.nat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.83/7.10 (declare-fun tptp.nth_list_nat (tptp.list_list_nat tptp.nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.83/7.10 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.83/7.10 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.83/7.10 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.83/7.10 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.83/7.10 (declare-fun tptp.nth_Pr8326237132889035090at_num (tptp.list_P1726324292696863441at_num tptp.nat) tptp.product_prod_nat_num)
% 6.83/7.10 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 6.83/7.10 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.83/7.10 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.83/7.10 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.83/7.10 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.83/7.10 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.83/7.10 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.83/7.10 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.83/7.10 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.83/7.10 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.83/7.10 (declare-fun tptp.product_nat_num (tptp.list_nat tptp.list_num) tptp.list_P1726324292696863441at_num)
% 6.83/7.10 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.83/7.10 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 6.83/7.10 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.83/7.10 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.83/7.10 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.83/7.10 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.83/7.10 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.83/7.10 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.83/7.10 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.take_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.83/7.10 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.83/7.10 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.83/7.10 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.83/7.10 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.83/7.10 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s3941691890525107288d_enat (tptp.list_Extended_enat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s3023201423986296836st_nat (tptp.list_list_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.83/7.10 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.83/7.10 (declare-fun tptp.nat_list_decode (tptp.nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.nat_list_decode_rel (tptp.nat tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.83/7.10 (declare-fun tptp.nat_prod_decode (tptp.nat) tptp.product_prod_nat_nat)
% 6.83/7.10 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.83/7.10 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.83/7.10 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.83/7.10 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.83/7.10 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.83/7.10 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.83/7.10 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.83/7.10 (declare-fun tptp.one () tptp.num)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.83/7.10 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.83/7.10 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.83/7.10 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.83/7.10 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.83/7.10 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.83/7.10 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.83/7.10 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.83/7.10 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.83/7.10 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.83/7.10 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.83/7.10 (declare-fun tptp.none_num () tptp.option_num)
% 6.83/7.10 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.83/7.10 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.83/7.10 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.83/7.10 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.83/7.10 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.83/7.10 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.83/7.10 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.83/7.10 (declare-fun tptp.bot_bo7653980558646680370d_enat () tptp.set_Extended_enat)
% 6.83/7.10 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.83/7.10 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.83/7.10 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.83/7.10 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.83/7.10 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.83/7.10 (declare-fun tptp.ord_Le1955565732374568822d_enat ((-> tptp.extended_enat Bool)) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.83/7.10 (declare-fun tptp.ord_Least_real ((-> tptp.real Bool)) tptp.real)
% 6.83/7.10 (declare-fun tptp.ord_less_complex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le8499522857272258027enat_o ((-> tptp.extended_enat Bool) (-> tptp.extended_enat Bool)) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le2529575680413868914d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le7203529160286727270d_enat (tptp.set_Extended_enat tptp.set_Extended_enat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.83/7.10 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.83/7.10 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.83/7.10 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 6.83/7.10 (declare-fun tptp.order_4130057895858720880d_enat ((-> tptp.extended_enat tptp.extended_enat)) Bool)
% 6.83/7.10 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.83/7.10 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 6.83/7.10 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.83/7.10 (declare-fun tptp.order_7092887310737990675l_real ((-> tptp.real tptp.real)) Bool)
% 6.83/7.10 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.top_to3028658606643905974d_enat () tptp.extended_enat)
% 6.83/7.10 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.83/7.10 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.83/7.10 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.83/7.10 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.83/7.10 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.83/7.10 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.83/7.10 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.83/7.10 (declare-fun tptp.produc851828971589881931at_num ((-> tptp.nat tptp.num tptp.num) tptp.produc2963631642982155120at_num) tptp.produc3368934014287244435at_num)
% 6.83/7.10 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.83/7.10 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.83/7.10 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.83/7.10 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.83/7.10 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.83/7.10 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.83/7.10 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.83/7.10 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.83/7.10 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.83/7.10 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.83/7.10 (declare-fun tptp.produc1195630363706982562at_num (tptp.nat tptp.product_prod_nat_num) tptp.produc2963631642982155120at_num)
% 6.83/7.10 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.83/7.10 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 6.83/7.10 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.83/7.10 (declare-fun tptp.produc581526299967858633d_enat (tptp.vEBT_VEBT tptp.extended_enat) tptp.produc7272778201969148633d_enat)
% 6.83/7.10 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.83/7.10 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.83/7.10 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.83/7.10 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.83/7.10 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.83/7.10 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.83/7.10 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.83/7.10 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.83/7.10 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.83/7.10 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.83/7.10 (declare-fun tptp.produc6771430404735790350plex_o ((-> tptp.complex tptp.complex Bool) tptp.produc4411394909380815293omplex) Bool)
% 6.83/7.10 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.83/7.10 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.83/7.10 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.83/7.10 (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)
% 6.83/7.10 (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)
% 6.83/7.10 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.83/7.10 (declare-fun tptp.produc2761476792215241774st_nat ((-> tptp.nat tptp.nat tptp.list_nat) tptp.product_prod_nat_nat) tptp.list_nat)
% 6.83/7.10 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.83/7.10 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.83/7.10 (declare-fun tptp.produc5414030515140494994real_o ((-> tptp.real tptp.real Bool) tptp.produc2422161461964618553l_real) Bool)
% 6.83/7.10 (declare-fun tptp.produc8508995932063986495nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.83/7.10 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.produc6174133586879617921nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.83/7.10 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 6.83/7.10 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.83/7.10 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.83/7.10 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.83/7.10 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.83/7.10 (declare-fun tptp.field_7254667332652039916t_real (tptp.rat) tptp.real)
% 6.83/7.10 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.83/7.10 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 6.83/7.10 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.83/7.10 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.83/7.10 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.83/7.10 (declare-fun tptp.real2 ((-> tptp.nat tptp.rat)) tptp.real)
% 6.83/7.10 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 6.83/7.10 (declare-fun tptp.cr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.83/7.10 (declare-fun tptp.pcr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.83/7.10 (declare-fun tptp.positive2 (tptp.real) Bool)
% 6.83/7.10 (declare-fun tptp.realrel ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.83/7.10 (declare-fun tptp.rep_real (tptp.real tptp.nat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 6.83/7.10 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.83/7.10 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.83/7.10 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 6.83/7.10 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.83/7.10 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.83/7.10 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.transp_nat_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool)) Bool)
% 6.83/7.10 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 6.83/7.10 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.83/7.10 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.83/7.10 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.83/7.10 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.83/7.10 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.83/7.10 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.83/7.10 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.83/7.10 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.83/7.10 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.83/7.10 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.83/7.10 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.83/7.10 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.83/7.10 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.83/7.10 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.83/7.10 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.83/7.10 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 6.83/7.10 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.83/7.10 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.83/7.10 (declare-fun tptp.collec4429806609662206161d_enat ((-> tptp.extended_enat Bool)) tptp.set_Extended_enat)
% 6.83/7.10 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.83/7.10 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.collec8663557070575231912omplex ((-> tptp.produc4411394909380815293omplex Bool)) tptp.set_Pr5085853215250843933omplex)
% 6.83/7.10 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.83/7.10 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.83/7.10 (declare-fun tptp.collec3799799289383736868l_real ((-> tptp.produc2422161461964618553l_real Bool)) tptp.set_Pr6218003697084177305l_real)
% 6.83/7.10 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.collect_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool)) tptp.set_VEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.image_80655429650038917d_enat ((-> tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat) tptp.set_Extended_enat)
% 6.83/7.10 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.83/7.10 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.83/7.10 (declare-fun tptp.image_5971271580939081552omplex ((-> tptp.real tptp.filter6041513312241820739omplex) tptp.set_real) tptp.set_fi4554929511873752355omplex)
% 6.83/7.10 (declare-fun tptp.image_2178119161166701260l_real ((-> tptp.real tptp.filter2146258269922977983l_real) tptp.set_real) tptp.set_fi7789364187291644575l_real)
% 6.83/7.10 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.83/7.10 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.83/7.10 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.set_or5403411693681687835d_enat (tptp.extended_enat tptp.extended_enat) tptp.set_Extended_enat)
% 6.83/7.10 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.83/7.10 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.83/7.10 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.83/7.10 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.83/7.10 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.83/7.10 (declare-fun tptp.abort_real (tptp.literal (-> tptp.product_unit tptp.real)) tptp.real)
% 6.83/7.10 (declare-fun tptp.literal2 (Bool Bool Bool Bool Bool Bool Bool tptp.literal) tptp.literal)
% 6.83/7.10 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.83/7.10 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.83/7.10 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.83/7.10 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.83/7.10 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.83/7.10 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.83/7.10 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.83/7.10 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.83/7.10 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.83/7.10 (declare-fun tptp.topolo7531315842566124627t_real ((-> tptp.nat tptp.real)) Bool)
% 6.83/7.10 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.83/7.10 (declare-fun tptp.topolo6517432010174082258omplex ((-> tptp.nat tptp.complex)) Bool)
% 6.83/7.10 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.83/7.10 (declare-fun tptp.topolo896644834953643431omplex () tptp.filter6041513312241820739omplex)
% 6.83/7.10 (declare-fun tptp.topolo1511823702728130853y_real () tptp.filter2146258269922977983l_real)
% 6.83/7.10 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.cosh_complex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.cot_complex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.pi () tptp.real)
% 6.83/7.10 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.powr_real2 (tptp.real tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.83/7.10 (declare-fun tptp.sinh_complex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.83/7.10 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.83/7.10 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.83/7.10 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.83/7.10 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.83/7.10 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_elim_dead (tptp.vEBT_VEBT tptp.extended_enat) tptp.vEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.vEBT_V312737461966249ad_rel (tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.83/7.10 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.83/7.10 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.83/7.10 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.83/7.10 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.83/7.10 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.83/7.10 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.83/7.10 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.83/7.10 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.83/7.10 (declare-fun tptp.accp_P6183159247885693666d_enat ((-> tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat Bool) tptp.produc7272778201969148633d_enat) Bool)
% 6.83/7.10 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.83/7.10 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.83/7.10 (declare-fun tptp.less_than () tptp.set_Pr1261947904930325089at_nat)
% 6.83/7.10 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.83/7.10 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.83/7.10 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.83/7.10 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 6.83/7.10 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.83/7.10 (declare-fun tptp.member_Extended_enat (tptp.extended_enat tptp.set_Extended_enat) Bool)
% 6.83/7.10 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.83/7.10 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.83/7.10 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.83/7.10 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.83/7.10 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.83/7.10 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.83/7.10 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.83/7.10 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.83/7.10 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.83/7.10 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.83/7.10 (declare-fun tptp.deg () tptp.nat)
% 6.83/7.10 (declare-fun tptp.m () tptp.nat)
% 6.83/7.10 (declare-fun tptp.ma () tptp.nat)
% 6.83/7.10 (declare-fun tptp.mi () tptp.nat)
% 6.83/7.10 (declare-fun tptp.miny () tptp.nat)
% 6.83/7.10 (declare-fun tptp.na () tptp.nat)
% 6.83/7.10 (declare-fun tptp.res () tptp.nat)
% 6.83/7.10 (declare-fun tptp.sc () tptp.nat)
% 6.83/7.10 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.83/7.10 (declare-fun tptp.xa () tptp.nat)
% 6.83/7.10 (declare-fun tptp.za () tptp.nat)
% 6.83/7.10 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_VEBT_high tptp.za) _let_1)) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1))))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 6.83/7.10 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1)) (@ (@ tptp.vEBT_VEBT_high tptp.za) _let_1))))
% 6.83/7.10 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat)) (and (@ (@ tptp.member_nat X) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat Y) X)))))))
% 6.83/7.10 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat)) (and (@ (@ tptp.member_nat X) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat X) Y)))))))
% 6.83/7.10 (assert (= (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))
% 6.83/7.10 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (= tptp.vEBT_VEBT_high (lambda ((X tptp.nat) (N2 tptp.nat)) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.za) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) tptp.sc))
% 6.83/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.83/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.83/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.83/7.10 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X2) (@ tptp.bit0 Y2)) (= X2 Y2))))
% 6.83/7.10 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 6.83/7.10 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 6.83/7.10 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 6.83/7.10 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 6.83/7.10 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 6.83/7.10 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_nat tptp.za) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.83/7.10 (assert (forall ((B tptp.real) (A2 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B) A2)) (@ (@ tptp.ord_less_real A2) B))))
% 6.83/7.10 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B) A2)) (@ (@ tptp.ord_less_rat A2) B))))
% 6.83/7.10 (assert (forall ((B tptp.num) (A2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B) A2)) (@ (@ tptp.ord_less_num A2) B))))
% 6.83/7.10 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B) A2)) (@ (@ tptp.ord_less_nat A2) B))))
% 6.83/7.10 (assert (forall ((B tptp.int) (A2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B) A2)) (@ (@ tptp.ord_less_int A2) B))))
% 6.83/7.10 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.83/7.10 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.83/7.10 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.83/7.10 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.83/7.10 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.83/7.10 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.83/7.10 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.83/7.10 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_rat A) B2)) (not (@ (@ tptp.ord_less_eq_rat B2) A)))))
% 6.83/7.10 (assert (forall ((A tptp.num) (B2 tptp.num)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_num A) B2)) (not (@ (@ tptp.ord_less_eq_num B2) A)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_nat A) B2)) (not (@ (@ tptp.ord_less_eq_nat B2) A)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_int A) B2)) (not (@ (@ tptp.ord_less_eq_int B2) A)))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((X2 tptp.num)) (not (= tptp.one (@ tptp.bit0 X2)))))
% 6.83/7.10 (assert (= (@ (@ tptp.vEBT_VEBT_high tptp.res) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.sc))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_nat tptp.xa) tptp.res))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_nat tptp.sc) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.83/7.10 (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))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((B2 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 B2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A) B2)) (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 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) B2))) (@ _let_1 A)) (@ _let_1 B2)))))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.na))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.xa))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.83/7.10 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.83/7.10 (assert (not (= tptp.za tptp.mi)))
% 6.83/7.10 (assert (not (= tptp.mi tptp.ma)))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_eq_nat tptp.res) tptp.ma))
% 6.83/7.10 (assert (forall ((A tptp.extended_enat) (P (-> tptp.extended_enat Bool))) (= (@ (@ tptp.member_Extended_enat A) (@ tptp.collec4429806609662206161d_enat P)) (@ P A))))
% 6.83/7.10 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.83/7.10 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.83/7.10 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.83/7.10 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.83/7.10 (assert (forall ((A3 tptp.set_Extended_enat)) (= (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) A3))) A3)))
% 6.83/7.10 (assert (forall ((A3 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A3))) A3)))
% 6.83/7.10 (assert (forall ((A3 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A3))) A3)))
% 6.83/7.10 (assert (forall ((A3 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A3))) A3)))
% 6.83/7.10 (assert (forall ((A3 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A3))) A3)))
% 6.83/7.10 (assert (forall ((A3 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A3))) A3)))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_nat tptp.mi) tptp.res))
% 6.83/7.10 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.83/7.10 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.83/7.10 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.83/7.10 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.83/7.10 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.83/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.83/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.83/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.83/7.10 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 6.83/7.10 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.83/7.10 (assert (= tptp.m (@ tptp.suc tptp.na)))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (@ (@ tptp.ord_less_real (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X4) Y3))))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2) (= (@ (@ tptp.ord_less_rat (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X4) Y3))))))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_nat (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X4) Y3))))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_int (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_nat X4) Y3))))))
% 6.83/7.10 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.83/7.10 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.83/7.10 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.83/7.10 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.83/7.10 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X4) Y3))))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X4) Y3))))))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B2) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X4) Y3))))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B2) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_nat X4) Y3))))))
% 6.83/7.10 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 6.83/7.10 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X4))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.83/7.10 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X4))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.83/7.10 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X4))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.83/7.10 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X4))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.83/7.10 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X4))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.83/7.10 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X4) tptp.one) (= X4 tptp.one))))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.83/7.10 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.83/7.10 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.83/7.10 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.83/7.10 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.83/7.10 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N3)))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N3)))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N3)))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N3)))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N3)))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N3)))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N3)))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N3)))))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 6.83/7.10 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.83/7.10 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.83/7.10 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.83/7.10 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.83/7.10 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.83/7.10 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))))))))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B2) (=> (@ _let_1 K) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N4)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat)))))))))))
% 6.83/7.10 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X4) Y3)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y3) X4)) _let_1)))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) Y3)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y3) X4)) _let_1)))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X4) Y3)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y3) X4)) _let_1)))))
% 6.83/7.10 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X4) Y3)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y3) X4)) _let_1)))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.83/7.10 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.83/7.10 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.83/7.10 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.83/7.10 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (assert (forall ((A tptp.complex) (B2 tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B2)) N) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B2) N)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B2)) N) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B2) N)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B2)) N) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B2) N)))))
% 6.83/7.10 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 6.83/7.10 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K)))))
% 6.83/7.10 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.minus_minus_real A) B2)) A))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A) (= (@ (@ tptp.plus_plus_rat B2) (@ (@ tptp.minus_minus_rat A) B2)) A))))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A) B2)) A))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A) B2)) A))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) B2) A))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B2)) B2) A))))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B2)) B2) A))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) B2) A))))
% 6.83/7.10 (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))))))))
% 6.83/7.10 (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))))))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) Y3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat) (N tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X4) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y3) _let_1)) X4)) N) Y3)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat)) (=> (forall ((N4 tptp.nat)) (not (= X4 (@ (@ tptp.plus_plus_nat N4) N4)))) (not (forall ((N4 tptp.nat)) (not (= X4 (@ (@ tptp.plus_plus_nat N4) (@ tptp.suc N4)))))))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X4) D)) (@ (@ tptp.vEBT_VEBT_low X4) D)) D) X4)))
% 6.83/7.10 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 6.83/7.10 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Z))))
% 6.83/7.10 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Z))))
% 6.83/7.10 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.83/7.10 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.83/7.10 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Z))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat) (N tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X4) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y3) _let_1)) X4)) N) X4)))))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.83/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.83/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.83/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.83/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.83/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (forall ((V tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B2) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((V tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((V tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((V tptp.num) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((V tptp.num) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.complex) (B2 tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B2)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B2) _let_1))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B2) _let_1))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B2)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B2) _let_1))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B2) _let_1))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B2) _let_1))))))
% 6.83/7.10 (assert (forall ((A tptp.complex) (B2 tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B2)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B2) _let_1))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B2) _let_1))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B2)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B2) _let_1))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B2) _let_1))))))
% 6.83/7.10 (assert (forall ((V tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B2) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((V tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((V tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((V tptp.num) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 6.83/7.10 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B2) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B2)))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B2) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B2) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B2)))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) _let_1)) A) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.83/7.10 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I))))))
% 6.83/7.10 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) (@ tptp.suc J))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B2 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))) B2)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B2 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))) B2)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B2 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))) B2)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B2 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))) B2)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B2 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))) B2)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B2)))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= (@ tptp.suc X4) (@ tptp.suc Y3)) (= X4 Y3))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (E tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B2)) E)) C))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (E tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B2)) E)) C))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (E tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B2)) E)) C))))
% 6.83/7.10 (assert (forall ((A tptp.int) (E tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B2)) E)) C))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B2)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B2) A)) (@ (@ tptp.times_times_real C) A)))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) C)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B2) A)) (@ (@ tptp.times_times_rat C) A)))))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B2) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B2) A)) (@ (@ tptp.times_times_nat C) A)))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B2) A)) (@ (@ tptp.times_times_int C) A)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) (@ _let_1 C))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (or (@ P N) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) N) (@ P I2)))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (@ P N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P I2)))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M2 tptp.nat)) (and (= M (@ tptp.suc M2)) (@ (@ tptp.ord_less_nat N) M2))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I3 tptp.nat)) (@ (@ P I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I3))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I) J))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I3 tptp.nat)) (=> (= J (@ tptp.suc I3)) (@ P I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ P (@ tptp.suc I3)) (@ P I3)))) (@ P I))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M3) (exists ((M4 tptp.nat)) (= M3 (@ tptp.suc M4))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M5)) N4) (@ P M5))) (@ P N4))) (@ P N))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N4) (=> (@ P N4) (@ P (@ tptp.suc N4))))) (@ P N))))))
% 6.83/7.10 (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) (Y4 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z2) (@ _let_1 Z2))))) (=> (forall ((N4 tptp.nat)) (@ (@ R N4) (@ tptp.suc N4))) (@ (@ R M) N)))))))
% 6.83/7.10 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.83/7.10 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) L2))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))))
% 6.83/7.10 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ tptp.suc A3) (@ _let_1 (@ tptp.suc A)))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N4 tptp.nat)) (=> (@ P (@ tptp.suc N4)) (@ P N4))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((A tptp.complex) (B2 tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B2)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B2) N)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B2)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B2) N)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A) B2)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B2) N)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B2)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B2) N)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B2)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B2) N)))))
% 6.83/7.10 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X4) N))) (let ((_let_2 (@ tptp.times_times_complex Y3))) (=> (= (@ (@ tptp.times_times_complex X4) Y3) (@ _let_2 X4)) (= (@ (@ tptp.times_times_complex _let_1) Y3) (@ _let_2 _let_1)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X4) N))) (let ((_let_2 (@ tptp.times_times_real Y3))) (=> (= (@ (@ tptp.times_times_real X4) Y3) (@ _let_2 X4)) (= (@ (@ tptp.times_times_real _let_1) Y3) (@ _let_2 _let_1)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X4) N))) (let ((_let_2 (@ tptp.times_times_rat Y3))) (=> (= (@ (@ tptp.times_times_rat X4) Y3) (@ _let_2 X4)) (= (@ (@ tptp.times_times_rat _let_1) Y3) (@ _let_2 _let_1)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X4) N))) (let ((_let_2 (@ tptp.times_times_nat Y3))) (=> (= (@ (@ tptp.times_times_nat X4) Y3) (@ _let_2 X4)) (= (@ (@ tptp.times_times_nat _let_1) Y3) (@ _let_2 _let_1)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X4) N))) (let ((_let_2 (@ tptp.times_times_int Y3))) (=> (= (@ (@ tptp.times_times_int X4) Y3) (@ _let_2 X4)) (= (@ (@ tptp.times_times_int _let_1) Y3) (@ _let_2 _let_1)))))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I) J)) U)) K))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) E)) C) D))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B2)) E)) C) D))))
% 6.83/7.10 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) E)) C) D))))
% 6.83/7.10 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B2) E)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) E)) D)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B2) E)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A)) E)) D)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) E)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A)) E)) D)))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y3) Y3)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.minus_minus_real X4) Y3)))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y3) Y3)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X4) Y3)) (@ (@ tptp.minus_minus_rat X4) Y3)))))
% 6.83/7.10 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y3) Y3)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X4) Y3)) (@ (@ tptp.minus_minus_int X4) Y3)))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X4))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y3)) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y3) B2))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X4) A)) B2))))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X4))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y3)) (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y3) B2))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X4) A)) B2))))))
% 6.83/7.10 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X4))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y3)) (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y3) B2))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X4) A)) B2))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_real (@ F N)) (@ F N5))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N5))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_num (@ F N)) (@ F N5))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N5))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_int (@ F N)) (@ F N5))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N4)) (@ F (@ tptp.suc N4)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N)) (@ F N5))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N5))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N5))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N5))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N5))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N5)) (@ F N))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N))))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N4))) (@ F N4))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N4) (=> (@ (@ tptp.ord_less_nat N4) J) (=> (@ P N4) (@ P (@ tptp.suc N4)))))) (@ P J))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N4) (=> (@ (@ tptp.ord_less_nat N4) J) (=> (@ P (@ tptp.suc N4)) (@ P N4))))) (@ P I))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 6.83/7.10 (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)))))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))
% 6.83/7.10 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.83/7.10 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) E)) D)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A)) E)) D)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A)) E)) D)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) E)) C)) D))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B2)) E)) C)) D))))
% 6.83/7.10 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) E)) C)) D))))
% 6.83/7.10 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) E)) D)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B2) A)) E)) D)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B2) A)) E)) D)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B2)) E)) C)) D))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B2)) E)) C)) D))))
% 6.83/7.10 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B2 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 B2) E)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B2)) E)) C)) D))))
% 6.83/7.10 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) X4)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X4) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X4) tptp.one_one_complex)))))
% 6.83/7.10 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) X4)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) X4)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)))))
% 6.83/7.10 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X4) X4)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X4) tptp.one_one_int)))))
% 6.83/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.83/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.83/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.83/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.83/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.83/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.83/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.83/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.83/7.10 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X4) Y3) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X4) N)) (@ (@ tptp.power_power_complex Y3) N)) tptp.one_one_complex))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X4) Y3) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X4) N)) (@ (@ tptp.power_power_real Y3) N)) tptp.one_one_real))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X4) Y3) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X4) N)) (@ (@ tptp.power_power_rat Y3) N)) tptp.one_one_rat))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X4) Y3) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X4) N)) (@ (@ tptp.power_power_nat Y3) N)) tptp.one_one_nat))))
% 6.83/7.10 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X4) Y3) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X4) N)) (@ (@ tptp.power_power_int Y3) N)) tptp.one_one_int))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) I))))
% 6.83/7.10 (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)))
% 6.83/7.10 (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)))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_real X4) Y3)) (@ (@ tptp.ord_less_real Y3) X4)))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_rat X4) Y3)) (@ (@ tptp.ord_less_rat Y3) X4)))))
% 6.83/7.10 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_int X4) Y3)) (@ (@ tptp.ord_less_int Y3) X4)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.83/7.10 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.83/7.10 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.83/7.10 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M) N)))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 6.83/7.10 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.83/7.10 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N4) (@ P M5))) (@ P N4))) (@ P N))))
% 6.83/7.10 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (not (@ P N4)) (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N4) (not (@ P M5)))))) (@ P N))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_nat X4) Y3)) (@ (@ tptp.ord_less_nat Y3) X4)))))
% 6.83/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.83/7.10 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B2))) (exists ((X3 tptp.nat)) (and (@ P X3) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X3)))))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 6.83/7.10 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B2)))))
% 6.83/7.10 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.83/7.10 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.83/7.10 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.83/7.10 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.83/7.10 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.83/7.10 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.83/7.10 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.83/7.10 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.83/7.10 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.83/7.10 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.83/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.83/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.83/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.83/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.83/7.10 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.power_power_complex X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X4) X4)) X4)) X4))))
% 6.83/7.10 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X4) X4)) X4)) X4))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X4) X4)) X4)) X4))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat)) (= (@ (@ tptp.power_power_nat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X4) X4)) X4)) X4))))
% 6.83/7.10 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X4) X4)) X4)) X4))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.83/7.10 (assert (forall ((X4 tptp.complex) (Y3 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 X4) Y3)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X4) _let_2)) (@ (@ tptp.power_power_complex Y3) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X4)) Y3)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 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 X4) Y3)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y3) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) Y3)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat) (Y3 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 X4) Y3)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_2)) (@ (@ tptp.power_power_rat Y3) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X4)) Y3)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X4) Y3)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X4) _let_1)) (@ (@ tptp.power_power_nat Y3) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X4)) Y3))))))
% 6.83/7.10 (assert (forall ((X4 tptp.int) (Y3 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 X4) Y3)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X4) _let_2)) (@ (@ tptp.power_power_int Y3) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X4)) Y3)))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.minus_minus_real C) D)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) D)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B2)) (@ (@ tptp.minus_minus_rat C) D)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.minus_minus_int C) D)))))
% 6.83/7.10 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (not (= M6 N2))))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.83/7.10 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N2) (= M6 N2)))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (@ (@ tptp.ord_less_nat (@ F I3)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 6.83/7.10 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (forall ((K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (exists ((N4 tptp.nat)) (= L2 (@ (@ tptp.plus_plus_nat K) N4))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.83/7.10 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M6) K3))))))
% 6.83/7.10 (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))))))))
% 6.83/7.10 (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))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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))))))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 6.83/7.10 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (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 B2)) (@ _let_1 A))))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((X4 tptp.complex) (Y3 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 X4) Y3)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X4) _let_2)) (@ (@ tptp.power_power_complex Y3) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X4)) Y3)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 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 X4) Y3)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y3) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) Y3)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat) (Y3 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 X4) Y3)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_2)) (@ (@ tptp.power_power_rat Y3) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X4)) Y3)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.int) (Y3 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 X4) Y3)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X4) _let_2)) (@ (@ tptp.power_power_int Y3) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X4)) Y3)))))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 6.83/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 6.83/7.10 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K)) J)))))))))
% 6.83/7.10 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K)) J)))))))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K)) J)))))))))
% 6.83/7.10 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K)) J)))))))))
% 6.83/7.10 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N) (@ (@ tptp.ord_less_eq_real I) (@ (@ tptp.minus_minus_real N) K)))))
% 6.83/7.10 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N) (@ (@ tptp.ord_less_eq_rat I) (@ (@ tptp.minus_minus_rat N) K)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N) K)))))
% 6.83/7.10 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N) K)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B2) tptp.one_one_real)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B2) tptp.one_one_rat)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B2) tptp.one_one_nat)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B2) tptp.one_one_int)))))
% 6.83/7.10 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.83/7.10 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.83/7.10 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B2)) (= (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.minus_minus_real A) B2)) A))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A) B2)) (= (@ (@ tptp.plus_plus_rat B2) (@ (@ tptp.minus_minus_rat A) B2)) A))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B2)) (= (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.minus_minus_nat A) B2)) A))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B2)) (= (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.minus_minus_int A) B2)) A))))
% 6.83/7.10 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N4) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B2) C))))))
% 6.83/7.10 (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))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) J))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.minus_minus_nat J) I) K) (= J (@ (@ tptp.plus_plus_nat K) I))))))
% 6.83/7.10 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I)))))
% 6.83/7.10 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 6.83/7.10 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 6.83/7.10 (assert (forall ((J tptp.nat) (K tptp.nat) (I tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I) K)))))
% 6.83/7.10 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I) K))))))
% 6.83/7.10 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X4))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X4) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X4))))
% 6.83/7.10 (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.sc)) tptp.miny))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 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)) X4)) Y3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y3) _let_2)))))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat) (Y3 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)) X4)) Y3)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_2)) (@ (@ tptp.power_power_rat Y3) _let_2)))))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) B2) A)))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B2)) B2) A)))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) B2) A)))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) B2) A)))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B2)) B2) A)))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) B2) A)))
% 6.83/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_real A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_rat A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_nat A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.minus_minus_int A) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) A) B2)))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B2)) A) B2)))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B2)) A) B2)))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) A) B2)))
% 6.83/7.10 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.minus_minus_real A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.minus_minus_rat A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.minus_minus_nat A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.minus_minus_int A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B2)) B2) A)))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B2)) B2) A)))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) A)))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B2)) B2) A)))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A) (@ (@ tptp.plus_plus_real C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A) (@ (@ tptp.plus_plus_rat C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A) (@ (@ tptp.plus_plus_nat C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_eq_real A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_eq_rat A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_eq_nat A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_eq_int A) B2))))
% 6.83/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_real A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_rat A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A) B2))))
% 6.83/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.83/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.83/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.83/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.83/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.83/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.83/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.83/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.83/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.83/7.10 (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))))))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 6.83/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.83/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (assert (forall ((S2 tptp.set_real)) (=> (exists ((X5 tptp.real)) (@ (@ tptp.member_real X5) S2)) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (@ (@ tptp.ord_less_eq_real X3) Z3)))) (exists ((Y4 tptp.real)) (and (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (@ (@ tptp.ord_less_eq_real X5) Y4))) (forall ((Z3 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S2) (@ (@ tptp.ord_less_eq_real X3) Z3))) (@ (@ tptp.ord_less_eq_real Y4) Z3)))))))))
% 6.83/7.10 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.power_power_real X4) N4))))))
% 6.83/7.10 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 6.83/7.10 (assert (forall ((Z tptp.extended_enat) (Y3 tptp.extended_enat) (X4 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X4))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y3) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y3) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y3)) Z))))))
% 6.83/7.10 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N4 tptp.extended_enat)) (=> (forall ((M5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M5) N4) (@ P M5))) (@ P N4))) (@ P N))))
% 6.83/7.10 (assert (forall ((X4 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 X4) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) _let_2))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (C tptp.real) (B2 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 B2) 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 B2) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (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)))))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B2))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B2))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.10 (assert (= tptp.times_times_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real B3) A4))))
% 6.83/7.10 (assert (= tptp.times_times_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat B3) A4))))
% 6.83/7.10 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A4))))
% 6.83/7.10 (assert (= tptp.times_times_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.times_times_int B3) A4))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_rat B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_rat B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))))
% 6.83/7.10 (assert (forall ((X4 tptp.complex)) (= (= tptp.one_one_complex X4) (= X4 tptp.one_one_complex))))
% 6.83/7.10 (assert (forall ((X4 tptp.real)) (= (= tptp.one_one_real X4) (= X4 tptp.one_one_real))))
% 6.83/7.10 (assert (forall ((X4 tptp.rat)) (= (= tptp.one_one_rat X4) (= X4 tptp.one_one_rat))))
% 6.83/7.10 (assert (forall ((X4 tptp.nat)) (= (= tptp.one_one_nat X4) (= X4 tptp.one_one_nat))))
% 6.83/7.10 (assert (forall ((X4 tptp.int)) (= (= tptp.one_one_int X4) (= X4 tptp.one_one_int))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B2) A) (@ (@ tptp.plus_plus_real C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B2) A) (@ (@ tptp.plus_plus_rat C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B2) A) (@ (@ tptp.plus_plus_nat C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B2))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B2))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.10 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B2))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B2))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.10 (assert (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real B3) A4))))
% 6.83/7.10 (assert (= tptp.plus_plus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat B3) A4))))
% 6.83/7.10 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat B3) A4))))
% 6.83/7.10 (assert (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int B3) A4))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A) (@ (@ tptp.plus_plus_real C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A) (@ (@ tptp.plus_plus_rat C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 6.83/7.10 (assert (forall ((B4 tptp.real) (K tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B4 (@ _let_2 B2)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B2))))))))
% 6.83/7.10 (assert (forall ((B4 tptp.rat) (K tptp.rat) (B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B4 (@ _let_2 B2)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B2))))))))
% 6.83/7.10 (assert (forall ((B4 tptp.nat) (K tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B4 (@ _let_2 B2)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B2))))))))
% 6.83/7.10 (assert (forall ((B4 tptp.int) (K tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B4 (@ _let_2 B2)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B2))))))))
% 6.83/7.10 (assert (forall ((A3 tptp.real) (K tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A3) B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))))
% 6.83/7.10 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A3) B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B2)))))))
% 6.83/7.10 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A3) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 6.83/7.10 (assert (forall ((A3 tptp.int) (K tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A3) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 6.83/7.10 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_rat I) K) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B2) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B2) (@ (@ tptp.minus_minus_real C) D)) (= (= A B2) (= C D)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B2) (@ (@ tptp.minus_minus_rat C) D)) (= (= A B2) (= C D)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B2) (@ (@ tptp.minus_minus_int C) D)) (= (= A B2) (= C D)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_eq_real A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_eq_rat A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_eq_nat A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_eq_int A) B2))))
% 6.83/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_rat A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_nat A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_int A) B2)))))
% 6.83/7.10 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (exists ((C2 tptp.nat)) (= B3 (@ (@ tptp.plus_plus_nat A4) C2))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (not (forall ((C3 tptp.nat)) (not (= B2 (@ (@ tptp.plus_plus_nat A) C3))))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) D))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))))
% 6.83/7.10 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (= K L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B2) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real C) D)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B2) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_eq_rat A) B2) (@ (@ tptp.ord_less_eq_rat C) D)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B2) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int C) D)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) C)))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B2) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) D))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat D) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B2) D))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) D))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.ord_less_real A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.ord_less_rat A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A) B2))))
% 6.83/7.10 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A) B2))))
% 6.83/7.10 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_rat A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A) B2)))))
% 6.83/7.10 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A) B2)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B2) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) D))))))
% 6.83/7.10 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))))
% 6.83/7.10 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (= K L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (= K L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.83/7.10 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B2) C)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) C)))))
% 6.83/7.10 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B2) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B2) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B2) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B2) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real C) D)))))
% 6.83/7.10 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B2) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_rat A) B2) (@ (@ tptp.ord_less_rat C) D)))))
% 6.83/7.10 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B2) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int C) D)))))
% 6.83/7.10 (assert (forall ((A tptp.real) (B2 tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat D) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.83/7.11 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B2) A) (= C (@ (@ tptp.minus_minus_real A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B2) A) (= C (@ (@ tptp.minus_minus_rat A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B2) A) (= C (@ (@ tptp.minus_minus_nat A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B2) A) (= C (@ (@ tptp.minus_minus_int A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B2)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B2) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B2) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B2) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B2)) (= (@ (@ tptp.plus_plus_real A) B2) C))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C) B2)) (= (@ (@ tptp.plus_plus_rat A) B2) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B2)) (= (@ (@ tptp.plus_plus_int A) B2) C))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B2) C) (= A (@ (@ tptp.plus_plus_real C) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B2) C) (= A (@ (@ tptp.plus_plus_rat C) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B2) C) (= A (@ (@ tptp.plus_plus_int C) B2)))))
% 6.83/7.11 (assert (forall ((A3 tptp.real) (K tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A3) B2) (@ _let_1 (@ (@ tptp.minus_minus_real A) B2)))))))
% 6.83/7.11 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A3) B2) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B2)))))))
% 6.83/7.11 (assert (forall ((A3 tptp.int) (K tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A3) B2) (@ _let_1 (@ (@ tptp.minus_minus_int A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))))
% 6.83/7.11 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.83/7.11 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.83/7.11 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.83/7.11 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.83/7.11 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.83/7.11 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.83/7.11 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.83/7.11 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B2)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A)) A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B2) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B2)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B2) A)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B2) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B2) A)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B2) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B2) A)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B2))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B2) A) C) (= B2 (@ (@ tptp.plus_plus_nat C) A))))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B2)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C) B2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) C))))
% 6.83/7.11 (assert (forall ((B2 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 B2) A)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B2) A)) _let_1)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 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) B2)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B2) A)) _let_1)))))
% 6.83/7.11 (assert (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B2) C)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B2) A)) C))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B2) A)) C))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B2) C)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B2) A)) C))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_complex B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_rat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B2) C)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B2) C)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B2) C)) (@ (@ tptp.divide_divide_rat (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B2)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B2)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B2))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (= tptp.vEBT_VEBT_low (lambda ((X tptp.nat) (N2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.83/7.11 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) B2))) (= (@ (@ tptp.modulo_modulo_nat _let_1) B2) _let_1))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B2))) (= (@ (@ tptp.modulo_modulo_int _let_1) B2) _let_1))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B2))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B2) _let_1))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) B2) (@ (@ tptp.modulo364778990260209775nteger A) B2))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B2) A)) B2) (@ (@ tptp.modulo364778990260209775nteger A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B2)) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B2)) B2) (@ (@ tptp.modulo364778990260209775nteger A) B2))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) C)) A)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) C)) A)) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) C)) A)) B2) (@ (@ tptp.modulo364778990260209775nteger A) B2))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B2)) A)) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B2)) A)) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B2)) A)) B2) (@ (@ tptp.modulo364778990260209775nteger A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B2) C))) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B2) C))) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B2) C))) B2) (@ (@ tptp.modulo364778990260209775nteger A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B2))) B2) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B2))) B2) (@ (@ tptp.modulo_modulo_int A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B2))) B2) (@ (@ tptp.modulo364778990260209775nteger A) B2))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.83/7.11 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.83/7.11 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.83/7.11 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.83/7.11 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.83/7.11 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B2) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B2) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) B2)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) B2)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B2)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B2)) C))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B2)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (A2 tptp.nat) (B2 tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A2) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B2) C) (@ (@ tptp.modulo_modulo_nat B) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B)) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B2 tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A2) C)) (=> (= (@ (@ tptp.modulo_modulo_int B2) C) (@ (@ tptp.modulo_modulo_int B) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B)) C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A2) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B2) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B2)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A2) B)) C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B2) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B2) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B2) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B2) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B2) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) B2)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) B2)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B2)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (A2 tptp.nat) (B2 tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A2) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B2) C) (@ (@ tptp.modulo_modulo_nat B) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) B)) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B2 tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A2) C)) (=> (= (@ (@ tptp.modulo_modulo_int B2) C) (@ (@ tptp.modulo_modulo_int B) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) B)) C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A2) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B2) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B2) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B2) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B2) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B2) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B2)) C)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) B2)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B2)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B2 tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A2) C)) (=> (= (@ (@ tptp.modulo_modulo_int B2) C) (@ (@ tptp.modulo_modulo_int B) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A2) B)) C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer) (B2 tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A2) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B2) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B2)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B)) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B2) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B2) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B2)) C))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B2)) N)) B2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B2)) N)) B2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B2)) N)) B2) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) B2))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X4) N) (@ (@ tptp.modulo_modulo_nat Y3) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X4) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y3) (@ _let_1 Q22))))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B2) C)) (not (forall ((D3 tptp.int)) (not (= B2 (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D3)))))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B2) C)) (not (forall ((D3 tptp.code_integer)) (not (= B2 (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D3)))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B2) C))) C)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B2) C))) C)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B2) C))) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B2) C))) C)))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P2 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P2) (=> (@ (@ tptp.ord_less_nat M) P2) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) P2) (=> (@ P N4) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N4)) P2))))) (@ P M)))))))
% 6.83/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (N tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X4) N) (@ (@ tptp.modulo_modulo_nat Y3) N)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X4) (exists ((Q3 tptp.nat)) (= X4 (@ (@ tptp.plus_plus_nat Y3) (@ (@ tptp.times_times_nat N) Q3))))))))
% 6.83/7.11 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (forall ((S3 tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S3))))))))))
% 6.83/7.11 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (forall ((S3 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q2) S3))))))))))
% 6.83/7.11 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N2)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) (@ (@ tptp.modulo_modulo_nat A) B2)) A)))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) (@ (@ tptp.modulo_modulo_int A) B2)) A)))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A) B2))) (@ (@ tptp.modulo364778990260209775nteger A) B2)) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) A)))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) A)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B2)) (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A) B2))) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) A)))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) A)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B2)) B2)) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2)) A)))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2)) A)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B2)) B2)) (@ (@ tptp.modulo364778990260209775nteger A) B2)) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B2)) B2)) (@ (@ tptp.modulo364778990260209775nteger A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B2)) B2)) (@ (@ tptp.modulo364778990260209775nteger A) B2))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) (@ (@ tptp.modulo_modulo_nat A) B2))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) (@ (@ tptp.modulo_modulo_int A) B2))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A) B2))) (@ (@ tptp.modulo364778990260209775nteger A) B2))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B2) C))) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B2) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) C))) C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B2) C))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B2) C))) C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2))) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2))) (@ (@ tptp.modulo_modulo_int A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A) B2))) (@ (@ tptp.modulo364778990260209775nteger A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B2)) (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B2)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B2)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) B2)) (@ (@ tptp.modulo_modulo_nat A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) B2)) (@ (@ tptp.modulo_modulo_int A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B2)) B2)) (@ (@ tptp.modulo364778990260209775nteger A) B2))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (assert (forall ((A3 tptp.nat) (N tptp.nat)) (= A3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A3) N)) N)) (@ (@ tptp.modulo_modulo_nat A3) N)))))
% 6.83/7.11 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N2)) N2)))))
% 6.83/7.11 (assert (forall ((X5 tptp.real)) (exists ((Y4 tptp.real)) (@ (@ tptp.ord_less_real Y4) X5))))
% 6.83/7.11 (assert (forall ((X5 tptp.rat)) (exists ((Y4 tptp.rat)) (@ (@ tptp.ord_less_rat Y4) X5))))
% 6.83/7.11 (assert (forall ((X5 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X5) X_1))))
% 6.83/7.11 (assert (forall ((X5 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X5) X_1))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (X4 tptp.nat) (M7 tptp.nat)) (=> (@ P X4) (=> (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)))))))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_complex C) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_real C) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.times_times_rat C) B2))))))
% 6.83/7.11 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X4) Y3)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X4) W)) (@ (@ tptp.times_times_complex Y3) Z)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X4) W)) (@ (@ tptp.times_times_real Y3) Z)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X4) Y3)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X4) W)) (@ (@ tptp.times_times_rat Y3) Z)))))
% 6.83/7.11 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y3)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X4) Z)) (@ (@ tptp.times_times_complex Y3) W)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real Y3) W)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X4) Y3)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat Y3) W)))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) B2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) B2)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) B2)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) B2)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B2) C)))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.83/7.11 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.83/7.11 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.83/7.11 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 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 B2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B2))))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 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 B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B2))))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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 B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B2))))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.pow K) L2)))))
% 6.83/7.11 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_real (@ (@ tptp.pow K) L2)))))
% 6.83/7.11 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.pow K) L2)))))
% 6.83/7.11 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.pow K) L2)))))
% 6.83/7.11 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ (@ tptp.pow K) L2)))))
% 6.83/7.11 (assert (forall ((U tptp.real) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X4) Y3)) (=> (@ _let_2 X4) (=> (@ _let_2 Y3) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.83/7.11 (assert (forall ((U tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X4) Y3)) (=> (@ _let_2 X4) (=> (@ _let_2 Y3) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) Y3)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.83/7.11 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 6.83/7.11 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B2) C)) (or (= C tptp.zero_zero_rat) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B2) C)) (or (= C tptp.zero_zero_nat) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= A B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_real) (= A B2))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_rat) (= A B2))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_nat) (= A B2))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_int) (= A B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B2) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.literal)) (= (@ (@ tptp.plus_plus_literal tptp.zero_zero_literal) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X4) Y3)) (and (= X4 tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X4) Y3) tptp.zero_zero_nat) (and (= X4 tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B2)) (= B2 tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B2)) (= B2 tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B2)) (= B2 tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B2)) (= B2 tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B2) A)) (= B2 tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B2) A)) (= B2 tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B2) A)) (= B2 tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B2) A)) (= B2 tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B2) A) (= B2 tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B2) A) (= B2 tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B2) A) (= B2 tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B2) A) (= B2 tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B2) A) A) (= B2 tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B2) A) A) (= B2 tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A) A) (= B2 tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) A) (= B2 tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.literal)) (= (@ (@ tptp.plus_plus_literal A) tptp.zero_zero_literal) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B2) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_complex) (= A B2))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_real) (= A B2))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (= (= (@ _let_1 A) (@ _let_1 B2)) (or (= C tptp.zero_zero_rat) (= A B2))))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B2) C)) (or (= C tptp.zero_zero_complex) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B2) C)) (or (= C tptp.zero_zero_real) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B2) C)) (or (= C tptp.zero_zero_rat) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B2) A)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) A)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) A)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) A)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) A)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) B2)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.83/7.11 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger B2) A)) (@ (@ tptp.divide6298287555418463151nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B2) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B2) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B2) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B2) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B2) C)))))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((X4 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X4) X4))) (= X4 tptp.zero_zero_real))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.83/7.11 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X4) M) _let_1) (or (= M tptp.zero_zero_nat) (= X4 _let_1))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X4) N)) (or (@ _let_1 X4) (= N tptp.zero_zero_nat))))))
% 6.83/7.11 (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)))))))))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.11 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.83/7.11 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.83/7.11 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B2) A)) B2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B2) A)) B2) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B2)) B2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B2)) B2) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B2) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B2) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B2) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B2) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.ord_less_eq_real B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B2)) (@ (@ tptp.ord_less_eq_rat B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.ord_less_eq_int B2) A))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B2) A)) B2) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B2) A)) B2) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) B2) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B2)) B2) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B2) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B2) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B2) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B2) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.ord_less_real B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B2)) (@ (@ tptp.ord_less_rat B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.ord_less_int B2) A))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (B2 tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B2)) (or (= C tptp.zero_zero_complex) (= B2 tptp.one_one_complex)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B2)) (or (= C tptp.zero_zero_real) (= B2 tptp.one_one_real)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B2)) (or (= C tptp.zero_zero_rat) (= B2 tptp.one_one_rat)))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B2)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (B2 tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B2) C)) (or (= C tptp.zero_zero_complex) (= B2 tptp.one_one_complex)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (= C (@ (@ tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (= B2 tptp.one_one_real)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B2) C)) (or (= C tptp.zero_zero_rat) (= B2 tptp.one_one_rat)))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (= C (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (= B2 tptp.one_one_int)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y3) Y3)) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y3) Y3)) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y3) Y3)) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B2)))) (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) B2)))))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B2)))) (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) B2)))))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 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 B2)) (@ (@ tptp.divide_divide_nat A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 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 B2)) (@ (@ tptp.divide_divide_int A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B2)) A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B2)) A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B2)) A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B2)) A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B2)) A) B2))))
% 6.83/7.11 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B2)) B2) A))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B2)) B2) A))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B2)) B2) A))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B2)) B2) A))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B2)) B2) A))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B2)))) (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) B2)))))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B2)))) (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) B2)))))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B2)))) (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) B2)))))))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.divide1717551699836669952omplex A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 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 B2)) (@ (@ tptp.divide_divide_real A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 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 B2)) (@ (@ tptp.divide_divide_rat A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A)) (@ (@ tptp.times_times_complex B2) C)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B2) C)) (@ (@ tptp.divide_divide_real A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B2) C)) (@ (@ tptp.divide_divide_rat A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B2) C)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (@ (@ tptp.divide_divide_real A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)) (@ (@ tptp.divide_divide_rat A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex C) B2)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B2)) (@ (@ tptp.divide_divide_real A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B2)) (@ (@ tptp.divide_divide_rat A) B2)))))
% 6.83/7.11 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.83/7.11 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.83/7.11 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.83/7.11 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.83/7.11 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.one_one_complex) (and (not (= B2 tptp.zero_zero_complex)) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.one_one_real) (and (not (= B2 tptp.zero_zero_real)) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B2) tptp.one_one_rat) (and (not (= B2 tptp.zero_zero_rat)) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (and (not (= B2 tptp.zero_zero_complex)) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B2)) (and (not (= B2 tptp.zero_zero_real)) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B2)) (and (not (= B2 tptp.zero_zero_rat)) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B2) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B2) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B2) A)) (and (not (= A tptp.zero_zero_real)) (= A B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B2) A)) (and (not (= A tptp.zero_zero_rat)) (= A B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B2) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B2) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B2) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 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 B2)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 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 B2)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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 B2)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B2) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A)) (@ _let_1 B2)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B2)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B2)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B2)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B2))))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 6.83/7.11 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.83/7.11 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B2)) tptp.one_one_Code_integer)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) tptp.one_one_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) tptp.one_one_int)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) B2)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B2)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B2)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B2)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B2)) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B2) (@ (@ tptp.times_3573771949741848930nteger C) A))) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B2) A)) B2) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B2) A)) B2) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B2) A)) B2) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B2)) B2) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B2)) B2) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B2)) B2) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B2) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B2) A)) A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) A)) A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) A)) A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B2) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B2) A)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B2) A)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B2) A)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B2)) tptp.one_one_Code_integer)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B2)) tptp.one_one_int)))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B2) C))))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger A) B2)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B2) C))))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B2)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B2)) B2) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B2)) B2) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B2)) B2) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B2)) B2) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B2)) B2) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B2)) B2) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (@ (@ tptp.modulo_modulo_nat B2) A) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (@ (@ tptp.modulo_modulo_int B2) A) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B2) (= (@ (@ tptp.modulo364778990260209775nteger B2) A) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.83/7.11 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.83/7.11 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.83/7.11 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.83/7.11 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.83/7.11 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_real A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A)) (@ (@ tptp.ord_less_rat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_real B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A)) (@ (@ tptp.ord_less_rat B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) A)) tptp.one_one_rat) (@ _let_1 B2))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((B2 tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B2) (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B2) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B2) (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B2))) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B2))) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B2) C))) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B2) C))) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B2)) A)) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B2)) A)) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) C)) A)) B2) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) C)) A)) B2) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B2) N)) (@ (@ tptp.ord_less_eq_real A) B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B2) N)) (@ (@ tptp.ord_less_eq_rat A) B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B2) N)) (@ (@ tptp.ord_less_eq_nat A) B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B2) N)) (@ (@ tptp.ord_less_eq_int A) B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B2) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B2) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B2) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B2) A)) A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) A)) A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) A)) A) B2))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_eq_real A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A)) (@ (@ tptp.ord_less_eq_rat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (@ (@ tptp.ord_less_eq_real B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A)) (@ (@ tptp.ord_less_eq_rat B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_real B2) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B2)) (or (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B2)) (or (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B2)) (or (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B2))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 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) B2))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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) B2))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) (= (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)) (= (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)) (= (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))
% 6.83/7.11 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.83/7.11 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.83/7.11 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.83/7.11 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_real B2) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat B2) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int B2) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 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 X4) (=> (@ _let_2 Y3) (= (= (@ (@ tptp.power_power_real X4) _let_1) (@ (@ tptp.power_power_real Y3) _let_1)) (= X4 Y3))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 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 X4) (=> (@ _let_2 Y3) (= (= (@ (@ tptp.power_power_rat X4) _let_1) (@ (@ tptp.power_power_rat Y3) _let_1)) (= X4 Y3))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 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 X4) (=> (@ _let_2 Y3) (= (= (@ (@ tptp.power_power_nat X4) _let_1) (@ (@ tptp.power_power_nat Y3) _let_1)) (= X4 Y3))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 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 X4) (=> (@ _let_2 Y3) (= (= (@ (@ tptp.power_power_int X4) _let_1) (@ (@ tptp.power_power_int Y3) _let_1)) (= X4 Y3))))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1)) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1)) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A) B2)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B2)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_2 (= A tptp.zero_zero_real)))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_2 (= A tptp.zero_zero_rat)))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_2 (= A tptp.zero_zero_int)))))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))))
% 6.83/7.11 (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))))))))))
% 6.83/7.11 (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))))))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I2 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J3))) (@ P I2)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I2 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J3))) (@ P I2))))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) R2) (= (@ (@ tptp.divide_divide_int A) B2) Q2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B2) (= (@ (@ tptp.divide_divide_int A) B2) Q2))))))
% 6.83/7.11 (assert (forall ((A3 tptp.int) (N tptp.int)) (= A3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A3) N)) N)) (@ (@ tptp.modulo_modulo_int A3) N)))))
% 6.83/7.11 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I2 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J3))) (@ (@ P I2) J3)))))))
% 6.83/7.11 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I2 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J3))) (@ (@ P I2) J3)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X4) K)) X4)))))
% 6.83/7.11 (assert (forall ((A3 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A3) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B4) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B4) N))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 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 B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B2))) (=> (@ (@ 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) B2)) C))) (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B2)) (and (@ (@ tptp.ord_less_eq_int B2) A) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B2)) (@ _let_1 A))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A) B2)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((K tptp.int) (I tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I) K)) (@ (@ tptp.ord_less_eq_int K) I))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L2) K) (=> (@ _let_1 L2) (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)))))))
% 6.83/7.11 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)) (or (= K tptp.zero_zero_int) (= L2 tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L2)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) B2) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A2) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B2)) (@ (@ tptp.divide_divide_int A) B2))))))
% 6.83/7.11 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 6.83/7.11 (assert (forall ((A3 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A3) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B4) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A3) N)) (@ (@ tptp.divide_divide_int B4) N))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) B2) (@ (@ tptp.ord_less_eq_int (@ _let_1 B2)) (@ _let_1 B))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B2)) (@ (@ tptp.divide_divide_int A2) B2))))))
% 6.83/7.11 (assert (= tptp.dvd_dvd_real (lambda ((A4 tptp.real) (B3 tptp.real)) (=> (= A4 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))
% 6.83/7.11 (assert (= tptp.dvd_dvd_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (=> (= A4 tptp.zero_zero_rat) (= B3 tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_nat B2) C) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_int B2) C) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) C) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 6.83/7.11 (assert (forall ((X4 tptp.literal)) (= (= tptp.zero_zero_literal X4) (= X4 tptp.zero_zero_literal))))
% 6.83/7.11 (assert (forall ((X4 tptp.real)) (= (= tptp.zero_zero_real X4) (= X4 tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat)) (= (= tptp.zero_zero_rat X4) (= X4 tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat)) (= (= tptp.zero_zero_nat X4) (= X4 tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((X4 tptp.int)) (= (= tptp.zero_zero_int X4) (= X4 tptp.zero_zero_int))))
% 6.83/7.11 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.83/7.11 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.83/7.11 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) A) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B2) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 6.83/7.11 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B2) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B2) A) (= (= (@ (@ tptp.divide_divide_rat A) B2) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B2) A))))
% 6.83/7.11 (assert (= tptp.dvd_dvd_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B3) A4) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (= tptp.dvd_dvd_int (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B3) A4) tptp.zero_zero_int))))
% 6.83/7.11 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B3) A4) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B2) A))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat)) (=> (not (= X4 tptp.zero_zero_nat)) (not (forall ((N4 tptp.nat)) (not (= X4 (@ tptp.suc N4))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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 B2))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B2) A)))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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 B2))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B2) tptp.one_one_int)) A))) tptp.one_one_int))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 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 (= B2 (@ (@ tptp.times_3573771949741848930nteger A) C3)))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C3 tptp.nat)) (not (= B2 (@ (@ tptp.times_times_nat A) C3)))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C3 tptp.int)) (not (= B2 (@ (@ tptp.times_times_int A) C3)))))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B2) (= (= (@ (@ tptp.divide6298287555418463151nteger B2) A) C) (= B2 (@ (@ tptp.times_3573771949741848930nteger C) A)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (= (= (@ (@ tptp.divide_divide_nat B2) A) C) (= B2 (@ (@ tptp.times_times_nat C) A)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (= (= (@ (@ tptp.divide_divide_int B2) A) C) (= B2 (@ (@ tptp.times_times_int C) A)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B2 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) A) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B2)) C) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger C) B2)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B2)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B2)))))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B2) (= (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B2) C)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B2) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (= (= (@ (@ tptp.divide6298287555418463151nteger B2) A) (@ (@ tptp.divide6298287555418463151nteger D) C)) (= (@ (@ tptp.times_3573771949741848930nteger B2) C) (@ (@ tptp.times_3573771949741848930nteger A) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (=> (@ (@ tptp.dvd_dvd_nat C) D) (= (= (@ (@ tptp.divide_divide_nat B2) A) (@ (@ tptp.divide_divide_nat D) C)) (= (@ (@ tptp.times_times_nat B2) C) (@ (@ tptp.times_times_nat A) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (=> (@ (@ tptp.dvd_dvd_int C) D) (= (= (@ (@ tptp.divide_divide_int B2) A) (@ (@ tptp.divide_divide_int D) C)) (= (@ (@ tptp.times_times_int B2) C) (@ (@ tptp.times_times_int A) D)))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B2) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B2) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A) B2) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B2)) C) (@ (@ tptp.dvd_dvd_Code_integer B2) C))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B2)) C) (@ (@ tptp.dvd_dvd_real B2) C))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B2)) C) (@ (@ tptp.dvd_dvd_rat B2) C))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat B2) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int B2) C))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B2) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B2) (=> (@ (@ tptp.dvd_dvd_real C) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B2) (=> (@ (@ tptp.dvd_dvd_rat C) D) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B2) (=> (@ (@ tptp.dvd_dvd_nat C) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B2) (=> (@ (@ tptp.dvd_dvd_int C) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B2))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B2)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B2)) C) (@ (@ tptp.dvd_dvd_real A) C))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B2)) C) (@ (@ tptp.dvd_dvd_rat A) C))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_rat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_rat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B2) C))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (= tptp.dvd_dvd_real (lambda ((B3 tptp.real) (A4 tptp.real)) (exists ((K3 tptp.real)) (= A4 (@ (@ tptp.times_times_real B3) K3))))))
% 6.83/7.11 (assert (= tptp.dvd_dvd_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (exists ((K3 tptp.rat)) (= A4 (@ (@ tptp.times_times_rat B3) K3))))))
% 6.83/7.11 (assert (= tptp.dvd_dvd_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (exists ((K3 tptp.nat)) (= A4 (@ (@ tptp.times_times_nat B3) K3))))))
% 6.83/7.11 (assert (= tptp.dvd_dvd_int (lambda ((B3 tptp.int) (A4 tptp.int)) (exists ((K3 tptp.int)) (= A4 (@ (@ tptp.times_times_int B3) K3))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B2) K)) (@ (@ tptp.dvd_dvd_Code_integer B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B2) K)) (@ (@ tptp.dvd_dvd_real B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B2) K)) (@ (@ tptp.dvd_dvd_rat B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B2) K)) (@ (@ tptp.dvd_dvd_nat B2) A))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B2) K)) (@ (@ tptp.dvd_dvd_int B2) A))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) A) (not (forall ((K2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B2) K2))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A) (not (forall ((K2 tptp.real)) (not (= A (@ (@ tptp.times_times_real B2) K2))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B2) A) (not (forall ((K2 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B2) K2))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (not (forall ((K2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B2) K2))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (not (forall ((K2 tptp.int)) (not (= A (@ (@ tptp.times_times_int B2) K2))))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B2))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B2))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B2))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.83/7.11 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B2) C)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B2) C)) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B2) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real B2) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat B2) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger C) B2)) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int C) B2)) (@ _let_1 (@ (@ tptp.minus_minus_int B2) C))))))
% 6.83/7.11 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X4))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y3) Z)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X4))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y3) Z)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X4))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y3) Z)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X4))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y3) Z)))))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B2) C)) (= A B2)))))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B2) C)) (= A B2)))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B2) C)) (= A B2)))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B2) C)) (= A B2)))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B2) C)) (= A B2)))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B2) C)) (= A B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (C tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B2) C)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2)))))))
% 6.83/7.11 (assert (forall ((D tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer D) B2) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 D)) (@ (@ tptp.divide6298287555418463151nteger B2) D)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((D tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B2) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B2) D)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((D tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B2) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B2) D)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X4) Y3) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X4) N)) (@ (@ tptp.power_8256067586552552935nteger Y3) N)))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X4) Y3) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X4) N)) (@ (@ tptp.power_power_nat Y3) N)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X4) Y3) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X4) N)) (@ (@ tptp.power_power_real Y3) N)))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X4) Y3) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X4) N)) (@ (@ tptp.power_power_int Y3) N)))))
% 6.83/7.11 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X4) Y3) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X4) N)) (@ (@ tptp.power_power_complex Y3) N)))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B2)) (@ _let_1 A))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B2)) (@ _let_1 A))))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 B2) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B2)) (@ _let_1 A))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B2)) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B2)) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B2)) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 B2)) C) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 B2)) C) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B2) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B2)) C) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X4)))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.11 (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)))))))))
% 6.83/7.11 (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)))))))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B2) C)) (= A B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B2) C)) (= A B2)))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B2) C)) (= A B2)))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B2) C)) (= A B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B2)) (= A B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B2 tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B2 tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B2) tptp.zero_zero_rat))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B2 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B2 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B2) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B2 tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B2) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B2 tptp.zero_zero_real))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B2) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B2 tptp.zero_zero_rat))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B2) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B2 tptp.zero_zero_nat))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B2) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B2 tptp.zero_zero_int))))))
% 6.83/7.11 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.83/7.11 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.83/7.11 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.83/7.11 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.83/7.11 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.83/7.11 (assert (= (lambda ((Y6 tptp.real) (Z4 tptp.real)) (= Y6 Z4)) (lambda ((A4 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real A4) B3) tptp.zero_zero_real))))
% 6.83/7.11 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A4) B3) tptp.zero_zero_rat))))
% 6.83/7.11 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int A4) B3) tptp.zero_zero_int))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N4 tptp.nat)) (=> (@ P (@ tptp.suc N4)) (@ P N4))) (@ P tptp.zero_zero_nat)))))
% 6.83/7.11 (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 ((Y4 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y4))) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ P X3) Y4) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y4)))) (@ (@ P M) N))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ tptp.suc N4)))) (@ P N)))))
% 6.83/7.11 (assert (forall ((Y3 tptp.nat)) (=> (not (= Y3 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y3 (@ tptp.suc Nat3))))))))
% 6.83/7.11 (assert (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (@ tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.83/7.11 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X2)))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (not (@ P N4)) (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N4) (not (@ P M5))))))) (@ P N)))))
% 6.83/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.83/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 6.83/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 6.83/7.11 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.83/7.11 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.83/7.11 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.83/7.11 (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 ((B5 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B5 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B5) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B5) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B5)))))))))))))))
% 6.83/7.11 (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 ((B5 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B5 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B5) tptp.one_one_nat) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_nat A) B5) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B5)))))))))))))))
% 6.83/7.11 (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 ((B5 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B5 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B5) tptp.one_one_int) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_int A) B5) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B5)))))))))))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger A) B2)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B2)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger B2) A)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B2) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B2) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B2))))))
% 6.83/7.11 (assert (forall ((X4 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X4))) (=> (not (= X4 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X4) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X4))) (=> (not (= X4 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X4) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (=> (not (= X4 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (X4 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X4 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X4) (@ (@ tptp.power_8256067586552552935nteger X4) N)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (X4 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X4 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X4) (@ (@ tptp.power_power_rat X4) N)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (X4 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X4 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X4) (@ (@ tptp.power_power_nat X4) N)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X4 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X4) (@ (@ tptp.power_power_real X4) N)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (X4 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X4 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X4) (@ (@ tptp.power_power_int X4) N)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (X4 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X4 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X4) (@ (@ tptp.power_power_complex X4) N)))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 6.83/7.11 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (N tptp.nat) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B2) N)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (N tptp.nat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B2) N)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (N tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B2) N)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (N tptp.nat) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B2) N)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B2))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (A tptp.real) (B2 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 B2) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B2) N)) (= A B2))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (A tptp.rat) (B2 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 B2) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B2) N)) (= A B2))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (A tptp.nat) (B2 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 B2) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B2) N)) (= A B2))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (A tptp.int) (B2 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 B2) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B2) N)) (= A B2))))))))
% 6.83/7.11 (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)))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B2)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int)))))
% 6.83/7.11 (assert (forall ((B2 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 B2) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B2)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B2)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B2)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B2)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.83/7.11 (assert (forall ((B2 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 B2) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B2) C)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 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) B2)) C) (@ (@ tptp.dvd_dvd_Code_integer B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B2)) C) (@ (@ tptp.dvd_dvd_int B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 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 B2) (@ _let_1 C)) (= B2 C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B2) A) (@ (@ tptp.times_3573771949741848930nteger C) A)) (= B2 C)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B2) A) (@ (@ tptp.times_times_nat C) A)) (= B2 C)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B2) A) (@ (@ tptp.times_times_int C) A)) (= B2 C)))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B2) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B2) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B2) A)) C)))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B2) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B2) A)) C)))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B2) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B2) A)) C)))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B2) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B2) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B2)) C))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C))))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B2) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B2) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B2) C)) (@ (@ tptp.times_times_nat (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B2) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B2) C)) (@ (@ tptp.times_times_int (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B2) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B2) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B2) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B2) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B2) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B2) C)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B2) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B2) C)))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B2)) (@ (@ tptp.divide6298287555418463151nteger C) D)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B2) D)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (=> (@ (@ tptp.dvd_dvd_nat D) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) (@ (@ tptp.divide_divide_nat C) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (=> (@ (@ tptp.dvd_dvd_int D) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) (@ (@ tptp.divide_divide_int C) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B2) A) (@ (@ tptp.divide6298287555418463151nteger C) A)) (= B2 C)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B2) A) (@ (@ tptp.divide_divide_nat C) A)) (= B2 C)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B2) A) (@ (@ tptp.divide_divide_int C) A)) (= B2 C)))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B2)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B2)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B2)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.83/7.11 (assert (forall ((B2 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 B2) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger C) B2)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B2)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B2)) (@ _let_1 C))))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B2) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B2) C))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B2) C))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B2) C))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B2) C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B2)) N) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B2)) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B2) N))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B2)) N) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B2) N))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ 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 B2) N)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ 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 B2) N)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ 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 B2) N)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ 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 B2) N)))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B2 tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N)) B2) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (N tptp.nat) (B2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B2) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (N tptp.nat) (B2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B2) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (N tptp.nat) (B2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B2) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (N tptp.nat) (B2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B2) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B2))))))
% 6.83/7.11 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X4) Y3) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X4) N)) (@ (@ tptp.power_8256067586552552935nteger Y3) M))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X4) Y3) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X4) N)) (@ (@ tptp.power_power_nat Y3) M))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X4) Y3) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X4) N)) (@ (@ tptp.power_power_real Y3) M))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X4) Y3) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X4) N)) (@ (@ tptp.power_power_int Y3) M))))))
% 6.83/7.11 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X4) Y3) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X4) N)) (@ (@ tptp.power_power_complex Y3) M))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B2) C)) (@ (@ tptp.dvd_dvd_int C) (@ (@ tptp.minus_minus_int A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B2) C)) (@ (@ tptp.dvd_dvd_Code_integer C) (@ (@ tptp.minus_8373710615458151222nteger A) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B2) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B2) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B2) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B2)))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (assert (= tptp.neg_numeral_dbl_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real X) X))))
% 6.83/7.11 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat X) X))))
% 6.83/7.11 (assert (= tptp.neg_numeral_dbl_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) X))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B2) A)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B2) A)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B2) A)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B2) A)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B2)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B2)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_rat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B2)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ 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 B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ 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 B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ 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 B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ 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 B2) C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) 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 B2) C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) 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 B2) C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) 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 B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B2) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.83/7.11 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 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) B2) (=> (@ (@ 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 B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 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) B2) (=> (@ (@ 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 B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 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) B2) (=> (@ (@ 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 B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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) B2) (=> (@ (@ 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 B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 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) B2) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 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) B2) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 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) B2) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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) B2) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 B2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B2)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (= (@ (@ tptp.plus_plus_real X4) Y3) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (= (@ (@ tptp.plus_plus_rat X4) Y3) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (= (@ (@ tptp.plus_plus_nat X4) Y3) tptp.zero_zero_nat) (and (= X4 tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (= (@ (@ tptp.plus_plus_int X4) Y3) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X4) Y3) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y3) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X4) Y3) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y3) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X4) Y3) tptp.zero_zero_nat) (and (= X4 tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y3) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X4) Y3) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B2)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B2)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A)))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B2) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 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 B2)) (@ (@ tptp.ord_less_real A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 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 B2)) (@ (@ tptp.ord_less_rat A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 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 B2)) (@ (@ tptp.ord_less_int A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 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 B2)) (@ (@ tptp.ord_less_real B2) A))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 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 B2)) (@ (@ tptp.ord_less_rat B2) A))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 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 B2)) (@ (@ tptp.ord_less_int B2) A))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B2) A)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B2) A)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B2) A)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B2) A)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B2)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B2)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B2)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B2)) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B2) A)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B2) A)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B2) A)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B2) A)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_real A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_rat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_nat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.times_times_int A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B2)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B2)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B2)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B2)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B2))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B2)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (not (forall ((C3 tptp.nat)) (=> (= B2 (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X4) Y3)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X4) Y3)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y3) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X4) Y3)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X4) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y3) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ 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 B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ 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 B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y3)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_rat X4) Y3)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y3)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_eq_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y3)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y3)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y3)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X4) Y3))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.divide_divide_real A) C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) C)) (@ (@ tptp.divide_divide_rat A) C))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B2) C))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B2)) (or (and (@ _let_1 A) (@ _let_1 B2)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)) (not (= C tptp.zero_zero_real))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B2) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A)) (not (= C tptp.zero_zero_rat))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B2)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) B2)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B2)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y3)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.divide_divide_rat X4) Y3)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Y3)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Y3)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Y3)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Y3)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X4) Y3))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ 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 B2) N))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ 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 B2) N))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ 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 B2) N))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ 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 B2) N))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X4 tptp.complex) (W tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X4) Y3) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X4) Z) (@ (@ tptp.times_times_complex W) Y3)))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X4 tptp.real) (W tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X4) Y3) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X4) Z) (@ (@ tptp.times_times_real W) Y3)))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X4 tptp.rat) (W tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X4) Y3) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X4) Z) (@ (@ tptp.times_times_rat W) Y3)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) A) (and (=> (not _let_1) (= B2 (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C) A) (and (=> (not _let_1) (= B2 (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B2) C) A) (and (=> (not _let_1) (= B2 (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.83/7.11 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) B2)) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B2) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B2)) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B2) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B2)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (B2 tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B2 (@ (@ tptp.times_times_complex A) C)) (= (@ (@ tptp.divide1717551699836669952omplex B2) C) A)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B2 (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B2) C) A)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B2 (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B2) C) A)))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C) B2) (= A (@ (@ tptp.divide1717551699836669952omplex B2) C))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B2) (= A (@ (@ tptp.divide_divide_real B2) C))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B2) (= A (@ (@ tptp.divide_divide_rat B2) C))))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (B2 tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) A) (= B2 (@ (@ tptp.times_times_complex A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B2) C) A) (= B2 (@ (@ tptp.times_times_real A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B2) C) A) (= B2 (@ (@ tptp.times_times_rat A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.complex) (A tptp.complex) (B2 tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) C)) (= (@ (@ tptp.times_times_complex A) C) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B2) C)) (= (@ (@ tptp.times_times_real A) C) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B2) C)) (= (@ (@ tptp.times_times_rat A) C) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) tptp.one_one_complex) (= A B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B2) tptp.one_one_real) (= A B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B2) tptp.one_one_rat) (= A B2)))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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 B2))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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 B2))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B2) tptp.one_one_int)) A))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A) B2)) A))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B2)) A))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B2)) A))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B2)) B2))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B2)) B2))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) B2)) B2))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.83/7.11 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B2) A) (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B2) A) (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B2) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B2) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (@ P tptp.zero_zero_nat) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P (@ tptp.suc I2))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (or (@ P tptp.zero_zero_nat) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) N) (@ P (@ tptp.suc I2))))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K2) (not (@ P I4)))) (@ P K2)))))))
% 6.83/7.11 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I) K2) J))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))
% 6.83/7.11 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K))))))
% 6.83/7.11 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))))
% 6.83/7.11 (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))))))))))
% 6.83/7.11 (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))))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.pow X4) tptp.one) X4)))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 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 X4) _let_1) (@ (@ tptp.divide_divide_nat Y3) _let_1)) (=> (= (@ _let_2 X4) (@ _let_2 Y3)) (= X4 Y3)))))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B2) C) (= A (@ (@ tptp.times_3573771949741848930nteger C) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B2) C) (= A (@ (@ tptp.times_times_nat C) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B2) C) (= A (@ (@ tptp.times_times_int C) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B2)) (= (@ (@ tptp.times_3573771949741848930nteger A) B2) C)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B2)) (= (@ (@ tptp.times_times_nat A) B2) C)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B2)) (= (@ (@ tptp.times_times_int A) B2) C)))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (B2 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 B2) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B2) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (B2 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 B2) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 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 B2) A) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B2)) C) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B2)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B2)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 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 B2) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B2)) C))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 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 B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 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 B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C))))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B2) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C)))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ 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 B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ 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 B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ 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 B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ 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 B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ 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 B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ 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 B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ 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 B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ 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 B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 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 B2)) (@ (@ tptp.ord_less_eq_real A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 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 B2)) (@ (@ tptp.ord_less_eq_rat A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 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 B2)) (@ (@ tptp.ord_less_eq_int A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 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 B2)) (@ (@ tptp.ord_less_eq_real B2) A))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 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 B2)) (@ (@ tptp.ord_less_eq_rat B2) A))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 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 B2)) (@ (@ tptp.ord_less_eq_int B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 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) B2) (=> (@ (@ 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 B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 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) B2) (=> (@ (@ 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 B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 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) B2) (=> (@ (@ 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 B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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) B2) (=> (@ (@ 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 B2) D)))))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A)))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) A)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B2) D))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D))))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B2))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A)))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A)))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) A)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B2))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B2) C) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.plus_plus_real A) C))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.plus_plus_rat A) C))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_nat B2) (@ (@ tptp.plus_plus_nat A) C))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_int B2) (@ (@ tptp.plus_plus_int A) C))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 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) B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 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) B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 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) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B2)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 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 B2) (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 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 B2) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 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 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B2)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B2)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.plus_plus_real Y3) E2)))) (@ (@ tptp.ord_less_eq_real X4) Y3))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.plus_plus_rat Y3) E2)))) (@ (@ tptp.ord_less_eq_rat X4) Y3))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B2)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B2) (= (@ (@ tptp.divide_divide_nat A) B2) tptp.zero_zero_nat)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B2) (= (@ (@ tptp.divide_divide_int A) B2) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y3)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y3)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y3)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (@ _let_1 (@ (@ tptp.divide_divide_rat X4) Y3)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y3)) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_rat Y3) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y3)) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B2) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Z)) (@ (@ tptp.divide_divide_real Y3) W)))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Z)) (@ (@ tptp.divide_divide_rat Y3) W)))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) Y3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Z)) (@ (@ tptp.divide_divide_real Y3) W))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_rat X4) Y3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Z)) (@ (@ tptp.divide_divide_rat Y3) W))))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (X4 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Z)) (@ (@ tptp.divide_divide_real Y3) W))))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y3) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Z)) (@ (@ tptp.divide_divide_rat Y3) W))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y3) X4)) X4)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y3) X4)) X4)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y3) X4)) X4)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X4) Y3)) X4)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X4) Y3)) X4)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X4) Y3)) X4)))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (=> (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B2)) tptp.one_one_real))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (=> (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B2)) tptp.one_one_rat))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B2)) tptp.one_one_nat))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B2)) tptp.one_one_int))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y3) Y3))) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y3) Y3))) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y3) Y3))) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y3) Y3)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y3) Y3)))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y3) Y3)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (N tptp.nat) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B2) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_real A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (N tptp.nat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B2) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_rat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (N tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B2) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_nat A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (N tptp.nat) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B2) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_int A) B2)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y3) Y3))) (or (not (= X4 tptp.zero_zero_real)) (not (= Y3 tptp.zero_zero_real))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y3) Y3))) (or (not (= X4 tptp.zero_zero_rat)) (not (= Y3 tptp.zero_zero_rat))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y3) Y3))) (or (not (= X4 tptp.zero_zero_int)) (not (= Y3 tptp.zero_zero_int))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y3) Y3))) tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y3) Y3))) tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y3) Y3))) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 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 B2) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B2)) C))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 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 B2) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B2)) C))))))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((B2 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 B2) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))))))
% 6.83/7.11 (assert (forall ((B2 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 B2) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B2)))))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y3)) X4) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X4) Y3))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y3)) X4) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X4) Y3))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (X4 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.times_times_real Z) Y3)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Y3)) Z)))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (=> (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.times_times_rat Z) Y3)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Y3)) Z)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B2) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) C)) A) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.times_times_rat A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B2) C)) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.times_times_rat A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 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 B2) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 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 B2) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.83/7.11 (assert (forall ((B2 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 B2) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B2)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.83/7.11 (assert (forall ((B2 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 B2) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B2)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.83/7.11 (assert (forall ((B2 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 B2) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B2)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) A)))))))
% 6.83/7.11 (assert (forall ((B2 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 B2) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B2)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) A)))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B2) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B2)) (= A tptp.zero_zero_real))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B2) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B2)) (= A tptp.zero_zero_rat))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((B2 tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.83/7.11 (assert (forall ((W tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.83/7.11 (assert (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.83/7.11 (assert (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.83/7.11 (assert (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B2) Z))) Z))))))))
% 6.83/7.11 (assert (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B2) Z))) Z))))))))
% 6.83/7.11 (assert (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B2) Z))) Z))))))))
% 6.83/7.11 (assert (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z)) B2)) Z))))))))
% 6.83/7.11 (assert (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z)) B2)) Z))))))))
% 6.83/7.11 (assert (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B2)) Z))))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X4 tptp.complex) (W tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y3)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X4) Z)) (@ (@ tptp.times_times_complex W) Y3))) (@ (@ tptp.times_times_complex Y3) Z)))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X4 tptp.real) (W tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y3))) (@ (@ tptp.times_times_real Y3) Z)))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X4 tptp.rat) (W tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X4) Y3)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y3))) (@ (@ tptp.times_times_rat Y3) Z)))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.complex) (X4 tptp.complex) (Z tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y3)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.times_times_complex Z) Y3))) Y3)))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (X4 tptp.real) (Z tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X4) Y3)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real Z) Y3))) Y3)))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X4) Y3)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.times_times_rat Z) Y3))) Y3)))))
% 6.83/7.11 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X4 tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X4) Y3)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.times_times_complex Z) Y3))) Y3)))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X4 tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real Z) Y3))) Y3)))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X4 tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X4) Y3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.times_times_rat Z) Y3))) Y3)))))
% 6.83/7.11 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.divide1717551699836669952omplex Y3) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X4) Z)) Y3)) Z)))))
% 6.83/7.11 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real Y3) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) Z)) Y3)) Z)))))
% 6.83/7.11 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.divide_divide_rat Y3) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) Z)) Y3)) Z)))))
% 6.83/7.11 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Z)) Y3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.times_times_complex Y3) Z))) Z)))))
% 6.83/7.11 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X4) Z)) Y3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real Y3) Z))) Z)))))
% 6.83/7.11 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X4) Z)) Y3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.times_times_rat Y3) Z))) Z)))))
% 6.83/7.11 (assert (forall ((A tptp.real) (N tptp.nat) (B2 tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (@ (@ tptp.ord_less_eq_real A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (N tptp.nat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (@ (@ tptp.ord_less_eq_rat A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (N tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (N tptp.nat) (B2 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B2) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int A) B2))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (N tptp.nat) (B2 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 B2) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (N tptp.nat) (B2 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 B2) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (N tptp.nat) (B2 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 B2) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (N tptp.nat) (B2 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 B2) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= A B2))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B2)) tptp.one_one_int)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B2)) tptp.one_one_nat)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B2)) tptp.one_one_int)))))
% 6.83/7.11 (assert (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z)) B2)) Z))))))))
% 6.83/7.11 (assert (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z)) B2)) Z))))))))
% 6.83/7.11 (assert (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B2) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B2)) Z))))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.complex) (Z tptp.complex) (X4 tptp.complex) (W tptp.complex)) (=> (not (= Y3 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y3)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) Z)) (@ (@ tptp.times_times_complex W) Y3))) (@ (@ tptp.times_times_complex Y3) Z)))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X4 tptp.real) (W tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y3))) (@ (@ tptp.times_times_real Y3) Z)))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X4 tptp.rat) (W tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X4) Y3)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y3))) (@ (@ tptp.times_times_rat Y3) Z)))))))
% 6.83/7.11 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.divide1717551699836669952omplex Y3) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) Z)) Y3)) Z)))))
% 6.83/7.11 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.divide_divide_real Y3) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) Y3)) Z)))))
% 6.83/7.11 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.divide_divide_rat Y3) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) Y3)) Z)))))
% 6.83/7.11 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Z)) Y3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex Y3) Z))) Z)))))
% 6.83/7.11 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X4) Z)) Y3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real Y3) Z))) Z)))))
% 6.83/7.11 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X4) Z)) Y3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat Y3) Z))) Z)))))
% 6.83/7.11 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B2)))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B2) (= (@ (@ tptp.modulo364778990260209775nteger A) B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B2) (= (@ (@ tptp.modulo_modulo_nat A) B2) A)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B2) (= (@ (@ tptp.modulo_modulo_int A) B2) A)))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.11 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) K2) (not (@ P I4)))) (@ P (@ tptp.suc K2))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))) N))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (@ P N4) (@ P (@ tptp.suc N4))))) (@ P N))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B2)) (and (=> (@ (@ tptp.ord_less_nat A) B2) (@ P tptp.zero_zero_nat)) (forall ((D2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B2) D2)) (@ P D2)))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B2)) (not (or (and (@ (@ tptp.ord_less_nat A) B2) (not (@ P tptp.zero_zero_nat))) (exists ((D2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B2) D2)) (not (@ P D2)))))))))
% 6.83/7.11 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I) (@ _let_1 (@ (@ tptp.power_power_nat I) N))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) N4)) Y3))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((A3 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A3) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B4) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A3) N)) (@ (@ tptp.divide_divide_nat B4) N))))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5))))))))
% 6.83/7.11 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5))))))))
% 6.83/7.11 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.83/7.11 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.83/7.11 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B2)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 6.83/7.11 (assert (= (lambda ((Y6 tptp.code_integer) (Z4 tptp.code_integer)) (= Y6 Z4)) (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide6298287555418463151nteger A4) _let_1) (@ (@ tptp.divide6298287555418463151nteger B3) _let_1))))))))
% 6.83/7.11 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide_divide_nat A4) _let_1) (@ (@ tptp.divide_divide_nat B3) _let_1))))))))
% 6.83/7.11 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A4 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide_divide_int A4) _let_1) (@ (@ tptp.divide_divide_int B3) _let_1))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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)))))))))))
% 6.83/7.11 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.one_one_real))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B2)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B2) tptp.one_one_real))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B2)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B2) tptp.one_one_rat))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B2)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B2) tptp.one_one_int))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B2) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B2) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B2) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B2)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) tptp.one_one_real))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B2)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) tptp.one_one_rat))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B2)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B2)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B2) tptp.one_one_int))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (=> (@ (@ tptp.ord_less_real Z2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z2) X4)) Y3)))) (@ (@ tptp.ord_less_eq_real X4) Y3))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (=> (@ (@ tptp.ord_less_rat Z2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) X4)) Y3)))) (@ (@ tptp.ord_less_eq_rat X4) Y3))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y3)) X4) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X4) Y3))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y3)) X4) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X4) Y3))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (X4 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.times_times_real Z) Y3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y3)) Z)))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (=> (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.times_times_rat Z) Y3)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y3)) Z)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B2) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) C)) A) (@ (@ tptp.ord_less_eq_rat B2) (@ (@ tptp.times_times_rat A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) C)) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B2) C)) (@ (@ tptp.ord_less_eq_rat B2) (@ (@ tptp.times_times_rat A) C))))))
% 6.83/7.11 (assert (forall ((C tptp.real) (B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B2)))))
% 6.83/7.11 (assert (forall ((C tptp.rat) (B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B2)))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B2) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((A tptp.real) (B2 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 B2) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 6.83/7.11 (assert (forall ((A tptp.rat) (B2 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 B2) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B2)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B2) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.83/7.11 (assert (forall ((B2 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 B2) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))))
% 6.83/7.11 (assert (forall ((B2 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 B2) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B2) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B2) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B2)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B2) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B2)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B2) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B2)) (= A tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B2) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B2)) (= A tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (A tptp.real) (Y3 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X4) A) (=> (@ (@ tptp.ord_less_eq_real Y3) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X4)) (@ (@ tptp.times_times_real V) Y3))) A)))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (A tptp.rat) (Y3 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X4) A) (=> (@ (@ tptp.ord_less_eq_rat Y3) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X4)) (@ (@ tptp.times_times_rat V) Y3))) A)))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (A tptp.int) (Y3 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X4) A) (=> (@ (@ tptp.ord_less_eq_int Y3) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X4)) (@ (@ tptp.times_times_int V) Y3))) A)))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B2) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B2)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.83/7.11 (assert (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.83/7.11 (assert (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X4 tptp.real) (W tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y3))) (@ (@ tptp.times_times_real Y3) Z))) tptp.zero_zero_real))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X4 tptp.rat) (W tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y3)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y3))) (@ (@ tptp.times_times_rat Y3) Z))) tptp.zero_zero_rat))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.real) (Z tptp.real) (X4 tptp.real) (W tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y3))) (@ (@ tptp.times_times_real Y3) Z))) tptp.zero_zero_real))))))
% 6.83/7.11 (assert (forall ((Y3 tptp.rat) (Z tptp.rat) (X4 tptp.rat) (W tptp.rat)) (=> (not (= Y3 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Y3)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y3))) (@ (@ tptp.times_times_rat Y3) Z))) tptp.zero_zero_rat))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N3)) (@ _let_1 N))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N3)) (@ _let_1 N))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N3)) (@ _let_1 N))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N3)) (@ _let_1 N))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ 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 N3)) (@ _let_1 N))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ 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 N3)) (@ _let_1 N))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ 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 N3)) (@ _let_1 N))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ 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 N3)) (@ _let_1 N))))))))
% 6.83/7.11 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.83/7.11 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.83/7.11 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.83/7.11 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.83/7.11 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.83/7.11 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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)))))))))))))
% 6.83/7.11 (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)))))))))))))
% 6.83/7.11 (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)))))))))))))
% 6.83/7.11 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N2))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I2 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I2)) J3)) (@ P I2))))))))))
% 6.83/7.11 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N2))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I2 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I2)) J3)) (@ P J3))))))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (A tptp.real) (B2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B2) N))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (A tptp.rat) (B2 tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B2) N))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B2) N))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (A tptp.real) (Y3 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X4) A) (=> (@ (@ tptp.ord_less_real Y3) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X4)) (@ (@ tptp.times_times_real V) Y3))) A)))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (A tptp.rat) (Y3 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X4) A) (=> (@ (@ tptp.ord_less_rat Y3) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X4)) (@ (@ tptp.times_times_rat V) Y3))) A)))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (A tptp.int) (Y3 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X4) A) (=> (@ (@ tptp.ord_less_int Y3) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X4)) (@ (@ tptp.times_times_int V) Y3))) A)))))))))
% 6.83/7.11 (assert (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.83/7.11 (assert (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S))) V))))))
% 6.83/7.11 (assert (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U))) S))) V))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 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 X4) _let_2) (@ (@ tptp.power_power_real Y3) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= X4 Y3))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 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 X4) _let_2) (@ (@ tptp.power_power_rat Y3) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= X4 Y3))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 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 X4) _let_2) (@ (@ tptp.power_power_nat Y3) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= X4 Y3))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 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 X4) _let_2) (@ (@ tptp.power_power_int Y3) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= X4 Y3))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_eq_real X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y3) (@ (@ tptp.ord_less_eq_rat X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X4) _let_1)) (@ (@ tptp.power_power_nat Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y3) (@ (@ tptp.ord_less_eq_nat X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (@ (@ tptp.ord_less_eq_int X4) Y3))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B2)) C))) (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B2))) (=> (@ (@ 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) B2)) C))) (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B2))) (=> (@ (@ 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) B2)) C))) (@ _let_1 B2))))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))))))))
% 6.83/7.11 (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))))))))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ (@ tptp.plus_plus_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 6.83/7.11 (assert (= tptp.power_power_complex (lambda ((P3 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P3) (@ (@ tptp.power_power_complex P3) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.83/7.11 (assert (= tptp.power_power_real (lambda ((P3 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P3) (@ (@ tptp.power_power_real P3) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.83/7.11 (assert (= tptp.power_power_rat (lambda ((P3 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P3) (@ (@ tptp.power_power_rat P3) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.83/7.11 (assert (= tptp.power_power_nat (lambda ((P3 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P3) (@ (@ tptp.power_power_nat P3) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.83/7.11 (assert (= tptp.power_power_int (lambda ((P3 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P3) (@ (@ tptp.power_power_int P3) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_Code_integer))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_nat))))))))
% 6.83/7.11 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_int))))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_real X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y3) (@ (@ tptp.ord_less_rat X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X4) _let_1)) (@ (@ tptp.power_power_nat Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y3) (@ (@ tptp.ord_less_nat X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (@ (@ tptp.ord_less_int X4) Y3))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y3 tptp.zero_zero_real))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1))) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y3 tptp.zero_zero_rat))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1))) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y3 tptp.zero_zero_int))))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) tptp.zero_zero_real)))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1))) tptp.zero_zero_rat)))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1))) tptp.zero_zero_int)))))
% 6.83/7.11 (assert (forall ((X4 tptp.real) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) (or (not (= X4 tptp.zero_zero_real)) (not (= Y3 tptp.zero_zero_real)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.rat) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1))) (or (not (= X4 tptp.zero_zero_rat)) (not (= Y3 tptp.zero_zero_rat)))))))
% 6.83/7.11 (assert (forall ((X4 tptp.int) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1))) (or (not (= X4 tptp.zero_zero_int)) (not (= Y3 tptp.zero_zero_int)))))))
% 6.83/7.11 (assert (forall ((B2 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))) B2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat _let_2) B2) (= _let_2 (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((B2 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))) B2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int _let_2) B2) (= _let_2 (@ _let_1 B2))))))))
% 6.83/7.11 (assert (forall ((B2 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))) B2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B2) (= _let_2 (@ _let_1 B2))))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ P N))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (assert (forall ((A3 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A3) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B4) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B4) N))))))
% 6.83/7.11 (assert (forall ((B2 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 B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B2) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B2)))))))))
% 6.83/7.11 (assert (forall ((B2 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 B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B2) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B2)))))))))
% 6.83/7.11 (assert (forall ((B2 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 B2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B2) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B2)))))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((M tptp.code_integer) (X4 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X4))) (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) X4) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 6.83/7.11 (assert (forall ((M tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X4))) (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) X4) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.83/7.11 (assert (forall ((M tptp.int) (X4 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X4))) (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) X4) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.83/7.11 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B2) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B2) (@ _let_1 B2)))))))))
% 6.83/7.11 (assert (forall ((A tptp.nat) (B2 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))) B2)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B2) (@ _let_1 B2)))))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 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))) B2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B2) (@ _let_1 B2)))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (A tptp.nat) (B2 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 B2) N)) (@ (@ tptp.dvd_dvd_nat A) B2)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (A tptp.int) (B2 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 B2) N)) (@ (@ tptp.dvd_dvd_int A) B2)))))
% 6.83/7.11 (assert (forall ((X4 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 X4) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X4) N)) (@ _let_1 N)))))))))
% 6.83/7.11 (assert (forall ((X4 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 X4) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X4) N)) (@ _let_1 M)))))))))
% 6.83/7.11 (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)))))))))
% 6.83/7.11 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.11 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.83/7.11 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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))))))))
% 6.83/7.11 (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)))))))))
% 6.83/7.11 (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)))))))))
% 6.83/7.11 (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)))))))))
% 6.83/7.11 (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)))))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.code_integer Bool)) (L2 tptp.code_integer)) (= (exists ((X tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L2) X))) (exists ((X tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L2) (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.zero_z3403309356797280102nteger)) (@ P X))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.real Bool)) (L2 tptp.real)) (= (exists ((X tptp.real)) (@ P (@ (@ tptp.times_times_real L2) X))) (exists ((X tptp.real)) (and (@ (@ tptp.dvd_dvd_real L2) (@ (@ tptp.plus_plus_real X) tptp.zero_zero_real)) (@ P X))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.rat Bool)) (L2 tptp.rat)) (= (exists ((X tptp.rat)) (@ P (@ (@ tptp.times_times_rat L2) X))) (exists ((X tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L2) (@ (@ tptp.plus_plus_rat X) tptp.zero_zero_rat)) (@ P X))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.nat Bool)) (L2 tptp.nat)) (= (exists ((X tptp.nat)) (@ P (@ (@ tptp.times_times_nat L2) X))) (exists ((X tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L2) (@ (@ tptp.plus_plus_nat X) tptp.zero_zero_nat)) (@ P X))))))
% 6.83/7.11 (assert (forall ((P (-> tptp.int Bool)) (L2 tptp.int)) (= (exists ((X tptp.int)) (@ P (@ (@ tptp.times_times_int L2) X))) (exists ((X tptp.int)) (and (@ (@ tptp.dvd_dvd_int L2) (@ (@ tptp.plus_plus_int X) tptp.zero_zero_int)) (@ P X))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N) K)) (@ _let_1 K)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N) K)) (@ _let_1 K)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N) K)) (@ _let_1 K)))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.83/7.11 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 6.83/7.11 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I2 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I2 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J3))) (@ P J3))))))))
% 6.83/7.11 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L2)) L2))))))
% 6.83/7.11 (assert (forall ((B 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 B) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ _let_1 Q5)))))))
% 6.83/7.11 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) R2) (= (@ (@ tptp.modulo_modulo_int A) B2) R2))))))
% 6.83/7.11 (assert (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B2) (= (@ (@ tptp.modulo_modulo_int A) B2) R2))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((D tptp.int) (P4 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P4 X3) (@ P4 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((X_12 tptp.int)) (@ P4 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (Q2 tptp.int) (R2 tptp.int) (B 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 B) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q2)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) B2) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 6.83/7.11 (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 ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.83/7.11 (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))))))))))
% 6.83/7.11 (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))))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (Q2 tptp.int) (R2 tptp.int) (B tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q2)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) B2) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 6.83/7.11 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (=> (@ (@ 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) B2) (=> (@ (@ tptp.ord_less_int R2) B2) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (let ((_let_2 (@ tptp.times_times_int B2))) (=> (@ (@ 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)))))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (assert (forall ((A tptp.int) (D tptp.int) (X4 tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X4))) (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))))))))
% 6.83/7.11 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 6.83/7.11 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L2) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (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)))))
% 6.83/7.11 (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))))
% 6.83/7.11 (assert (forall ((M tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K)) M))))
% 6.83/7.11 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I) K) I) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 6.83/7.11 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2)) (or (@ (@ tptp.dvd_dvd_int L2) K) (and (= L2 tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B2))))))
% 6.83/7.11 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B2))) (let ((_let_2 (@ tptp.ord_less_int B2))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))))
% 6.83/7.11 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N) (not (@ (@ tptp.dvd_dvd_int N) M))))))
% 6.83/7.11 (assert (forall ((Z tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z) N)))))
% 6.83/7.11 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.11 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L2) L2)))
% 6.83/7.11 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 6.83/7.11 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 6.83/7.11 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M) N)) (=> (@ _let_1 N) (@ _let_1 M))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.83/7.11 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.83/7.11 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 6.83/7.11 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 6.83/7.11 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.83/7.11 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 6.83/7.11 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.83/7.11 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 6.83/7.11 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 6.83/7.11 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 6.83/7.11 (assert (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))))
% 6.83/7.11 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 6.83/7.11 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I))))))
% 6.83/7.11 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I))))))
% 6.83/7.11 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 6.83/7.11 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I tptp.int)) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 6.83/7.11 (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))))))
% 6.83/7.11 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (not (@ (@ tptp.ord_less_real T) X5)))))))
% 6.83/7.11 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (not (@ (@ tptp.ord_less_rat T) X5)))))))
% 6.83/7.11 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (not (@ (@ tptp.ord_less_num T) X5)))))))
% 6.83/7.11 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (not (@ (@ tptp.ord_less_nat T) X5)))))))
% 6.83/7.11 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (not (@ (@ tptp.ord_less_int T) X5)))))))
% 6.83/7.11 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X5))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.83/7.11 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X5))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X5))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X5))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X5))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (= (or (@ P X5) (@ Q X5)) (or (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (= (or (@ P X5) (@ Q X5)) (or (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (= (or (@ P X5) (@ Q X5)) (or (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (= (or (@ P X5) (@ Q X5)) (or (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (= (or (@ P X5) (@ Q X5)) (or (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (= (and (@ P X5) (@ Q X5)) (and (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (= (and (@ P X5) (@ Q X5)) (and (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (= (and (@ P X5) (@ Q X5)) (and (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (= (and (@ P X5) (@ Q X5)) (and (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (= (and (@ P X5) (@ Q X5)) (and (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (@ (@ tptp.ord_less_real T) X5))))))
% 6.83/7.12 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (@ (@ tptp.ord_less_rat T) X5))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (@ (@ tptp.ord_less_num T) X5))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (@ (@ tptp.ord_less_nat T) X5))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (@ (@ tptp.ord_less_int T) X5))))))
% 6.83/7.12 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (not (@ (@ tptp.ord_less_real X5) T)))))))
% 6.83/7.12 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (not (@ (@ tptp.ord_less_rat X5) T)))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (not (@ (@ tptp.ord_less_num X5) T)))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (not (@ (@ tptp.ord_less_nat X5) T)))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (not (@ (@ tptp.ord_less_int X5) T)))))))
% 6.83/7.12 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (not (= X5 T)))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.real Bool)) (P4 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.rat Bool)) (P4 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.num Bool)) (P4 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P4 X5) (@ Q6 X5))))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat)) (=> (not (= X4 tptp.zero_zero_nat)) (=> (not (= X4 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X4 (@ tptp.suc (@ tptp.suc Va))))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ P A5) B5) (@ (@ P B5) A5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) tptp.zero_zero_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.plus_plus_nat A5) B5))))) (@ (@ P A) B2))))))
% 6.83/7.12 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (not (@ (@ tptp.ord_less_eq_real T) X5)))))))
% 6.83/7.12 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (not (@ (@ tptp.ord_less_eq_rat T) X5)))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (not (@ (@ tptp.ord_less_eq_num T) X5)))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (not (@ (@ tptp.ord_less_eq_nat T) X5)))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (not (@ (@ tptp.ord_less_eq_int T) X5)))))))
% 6.83/7.12 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (@ (@ tptp.ord_less_eq_real X5) T))))))
% 6.83/7.12 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (@ (@ tptp.ord_less_eq_rat X5) T))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (@ (@ tptp.ord_less_eq_num X5) T))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (@ (@ tptp.ord_less_eq_nat X5) T))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (@ (@ tptp.ord_less_eq_int X5) T))))))
% 6.83/7.12 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (@ (@ tptp.ord_less_eq_real T) X5))))))
% 6.83/7.12 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (@ (@ tptp.ord_less_eq_rat T) X5))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (@ (@ tptp.ord_less_eq_num T) X5))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (@ (@ tptp.ord_less_eq_nat T) X5))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (@ (@ tptp.ord_less_eq_int T) X5))))))
% 6.83/7.12 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (not (@ (@ tptp.ord_less_eq_real X5) T)))))))
% 6.83/7.12 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (not (@ (@ tptp.ord_less_eq_rat X5) T)))))))
% 6.83/7.12 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (not (@ (@ tptp.ord_less_eq_num X5) T)))))))
% 6.83/7.12 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (not (@ (@ tptp.ord_less_eq_nat X5) T)))))))
% 6.83/7.12 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (not (@ (@ tptp.ord_less_eq_int X5) T)))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (assert (forall ((P2 tptp.nat) (A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P2) (@ (@ tptp.times_times_nat A) B2)) (not (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (= P2 (@ (@ tptp.times_times_nat X3) Y4)) (=> (@ (@ tptp.dvd_dvd_nat X3) A) (not (@ (@ tptp.dvd_dvd_nat Y4) B2)))))))))
% 6.83/7.12 (assert (forall ((P2 tptp.int) (A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P2) (@ (@ tptp.times_times_int A) B2)) (not (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (= P2 (@ (@ tptp.times_times_int X3) Y4)) (=> (@ (@ tptp.dvd_dvd_int X3) A) (not (@ (@ tptp.dvd_dvd_int Y4) B2)))))))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B2) C)) (exists ((B6 tptp.nat) (C4 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B6) C4)) (@ (@ tptp.dvd_dvd_nat B6) B2) (@ (@ tptp.dvd_dvd_nat C4) C))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B2) C)) (exists ((B6 tptp.int) (C4 tptp.int)) (and (= A (@ (@ tptp.times_times_int B6) C4)) (@ (@ tptp.dvd_dvd_int B6) B2) (@ (@ tptp.dvd_dvd_int C4) C))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (@ (@ P N4) (@ (@ tptp.modulo_modulo_nat M4) N4)) (@ (@ P M4) N4)))) (@ (@ P M) N)))))
% 6.83/7.12 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X5) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S)))) (=> (@ (@ tptp.ord_less_real Z2) X5) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S)))) (=> (@ (@ tptp.ord_less_rat Z2) X5) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S)))) (=> (@ (@ tptp.ord_less_nat Z2) X5) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S)))) (=> (@ (@ tptp.ord_less_int Z2) X5) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X5) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S))))) (=> (@ (@ tptp.ord_less_real Z2) X5) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S))))) (=> (@ (@ tptp.ord_less_rat Z2) X5) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S))))) (=> (@ (@ tptp.ord_less_nat Z2) X5) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S))))) (=> (@ (@ tptp.ord_less_int Z2) X5) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X5) Z2) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S)))) (=> (@ (@ tptp.ord_less_real X5) Z2) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S)))) (=> (@ (@ tptp.ord_less_rat X5) Z2) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S)))) (=> (@ (@ tptp.ord_less_nat X5) Z2) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S)))) (=> (@ (@ tptp.ord_less_int X5) Z2) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X5) Z2) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S))))) (=> (@ (@ tptp.ord_less_real X5) Z2) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S))))) (=> (@ (@ tptp.ord_less_rat X5) Z2) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S))))) (=> (@ (@ tptp.ord_less_nat X5) Z2) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S))))) (=> (@ (@ tptp.ord_less_int X5) Z2) (= _let_1 _let_1)))))))
% 6.83/7.12 (assert (forall ((D tptp.nat) (A tptp.nat) (B2 tptp.nat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B2))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B2) (=> (or (= (@ _let_1 X4) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D)) (= (@ _let_2 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D))) (exists ((X3 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B2))) (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 Y4)) D)) (= (@ _let_3 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y4)) D)))))))))))))))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B2))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B2) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y4)) D3)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y4)) D3))))))))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B2) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) Y4)) D3))))))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B2))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B2) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X3)) (@ _let_2 Y4)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X3)) (@ _let_1 Y4)) D3)))))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (forall ((A5 tptp.real) (B5 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (=> (@ (@ P B5) C3) (=> (@ (@ tptp.ord_less_eq_real A5) B5) (=> (@ (@ tptp.ord_less_eq_real B5) C3) (@ _let_1 C3))))))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B2) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A5 tptp.real) (B5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A5) X3) (@ (@ tptp.ord_less_eq_real X3) B5) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B5) A5)) D5)) (@ (@ P A5) B5)))))))) (@ (@ P A) B2))))))
% 6.83/7.12 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real Y3) Z)) (@ (@ tptp.ord_less_eq_real X4) Y3)))))
% 6.83/7.12 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat Y3) Z)) (@ (@ tptp.ord_less_eq_rat X4) Y3)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X4) Z)) (@ (@ tptp.times_times_int Y3) Z)) (@ (@ tptp.ord_less_eq_int X4) Y3)))))
% 6.83/7.12 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3))))))
% 6.83/7.12 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_rat X4) Y3))))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_int X4) Y3))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))))))
% 6.83/7.12 (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))))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real B2)) B2)))
% 6.83/7.12 (assert (forall ((B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int B2)) B2)))
% 6.83/7.12 (assert (forall ((B2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex B2)) B2)))
% 6.83/7.12 (assert (forall ((B2 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger B2)) B2)))
% 6.83/7.12 (assert (forall ((B2 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.83/7.12 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B2)) (= A B2))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B2)) (= A B2))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B2)) (= A B2))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B2)) (= A B2))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B2)) (= A B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B2))))
% 6.83/7.12 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.83/7.12 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.83/7.12 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.83/7.12 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.83/7.12 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.83/7.12 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B2))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real (@ _let_1 B2))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ _let_1 B2))))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B2)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B2))))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B2))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat (@ _let_1 B2))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.times_times_int A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B2)) (@ (@ tptp.times_times_complex A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B2)) (@ (@ tptp.times_3573771949741848930nteger A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.times_times_rat A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B2) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B2) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B2) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B2) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B2)))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B2)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B2)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B2)) B2)))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B2)) (@ (@ tptp.minus_minus_real B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.minus_minus_int B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B2)) (@ (@ tptp.minus_minus_complex B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B2)) (@ (@ tptp.minus_8373710615458151222nteger B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B2)) (@ (@ tptp.minus_minus_rat B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.divide_divide_int A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B2)) (@ (@ tptp.divide6298287555418463151nteger A) B2))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X4))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y3)) (@ _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X4))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y3)) (@ _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X4))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y3)) (@ _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X4))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y3)) (@ _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X4))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y3)) (@ _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X4)) Y3) (@ (@ tptp.dvd_dvd_real X4) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X4)) Y3) (@ (@ tptp.dvd_dvd_int X4) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X4)) Y3) (@ (@ tptp.dvd_dvd_complex X4) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X4)) Y3) (@ (@ tptp.dvd_dvd_Code_integer X4) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X4)) Y3) (@ (@ tptp.dvd_dvd_rat X4) Y3))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B2)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X4) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X4 A))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.83/7.12 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.83/7.12 (assert (forall ((B2 tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B2) (@ tptp.uminus_uminus_real B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B2) (@ tptp.uminus_uminus_int B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B2) (@ tptp.uminus1482373934393186551omplex B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B2) (@ tptp.uminus1351360451143612070nteger B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B2) (@ tptp.uminus_uminus_rat B2))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.83/7.12 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.83/7.12 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.83/7.12 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.83/7.12 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.83/7.12 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.83/7.12 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.83/7.12 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.minus_minus_real B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.minus_minus_int B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B2) (@ (@ tptp.minus_minus_complex B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B2) (@ (@ tptp.minus_8373710615458151222nteger B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B2) (@ (@ tptp.minus_minus_rat B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.plus_plus_real A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.plus_plus_int A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B2)) (@ (@ tptp.plus_plus_complex A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B2)) (@ (@ tptp.plus_p5714425477246183910nteger A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.plus_plus_rat A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.divide_divide_real X4) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X4) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.divide_divide_rat X4) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int B2) A)) B2) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B2) A)) B2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B2))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.83/7.12 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.83/7.12 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.83/7.12 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.83/7.12 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.83/7.12 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.83/7.12 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.83/7.12 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.83/7.12 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.83/7.12 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y3)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y3)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y3)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y3)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y3))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y3)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y3)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y3)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y3)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y3)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y3)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y3)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y3)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y3)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y3)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y3)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y3)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y3)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y3)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y3))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num) (Y3 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y3)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y3))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B2)))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_eq_real B2) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B2) _let_1)) (@ (@ tptp.ord_less_eq_rat B2) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B2) _let_1) A) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B2) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B2)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B2)))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B2) _let_1)) (@ (@ tptp.ord_less_real B2) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B2) _let_1)) (@ (@ tptp.ord_less_rat B2) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.83/7.12 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.83/7.12 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.83/7.12 (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))
% 6.83/7.12 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.83/7.12 (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))
% 6.83/7.12 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))
% 6.83/7.12 (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)))
% 6.83/7.12 (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)))
% 6.83/7.12 (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)))
% 6.83/7.12 (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)))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= A B2) (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (= A B2) (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (= A B2) (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (= A B2) (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ tptp.uminus_uminus_real B2)) (= B2 (@ tptp.uminus_uminus_real A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.uminus_uminus_int B2)) (= B2 (@ tptp.uminus_uminus_int A)))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B2)) (= B2 (@ tptp.uminus1482373934393186551omplex A)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B2)) (= B2 (@ tptp.uminus1351360451143612070nteger A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B2)) (= B2 (@ tptp.uminus_uminus_rat A)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B2) (= (@ tptp.uminus_uminus_real B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B2) (= (@ tptp.uminus_uminus_int B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B2) (= (@ tptp.uminus1482373934393186551omplex B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B2) (= (@ tptp.uminus1351360451143612070nteger B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B2) (= (@ tptp.uminus_uminus_rat B2) A))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B2)) A))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B2) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B2)) A))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) A))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.ord_less_eq_real B2) (@ tptp.uminus_uminus_real A)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B2)) (@ (@ tptp.ord_le3102999989581377725nteger B2) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.ord_less_eq_rat B2) (@ tptp.uminus_uminus_rat A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.ord_less_eq_int B2) (@ tptp.uminus_uminus_int A)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) A))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B2)) A))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B2) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B2)) A))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.ord_less_real B2) (@ tptp.uminus_uminus_real A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.ord_less_int B2) (@ tptp.uminus_uminus_int A)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B2)) (@ (@ tptp.ord_le6747313008572928689nteger B2) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.ord_less_rat B2) (@ tptp.uminus_uminus_rat A)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat A)))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B2)))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B2) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B2) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B2) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B2) B2)) (or (= A B2) (= A (@ tptp.uminus_uminus_real B2))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B2) B2)) (or (= A B2) (= A (@ tptp.uminus_uminus_int B2))))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B2) B2)) (or (= A B2) (= A (@ tptp.uminus1482373934393186551omplex B2))))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) A) (@ (@ tptp.times_3573771949741848930nteger B2) B2)) (or (= A B2) (= A (@ tptp.uminus1351360451143612070nteger B2))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) A) (@ (@ tptp.times_times_rat B2) B2)) (or (= A B2) (= A (@ tptp.uminus_uminus_rat B2))))))
% 6.83/7.12 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.83/7.12 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.83/7.12 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.83/7.12 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.83/7.12 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B2)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B2)) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B2)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat A)))))
% 6.83/7.12 (assert (forall ((A3 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A3 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A3) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))))
% 6.83/7.12 (assert (forall ((A3 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A3 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A3) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 6.83/7.12 (assert (forall ((A3 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A3 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A3) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.83/7.12 (assert (forall ((A3 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A3 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A3) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))))
% 6.83/7.12 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A3 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A3) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B2)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B2)) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B2)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat A)))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B2)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B2)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B2)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B2)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B2)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B2)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B2)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ tptp.uminus_uminus_real (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus_uminus_real B2))))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B2))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ tptp.uminus_uminus_rat (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus_uminus_rat B2))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.divide_divide_real A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B2)) (@ (@ tptp.divide1717551699836669952omplex A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.divide_divide_rat A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B2)) (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B2))) B2) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B2))) B2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int) (A2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B2) (@ (@ tptp.modulo_modulo_int A2) B2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A2)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (A2 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B2) (@ (@ tptp.modulo364778990260209775nteger A2) B2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A2)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B2)))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.83/7.12 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.83/7.12 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.83/7.12 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.83/7.12 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.83/7.12 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.83/7.12 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B2) (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B2) (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B2) (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B2) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B2) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B2) (= (@ (@ tptp.plus_plus_rat A) B2) tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ tptp.uminus_uminus_real B2)) (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.uminus_uminus_int B2)) (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B2)) (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B2)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B2) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B2)) (= (@ (@ tptp.plus_plus_rat A) B2) tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B2) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B2) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B2) tptp.zero_zero_real) (= B2 (@ tptp.uminus_uminus_real A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B2) tptp.zero_zero_int) (= B2 (@ tptp.uminus_uminus_int A)))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B2) tptp.zero_zero_complex) (= B2 (@ tptp.uminus1482373934393186551omplex A)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B2) tptp.zero_z3403309356797280102nteger) (= B2 (@ tptp.uminus1351360451143612070nteger A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B2) tptp.zero_zero_rat) (= B2 (@ tptp.uminus_uminus_rat A)))))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.83/7.12 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.83/7.12 (assert (forall ((W tptp.num) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real X4) (@ tptp.uminus_uminus_real _let_1))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (X4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X4)) (@ (@ tptp.times_times_int X4) (@ tptp.uminus_uminus_int _let_1))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (X4 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex X4) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (X4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X4)) (@ (@ tptp.times_3573771949741848930nteger X4) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (X4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X4)) (@ (@ tptp.times_times_rat X4) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus_uminus_real B2)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B2)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B2 tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B2)) (@ _let_1 (@ tptp.uminus_uminus_rat B2)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.divide_divide_real A) B2)))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B2)) (@ (@ tptp.divide1717551699836669952omplex A) B2)))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.divide_divide_rat A) B2)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (= (@ (@ tptp.times_times_real X4) X4) tptp.one_one_real) (or (= X4 tptp.one_one_real) (= X4 (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.83/7.12 (assert (forall ((X4 tptp.int)) (= (= (@ (@ tptp.times_times_int X4) X4) tptp.one_one_int) (or (= X4 tptp.one_one_int) (= X4 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.83/7.12 (assert (forall ((X4 tptp.complex)) (= (= (@ (@ tptp.times_times_complex X4) X4) tptp.one_one_complex) (or (= X4 tptp.one_one_complex) (= X4 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X4) X4) tptp.one_one_Code_integer) (or (= X4 tptp.one_one_Code_integer) (= X4 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (= (= (@ (@ tptp.times_times_rat X4) X4) tptp.one_one_rat) (or (= X4 tptp.one_one_rat) (= X4 (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.83/7.12 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))
% 6.83/7.12 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))
% 6.83/7.12 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))
% 6.83/7.12 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))
% 6.83/7.12 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))
% 6.83/7.12 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))
% 6.83/7.12 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))
% 6.83/7.12 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))
% 6.83/7.12 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))
% 6.83/7.12 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))
% 6.83/7.12 (assert (forall ((B4 tptp.real) (K tptp.real) (B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B4 (@ (@ tptp.plus_plus_real K) B2)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((B4 tptp.int) (K tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B4 (@ (@ tptp.plus_plus_int K) B2)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((B4 tptp.complex) (K tptp.complex) (B2 tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B4 (@ (@ tptp.plus_plus_complex K) B2)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((B4 tptp.code_integer) (K tptp.code_integer) (B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B4 (@ (@ tptp.plus_p5714425477246183910nteger K) B2)) (= (@ _let_1 B4) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((B4 tptp.rat) (K tptp.rat) (B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B4 (@ (@ tptp.plus_plus_rat K) B2)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B2) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B2)) (@ tptp.uminus_uminus_real (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (@ (@ tptp.dvd_dvd_complex B2) A) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B2)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) A) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B2)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (@ (@ tptp.dvd_dvd_rat B2) A) (= (@ _let_1 (@ tptp.uminus_uminus_rat B2)) (@ tptp.uminus_uminus_rat (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B2) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B2) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2))))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B2) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B2))))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B2) A) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B2))))))
% 6.83/7.12 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B2) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.divide6298287555418463151nteger A) B2))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B2) A) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B2) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B2))))))
% 6.83/7.12 (assert (forall ((U tptp.real) (X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X4) X4))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L2) (@ tptp.uminus_uminus_int L2))))
% 6.83/7.12 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L2)) tptp.zero_zero_int)) (not (= (@ _let_1 L2) tptp.zero_zero_int))))))
% 6.83/7.12 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L2) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K) L2) tptp.zero_zero_int)))))
% 6.83/7.12 (assert (= tptp.minus_minus_real (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real Y)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.83/7.12 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.12 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.83/7.12 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.83/7.12 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.12 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.83/7.12 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.83/7.12 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.83/7.12 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.83/7.12 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B2))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B2) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B2))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B2) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B2))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B2) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B2) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B2) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B2) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B2) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B2))))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B2)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B2))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B2)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B2))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B2))) (= (@ (@ tptp.times_times_real C) B2) (@ tptp.uminus_uminus_real A))))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B2))) (= (@ (@ tptp.times_times_complex C) B2) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B2))) (= (@ (@ tptp.times_times_rat C) B2) (@ tptp.uminus_uminus_rat A))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real)) (= (@ (@ tptp.times_times_real B2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.int)) (= (@ (@ tptp.times_times_int B2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex)) (= (@ (@ tptp.times_times_complex B2) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B2) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat)) (= (@ (@ tptp.times_times_rat B2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B2) (@ tptp.uminus_uminus_real B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B2) (@ tptp.uminus_uminus_int B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B2) (@ tptp.uminus1482373934393186551omplex B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B2) (@ tptp.uminus1351360451143612070nteger B2))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B2) (@ tptp.uminus_uminus_rat B2))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B2 tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B2))))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B2 tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B2))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B2 tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B2))))))
% 6.83/7.12 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.83/7.12 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.83/7.12 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.83/7.12 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.83/7.12 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X4)) _let_1) (@ (@ tptp.power_power_real X4) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X4)) _let_1) (@ (@ tptp.power_power_int X4) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X4)) _let_1) (@ (@ tptp.power_power_complex X4) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X4)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X4) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X4)) _let_1) (@ (@ tptp.power_power_rat X4) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X4) Y3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y3) (@ tptp.uminus_uminus_real X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X4)) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X4)) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X4) Y3)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y3) (@ tptp.uminus_uminus_real X4)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B2)))) (let ((_let_4 (= _let_2 tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) B2))))))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B2))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B2))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int B2) _let_1)))))))))
% 6.83/7.12 (assert (forall ((C tptp.real) (B2 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 B2) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))))
% 6.83/7.12 (assert (forall ((C tptp.rat) (B2 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 B2) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.times_times_rat A) C))))))
% 6.83/7.12 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))))
% 6.83/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B2) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B2))))))
% 6.83/7.12 (assert (forall ((C tptp.real) (B2 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 B2) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))))
% 6.83/7.12 (assert (forall ((C tptp.rat) (B2 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 B2) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B2))))))
% 6.83/7.12 (assert (forall ((C tptp.real) (A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))))
% 6.83/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B2) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.times_times_rat A) C))))))
% 6.83/7.12 (assert (forall ((B2 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 B2))) (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 B2) 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)))))))))))))
% 6.83/7.12 (assert (forall ((B2 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 B2))) (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 B2) 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)))))))))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 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 B2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) 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)))))))))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 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 B2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B2) 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)))))))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B2) C) _let_1) (and (=> (not _let_2) (= B2 (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (B2 tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B2) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B2)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.83/7.12 (assert (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B2) Z))) Z))))))))
% 6.83/7.12 (assert (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B2) Z))) Z))))))))
% 6.83/7.12 (assert (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B2) Z))) Z))))))))
% 6.83/7.12 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X4) Z))) Y3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real Y3) Z))) Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X4) Z))) Y3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex Y3) Z))) Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X4) Z))) Y3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X4)) (@ (@ tptp.times_times_rat Y3) Z))) Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B2) Z))) Z))))))))
% 6.83/7.12 (assert (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B2) Z))) Z))))))))
% 6.83/7.12 (assert (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B2))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B2) Z))) Z))))))))
% 6.83/7.12 (assert (forall ((Z tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B2) Z))) Z))))))))
% 6.83/7.12 (assert (forall ((Z tptp.complex) (A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B2) Z))) Z))))))))
% 6.83/7.12 (assert (forall ((Z tptp.rat) (A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B2))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B2))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B2) Z))) Z))))))))
% 6.83/7.12 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X4) Z))) Y3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real Y3) Z))) Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y3 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X4) Z))) Y3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex Y3) Z))) Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X4) Z))) Y3) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X4)) (@ (@ tptp.times_times_rat Y3) Z))) Z)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X4) _let_1) (@ (@ tptp.power_power_real Y3) _let_1)) (or (= X4 Y3) (= X4 (@ tptp.uminus_uminus_real Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X4) _let_1) (@ (@ tptp.power_power_int Y3) _let_1)) (or (= X4 Y3) (= X4 (@ tptp.uminus_uminus_int Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X4) _let_1) (@ (@ tptp.power_power_complex Y3) _let_1)) (or (= X4 Y3) (= X4 (@ tptp.uminus1482373934393186551omplex Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X4) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1)) (or (= X4 Y3) (= X4 (@ tptp.uminus1351360451143612070nteger Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X4) _let_1) (@ (@ tptp.power_power_rat Y3) _let_1)) (or (= X4 Y3) (= X4 (@ tptp.uminus_uminus_rat Y3)))))))
% 6.83/7.12 (assert (forall ((A3 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B4) N)) (@ (@ tptp.divide_divide_int A3) N))))))
% 6.83/7.12 (assert (forall ((B2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.divide_divide_int _let_1) B2) _let_1)))))
% 6.83/7.12 (assert (forall ((C tptp.real) (B2 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 B2) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))))
% 6.83/7.12 (assert (forall ((C tptp.rat) (B2 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 B2) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.times_times_rat A) C))))))
% 6.83/7.12 (assert (forall ((C tptp.real) (A tptp.real) (B2 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 B2) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))))
% 6.83/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 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 B2) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B2))))))
% 6.83/7.12 (assert (forall ((C tptp.real) (B2 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 B2) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B2))))))
% 6.83/7.12 (assert (forall ((C tptp.rat) (B2 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 B2) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B2))))))
% 6.83/7.12 (assert (forall ((C tptp.real) (A tptp.real) (B2 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 B2) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B2)) (@ (@ tptp.times_times_real A) C))))))
% 6.83/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B2 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 B2) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B2)) (@ (@ tptp.times_times_rat A) C))))))
% 6.83/7.12 (assert (forall ((B2 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 B2))) (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 B2) 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))))))))))))
% 6.83/7.12 (assert (forall ((B2 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 B2))) (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 B2) 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))))))))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 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 B2))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B2) 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)))))))))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 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 B2))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B2) 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)))))))))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B2) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B2)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B2) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B2) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B2)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (assert (forall ((U tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X4) _let_1)))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (assert (forall ((B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B2) (@ (@ tptp.minus_minus_int B2) tptp.one_one_int)))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B2)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B2))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int))) (=> (not (= B2 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))))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B2)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B2)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B2) tptp.zero_zero_int))) (=> (not (= B2 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)))))))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B2) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B2)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B2) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B2) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B2) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B2) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B2)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X4) (=> (@ (@ tptp.ord_le3102999989581377725nteger X4) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X4) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X4) (=> (@ (@ tptp.ord_less_eq_int X4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real Y3) Z)) (@ (@ tptp.ord_less_real X4) Y3)))))
% 6.83/7.12 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat Y3) Z)) (@ (@ tptp.ord_less_rat X4) Y3)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X4) Z)) (@ (@ tptp.times_times_int Y3) Z)) (@ (@ tptp.ord_less_int X4) Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X4)) (@ tptp.uminus5710092332889474511et_nat Y3)) (@ (@ tptp.ord_less_eq_set_nat Y3) X4))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X4)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4)))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 6.83/7.12 (assert (forall ((X32 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X32) (@ tptp.bit1 Y32)) (= X32 Y32))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.83/7.12 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.83/7.12 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.83/7.12 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.83/7.12 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 6.83/7.12 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.83/7.12 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.83/7.12 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.83/7.12 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.83/7.12 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.83/7.12 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.83/7.12 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.83/7.12 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.83/7.12 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.83/7.12 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.83/7.12 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.83/7.12 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.83/7.12 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.83/7.12 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.83/7.12 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.83/7.12 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.83/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.83/7.12 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L2) L2)))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ _let_1 L2)))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P2))) P2)))
% 6.83/7.12 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P2))) P2)))
% 6.83/7.12 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P2))) P2)))
% 6.83/7.12 (assert (forall ((B2 Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.83/7.12 (assert (forall ((B2 Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((B2 Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B2)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X4)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))) tptp.one_one_int))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P2 Q2))))
% 6.83/7.12 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P2 Q2))))
% 6.83/7.12 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) (@ tptp.zero_n356916108424825756nteger Q2)) (= P2 Q2))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.83/7.12 (assert (forall ((X2 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X2) (@ tptp.bit1 X32)))))
% 6.83/7.12 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.83/7.12 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.83/7.12 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.83/7.12 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.83/7.12 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.83/7.12 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.83/7.12 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.83/7.12 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.83/7.12 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.83/7.12 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.83/7.12 (assert (forall ((P (-> tptp.complex Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P2)) (not (or (and P2 (not (@ P tptp.one_one_complex))) (and (not P2) (not (@ P tptp.zero_zero_complex))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.real Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P2)) (not (or (and P2 (not (@ P tptp.one_one_real))) (and (not P2) (not (@ P tptp.zero_zero_real))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.rat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P2)) (not (or (and P2 (not (@ P tptp.one_one_rat))) (and (not P2) (not (@ P tptp.zero_zero_rat))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.nat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P2)) (not (or (and P2 (not (@ P tptp.one_one_nat))) (and (not P2) (not (@ P tptp.zero_zero_nat))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.int Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P2)) (not (or (and P2 (not (@ P tptp.one_one_int))) (and (not P2) (not (@ P tptp.zero_zero_int))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.code_integer Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P2)) (not (or (and P2 (not (@ P tptp.one_one_Code_integer))) (and (not P2) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.complex Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P2)) (and (=> P2 (@ P tptp.one_one_complex)) (=> (not P2) (@ P tptp.zero_zero_complex))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.real Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P2)) (and (=> P2 (@ P tptp.one_one_real)) (=> (not P2) (@ P tptp.zero_zero_real))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.rat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P2)) (and (=> P2 (@ P tptp.one_one_rat)) (=> (not P2) (@ P tptp.zero_zero_rat))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.nat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P2)) (and (=> P2 (@ P tptp.one_one_nat)) (=> (not P2) (@ P tptp.zero_zero_nat))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.int Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P2)) (and (=> P2 (@ P tptp.one_one_int)) (=> (not P2) (@ P tptp.zero_zero_int))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.code_integer Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P2)) (and (=> P2 (@ P tptp.one_one_Code_integer)) (=> (not P2) (@ P tptp.zero_z3403309356797280102nteger))))))
% 6.83/7.12 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P3 Bool)) (@ (@ (@ tptp.if_complex P3) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.83/7.12 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P3 Bool)) (@ (@ (@ tptp.if_real P3) tptp.one_one_real) tptp.zero_zero_real))))
% 6.83/7.12 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P3 Bool)) (@ (@ (@ tptp.if_rat P3) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.83/7.12 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P3 Bool)) (@ (@ (@ tptp.if_nat P3) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.83/7.12 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P3 Bool)) (@ (@ (@ tptp.if_int P3) tptp.one_one_int) tptp.zero_zero_int))))
% 6.83/7.12 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P3 Bool)) (@ (@ (@ tptp.if_Code_integer P3) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((Y3 tptp.num)) (=> (not (= Y3 tptp.one)) (=> (forall ((X22 tptp.num)) (not (= Y3 (@ tptp.bit0 X22)))) (not (forall ((X33 tptp.num)) (not (= Y3 (@ tptp.bit1 X33)))))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X4)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X4) _let_1))))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X4)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X4) _let_1))))))
% 6.83/7.12 (assert (forall ((X4 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X4)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X4) _let_1))))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X4)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X4) _let_1))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X4)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X4) _let_1))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A5 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.nat) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B5)) (@ (@ tptp.times_times_nat _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.83/7.12 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A5 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A5) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.int) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B5)) (@ (@ tptp.times_times_int _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.83/7.12 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A5 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A5) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B5)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.set_nat) (X4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y3)) X4) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X4)) Y3))))
% 6.83/7.12 (assert (forall ((Y3 tptp.set_nat) (X4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) (@ tptp.uminus5710092332889474511et_nat X4)) (@ (@ tptp.ord_less_eq_set_nat X4) (@ tptp.uminus5710092332889474511et_nat Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X4) Y3) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y3)) (@ tptp.uminus5710092332889474511et_nat X4)))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.83/7.12 (assert (forall ((R2 tptp.real) (A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B2) (@ _let_1 D)))))))))
% 6.83/7.12 (assert (forall ((R2 tptp.rat) (A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B2) (@ _let_1 D)))))))))
% 6.83/7.12 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B2) (@ _let_1 D)))))))))
% 6.83/7.12 (assert (forall ((R2 tptp.int) (A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B2) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B2) (@ _let_1 D)))))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.83/7.12 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.83/7.12 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.83/7.12 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.83/7.12 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.83/7.12 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.83/7.12 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.83/7.12 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.83/7.12 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.83/7.12 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.83/7.12 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.83/7.12 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.83/7.12 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.83/7.12 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.83/7.12 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 6.83/7.12 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 6.83/7.12 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 6.83/7.12 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 6.83/7.12 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.83/7.12 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 6.83/7.12 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 6.83/7.12 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 6.83/7.12 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (A tptp.real)) (= (= B2 (@ (@ tptp.plus_plus_real B2) A)) (= A tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (= (= B2 (@ (@ tptp.plus_plus_rat B2) A)) (= A tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (= B2 (@ (@ tptp.plus_plus_nat B2) A)) (= A tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (= B2 (@ (@ tptp.plus_plus_int B2) A)) (= A tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B2))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B2))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_rat (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B2))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int B2))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B2)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.83/7.12 (assert (forall ((W tptp.real) (Y3 tptp.real) (X4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X4))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y3)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y3))) (or (= W X4) (= Y3 Z)))))))
% 6.83/7.12 (assert (forall ((W tptp.rat) (Y3 tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X4))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y3)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y3))) (or (= W X4) (= Y3 Z)))))))
% 6.83/7.12 (assert (forall ((W tptp.nat) (Y3 tptp.nat) (X4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X4))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y3))) (or (= W X4) (= Y3 Z)))))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Y3 tptp.int) (X4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X4))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y3)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y3))) (or (= W X4) (= Y3 Z)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (Z tptp.real)) (= (= X4 (@ (@ tptp.minus_minus_real Y3) Z)) (= Y3 (@ (@ tptp.plus_plus_real X4) Z)))))
% 6.83/7.12 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N)))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N)))))))
% 6.83/7.12 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N2 tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A4) _let_1)))))))
% 6.83/7.12 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A4) _let_1)))))))
% 6.83/7.12 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A4) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A4) _let_1)))))))
% 6.83/7.12 (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))))))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X4))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (U tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X4) _let_4) (=> (@ (@ tptp.ord_less_real Y3) _let_4) (=> (@ _let_3 X4) (=> (@ _let_3 Y3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y3) _let_2)))) U)))))))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 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 X4))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 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 X4))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)) A))))
% 6.83/7.12 (assert (forall ((X4 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 X4))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)) A))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)) A))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B2))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) B2) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B2))) (= (@ (@ tptp.bit_se727722235901077358nd_nat _let_1) B2) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 6.83/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (= (@ tptp.sqrt X4) (@ tptp.sqrt Y3)) (= X4 Y3))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.83/7.12 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X4) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X4) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.83/7.12 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.sqrt X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y3)) (@ (@ tptp.ord_less_real X4) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3))))
% 6.83/7.12 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.sqrt X4) tptp.one_one_real) (= X4 tptp.one_one_real))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B2)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X4) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X4)))
% 6.83/7.12 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X4) (@ tptp.uminus_uminus_int tptp.one_one_int)) X4)))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.83/7.12 (assert (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) tptp.one_one_int) tptp.one_one_int)))
% 6.83/7.12 (assert (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.83/7.12 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.83/7.12 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.83/7.12 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.83/7.12 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y3)) (@ _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y3)) (@ _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.83/7.12 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.83/7.12 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.83/7.12 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y3)) (@ _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y3)) (@ _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W) (@ tptp.ring_1_of_int_rat X4)) (= (@ (@ tptp.power_power_int B2) W) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W) (@ tptp.ring_1_of_int_real X4)) (= (@ (@ tptp.power_power_int B2) W) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W) (@ tptp.ring_1_of_int_int X4)) (= (@ (@ tptp.power_power_int B2) W) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B2)) W) (@ tptp.ring_17405671764205052669omplex X4)) (= (@ (@ tptp.power_power_int B2) W) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X4) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W)) (= X4 (@ (@ tptp.power_power_int B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X4) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W)) (= X4 (@ (@ tptp.power_power_int B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X4) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W)) (= X4 (@ (@ tptp.power_power_int B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X4) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B2)) W)) (= X4 (@ (@ tptp.power_power_int B2) W)))))
% 6.83/7.12 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))))
% 6.83/7.12 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y3))) tptp.one_one_int)))
% 6.83/7.12 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3))) tptp.one_one_nat)))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) tptp.one_one_int) tptp.one_one_int)))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.83/7.12 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.83/7.12 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y3))) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) tptp.zero_zero_nat)))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y3))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y3))))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 6.83/7.12 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.83/7.12 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.83/7.12 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.83/7.12 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 6.83/7.12 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.83/7.12 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.83/7.12 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N) (@ tptp.ring_17405671764205052669omplex Y3)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N) (@ tptp.ring_1_of_int_real Y3)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N) (@ tptp.ring_1_of_int_rat Y3)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y3)) (= _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y3) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y3) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y3) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N))) (= (= (@ tptp.ring_1_of_int_int Y3) _let_1) (= Y3 _let_1)))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W)) (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W)) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W)) (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W)) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W)) (@ tptp.ring_1_of_int_int X4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B2) W)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W)) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.power_power_int B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W)) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.power_power_int B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X4)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W)) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.power_power_int B2) W)))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W)) (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W)) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W)) (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W)) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W)) (@ tptp.ring_1_of_int_int X4)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B2) W)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B2)) W)) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.power_power_int B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B2)) W)) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.power_power_int B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (B2 tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X4)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B2)) W)) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.power_power_int B2) W)))))
% 6.83/7.12 (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)))
% 6.83/7.12 (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)))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y3))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y3))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y3))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1745604003318907178nteger N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.83/7.12 (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)))
% 6.83/7.12 (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)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)) A))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)) A))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 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 X4)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 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 X4)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)) A))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)) A))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y3) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N))) (= (= (@ tptp.ring_1_of_int_int Y3) _let_1) (= Y3 _let_1)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y3) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X4))) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y3) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N) (@ tptp.ring_1_of_int_real Y3)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y3)) (= _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X4))) N) (@ tptp.ring_17405671764205052669omplex Y3)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N) (@ tptp.ring_18347121197199848620nteger Y3)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N) (@ tptp.ring_1_of_int_rat Y3)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y3))) (@ (@ 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 X4)) (@ tptp.numeral_numeral_int Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y3)))))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N))) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 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 X4))) 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 X4))) N)) A))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)) A))))
% 6.83/7.12 (assert (forall ((X4 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 X4))) 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 X4))) N)) A))))
% 6.83/7.12 (assert (forall ((X4 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 X4))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 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 X4))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 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 X4))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (X4 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.83/7.12 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A4) (@ tptp.bit_se2000444600071755411sk_int N2)))))
% 6.83/7.12 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A4) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.83/7.12 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int B2))) (let ((_let_2 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat B2))) (let ((_let_2 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.12 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B3) A4))))
% 6.83/7.12 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B3) A4))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int B2) C))))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat B2) C))))))
% 6.83/7.12 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L2)))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B2))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (=> (= (@ _let_2 A) (@ _let_2 B2)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B2))))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.nat) (B2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N))) (=> (= (@ _let_2 A) (@ _let_2 B2)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B2))))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X4))) (= (@ (@ tptp.times_times_real _let_1) Y3) (@ (@ tptp.times_times_real Y3) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X4))) (= (@ (@ tptp.times_times_rat _let_1) Y3) (@ (@ tptp.times_times_rat Y3) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X4))) (= (@ (@ tptp.times_times_int _let_1) Y3) (@ (@ tptp.times_times_int Y3) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X4) Y3)) (@ (@ tptp.times_times_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X4) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) K))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X4)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X4)))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) B2)) (@ _let_1 B2)))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int) (R2 tptp.int) (S tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ tptp.bit_concat_bit N))) (= (= (@ (@ _let_2 K) L2) (@ (@ _let_2 R2) S)) (and (= (@ _let_1 K) (@ _let_1 R2)) (= L2 S)))))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (= (@ (@ tptp.bit_se3949692690581998587nteger A) B2) _let_1) (and (= A _let_1) (= B2 _let_1))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) B2) _let_1) (and (= A _let_1) (= B2 _let_1))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.sqrt X4))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.sqrt X4))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (= (@ tptp.sqrt X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.sqrt X4))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (Z tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y3)) Z)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y3) Ya)) Z)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y3)) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y3)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X4) Y3))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N))) (= (= (@ _let_2 A) (@ _let_2 B2)) (= (@ _let_1 A) (@ _let_1 B2)))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ _let_1 tptp.zero_zero_int)))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N) M)) _let_2) _let_1) A))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sqrt X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.divide_divide_real X4) _let_1) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X4) Y3))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y3))))))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) A)) (@ _let_1 A))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y3) Y3))))))
% 6.83/7.12 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) K))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (=> (@ (@ tptp.ord_less_int Y3) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y3) Ya)) Z)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (Z tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (=> (@ (@ tptp.ord_less_int Y3) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y3)) Z)))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X4))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X4)))))
% 6.83/7.12 (assert (forall ((D tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B2)) (or (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B2)) (or (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B2)) (or (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.12 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))))
% 6.83/7.12 (assert (= tptp.ord_less_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N2)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))))
% 6.83/7.12 (assert (forall ((X4 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 X4)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X4) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X4) D))) _let_1))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A4 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A4) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)))))
% 6.83/7.12 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (@ (@ tptp.modulo_modulo_int A4) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.83/7.12 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.one_one_int) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.one_one_nat) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y3) (@ (@ tptp.ord_less_real X4) (@ tptp.sqrt Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y3) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.sqrt Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) Y3) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.power_power_real Y3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.83/7.12 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X4))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X4))))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 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 X4))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X4)))) tptp.one_one_real)))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) A))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) A))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) A))))
% 6.83/7.12 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (= (@ tptp.sqrt X4) Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.power_power_real Y3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) Y3)))))))
% 6.83/7.12 (assert (forall ((U tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) U) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) U))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) Y3) (= X4 tptp.zero_zero_real)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) X4) (= Y3 tptp.zero_zero_real)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.real) (C tptp.real) (B2 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 B2) D)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B2) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D) _let_1))))))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N)) (= N tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N)) (= N tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N)) (= N tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.power_power_real Y3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 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 X4) (=> (@ _let_2 Y3) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))) (@ (@ tptp.plus_plus_real X4) Y3))))))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (X4 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) X4) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) N) (@ (@ tptp.power_power_real X4) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X4) Y3))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer))))))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int))))))))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat))))))))))
% 6.83/7.12 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.83/7.12 (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)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X4)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X4))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y3)) (@ (@ tptp.ord_less_real X4) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3))))
% 6.83/7.12 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.83/7.12 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.exp_real X4) tptp.one_one_real) (= X4 tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.83/7.12 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) tptp.zero_zero_nat)))
% 6.83/7.12 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3))) tptp.one_one_nat)))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.83/7.12 (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))))))
% 6.83/7.12 (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))))))
% 6.83/7.12 (assert (forall ((A3 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A3))) (= (@ (@ tptp.times_times_complex _let_1) A3) (@ (@ tptp.times_times_complex A3) _let_1)))))
% 6.83/7.12 (assert (forall ((A3 tptp.real)) (let ((_let_1 (@ tptp.exp_real A3))) (= (@ (@ tptp.times_times_real _let_1) A3) (@ (@ tptp.times_times_real A3) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y3)) (@ (@ tptp.ord_less_real X4) Y3))))
% 6.83/7.12 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.83/7.12 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X4)) (@ tptp.exp_complex Y3)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X4) Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y3)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X4) Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X4) Y3) (@ (@ tptp.times_times_complex Y3) X4)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X4) Y3)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X4)) (@ tptp.exp_complex Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (= (@ (@ tptp.times_times_real X4) Y3) (@ (@ tptp.times_times_real Y3) X4)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.times_times_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X4) Y3)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X4)) (@ tptp.exp_complex Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X4) Y3)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X4))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (exists ((X3 tptp.real)) (= (@ tptp.exp_real X3) Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X4)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X4))) tptp.one_one_real)))
% 6.83/7.12 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X4)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X4))) tptp.one_one_complex)))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ tptp.exp_real X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ tptp.exp_real X4)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y3) (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 Y3) tptp.one_one_real)) (= (@ tptp.exp_real X3) Y3))))))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.83/7.12 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.83/7.12 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.83/7.12 (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)))
% 6.83/7.12 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X3)) X4) (@ (@ tptp.ord_less_real X4) (@ 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)) X4) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X3)) X4) (@ (@ tptp.ord_less_rat X4) (@ 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)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X4) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.83/7.12 (assert (forall ((X4 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) X4) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X4)))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X4)) (@ tptp.tanh_real Y3)) (@ (@ tptp.ord_less_real X4) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X4)) (@ tptp.tanh_real Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3))))
% 6.83/7.12 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (= (@ tptp.ln_ln_real X4) (@ tptp.ln_ln_real Y3)) (= X4 Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y3)) (@ (@ tptp.ord_less_real X4) Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X4)) (@ _let_1 X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X4)) (@ _let_1 X4)))))
% 6.83/7.12 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (= (@ tptp.ln_ln_real X4) tptp.zero_zero_real) (= X4 tptp.one_one_real)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (= (@ _let_1 (@ tptp.ln_ln_real X4)) (@ (@ tptp.ord_less_real tptp.one_one_real) X4))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.exp_real (@ tptp.ln_ln_real X4)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X4)) X4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.inc M)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.inc M)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 6.83/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.inc M)))))
% 6.83/7.12 (assert (forall ((P (-> tptp.num Bool)) (X4 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X3 tptp.num)) (=> (@ P X3) (@ P (@ tptp.inc X3)))) (@ P X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X4))) (= (@ _let_1 (@ tptp.inc Y3)) (@ tptp.inc (@ _let_1 Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X4)) tptp.one_one_real)))
% 6.83/7.12 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X4)) (@ tptp.bit1 X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X4)) (@ tptp.bit0 (@ tptp.inc X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) tptp.zero_zero_real)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X4)) (=> (@ _let_1 X4) (@ (@ tptp.ord_less_real tptp.one_one_real) X4))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.plus_plus_num X4) tptp.one) (@ tptp.inc X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (let ((_let_1 (@ tptp.times_times_num X4))) (= (@ _let_1 (@ tptp.inc Y3)) (@ (@ tptp.plus_plus_num (@ _let_1 Y3)) X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X4) Y3)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y3))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (= (@ tptp.ln_ln_real X4) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (= X4 tptp.one_one_real)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y3))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real Y3) (@ tptp.ln_ln_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y3)) X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y3)) Y3)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X4)) X4))))))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X4)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X4)) tptp.one_one_complex))))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X4)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X4)) tptp.one_one_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X4)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X4)) tptp.one_one_rat))))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X4)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X4)) tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X4)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X4)) tptp.one_one_int))))
% 6.83/7.12 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y3))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X4) Y3)) Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (= (@ tptp.arcosh_real X4) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X4) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X4))) (@ tptp.uminus_uminus_real X4))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.ln_ln_real (@ tptp.sqrt X4)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N4 tptp.nat)) (and (not (@ P N4)) (@ P (@ tptp.suc N4))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real Z2)))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real Z2)))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.83/7.12 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))) (let ((_let_2 (@ tptp.exp_real X))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.83/7.12 (assert (= tptp.tanh_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))) (let ((_let_2 (@ tptp.exp_complex X))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)))))))
% 6.83/7.12 (assert (= tptp.artanh_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((X4 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))) X4) (=> (@ (@ tptp.ord_less_eq_real X4) 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) X4))) X4))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 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 Y3))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X4) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X4) _let_1)) (= (@ tptp.archim8280529875227126926d_real X4) Y3)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (Y3 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 Y3))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X4) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X4) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X4) Y3)))))))
% 6.83/7.12 (assert (= tptp.arsinh_real (lambda ((X tptp.real)) (@ tptp.ln_ln_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)))))))
% 6.83/7.12 (assert (forall ((X4 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 X4)) (@ (@ 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) X4))) X4))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X4) (@ (@ 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 X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ 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 X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X4) (@ (@ 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 X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ 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 X4)))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.83/7.12 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B2)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B2)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.83/7.12 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.83/7.12 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 6.83/7.12 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 6.83/7.12 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M)) K) (@ (@ tptp.dvd_dvd_Code_integer M) K))))
% 6.83/7.12 (assert (forall ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))))
% 6.83/7.12 (assert (forall ((M tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))))
% 6.83/7.12 (assert (forall ((M tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))))
% 6.83/7.12 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K)) (@ _let_1 K)))))
% 6.83/7.12 (assert (forall ((M tptp.rat) (K tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M))) (= (@ _let_1 (@ tptp.abs_abs_rat K)) (@ _let_1 K)))))
% 6.83/7.12 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X4) X4)) (@ tptp.abs_abs_real X4))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 6.83/7.12 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.83/7.12 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 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 B2))) (or (@ _let_1 A) (= B2 tptp.zero_zero_real))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 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 B2))) (or (@ _let_1 A) (= B2 tptp.zero_zero_rat))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B2))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B2))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X4)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X4))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((W tptp.num) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X4))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2) (@ (@ tptp.ord_less_eq_real A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B2) (@ (@ tptp.ord_le3102999989581377725nteger A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B2) (@ (@ tptp.ord_less_eq_rat A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2) (@ (@ tptp.ord_less_eq_int A) B2))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.83/7.12 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B2)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B2) A)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B2) A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B2)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B2) A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B2) A)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (= (@ tptp.abs_abs_real X4) (@ tptp.abs_abs_real Y3)) (or (= X4 Y3) (= X4 (@ tptp.uminus_uminus_real Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (= (@ tptp.abs_abs_int X4) (@ tptp.abs_abs_int Y3)) (or (= X4 Y3) (= X4 (@ tptp.uminus_uminus_int Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X4) (@ tptp.abs_abs_Code_integer Y3)) (or (= X4 Y3) (= X4 (@ tptp.uminus1351360451143612070nteger Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (= (@ tptp.abs_abs_rat X4) (@ tptp.abs_abs_rat Y3)) (or (= X4 Y3) (= X4 (@ tptp.uminus_uminus_rat Y3))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((L2 tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L2) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L2) K))))
% 6.83/7.12 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L2) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L2) K))))
% 6.83/7.12 (assert (forall ((L2 tptp.code_integer) (K tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L2) (@ tptp.abs_abs_Code_integer K)) (@ (@ tptp.dvd_dvd_Code_integer L2) K))))
% 6.83/7.12 (assert (forall ((L2 tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L2) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L2) K))))
% 6.83/7.12 (assert (forall ((Z tptp.real) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M)))))))
% 6.83/7.12 (assert (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B2))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B2))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B2))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B2))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B2 tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B2))) (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))))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (C tptp.real) (B2 tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B2))) (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))))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B2 tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B2))) (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))))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B2))) (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))))))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B2))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 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 B2)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B2))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B2) A)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B2) A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B2) A)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B2) A)))))
% 6.83/7.12 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))))))
% 6.83/7.12 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B2)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2))))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2) (and (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B2) (and (@ (@ tptp.ord_le3102999989581377725nteger A) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B2) (and (@ (@ tptp.ord_less_eq_rat A) B2) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2) (and (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B2) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B2) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B2) (and (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B2) (and (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) B2) (and (@ (@ tptp.ord_le6747313008572928689nteger A) B2) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) B2) (and (@ (@ tptp.ord_less_rat A) B2) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B2)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) E2))) (= X4 tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X4)) E2))) (= X4 tptp.zero_zero_rat))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 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 B2) (@ (@ tptp.ord_le3102999989581377725nteger B2) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B2)))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 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 B2) (@ (@ tptp.ord_less_eq_real B2) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 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 B2) (@ (@ tptp.ord_less_eq_rat B2) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2)))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 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 B2) (@ (@ tptp.ord_less_eq_int B2) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X4) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y3)) X4) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y3) X4))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y3)) X4) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y3) X4))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y3)) X4) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y3) X4))))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y3)) X4) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y3) X4))))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.83/7.12 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= A (@ tptp.abs_abs_real B2)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B2 A) (= B2 (@ tptp.uminus_uminus_real A)))))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= A (@ tptp.abs_abs_Code_integer B2)) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (or (= B2 A) (= B2 (@ tptp.uminus1351360451143612070nteger A)))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= A (@ tptp.abs_abs_rat B2)) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (or (= B2 A) (= B2 (@ tptp.uminus_uminus_rat A)))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.abs_abs_int B2)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (or (= B2 A) (= B2 (@ tptp.uminus_uminus_int A)))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.abs_abs_real A) B2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B2) (or (= A B2) (= A (@ tptp.uminus_uminus_real B2)))))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) B2) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B2) (or (= A B2) (= A (@ tptp.uminus1351360451143612070nteger B2)))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ tptp.abs_abs_rat A) B2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B2) (or (= A B2) (= A (@ tptp.uminus_uminus_rat B2)))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.abs_abs_int A) B2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (or (= A B2) (= A (@ tptp.uminus_uminus_int B2)))))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X4)) Y3) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X4) Y3))))))
% 6.83/7.12 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y3) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X4)) Y3) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X4) Y3))))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.83/7.12 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B2))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B2)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B2))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2)))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B2))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2)))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B2))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (B2 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) B2)) (@ (@ 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 B2) D))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 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) B2)) (@ (@ 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 B2) D))))))
% 6.83/7.12 (assert (forall ((A tptp.rat) (B2 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) B2)) (@ (@ 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 B2) D))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 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) B2)) (@ (@ 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 B2) D))))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X4) A))) R2) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X4) (@ (@ tptp.ord_le3102999989581377725nteger X4) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X4) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) A))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R2)) X4) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X4) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X4) A))) R2) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X4) (@ (@ tptp.ord_le6747313008572928689nteger X4) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) A))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R2)) X4) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X4) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X4)) (@ tptp.archim7778729529865785530nd_rat Y3)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y5))) D3) (and (@ (@ tptp.ord_less_real A) Y5) (@ (@ tptp.ord_less_real Y5) B2))))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (U tptp.real) (V tptp.real)) (=> (= X4 Y3) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X4) U)) Y3))) V)))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X4)))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X4) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X4)))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X4) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X4) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4)))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X4) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X4)))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X4) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X4)))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X4) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X4)))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X4) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X4)))))
% 6.83/7.12 (assert (forall ((N tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X4) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X4)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y5))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y5) (@ (@ tptp.ord_less_eq_real Y5) B2))))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X4))) X4))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X4))) X4))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) (@ 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 X4) N))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) (@ 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 X4) N))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X4)) (@ tptp.abs_abs_Code_integer Y3)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X4) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) (@ tptp.abs_abs_real Y3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X4)) (@ tptp.abs_abs_rat Y3)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1))))))
% 6.83/7.12 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X4)) (@ tptp.abs_abs_int Y3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1))))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X4) tptp.one_one_Code_integer))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (= (= (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X4) tptp.one_one_rat))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (= (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X4) tptp.one_one_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.int)) (= (= (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X4) tptp.one_one_int))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.code_integer) (X4 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y3) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X4) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y3) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X4)) Y3))))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) Y3))))))
% 6.83/7.12 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y3) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y3) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X4)) Y3))))))
% 6.83/7.12 (assert (forall ((Y3 tptp.int) (X4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y3) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X4)) Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X4)) tptp.one_one_Code_integer))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X4)) tptp.one_one_rat))))
% 6.83/7.12 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X4)) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X4)) tptp.one_one_Code_integer))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X4)) tptp.one_one_rat))))
% 6.83/7.12 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X4)) tptp.one_one_int))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B2 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 B2)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B2) N))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.real) (B2 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 B2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B2) N))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.rat) (B2 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 B2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B2) N))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (A tptp.int) (B2 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 B2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B2) N))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) (@ tptp.sqrt Y3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))))
% 6.83/7.12 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 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 X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X4)) (@ tptp.abs_abs_real Y3))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (Y3 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 X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))) tptp.one_one_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (U tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y3)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y3) _let_2)))) U))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) 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) X4))) X4))) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X4))) (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X4))) (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X4 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 X4)) (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X4 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 X4)) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X4 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 X4)) (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.83/7.12 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X4 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 X4)) (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.83/7.12 (assert (forall ((X4 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 X4)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X4)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X4)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.83/7.12 (assert (= tptp.arctan (lambda ((X 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 X) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.83/7.12 (assert (forall ((X4 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) X4) (= (@ (@ tptp.log _let_1) X4) (@ (@ 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 X4)))))))
% 6.83/7.12 (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))))))))
% 6.83/7.12 (assert (forall ((X4 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) X4) (= (@ _let_1 X4) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X4)))))))
% 6.83/7.12 (assert (forall ((X4 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X4) _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 X4) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X4))))))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) (@ tptp.semiri8010041392384452111omplex N)) (= M N))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) (@ tptp.semiri681578069525770553at_rat N)) (= M N))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 6.83/7.12 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.83/7.12 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.83/7.12 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.83/7.12 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.83/7.12 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.83/7.12 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.83/7.12 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.83/7.12 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.83/7.12 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B2)) W) (@ tptp.semiri8010041392384452111omplex X4)) (= (@ (@ tptp.power_power_nat B2) W) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W) (@ tptp.semiri5074537144036343181t_real X4)) (= (@ (@ tptp.power_power_nat B2) W) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B2)) W) (@ tptp.semiri681578069525770553at_rat X4)) (= (@ (@ tptp.power_power_nat B2) W) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W) (@ tptp.semiri1316708129612266289at_nat X4)) (= (@ (@ tptp.power_power_nat B2) W) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W) (@ tptp.semiri1314217659103216013at_int X4)) (= (@ (@ tptp.power_power_nat B2) W) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X4) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B2)) W)) (= X4 (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X4) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W)) (= X4 (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat X4) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B2)) W)) (= X4 (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X4) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W)) (= X4 (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X4) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W)) (= X4 (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 6.83/7.12 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X4)) (@ _let_1 X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X4)) (@ _let_1 X4)))))
% 6.83/7.12 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.83/7.12 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.83/7.12 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.83/7.12 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real) (Y3 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 X4) (=> (@ _let_2 Y3) (= (@ (@ tptp.ord_less_real (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_real X4) Y3)))))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) A))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ _let_1 (@ (@ tptp.log A) X4)) (@ (@ tptp.ord_less_real A) X4)))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 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 X4) (= (@ _let_2 (@ (@ tptp.log A) X4)) (@ _let_1 X4))))))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W)) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B2)) W)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W)) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W)) (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W)) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B2) W)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B2)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.nat) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y3) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N)) (= Y3 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.nat) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y3) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N)) (= Y3 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.nat) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y3) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N)) (= Y3 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.nat) (X4 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y3) _let_1) (= Y3 _let_1)))))
% 6.83/7.12 (assert (forall ((Y3 tptp.nat) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)) (= Y3 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N)))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N) (@ tptp.semiri8010041392384452111omplex Y3)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N) (@ tptp.semiri5074537144036343181t_real Y3)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N) (@ tptp.semiri681578069525770553at_rat Y3)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N) Y3))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y3)) (= _let_1 Y3)))))
% 6.83/7.12 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N) (@ tptp.semiri1314217659103216013at_int Y3)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N) Y3))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W)) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B2)) W)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W)) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W)) (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W)) X4))))
% 6.83/7.12 (assert (forall ((B2 tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B2) W)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B2)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B2)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B2)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (B2 tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B2)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B2) W)))))
% 6.83/7.12 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N))))
% 6.83/7.12 (assert (forall ((N tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W)))))
% 6.83/7.12 (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))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X4)) (@ (@ tptp.ord_less_eq_real A) X4))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) A))))))
% 6.83/7.12 (assert (forall ((A tptp.real) (X4 tptp.real) (Y3 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 X4) (=> (@ _let_2 Y3) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3)))))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N)))))
% 6.83/7.12 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N)))))
% 6.83/7.12 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N))))
% 6.83/7.12 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N)))))
% 6.83/7.12 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N)))))
% 6.83/7.12 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X4)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (= N tptp.zero_zero_nat)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X4)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (= N tptp.zero_zero_nat)))))
% 6.83/7.12 (assert (forall ((X4 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 X4)) N)) (or (@ _let_1 X4) (= N tptp.zero_zero_nat))))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X4)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (= N tptp.zero_zero_nat)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))))
% 6.83/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))))
% 6.83/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))))
% 6.83/7.12 (assert (forall ((A tptp.real) (B2 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) B2)) (@ tptp.semiri5074537144036343181t_real B2))))))
% 6.83/7.12 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N)))))
% 6.83/7.12 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N))))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (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)))))
% 6.83/7.12 (assert (forall ((I tptp.num) (N tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X4))))
% 6.83/7.12 (assert (forall ((I tptp.num) (N tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X4))))
% 6.83/7.12 (assert (forall ((I tptp.num) (N tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X4)) (@ _let_1 X4)))))
% 6.83/7.12 (assert (forall ((I tptp.num) (N tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X4)) _let_1) (@ (@ tptp.ord_less_nat X4) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.83/7.12 (assert (forall ((I tptp.num) (N tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X4))))
% 6.83/7.12 (assert (forall ((I tptp.num) (N tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X4))))
% 6.83/7.12 (assert (forall ((I tptp.num) (N tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X4)) (@ _let_1 X4)))))
% 6.83/7.12 (assert (forall ((I tptp.num) (N tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X4))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X4)) _let_1) (@ (@ tptp.ord_less_eq_nat X4) _let_1)))))
% 6.83/7.12 (assert (forall ((X4 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.83/7.12 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.83/7.12 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.83/7.12 (assert (forall ((M tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))) (= _let_1 _let_1))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 6.83/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 6.83/7.12 (assert (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (=> (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N4)) (not (@ (@ tptp.bit_se1146084159140164899it_int B2) N4)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B2)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B2) N))))))
% 6.83/7.12 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (forall ((N4 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N4)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B2) N4)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B2)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B2) N))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.semiri5074537144036343181t_real N4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.semiri681578069525770553at_rat N4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real X4) (@ tptp.semiri5074537144036343181t_real N4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_rat X4) (@ tptp.semiri681578069525770553at_rat N4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X4))) (= (@ (@ tptp.times_times_complex _let_1) Y3) (@ (@ tptp.times_times_complex Y3) _let_1)))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X4))) (= (@ (@ tptp.times_times_real _let_1) Y3) (@ (@ tptp.times_times_real Y3) _let_1)))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X4))) (= (@ (@ tptp.times_times_rat _let_1) Y3) (@ (@ tptp.times_times_rat Y3) _let_1)))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X4))) (= (@ (@ tptp.times_times_nat _let_1) Y3) (@ (@ tptp.times_times_nat Y3) _let_1)))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X4))) (= (@ (@ tptp.times_times_int _let_1) Y3) (@ (@ tptp.times_times_int Y3) _let_1)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int A) B2)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B2) N)))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se727722235901077358nd_nat A) B2)) N) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B2) N)))))
% 6.83/7.13 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X4)) (@ tptp.arctan Y3)) (@ (@ tptp.ord_less_real X4) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ tptp.arctan X4)) (@ tptp.arctan Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X4)) (@ tptp.arctan Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X4)) (@ tptp.arctan Y3)))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se4203085406695923979it_int M) A)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N) (not (= M N))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) N) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (not (= M N))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B2) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B2) M))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B2) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B2) _let_1)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X4))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X4))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X4)) (@ _let_1 X4)))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B2) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B2) M))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X4) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X4)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ _let_1 (@ (@ tptp.power_power_real X4) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X4)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N) (= N tptp.zero_zero_nat))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N) (= N tptp.zero_zero_nat))))
% 6.83/7.13 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N)))))
% 6.83/7.13 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 6.83/7.13 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.83/7.13 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.83/7.13 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N) (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N) (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 6.83/7.13 (assert (forall ((B2 Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B2)) N) (and B2 (= N tptp.zero_zero_nat)))))
% 6.83/7.13 (assert (forall ((B2 Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B2)) N) (and B2 (= N tptp.zero_zero_nat)))))
% 6.83/7.13 (assert (forall ((B2 Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) N) (and B2 (= N tptp.zero_zero_nat)))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I)) (@ tptp.semiri5074537144036343181t_real J)))))
% 6.83/7.13 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I)) (@ tptp.semiri681578069525770553at_rat J)))))
% 6.83/7.13 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 6.83/7.13 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (= tptp.log (lambda ((A4 tptp.real) (X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real A4)))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) A) (@ (@ tptp.bit_se2923211474154528505it_int N) A)))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y3) X4) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X4) Y3)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X4)) (@ tptp.abs_abs_int Y3))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B2) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B2) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N) M)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (B2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B2) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B2) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_rat Y3) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N4)) X4))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X4)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X4)) N))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X4)) (@ (@ tptp.power_power_real (@ tptp.exp_real X4)) N))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X4) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X4)) N))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X4) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X4)) N))))
% 6.83/7.13 (assert (= tptp.abs_abs_int (lambda ((I2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I2)) I2))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (forall ((Y5 tptp.real)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y5) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) X4)))))))
% 6.83/7.13 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X4))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X4)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A4) N2)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N2) A4))))
% 6.83/7.13 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N2 tptp.nat) (A4 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A4) N2)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N2) A4))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (X4 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 B2) X4) (@ (@ tptp.divide_divide_real (@ _let_1 X4)) (@ _let_1 B2))))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))))
% 6.83/7.13 (assert (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X4)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X4) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X4) D))) _let_1))))))
% 6.83/7.13 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N2) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) N))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (=> (forall ((N4 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N4) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (=> (forall ((N4 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N4) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (=> (forall ((N4 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N4) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real) (Y3 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 X4) (=> (@ _let_2 Y3) (= (@ _let_1 (@ (@ tptp.times_times_real X4) Y3)) (@ (@ tptp.plus_plus_real (@ _let_1 X4)) (@ _let_1 Y3)))))))))))
% 6.83/7.13 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N4 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) E)))))))
% 6.83/7.13 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N4 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N4)))) E)))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((K tptp.int)) (not (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M5 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N4) M5) (= (@ _let_1 M5) (@ _let_1 N4))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (not (@ _let_1 N4)))))))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real) (Y3 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 X4) (=> (@ _let_2 Y3) (= (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.minus_minus_real (@ _let_1 X4)) (@ _let_1 Y3)))))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X4) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X4)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X4) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X4)))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _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)) X4)) C))) (= X4 tptp.zero_zero_real)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 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 X4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X4))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X4)))) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X4) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X4))))))
% 6.83/7.13 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A4) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))))
% 6.83/7.13 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A4 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 A4) (@ (@ tptp.power_power_int _let_1) N2))))))))
% 6.83/7.13 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 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 A4) (@ (@ tptp.power_power_nat _let_1) N2))))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B2) (=> (not (= B2 tptp.one_one_real)) (=> (@ _let_1 X4) (= (@ (@ tptp.log A) X4) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B2)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B2) X4)))))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (assert (forall ((D tptp.int) (X4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X4))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 6.83/7.13 (assert (forall ((D tptp.int) (Z tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X4) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) Z))) tptp.one_one_int)) D))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X4)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) N)))))
% 6.83/7.13 (assert (forall ((X4 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)) X4) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X4))) (@ (@ tptp.power_power_real (@ _let_1 X4)) N))))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) N) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N) (= N tptp.zero_zero_nat))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (= N tptp.zero_zero_nat))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (= N tptp.zero_zero_nat))))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (or (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.minus_8373710615458151222nteger A) tptp.one_one_Code_integer)) N) (= N tptp.zero_zero_nat))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (or (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) N) (= N tptp.zero_zero_nat))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.minus_minus_nat A) tptp.one_one_nat)) N) (= N tptp.zero_zero_nat))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B2))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N))))))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B2))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N))))))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B2))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N))))))))))
% 6.83/7.13 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A4) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))))
% 6.83/7.13 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A4) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))))
% 6.83/7.13 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A4) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X4)) (@ tptp.arctan Y3)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X4) Y3)))))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 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)) X4))) (@ (@ tptp.power_power_real (@ _let_1 X4)) N))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ 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 X4) _let_1))) N)) (@ tptp.exp_real X4)))))))
% 6.83/7.13 (assert (forall ((H2 tptp.real) (Z tptp.real) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N)) (@ _let_4 N))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))))
% 6.83/7.13 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N)) (@ _let_3 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))))
% 6.83/7.13 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))))
% 6.83/7.13 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X4)) X4) (exists ((N2 tptp.int)) (= X4 (@ tptp.ring_1_of_int_real N2))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X4)) X4) (exists ((N2 tptp.int)) (= X4 (@ tptp.ring_1_of_int_rat N2))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X4)) X4) (exists ((N2 tptp.int)) (= X4 (@ tptp.ring_1_of_int_rat N2))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X4)) X4) (exists ((N2 tptp.int)) (= X4 (@ tptp.ring_1_of_int_real N2))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.83/7.13 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.83/7.13 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.83/7.13 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 6.83/7.13 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 6.83/7.13 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.83/7.13 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.83/7.13 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 6.83/7.13 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) Z))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) Z))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X4) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X4)) Z))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X4) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X4)) Z))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X4) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X4)) Z))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X4) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X4)) Z))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X4) tptp.zero_zero_rat))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real V)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X4) (@ tptp.numeral_numeral_rat V)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real V)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.numeral_numeral_rat V)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.83/7.13 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X4) tptp.one_one_rat))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real tptp.one_one_real) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X4) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.numeral_numeral_int V)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X4) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.numeral_numeral_int V)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X4) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X4) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B2))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B2)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X4))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B2))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B2))))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X4) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X4) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X4) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X4))))
% 6.83/7.13 (assert (forall ((B2 tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B2))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B2)))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B2)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B2)))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B2)))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B2))))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X4))))
% 6.83/7.13 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X4))))
% 6.83/7.13 (assert (forall ((B2 tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B2)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int B2)))))
% 6.83/7.13 (assert (forall ((P Bool) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ (@ tptp.if_nat P) A) B2)))) (and (=> P (= _let_1 (@ tptp.semiri1314217659103216013at_int A))) (=> (not P) (= _let_1 (@ tptp.semiri1314217659103216013at_int B2)))))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int A4) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.83/7.13 (assert (forall ((Z tptp.int)) (not (forall ((M4 tptp.nat) (N4 tptp.nat)) (not (= Z (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M4)) (@ tptp.semiri1314217659103216013at_int N4))))))))
% 6.83/7.13 (assert (= tptp.archim7802044766580827645g_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (@ (@ (@ tptp.if_int (= X (@ tptp.ring_1_of_int_real _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.83/7.13 (assert (= tptp.archim2889992004027027881ng_rat (lambda ((X tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (@ (@ (@ tptp.if_int (= X (@ tptp.ring_1_of_int_rat _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim6058952711729229775r_real X4))) tptp.one_one_int)))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.archim3151403230148437115or_rat X4))) tptp.one_one_int)))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X4))) X4)))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X4))) X4)))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y3)) (@ (@ tptp.ord_less_real X4) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y3)) (@ (@ tptp.ord_less_rat X4) Y3))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y3) X4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y3)) (@ tptp.archim7802044766580827645g_real X4)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y3)) (@ tptp.archim2889992004027027881ng_rat X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.archim2889992004027027881ng_rat Y3)) (@ (@ tptp.ord_less_rat X4) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim7802044766580827645g_real Y3)) (@ (@ tptp.ord_less_real X4) Y3))))
% 6.83/7.13 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X4))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.83/7.13 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X4) N))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X4) N))))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X4) N))))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X4) N))))))
% 6.83/7.13 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.83/7.13 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N4 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N4))) (=> (forall ((N4 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))) (@ P Z)))))
% 6.83/7.13 (assert (forall ((Z tptp.int)) (=> (forall ((N4 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N4)))) (not (forall ((N4 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))))
% 6.83/7.13 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 6.83/7.13 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 6.83/7.13 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B2) A))) (@ tptp.real_V1022390504157884413omplex B2))) (@ tptp.real_V1022390504157884413omplex A))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N))) Z))))
% 6.83/7.13 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat A) B2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.83/7.13 (assert (= tptp.ord_less_eq_int (lambda ((W2 tptp.int) (Z5 tptp.int)) (exists ((N2 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W2) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat A) B2)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat A) B2)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.83/7.13 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X4))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) Z) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real Z)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) Z) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat Z)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y3))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y3))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) Y3)))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X4)))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) (@ tptp.ring_1_of_int_real Z))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) Z) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) (@ tptp.ring_1_of_int_rat Z))))))
% 6.83/7.13 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real K)) (@ tptp.ring_1_of_int_real L2))) (@ (@ tptp.divide_divide_int K) L2))))
% 6.83/7.13 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K)) (@ tptp.ring_1_of_int_rat L2))) (@ (@ tptp.divide_divide_int K) L2))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X4))) (=> (= X4 (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X4) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X4))) (=> (= X4 (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X4) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) A))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) A))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) Z) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real Z)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) Z) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat Z)))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X4))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) Y3))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.archim2889992004027027881ng_rat Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) Y3))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim7802044766580827645g_real Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X4) N)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X4) N)))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X4) N)))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X4) N)))))
% 6.83/7.13 (assert (forall ((M tptp.int)) (=> (forall ((N4 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N4)))) (not (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.83/7.13 (assert (= tptp.ord_less_int (lambda ((W2 tptp.int) (Z5 tptp.int)) (exists ((N2 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W2) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X4))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X4))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)))))
% 6.83/7.13 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R2))) (@ (@ tptp.plus_plus_real R2) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R2))) (@ (@ tptp.plus_plus_rat R2) tptp.one_one_rat))))
% 6.83/7.13 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R2))) tptp.one_one_real)) R2)))
% 6.83/7.13 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R2))) tptp.one_one_rat)) R2)))
% 6.83/7.13 (assert (forall ((N tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X4) N))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B2))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B2)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B2))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B2)))))
% 6.83/7.13 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (= K (@ tptp.semiri1314217659103216013at_int N4)))))))
% 6.83/7.13 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N4)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4))))))))
% 6.83/7.13 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N4 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N4)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4)))) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4)))))))))
% 6.83/7.13 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.83/7.13 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.83/7.13 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) tptp.zero_zero_int) (exists ((N4 tptp.nat)) (= X4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ _let_1 N))))))
% 6.83/7.13 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))))
% 6.83/7.13 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))))
% 6.83/7.13 (assert (forall ((Z tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A) B2)))) (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))))))))))
% 6.83/7.13 (assert (forall ((Z tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N))) M))))))
% 6.83/7.13 (assert (forall ((Z tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) M))))))
% 6.83/7.13 (assert (forall ((Z tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) M))))))
% 6.83/7.13 (assert (forall ((Z tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) M))))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) M))))))
% 6.83/7.13 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I2))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I2)))))))
% 6.83/7.13 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I2))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T) (@ (@ tptp.ord_less_rat T) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I2)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X4) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X4) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X4) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X4) Z))))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X4) (=> (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X4) Z))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B2))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B2))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B2))))))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X4))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) Z) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) Z) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X4))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X4) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X4))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.83/7.13 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I2))) (=> (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) T) (@ (@ tptp.ord_less_eq_real T) _let_1)) (@ P I2)))))))
% 6.83/7.13 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I2))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T) (@ (@ tptp.ord_less_eq_rat T) _let_1)) (@ P I2)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X4) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X4) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X4) (@ (@ tptp.ord_less_eq_rat X4) _let_1))))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.archim7802044766580827645g_real X4) Z))))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X4) (=> (@ (@ tptp.ord_less_eq_rat X4) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X4) Z))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X4)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X4)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X4) (@ (@ tptp.ord_less_eq_rat X4) _let_1)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B2))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B2))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B2))))))))
% 6.83/7.13 (assert (forall ((B2 tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ 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))) B2) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) Z) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) Z) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X4))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X4))))
% 6.83/7.13 (assert (forall ((N tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X4) N))))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B2) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A) (@ tptp.ring_1_of_int_real B2))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A)) B2)))))
% 6.83/7.13 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4))))))))
% 6.83/7.13 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.83/7.13 (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)))
% 6.83/7.13 (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)))
% 6.83/7.13 (assert (forall ((P (-> tptp.int Bool)) (X4 tptp.nat) (Y3 tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X4) Y3))) (and (=> (@ (@ tptp.ord_less_eq_nat Y3) X4) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X4)) (@ tptp.semiri1314217659103216013at_int Y3)))) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ P tptp.zero_zero_int))))))
% 6.83/7.13 (assert (forall ((B2 tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ 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))))))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 6.83/7.13 (assert (forall ((Q2 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q2)))) Q2)) P2))))
% 6.83/7.13 (assert (forall ((Q2 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q2)))) Q2)) P2))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (assert (forall ((Q2 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real P2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q2)))) Q2)))))
% 6.83/7.13 (assert (forall ((Q2 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_eq_rat P2) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q2)))) Q2)))))
% 6.83/7.13 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N2))))))))
% 6.83/7.13 (assert (forall ((B2 tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ 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))) B2) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 6.83/7.13 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.83/7.13 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))
% 6.83/7.13 (assert (forall ((B2 tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B2))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B2)) (@ 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))))))))))
% 6.83/7.13 (assert (forall ((Q2 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real P2) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q2)))) tptp.one_one_real)) Q2)))))
% 6.83/7.13 (assert (forall ((Q2 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_rat P2) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q2)))) tptp.one_one_rat)) Q2)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (= tptp.archim8280529875227126926d_real (lambda ((X tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.83/7.13 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.83/7.13 (assert (forall ((Q2 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q2)))) tptp.one_one_real)) Q2)) P2))))
% 6.83/7.13 (assert (forall ((Q2 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q2)))) tptp.one_one_rat)) Q2)) P2))))
% 6.83/7.13 (assert (forall ((N tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X4) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X4) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 6.83/7.13 (assert (forall ((N tptp.int) (X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N))) (=> (@ (@ tptp.ord_less_rat _let_1) X4) (=> (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X4) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 6.83/7.13 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))))
% 6.83/7.13 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))))
% 6.83/7.13 (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))
% 6.83/7.13 (assert (forall ((B2 tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B2)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B2) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K)))))
% 6.83/7.13 (assert (forall ((B2 tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B2)) 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 B2) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B2)) 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 B2) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 6.83/7.13 (assert (forall ((B2 tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B2)) 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 B2) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B2)) 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 B2) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))))
% 6.83/7.13 (assert (forall ((B2 tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B2) (@ 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 B2)) K)))))
% 6.83/7.13 (assert (forall ((B2 tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B2) (@ 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 B2)) K)))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B2) (@ 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 B2)) K)))))
% 6.83/7.13 (assert (forall ((B2 tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B2) (@ 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 B2)) K)))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B2) (@ 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 B2)) K)))))
% 6.83/7.13 (assert (forall ((Y3 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 Y3))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y3))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 6.83/7.13 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.83/7.13 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.83/7.13 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A))))))
% 6.83/7.13 (assert (forall ((W tptp.num) (A tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) (@ tptp.real_V1022390504157884413omplex A)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X4)) tptp.zero_zero_real) (= X4 tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) tptp.zero_zero_real) (= X4 tptp.zero_zero_complex))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 6.83/7.13 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.83/7.13 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.83/7.13 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.83/7.13 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X4)) (not (= X4 tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X4)) (not (= X4 tptp.zero_zero_complex)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B2)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B2)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B2) A)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X4) Y3)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X4) Y3)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y3)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B2)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B2)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X4) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X4)) N))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X4) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X4)) N))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X4)) Y3)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X4)) Y3)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y3)))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B2))))))
% 6.83/7.13 (assert (forall ((B2 tptp.complex) (A tptp.complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B2))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (N tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N) (@ (@ tptp.power_power_real Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 6.83/7.13 (assert (forall ((W tptp.complex) (N tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N) (@ (@ tptp.power_power_complex Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (R2 tptp.real) (Y3 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y3)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X4) Y3))) (@ (@ tptp.times_times_real R2) S))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (R2 tptp.real) (Y3 tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y3)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X4) Y3))) (@ (@ tptp.times_times_real R2) S))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X4) Y3))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X4) Y3))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y3))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y3))) E))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y3))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y3))) E))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (R2 tptp.real) (Y3 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y3)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y3))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (R2 tptp.real) (Y3 tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y3)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y3))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X4) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X4)) N))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X4) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X4)) N))))
% 6.83/7.13 (assert (forall ((A tptp.real) (R2 tptp.real) (B2 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B2)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B2))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (R2 tptp.real) (B2 tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B2)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B2))) (@ (@ tptp.plus_plus_real R2) S))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y3))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y3))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y3))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y3))) E))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y3))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y3))) E))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B2))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B2))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X4))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y3))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y3) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X4))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y3))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y3) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X4)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y3)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X4) Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y3)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X4) Y3))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B2))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B2)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B2))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B2)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y3))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y3) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y3))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y3) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y3))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X4) Y3))) E))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y3))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X4) Y3))) E))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B2))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B2)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B2))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B2)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B2))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B2)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B2))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B2)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B2))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B2)) (@ _let_1 A)))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.83/7.13 (assert (forall ((W tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 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) B2)) (@ (@ 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 B2) D))))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 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) B2)) (@ (@ 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 B2) D))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B2)))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B2)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B2)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B2)))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (= (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X4) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X4) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((Z tptp.real) (W tptp.real) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real Z) M)) (@ (@ tptp.power_power_real W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z) W))))))))
% 6.83/7.13 (assert (forall ((Z tptp.complex) (W tptp.complex) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z) M)) (@ (@ tptp.power_power_complex W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z) W))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (= tptp.archim8280529875227126926d_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.archim2898591450579166408c_real X))) (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim6058952711729229775r_real X)))))
% 6.83/7.13 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.archimedean_frac_rat X))) (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim3151403230148437115or_rat X)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (B2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B2) X4)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X4) (@ (@ tptp.ord_less_eq_real X4) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) 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)) (= X4 (@ (@ 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)) (= X4 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X4)) tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 6.83/7.13 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.83/7.13 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X4) tptp.zero_zero_real))) (let ((_let_2 (= X4 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X4) A)) (not (= X4 tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X4)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_real A) B2))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real tptp.pi) X4)) (@ tptp.sin_real X4))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X4) tptp.one_one_real) (= X4 tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) tptp.one_one_real) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ (@ tptp.powr_real X4) tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_eq_real A) B2))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X4)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X4)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X4) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real tptp.pi) X4)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X4) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X4) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X4))) (let ((_let_2 (@ tptp.cos_complex X4))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sin_real X4))) (let ((_let_2 (@ tptp.cos_real X4))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y3)) Y3)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X4) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X4)) X4)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.83/7.13 (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)))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat N))))))
% 6.83/7.13 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.83/7.13 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.83/7.13 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.83/7.13 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X4)) (@ tptp.cos_real X4))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1)) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1)) tptp.one_one_complex))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1)) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1)) tptp.one_one_complex))))
% 6.83/7.13 (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)))
% 6.83/7.13 (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)))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X4)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X4)))))
% 6.83/7.13 (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)))
% 6.83/7.13 (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)))
% 6.83/7.13 (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))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X4)))))
% 6.83/7.13 (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)))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.cos_real Y3))) (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.sin_real Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X4) Y3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.cos_real Y3))) (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.sin_real Y3))))))
% 6.83/7.13 (assert (= tptp.cot_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X)) (@ tptp.sin_complex X)))))
% 6.83/7.13 (assert (= tptp.cot_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (exists ((R3 tptp.real) (A5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X4 (@ _let_1 (@ tptp.cos_real A5))) (= Y3 (@ _let_1 (@ tptp.sin_real A5))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (=> (= (@ tptp.cos_complex X4) tptp.one_one_complex) (= (@ tptp.sin_complex X4) tptp.zero_zero_complex))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (= (@ tptp.cos_real X4) tptp.one_one_real) (= (@ tptp.sin_real X4) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B2) (@ _let_1 (@ (@ tptp.times_times_real A) B2))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y3))) (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X4) Y3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y3))) (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X4)) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (=> (= (@ tptp.sin_complex X4) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X4)) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X4)) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X4)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X4))) (@ tptp.cos_complex X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X4)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X4))) (@ tptp.cos_real X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (exists ((Y4 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y4) (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ tptp.sin_real Y4) (@ tptp.sin_real X4)) (= (@ tptp.cos_real Y4) (@ tptp.cos_real X4))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y3) A)) (@ (@ tptp.powr_real X4) A)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X4)) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y3) A))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X4) Y3))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real A) B2))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B2)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X4)) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X4))) (@ tptp.abs_abs_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y3))) (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y3))))) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X4)) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X4)) tptp.one_one_rat)))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)) (@ tptp.archimedean_frac_rat X4))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y3) A)) (@ (@ tptp.powr_real X4) A)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y3) A)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (@ _let_1 (@ (@ tptp.powr_real X4) Y3)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real) (Y3 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 X4) (@ _let_1 Y3)) (= X4 Y3)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X4) A)) tptp.one_one_real)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y3) B2))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X4) A)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X4) Y3)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y3) A))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X4) Y3)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y3) A))))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.powr_real B2))) (= (@ (@ tptp.divide_divide_real A) (@ _let_1 C)) (@ (@ tptp.times_times_real A) (@ _let_1 (@ tptp.uminus_uminus_real C)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) tptp.pi) (@ _let_1 (@ tptp.sin_real X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X4)) (@ tptp.sin_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (@ _let_1 (@ tptp.sin_real X4)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (X4 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.log (@ (@ tptp.powr_real A) B2)) X4) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X4)) B2)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (not (= X4 tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X4) Y3)) (@ (@ tptp.times_times_real Y3) (@ tptp.ln_ln_real X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (B2 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (=> (not (= X4 tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X4) Y3)) (@ (@ tptp.times_times_real Y3) (@ _let_1 X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X4))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y3))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (=> (@ _let_2 Y3) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y3)) (@ _let_1 X4))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (=> (= (@ tptp.cos_real X4) (@ tptp.cos_real Y3)) (= X4 Y3)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X4))) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X4))) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z) W)) _let_1)))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z) W)) _let_1)))))))
% 6.83/7.13 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))))))
% 6.83/7.13 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 6.83/7.13 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((X4 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)) X4)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_2)))))))
% 6.83/7.13 (assert (forall ((X4 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)) X4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_2)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (Z1 tptp.real) (Z22 tptp.real)) (let ((_let_1 (@ tptp.powr_real W))) (= (@ _let_1 (@ (@ tptp.minus_minus_real Z1) Z22)) (@ (@ tptp.divide_divide_real (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.83/7.13 (assert (forall ((W tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.sin_complex W)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.83/7.13 (assert (forall ((W tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.sin_real W)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X4) N)))))
% 6.83/7.13 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.log B2) X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B2) Y3)) X4))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B2) X4)) Y3) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.powr_real B2) Y3)))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real X4) (@ (@ tptp.powr_real B2) Y3)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B2) X4)) Y3))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B2) Y3)) X4) (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.log B2) X4)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_real Y3) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y3)) (@ (@ tptp.ord_less_real Y3) X4)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.pi) (=> (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.pi) (= (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y3)) (@ tptp.cos_real X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.sin_real X4) tptp.zero_zero_real) (exists ((I2 tptp.int)) (= X4 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))))))
% 6.83/7.13 (assert (= tptp.archim2898591450579166408c_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X))))))
% 6.83/7.13 (assert (= tptp.archimedean_frac_rat (lambda ((X tptp.rat)) (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) tptp.one_one_real) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_eq_real T2) tptp.pi) (= X4 (@ tptp.cos_real T2)) (= Y3 (@ tptp.sin_real T2)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sin_real X4))) (=> (@ (@ 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 X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X4))) (= (@ 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))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X4))) (= (@ 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)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.times_times_real X4) (@ _let_1 Y3)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y3)))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B2) Y3)) X4) (@ (@ tptp.ord_less_eq_real Y3) (@ (@ tptp.log B2) X4)))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.powr_real B2) Y3)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B2) X4)) Y3))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B2) X4)) Y3) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.powr_real B2) Y3)))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real Y3) (@ (@ tptp.log B2) X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B2) Y3)) X4))))))
% 6.83/7.13 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.83/7.13 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (=> (@ (@ tptp.ord_less_real Y3) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y3)) (@ tptp.cos_real X4)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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) Y3) (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) Y3)) (= Y5 X3)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X4) X4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X4) X4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X4)) (@ tptp.archim2898591450579166408c_real Y3)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X4) Y3)))) (let ((_let_3 (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X4)) (@ tptp.archimedean_frac_rat Y3)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X4) Y3)))) (let ((_let_3 (@ (@ tptp.ord_less_rat _let_1) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 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 X4) (=> (@ _let_2 Y3) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) tptp.one_one_real) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_eq_real T2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X4 (@ tptp.cos_real T2)) (= Y3 (@ tptp.sin_real T2)))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) tptp.one_one_real) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_eq_real T2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X4 (@ tptp.cos_real T2)) (= Y3 (@ tptp.sin_real T2))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)) tptp.one_one_real) (not (forall ((T2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T2) (=> (@ (@ tptp.ord_less_real T2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X4 (@ tptp.cos_real T2)) (not (= Y3 (@ tptp.sin_real T2))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X4) A)) A))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X4)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X4))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B2) (=> (not (= B2 tptp.one_one_real)) (=> (@ _let_2 X4) (= (@ (@ tptp.plus_plus_real (@ _let_1 X4)) Y3) (@ _let_1 (@ (@ tptp.times_times_real X4) (@ (@ tptp.powr_real B2) Y3)))))))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B2) (=> (not (= B2 tptp.one_one_real)) (=> (@ _let_2 X4) (= (@ (@ tptp.plus_plus_real Y3) (@ _let_1 X4)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B2) Y3)) X4))))))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B2) (=> (not (= B2 tptp.one_one_real)) (=> (@ _let_2 X4) (= (@ (@ tptp.minus_minus_real Y3) (@ _let_1 X4)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B2) Y3)) X4))))))))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (= tptp.powr_real (lambda ((X tptp.real) (A4 tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A4) (@ tptp.ln_ln_real X)))))))
% 6.83/7.13 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 6.83/7.13 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X4)) tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X4))) tptp.one_one_real))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X4)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 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)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y3)) (@ tptp.sin_real X4))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X4))) (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 X4) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y3)) (@ _let_1 Y3)))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 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 X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (=> (@ _let_2 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) _let_1) (=> (= (@ tptp.sin_real X4) (@ tptp.sin_real Y3)) (= X4 Y3))))))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B2) (=> (not (= B2 tptp.one_one_real)) (=> (@ _let_2 X4) (= (@ (@ tptp.minus_minus_real (@ _let_1 X4)) Y3) (@ _let_1 (@ (@ tptp.times_times_real X4) (@ (@ tptp.powr_real B2) (@ tptp.uminus_uminus_real Y3))))))))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) tptp.one_one_real) (exists ((X tptp.int)) (= X4 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.83/7.13 (assert (forall ((W tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W)) (@ (@ tptp.minus_minus_complex (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.cos_complex W)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_complex))))))
% 6.83/7.13 (assert (forall ((W tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W)) (@ (@ tptp.minus_minus_real (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.cos_real W)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_real))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X4))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X4)) (@ (@ 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))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.cos_real X4))) (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 X4)) (@ (@ 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))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat N)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X4)) tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 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)) Y3) (=> (@ (@ tptp.ord_less_real Y3) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y3)) (@ tptp.sin_real X4))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 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 X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (=> (@ _let_2 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y3)) (@ (@ tptp.ord_less_real X4) Y3))))))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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) Y3) (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) Y3)) (= Y5 X3)))))))))))
% 6.83/7.13 (assert (forall ((X4 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)) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X4)))))))
% 6.83/7.13 (assert (forall ((X4 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)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) tptp.one_one_real) (or (exists ((X tptp.nat)) (= X4 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X tptp.nat)) (= X4 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y3)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) Y3)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X4)) (@ tptp.archim2898591450579166408c_real Y3))) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y3)))) (let ((_let_2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) Y3)))) (let ((_let_3 (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X4)) (@ tptp.archimedean_frac_rat Y3))) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X4)) (@ (@ tptp.divide_divide_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (B2 tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B2) X4)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X4) (@ (@ tptp.ord_less_real X4) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X4)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.sin_real X4) tptp.zero_zero_real) (exists ((I2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I2) (= X4 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) tptp.zero_zero_real) (exists ((I2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I2)) (= X4 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (= (@ tptp.sin_real X4) tptp.zero_zero_real) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X4 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.sin_real X4) 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) (= X4 (@ (@ 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) (= X4 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (= (@ tptp.cos_real X4) tptp.zero_zero_real) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X4 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X4))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X4))) (=> (not (= (@ tptp.cos_complex X4) 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)))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X4))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X4))) (=> (not (= (@ tptp.cos_real X4) 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)))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X4))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X4) (@ (@ 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)))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X4) (@ (@ 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 X4)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.83/7.13 (assert (= tptp.arcosh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.83/7.13 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T2) (=> (@ (@ tptp.ord_less_real T2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T2)) (@ tptp.sin_real T2)))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X4)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.83/7.13 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 6.83/7.13 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X4) tptp.one_one_real) (= X4 tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X4) tptp.one_one_complex) (= X4 tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.times_times_real X4) Y3)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real X4) Y3)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y3)))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X4) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X4)) N))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X4) N)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X4)) N))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.minus_minus_real X4) Y3)) (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.minus_minus_real X4) Y3)) (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X4) tptp.pi)) (@ tptp.tan_real X4))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 6.83/7.13 (assert (= (@ tptp.cos_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.83/7.13 (assert (= (@ tptp.cos_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X4))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y3)) Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (I tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) tptp.pi))) (@ tptp.tan_real X4))))
% 6.83/7.13 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X4)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X4)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (B2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B2))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X4)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (B2 tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.numera6690914467698888265omplex B2))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) (@ tptp.numeral_numeral_real B2))))))
% 6.83/7.13 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X4))))
% 6.83/7.13 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.83/7.13 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 6.83/7.13 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.83/7.13 (assert (= (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.one_one_complex))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((R2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X4) Y3)) (@ (@ tptp.complex2 (@ _let_1 X4)) (@ _let_1 Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X4) Y3)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X4) R2)) (@ (@ tptp.times_times_real Y3) R2)))))
% 6.83/7.13 (assert (forall ((R2 tptp.real) (X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X4) Y3)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R2) X4)) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X4) Y3)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X4) R2)) Y3))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.complex2 A) B2)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B2) D)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.complex2 A) B2) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B2 tptp.zero_zero_real)))))
% 6.83/7.13 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B2) (@ tptp.numera6690914467698888265omplex W)) (and (= A (@ tptp.numeral_numeral_real W)) (= B2 tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 A) B2)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B2) D)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y3))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (not (= Y3 tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y3))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.complex2 A) B2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B2 tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B2) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (and (= A (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (= B2 tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B2))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B2)) (@ (@ 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))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X4)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (= (@ tptp.arcsin X4) (@ tptp.arcsin Y3)) (= X4 Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X4))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X4))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 6.83/7.13 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex X)))))
% 6.83/7.13 (assert (= tptp.tan_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X)) (@ tptp.cos_real X)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y3)) (@ (@ tptp.ord_less_real X4) Y3))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real B2)) (@ tptp.real_V1803761363581548252l_real A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B2) A)))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex B2)) (@ tptp.real_V4546457046886955230omplex A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B2) A)))))
% 6.83/7.13 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((M tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.cos_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X4))) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real (@ _let_1 X4)))))))
% 6.83/7.13 (assert (forall ((M tptp.int) (X4 tptp.real)) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X4))) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X4))))))
% 6.83/7.13 (assert (forall ((M tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.sin_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X4))) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real (@ _let_1 X4)))))))
% 6.83/7.13 (assert (forall ((M tptp.int) (X4 tptp.real)) (= (@ tptp.sin_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X4))) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X4)) tptp.zero_zero_real))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (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 Y3) (@ tptp.tan_real X3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X4)))))))
% 6.83/7.13 (assert (forall ((Y3 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) Y3) (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) Y3)) (= Y5 X3)))))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 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)) Y3) (=> (@ (@ tptp.ord_less_real Y3) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y3)) (@ tptp.tan_real X4))))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y3))) (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 Y3) (=> (@ _let_1 _let_2) (=> (@ _let_3 X4) (=> (@ (@ tptp.ord_less_real X4) _let_2) (= (@ _let_1 X4) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y3)) (@ tptp.tan_real X4))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (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 X4) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y3) (=> (@ (@ tptp.ord_less_real Y3) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y3)) (@ _let_1 Y3)))))))))))
% 6.83/7.13 (assert (forall ((Y3 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) Y3))))))
% 6.83/7.13 (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)))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y3)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X4) Y3)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y3) _let_1)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y3))) (let ((_let_2 (@ tptp.cos_complex X4))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X4)) (@ tptp.tan_complex Y3)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X4) Y3))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y3))) (let ((_let_2 (@ tptp.cos_real X4))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y3)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X4) Y3))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4)) (@ tptp.cot_real X4))))
% 6.83/7.13 (assert (= tptp.sin_real (lambda ((X tptp.real)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))))
% 6.83/7.13 (assert (= tptp.sin_complex (lambda ((X tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))))
% 6.83/7.13 (assert (= tptp.cos_real (lambda ((X tptp.real)) (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))))
% 6.83/7.13 (assert (= tptp.cos_complex (lambda ((X tptp.complex)) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X4)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (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) Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X4)) tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 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)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (=> (@ (@ tptp.ord_less_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y3))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 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 X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (=> (@ _let_2 Y3) (=> (@ (@ tptp.ord_less_real Y3) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) (@ (@ 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 X4))) tptp.one_one_real))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arctan Y3))) (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) Y3))))))
% 6.83/7.13 (assert (forall ((X4 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)) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X4)) X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 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)) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (=> (= (@ tptp.tan_real X4) Y3) (= (@ tptp.arctan Y3) X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y3))) (let ((_let_2 (@ tptp.cos_complex X4))) (=> (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 X4)) (@ tptp.tan_complex Y3))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X4) Y3))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y3))) (let ((_let_2 (@ tptp.cos_real X4))) (=> (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 X4)) (@ tptp.tan_real Y3))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) Y3))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y3))) (let ((_let_2 (@ tptp.tan_complex X4))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X4) Y3))) (=> (not (= (@ tptp.cos_complex X4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y3) 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))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y3))) (let ((_let_2 (@ tptp.tan_real X4))) (let ((_let_3 (@ (@ tptp.minus_minus_real X4) Y3))) (=> (not (= (@ tptp.cos_real X4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y3) 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))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y3))) (let ((_let_2 (@ tptp.tan_complex X4))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X4) Y3))) (=> (not (= (@ tptp.cos_complex X4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y3) 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))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y3))) (let ((_let_2 (@ tptp.tan_real X4))) (let ((_let_3 (@ (@ tptp.plus_plus_real X4) Y3))) (=> (not (= (@ tptp.cos_real X4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y3) 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))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X4)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X4)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (exists ((Z2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z2) (@ (@ tptp.ord_less_real Z2) _let_1) (= (@ tptp.tan_real Z2) X4)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y3))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_real Y3) 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))))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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 Y3))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y3))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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))))))))
% 6.83/7.13 (assert (forall ((X4 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)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X4)) X4))))))
% 6.83/7.13 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 6.83/7.13 (assert (= tptp.tan_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y3))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y3) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y3)) X4))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X4))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X4)) Y3) (@ _let_1 (@ tptp.sin_real Y3)))))))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y3))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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) Y3)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y3))) (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)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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) Y3))))))))
% 6.83/7.13 (assert (= tptp.arsinh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y3)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X4)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.83/7.13 (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))))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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)))))))))))))))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ tptp.sgn_sgn_int _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.sgn_sgn_complex A))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1))))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 6.83/7.13 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B2)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B2)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.divide_divide_rat A) B2)) (@ (@ tptp.divide_divide_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B2)))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real A)))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ tptp.sgn_sgn_int A)))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sgn_sgn_complex A)))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ tptp.sgn_sgn_Code_integer A)))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.sgn_sgn_rat A)))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.sgn_sgn_Code_integer A)) N))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat (@ tptp.sgn_sgn_rat A)) N))))
% 6.83/7.13 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.sgn_sgn_real A)) N))))
% 6.83/7.13 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.sgn_sgn_int A)) N))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ tptp.sgn_sgn_Code_integer A)) (@ _let_1 A)))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real A)) (@ _let_1 A)))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.sgn_sgn_rat A)) (@ _let_1 A)))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.sgn_sgn_int A)) (@ _let_1 A)))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.sgn_sgn_Code_integer A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sgn_sgn_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.sgn_sgn_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.sgn_sgn_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B2))) (= (@ (@ tptp.divide_divide_real A) _let_1) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B2))) (= (@ (@ tptp.divide_divide_rat A) _let_1) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.83/7.13 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.83/7.13 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.83/7.13 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.83/7.13 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.83/7.13 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.83/7.13 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.83/7.13 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.83/7.13 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.83/7.13 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.83/7.13 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.83/7.13 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.sgn_sgn_real A) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) tptp.one_one_Code_integer))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) tptp.one_one_rat))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))))
% 6.83/7.13 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.83/7.13 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.83/7.13 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.83/7.13 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.83/7.13 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri5044797733671781792omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.semiri5044797733671781792omplex N))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat)))))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int)))))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger)))))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.abs_abs_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.abs_abs_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.abs_abs_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.abs_abs_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.abs_abs_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))))
% 6.83/7.13 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.zero_n3304061248610475627l_real (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.zero_n2052037380579107095ol_rat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.semiri4939895301339042750nteger N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y3)) Y3)))))
% 6.83/7.13 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.83/7.13 (assert (forall ((Z tptp.complex)) (exists ((A5 tptp.complex) (R3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ tptp.exp_complex A5))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (= (@ tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex X4) Y3)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex X4)) (@ tptp.sgn_sgn_complex Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real X4) Y3)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X4)) (@ tptp.sgn_sgn_real Y3)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B2)))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.sgn_sgn_Code_integer B2)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B2)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B2)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B2)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B2)))))
% 6.83/7.13 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (=> (= (@ tptp.sgn_sgn_Code_integer B2) _let_1) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) _let_1)))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (=> (= (@ tptp.sgn_sgn_real B2) _let_1) (= (@ tptp.sgn_sgn_real (@ (@ tptp.plus_plus_real A) B2)) _let_1)))))
% 6.83/7.13 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (=> (= (@ tptp.sgn_sgn_rat B2) _let_1) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.plus_plus_rat A) B2)) _let_1)))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (=> (= (@ tptp.sgn_sgn_int B2) _let_1) (= (@ tptp.sgn_sgn_int (@ (@ tptp.plus_plus_int A) B2)) _let_1)))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B2))) (let ((_let_2 (@ tptp.sgn_sgn_real A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int B2))) (let ((_let_2 (@ tptp.sgn_sgn_int A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.83/7.13 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer B2))) (let ((_let_2 (@ tptp.sgn_sgn_Code_integer A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.83/7.13 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B2))) (let ((_let_2 (@ tptp.sgn_sgn_rat A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_rat)) (=> (not (= _let_1 tptp.zero_zero_rat)) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.sgn_sgn_real _let_1) _let_1)))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.sgn_sgn_int _let_1) _let_1)))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1)))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1)))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1)))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.83/7.13 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger K3) (@ tptp.sgn_sgn_Code_integer K3)))))
% 6.83/7.13 (assert (= tptp.abs_abs_real (lambda ((K3 tptp.real)) (@ (@ tptp.times_times_real K3) (@ tptp.sgn_sgn_real K3)))))
% 6.83/7.13 (assert (= tptp.abs_abs_rat (lambda ((K3 tptp.rat)) (@ (@ tptp.times_times_rat K3) (@ tptp.sgn_sgn_rat K3)))))
% 6.83/7.13 (assert (= tptp.abs_abs_int (lambda ((K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ tptp.sgn_sgn_int K3)))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.sgn_sgn_complex A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.sgn_sgn_Code_integer A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.sgn_sgn_real A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.sgn_sgn_rat A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.abs_abs_complex A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.abs_abs_Code_integer A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.abs_abs_real A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.abs_abs_rat A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)))
% 6.83/7.13 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer X4)) (@ tptp.abs_abs_Code_integer X4)) X4)))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X4)) (@ tptp.abs_abs_real X4)) X4)))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat X4)) (@ tptp.abs_abs_rat X4)) X4)))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X4)) (@ tptp.abs_abs_int X4)) X4)))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.83/7.13 (assert (forall ((K tptp.int)) (not (forall ((N4 tptp.nat) (L3 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L3)) (@ tptp.semiri1314217659103216013at_int N4))))))))
% 6.83/7.13 (assert (forall ((B2 tptp.code_integer) (A tptp.code_integer)) (=> (= (@ tptp.sgn_sgn_Code_integer B2) (@ tptp.sgn_sgn_Code_integer A)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B2))))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (= (@ tptp.sgn_sgn_real B2) (@ tptp.sgn_sgn_real A)) (= (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B2)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B2))))))
% 6.83/7.13 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (= (@ tptp.sgn_sgn_rat B2) (@ tptp.sgn_sgn_rat A)) (= (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B2)) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B2))))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (= (@ tptp.sgn_sgn_int B2) (@ tptp.sgn_sgn_int A)) (= (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B2))))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L2)) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.83/7.13 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 6.83/7.13 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.83/7.13 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.83/7.13 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)))) (let ((_let_2 (= A tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer)))))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)))) (let ((_let_2 (= A tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 tptp.one_one_int)))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y3)) (@ tptp.arccos X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real)) (= (= (@ tptp.arccos X4) (@ tptp.arccos Y3)) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X4)) (@ tptp.arccos Y3)) (@ (@ tptp.ord_less_eq_real Y3) X4))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (assert (= tptp.sgn_sgn_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.83/7.13 (assert (= tptp.sgn_sgn_int (lambda ((X tptp.int)) (@ (@ (@ tptp.if_int (= X tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.83/7.13 (assert (= tptp.sgn_sgn_Code_integer (lambda ((X tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.83/7.13 (assert (= tptp.sgn_sgn_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_rat (= X tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.83/7.13 (assert (= tptp.sgn_sgn_int (lambda ((I2 tptp.int)) (@ (@ (@ tptp.if_int (= I2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I2)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X4)))) (let ((_let_2 (= X4 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X4)))) (let ((_let_2 (= X4 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y3)) (@ tptp.arccos X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X4)) (@ tptp.arccos Y3)) (@ (@ tptp.ord_less_real Y3) X4))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y3)) tptp.pi)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X4)) X4)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y3)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y3)) Y3))))
% 6.83/7.13 (assert (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arccos Y3))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_real Y3) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arccos Y3))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X4)) tptp.zero_zero_real))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X4) (= (@ tptp.arccos (@ tptp.cos_real X4)) (@ tptp.uminus_uminus_real X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X4)))))))
% 6.83/7.13 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M6)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.83/7.13 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M6)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.83/7.13 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.83/7.13 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M6)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.83/7.13 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M6)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri5044797733671781792omplex N) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (let ((_let_1 (@ tptp.arccos Y3))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) 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) Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X4))))))
% 6.83/7.13 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L2))) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K)))))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.83/7.13 (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)))))))))))))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))
% 6.83/7.13 (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))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X4)) (@ _let_1 X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.83/7.13 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 6.83/7.13 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X4) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X4)) (@ tptp.uminus1482373934393186551omplex X4)))))
% 6.83/7.13 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.83/7.13 (assert (forall ((Z tptp.complex) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ (@ tptp.divide1717551699836669952omplex Z) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z))) _let_1)))))
% 6.83/7.13 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.83/7.13 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.83/7.13 (assert (= tptp.sgn_sgn_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real X) (@ tptp.abs_abs_real X)))))
% 6.83/7.13 (assert (= tptp.sgn_sgn_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex Z5) (@ tptp.real_V4546457046886955230omplex (@ tptp.real_V1022390504157884413omplex Z5))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (= (@ _let_1 W) Z) (= W (@ tptp.uminus1482373934393186551omplex (@ _let_1 Z)))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (= (@ (@ tptp.complex2 X4) Y3) tptp.imaginary_unit) (and (= X4 tptp.zero_zero_real) (= Y3 tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.complex2 A) B2)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B2)) A))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B2)) tptp.imaginary_unit) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B2)) A))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (N tptp.nat) (X4 tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X4) (=> (= X4 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B2)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B2))))))
% 6.83/7.13 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F2 (-> 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 F2) (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) B3) (@ (@ F2 A4) Acc))))))
% 6.83/7.13 (assert (forall ((X4 (-> tptp.nat tptp.nat tptp.nat)) (Xa tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X4))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa))) (=> (= (@ (@ (@ _let_1 Xa) Xb) Xc) Y3) (and (=> _let_2 (= Y3 Xc)) (=> (not _let_2) (= Y3 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa) tptp.one_one_nat)) Xb) (@ (@ X4 Xa) Xc))))))))))
% 6.83/7.13 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.83/7.13 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A5 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A5))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A5)))))))))
% 6.83/7.13 (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)))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (not (= X4 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X4)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X4))))))
% 6.83/7.13 (assert (= tptp.semiri5044797733671781792omplex (lambda ((N2 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.one_one_nat)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.83/7.13 (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)))
% 6.83/7.13 (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)))))))))))
% 6.83/7.13 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 6.83/7.13 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.83/7.13 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 _let_1)) (@ tptp.ring_17405671764205052669omplex _let_1)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_real _let_1)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_rat _let_1)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_int _let_1)))))
% 6.83/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.83/7.13 (assert (forall ((V tptp.num) (V2 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V2)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V2))))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (N tptp.nat) (Y3 tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N) (@ tptp.nat2 Y3)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N) Y3))))
% 6.83/7.13 (assert (forall ((Y3 tptp.int) (X4 tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N)) (= Y3 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))))
% 6.83/7.13 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X4))) A) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.83/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)) A))))
% 6.83/7.13 (assert (forall ((A tptp.int) (X4 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)) A))))
% 6.83/7.13 (assert (forall ((A tptp.int) (X4 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N)))))
% 6.83/7.13 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.83/7.13 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cis A)) (@ tptp.cis B2)) (@ tptp.cis (@ (@ tptp.minus_minus_real A) B2)))))
% 6.83/7.13 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 6.83/7.13 (assert (= tptp.numeral_numeral_nat (lambda ((I2 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I2)))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y3)))))
% 6.83/7.13 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.83/7.13 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.83/7.13 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis _let_1)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi))))))
% 6.83/7.13 (assert (forall ((Z tptp.complex) (X4 tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X4)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (= (@ tptp.arg Z) X4))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.cis A)) (@ tptp.cis B2)) (@ tptp.cis (@ (@ tptp.plus_plus_real A) B2)))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.83/7.13 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real R2) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real R2))))))
% 6.83/7.13 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat R2) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim2889992004027027881ng_rat R2))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X4)) N) (@ (@ tptp.ord_less_eq_int X4) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2))) (@ (@ tptp.plus_plus_nat A) B2))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W))) (@ tptp.nat2 (@ tptp.abs_abs_int Z))))))
% 6.83/7.13 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X4))))))
% 6.83/7.13 (assert (forall ((R2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real R2)))) R2))))
% 6.83/7.13 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat R2)))) R2))))
% 6.83/7.13 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.83/7.13 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int W) Z)))))
% 6.83/7.13 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N2 tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N2)) (@ P N2))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real B2)))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B2))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat A))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat B2)))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B2))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z6) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z6)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))
% 6.83/7.13 (assert (= tptp.suc (lambda ((A4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) tptp.one_one_int)))))
% 6.83/7.13 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z6) (=> (@ (@ tptp.ord_less_eq_int Z6) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z6)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X4) Y3)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y3))))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X4) Y3)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y3))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y3) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X4) Y3)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y3))))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X4)) tptp.zero_zero_nat))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X4) Y3)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y3))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X4)) N)))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X4)) A) (@ (@ tptp.ord_less_eq_nat X4) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.83/7.13 (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.modulo_modulo_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.83/7.13 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K))))))
% 6.83/7.13 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K))))))
% 6.83/7.13 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.83/7.13 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.83/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.suc (@ tptp.nat2 Z)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z))))))
% 6.83/7.13 (assert (forall ((W tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M))))))
% 6.83/7.13 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z6)))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B2))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B2) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B2))))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X4)) N)))))
% 6.83/7.13 (assert (= tptp.cis (lambda ((B3 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B3))))))
% 6.83/7.13 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 K3))))))
% 6.83/7.13 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 K3))))))
% 6.83/7.13 (assert (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 K3))))))
% 6.83/7.13 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 K3))))))
% 6.83/7.13 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 K3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X4)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X4))))))
% 6.83/7.13 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ (@ tptp.powr_real X4) (@ tptp.ring_1_of_int_real I)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I)))))))))))))
% 6.83/7.13 (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))))))))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ (@ tptp.powr_real X4) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A)))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B2)) (= A B2))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B2)) (= A B2))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B2)) (= A B2))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int X4))) (= (@ _let_1 (@ _let_1 Y3)) Y3))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.83/7.13 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.83/7.13 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.83/7.13 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B2)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex B2)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B2)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.inverse_inverse_real X4) tptp.one_one_real) (= X4 tptp.one_one_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X4) tptp.one_one_complex) (= X4 tptp.one_one_complex))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X4) tptp.one_one_rat) (= X4 tptp.one_one_rat))))
% 6.83/7.13 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 6.83/7.13 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.83/7.13 (assert (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B2)) (@ (@ tptp.divide_divide_real B2) A))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B2)) (@ (@ tptp.divide1717551699836669952omplex B2) A))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.divide_divide_rat A) B2)) (@ (@ tptp.divide_divide_rat B2) A))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A)))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A)))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A)))))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.zero_zero_nat) A)))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.zero_zero_int) A)))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.zero_zero_nat) A) A)))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.zero_zero_int) A) A)))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) A) tptp.zero_zero_nat)))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) A) tptp.zero_zero_int)))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X4) X4) tptp.zero_zero_int)))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A)))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.abs_abs_complex A)))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A)))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.inverse_inverse_real _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.sgn_sgn_real A)))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.sgn_sgn_complex A)))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.sgn_sgn_rat A)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B2)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B2)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B2))) (=> (@ (@ 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 B2)) (@ _let_1 A)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B2))) (=> (@ (@ 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 B2)) (@ _let_1 A)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B2)) (@ (@ tptp.ord_less_real B2) A)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B2)) (@ (@ tptp.ord_less_rat B2) A)))))))
% 6.83/7.13 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.83/7.13 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 6.83/7.13 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.83/7.13 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.83/7.13 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.83/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B2)) (@ (@ tptp.ord_less_eq_real B2) A)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B2)) (@ (@ tptp.ord_less_eq_rat B2) A)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B2)) (@ (@ tptp.ord_less_eq_real B2) A))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B2)) (@ (@ tptp.ord_less_eq_rat B2) A))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (or (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (@ (@ tptp.member_real Y3) tptp.ring_1_Ints_real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (or (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat Y3) tptp.ring_1_Ints_rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) Y3)) (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X4)) (not (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X4)) (not (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat)))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.83/7.13 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y3))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y3))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y3))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y3))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y3))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y3))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y3))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y3))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y3)))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex A)) N) (@ tptp.invers8013647133539491842omplex (@ (@ tptp.power_power_complex A) N)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real Y3))) (let ((_let_2 (@ tptp.times_times_real X4))) (=> (= (@ (@ tptp.times_times_real Y3) X4) (@ _let_2 Y3)) (= (@ (@ tptp.times_times_real _let_1) X4) (@ _let_2 _let_1)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.complex) (X4 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex Y3))) (let ((_let_2 (@ tptp.times_times_complex X4))) (=> (= (@ (@ tptp.times_times_complex Y3) X4) (@ _let_2 Y3)) (= (@ (@ tptp.times_times_complex _let_1) X4) (@ _let_2 _let_1)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat Y3))) (let ((_let_2 (@ tptp.times_times_rat X4))) (=> (= (@ (@ tptp.times_times_rat Y3) X4) (@ _let_2 Y3)) (= (@ (@ tptp.times_times_rat _let_1) X4) (@ _let_2 _let_1)))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se6528837805403552850or_nat M) N)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se6528837805403552850or_nat M) N)) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.83/7.13 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L2)))))
% 6.83/7.13 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se6528837805403552850or_nat B2))) (let ((_let_2 (@ tptp.bit_se6528837805403552850or_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int B2))) (let ((_let_2 (@ tptp.bit_se6526347334894502574or_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.83/7.13 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat B3) A4))))
% 6.83/7.13 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int B3) A4))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se6528837805403552850or_nat A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat B2) C))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int A))) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int B2) C))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B2)) (= A B2))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B2)) (= A B2))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B2)) (= A B2))))
% 6.83/7.13 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.83/7.13 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.83/7.13 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B2)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B2 tptp.zero_zero_real)) (= A B2))))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B2)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= A B2))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B2)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= A B2))))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex)))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))))
% 6.83/7.13 (assert (forall ((N tptp.num)) (@ (@ tptp.member_complex (@ tptp.numera6690914467698888265omplex N)) tptp.ring_1_Ints_complex)))
% 6.83/7.13 (assert (forall ((N tptp.num)) (@ (@ tptp.member_real (@ tptp.numeral_numeral_real N)) tptp.ring_1_Ints_real)))
% 6.83/7.13 (assert (forall ((N tptp.num)) (@ (@ tptp.member_rat (@ tptp.numeral_numeral_rat N)) tptp.ring_1_Ints_rat)))
% 6.83/7.13 (assert (forall ((N tptp.num)) (@ (@ tptp.member_int (@ tptp.numeral_numeral_int N)) tptp.ring_1_Ints_int)))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B2) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.times_times_complex A) B2)) tptp.ring_1_Ints_complex)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B2) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.times_times_real A) B2)) tptp.ring_1_Ints_real)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B2) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.times_times_rat A) B2)) tptp.ring_1_Ints_rat)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B2) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.times_times_int A) B2)) tptp.ring_1_Ints_int)))))
% 6.83/7.13 (assert (@ (@ tptp.member_complex tptp.one_one_complex) tptp.ring_1_Ints_complex))
% 6.83/7.13 (assert (@ (@ tptp.member_rat tptp.one_one_rat) tptp.ring_1_Ints_rat))
% 6.83/7.13 (assert (@ (@ tptp.member_int tptp.one_one_int) tptp.ring_1_Ints_int))
% 6.83/7.13 (assert (@ (@ tptp.member_real tptp.one_one_real) tptp.ring_1_Ints_real))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B2) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.plus_plus_complex A) B2)) tptp.ring_1_Ints_complex)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B2) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real A) B2)) tptp.ring_1_Ints_real)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B2) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.plus_plus_rat A) B2)) tptp.ring_1_Ints_rat)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B2) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int A) B2)) tptp.ring_1_Ints_int)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X4)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X4)))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B2) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.minus_minus_complex A) B2)) tptp.ring_1_Ints_complex)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B2) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real A) B2)) tptp.ring_1_Ints_real)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B2) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat A) B2)) tptp.ring_1_Ints_rat)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B2) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int A) B2)) tptp.ring_1_Ints_int)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.power_power_real A) N)) tptp.ring_1_Ints_real))))
% 6.83/7.13 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.power_power_int A) N)) tptp.ring_1_Ints_int))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.power_power_complex A) N)) tptp.ring_1_Ints_complex))))
% 6.83/7.13 (assert (forall ((Y3 tptp.int) (Z tptp.int) (X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se6526347334894502574or_int Y3) Z)) X4) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.bit_se725231765392027082nd_int Y3) X4)) (@ (@ tptp.bit_se725231765392027082nd_int Z) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int X4))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int Y3) Z)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 Y3)) (@ _let_1 Z))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se6528837805403552850or_nat A) B2)) N) (not (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B2) N))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int A) B2)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B2) N))))))
% 6.83/7.13 (assert (forall ((R2 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real R2) (@ tptp.real_V7735802525324610683m_real X4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real X4))) (@ tptp.inverse_inverse_real R2))))))
% 6.83/7.13 (assert (forall ((R2 tptp.real) (X4 tptp.complex)) (=> (@ (@ tptp.ord_less_eq_real R2) (@ tptp.real_V1022390504157884413omplex X4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex X4))) (@ tptp.inverse_inverse_real R2))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B2)) (@ tptp.inverse_inverse_real A))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B2)) (@ tptp.inverse_inverse_rat A))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B2))) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B2)) (=> (@ _let_1 tptp.zero_zero_real) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B2))) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B2)) (=> (@ _let_1 tptp.zero_zero_rat) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B2)) (@ tptp.inverse_inverse_real A))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B2)) (@ tptp.inverse_inverse_rat A))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B2 tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B2)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B2)) (@ tptp.inverse_inverse_real A)))))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B2 tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B2)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B2)) (@ tptp.invers8013647133539491842omplex A)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B2 tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B2)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B2)) (@ tptp.inverse_inverse_rat A)))))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A))))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A))))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A))))))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.numeral_numeral_real tptp.one))) (= (@ tptp.inverse_inverse_real _let_1) _let_1)))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.numera6690914467698888265omplex tptp.one))) (= (@ tptp.invers8013647133539491842omplex _let_1) _let_1)))
% 6.83/7.13 (assert (let ((_let_1 (@ tptp.numeral_numeral_rat tptp.one))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1)))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B2) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B2))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B2) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B2))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B2) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B2))))
% 6.83/7.13 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B3)) A4))))
% 6.83/7.13 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B3)) A4))))
% 6.83/7.13 (assert (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B3)) A4))))
% 6.83/7.13 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real A4) (@ tptp.inverse_inverse_real B3)))))
% 6.83/7.13 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex A4) (@ tptp.invers8013647133539491842omplex B3)))))
% 6.83/7.13 (assert (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat A4) (@ tptp.inverse_inverse_rat B3)))))
% 6.83/7.13 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real A4) (@ tptp.inverse_inverse_real B3)))))
% 6.83/7.13 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex A4) (@ tptp.invers8013647133539491842omplex B3)))))
% 6.83/7.13 (assert (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat A4) (@ tptp.inverse_inverse_rat B3)))))
% 6.83/7.13 (assert (= tptp.inverse_inverse_real (@ tptp.divide_divide_real tptp.one_one_real)))
% 6.83/7.13 (assert (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)))
% 6.83/7.13 (assert (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X4) M))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X4)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X4) M))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X4)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X4) M))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X4)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X4) M))) (let ((_let_2 (@ tptp.inverse_inverse_real X4))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X4) M))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X4))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X4) M))) (let ((_let_2 (@ tptp.inverse_inverse_rat X4))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.83/7.13 (assert (forall ((Xa tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa)))) (= (@ (@ tptp.times_times_real _let_1) X4) (@ (@ tptp.times_times_real X4) _let_1)))))
% 6.83/7.13 (assert (forall ((Xa tptp.nat) (X4 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa)))) (= (@ (@ tptp.times_times_complex _let_1) X4) (@ (@ tptp.times_times_complex X4) _let_1)))))
% 6.83/7.13 (assert (forall ((Xa tptp.nat) (X4 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat Xa)))) (= (@ (@ tptp.times_times_rat _let_1) X4) (@ (@ tptp.times_times_rat X4) _let_1)))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A))))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A))))))
% 6.83/7.13 (assert (forall ((Xa tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.ring_1_of_int_real Xa)))) (= (@ (@ tptp.times_times_real _let_1) X4) (@ (@ tptp.times_times_real X4) _let_1)))))
% 6.83/7.13 (assert (forall ((Xa tptp.int) (X4 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.ring_17405671764205052669omplex Xa)))) (= (@ (@ tptp.times_times_complex _let_1) X4) (@ (@ tptp.times_times_complex X4) _let_1)))))
% 6.83/7.13 (assert (forall ((Xa tptp.int) (X4 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.ring_1_of_int_rat Xa)))) (= (@ (@ tptp.times_times_rat _let_1) X4) (@ (@ tptp.times_times_rat X4) _let_1)))))
% 6.83/7.13 (assert (= tptp.divide_divide_real (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.times_times_real X) (@ tptp.inverse_inverse_real Y)))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (= (= (@ (@ tptp.plus_plus_complex A) A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B2)) (@ tptp.inverse_inverse_real A))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B2)) (@ tptp.inverse_inverse_rat A))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B2)) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B2)) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real B2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B2)) (@ tptp.inverse_inverse_real A))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_rat B2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B2)) (@ tptp.inverse_inverse_rat A))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X4)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X4)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X4)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X4)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat)))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B2))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B2 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) B2))) _let_1))))))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B2))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B2 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) B2))) _let_1))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B2))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B2 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) B2))) _let_1))))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B2))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B2 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) B2)) _let_2)) _let_1))))))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B2))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B2 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) B2)) _let_2)) _let_1))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B2))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B2 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) B2)) _let_2)) _let_1))))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B2))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B2 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 B2) A))) _let_1))))))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B2))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B2 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 B2) A))) _let_1))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B2))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B2 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 B2) A))) _let_1))))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y3)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y3) A))))))
% 6.83/7.13 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (not (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) A)) A) tptp.zero_zero_complex)))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (not (= (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A) tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (not (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A) tptp.zero_zero_rat)))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A) tptp.zero_zero_int)))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.ring_17405671764205052669omplex A)) (@ tptp.ring_17405671764205052669omplex B2))) tptp.ring_1_Ints_complex))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B2))) tptp.ring_1_Ints_real))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (@ (@ tptp.member_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B2))) tptp.ring_1_Ints_rat))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B2) A) (@ (@ tptp.member_int (@ (@ tptp.divide_divide_int (@ tptp.ring_1_of_int_int A)) (@ tptp.ring_1_of_int_int B2))) tptp.ring_1_Ints_int))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B2))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real B2) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B2)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B2))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat B2) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B2)))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B2))) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B2)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real B2) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) B2)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B2))) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B2)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat B2) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) B2)))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real X4)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat X4)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real X4)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X4)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_eq_rat X4) tptp.one_one_rat)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B2))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B2 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) B2))) _let_1)))))))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B2))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B2 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) B2))) _let_1)))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B2))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B2 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) B2))) _let_1)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N4)))) X4)))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex _let_3) A) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex A) _let_3) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (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 ((N4 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.83/7.13 (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 ((N4 tptp.nat)) (=> (not (= N4 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N4))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.83/7.13 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2)))) (and (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3222712562003087583nteger A) B2)) (= (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B2)) (= (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B2)) (= (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sqrt X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.divide_divide_real _let_1) X4) (@ tptp.inverse_inverse_real _let_1))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X4)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X4))))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.83/7.13 (assert (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) tptp.ring_11222124179247155820nteger) (=> (not (= X4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (=> (not (= X4 tptp.zero_zero_real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.abs_abs_real X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (=> (not (= X4 tptp.zero_zero_rat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) tptp.ring_1_Ints_int) (=> (not (= X4 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.abs_abs_int X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X4)) tptp.one_one_Code_integer) (= X4 tptp.zero_z3403309356797280102nteger)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= X4 tptp.zero_zero_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X4)) tptp.one_one_rat) (= X4 tptp.zero_zero_rat)))))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) tptp.ring_1_Ints_int) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X4)) tptp.one_one_int) (= X4 tptp.zero_zero_int)))))
% 6.83/7.13 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.member_Code_integer Y3) tptp.ring_11222124179247155820nteger) (= (= X4 Y3) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X4) Y3))) tptp.one_one_Code_integer))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real Y3) tptp.ring_1_Ints_real) (= (= X4 Y3) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y3))) tptp.one_one_real))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat Y3) tptp.ring_1_Ints_rat) (= (= X4 Y3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) Y3))) tptp.one_one_rat))))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.member_int X4) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int Y3) tptp.ring_1_Ints_int) (= (= X4 Y3) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) Y3))) tptp.one_one_int))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X4) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N4))) X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat N4))) X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (=> (not (= X4 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 X4)) M))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (=> (not (= X4 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 X4)) M))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (=> (not (= X4 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 X4)) M))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (X4 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 X4) (= (@ _let_1 (@ tptp.inverse_inverse_real X4)) (@ tptp.uminus_uminus_real (@ _let_1 X4))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.archim2898591450579166408c_real (@ tptp.uminus_uminus_real X4)))) (let ((_let_2 (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.archim2898591450579166408c_real X4)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.archimedean_frac_rat (@ tptp.uminus_uminus_rat X4)))) (let ((_let_2 (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.archimedean_frac_rat X4)))))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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))))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real X4))) (@ (@ 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))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B2)))) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B2)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B2)))) (@ tptp.ring_1_of_int_int (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B2)))) (@ tptp.ring_1_of_int_real (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B2)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B2)))) (@ tptp.ring_1_of_int_int (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B2))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (A tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X4) A) (and (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real X4) A)) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real A) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (A tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X4) A) (and (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat X4) A)) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B2)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B2)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B2)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B2)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B2)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B2))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B2)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B2))))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X4) (@ tptp.inverse_inverse_real X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X4)))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X4)))))
% 6.83/7.13 (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))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.83/7.13 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M6)) (not (@ _let_2 N2)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger A) tptp.one_one_Code_integer) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.one_one_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.one_one_int) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger tptp.one_one_Code_integer) A) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real X4))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) (@ 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))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_real X4))) (=> (not (= _let_2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real _let_2)) _let_1)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_complex X4))) (=> (not (= _let_2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.tan_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex _let_2)) _let_1)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X4) (@ tptp.inverse_inverse_real X4))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ tptp.inverse_inverse_real X4))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.cosh_real X4) tptp.zero_zero_real) (= (@ (@ tptp.power_power_real (@ tptp.exp_real X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (= (= (@ tptp.cosh_complex X4) tptp.zero_zero_complex) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (=> (not (= A3 B4)) (@ (@ tptp.ord_less_set_nat A3) B4)))))
% 6.83/7.13 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1))))))
% 6.83/7.13 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ _let_1 K)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se545348938243370406it_int N) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se547839408752420682it_nat N) A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) A)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.plus_plus_nat M) N)) A))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat M) (@ (@ tptp.bit_se547839408752420682it_nat N) A)) (@ (@ tptp.bit_se547839408752420682it_nat (@ (@ tptp.plus_plus_nat M) N)) A))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B2)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B2)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B2)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L2) (@ (@ tptp.bit_se545348938243370406it_int N) L2))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X4)) (@ tptp.sinh_real Y3)) (@ (@ tptp.ord_less_real X4) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X4)) (@ tptp.sinh_real Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3))))
% 6.83/7.13 (assert (= (@ tptp.cosh_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.83/7.13 (assert (= (@ tptp.cosh_real tptp.zero_zero_real) tptp.one_one_real))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X4)) (@ _let_1 X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X4)) (@ _let_1 X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.83/7.13 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) (= (@ _let_1 K) (@ _let_1 L2))))))
% 6.83/7.13 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int K)) (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.suc N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K))) (@ (@ tptp.bit_se7788150548672797655nteger N) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))))
% 6.83/7.13 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int K)) (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))))))
% 6.83/7.13 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N)) A) (@ (@ tptp.bit_se545348938243370406it_int N) (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N)) A) (@ (@ tptp.bit_se547839408752420682it_nat N) (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7788150548672797655nteger N) A)) (or (not (= N tptp.zero_zero_nat)) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) A)) (or (not (= N tptp.zero_zero_nat)) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se547839408752420682it_nat N) A)) (or (not (= N tptp.zero_zero_nat)) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K))) (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.pred_numeral L2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))))
% 6.83/7.13 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.cosh_complex X4)) (@ tptp.sinh_complex X4)) (@ tptp.exp_complex X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.cosh_real X4)) (@ tptp.sinh_real X4)) (@ tptp.exp_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.sinh_complex X4)) (@ tptp.cosh_complex X4)) (@ tptp.exp_complex X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real X4)) (@ tptp.exp_real X4))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ (@ tptp.ord_le2529575680413868914d_enat A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_complex) (B4 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_less_set_complex A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_real) (B4 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_int) (B4 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real X4))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se547839408752420682it_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int M) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat M))) (= (@ tptp.semiri1316708129612266289at_nat (@ _let_1 N)) (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se547839408752420682it_nat N) M)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le2529575680413868914d_enat A3) B4) (exists ((B5 tptp.extended_enat)) (@ (@ tptp.member_Extended_enat B5) (@ (@ tptp.minus_925952699566721837d_enat B4) A3))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_complex) (B4 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A3) B4) (exists ((B5 tptp.complex)) (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B4) A3))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_real) (B4 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A3) B4) (exists ((B5 tptp.real)) (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B4) A3))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A3) B4) (exists ((B5 tptp.int)) (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B4) A3))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A3) B4) (exists ((B5 tptp.nat)) (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B4) A3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.minus_minus_real X4) Y3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real Y3))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X4)) (@ tptp.sinh_real Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.minus_minus_real X4) Y3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y3))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X4)) (@ tptp.sinh_real Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real Y3))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X4)) (@ tptp.sinh_real Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y3))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X4)) (@ tptp.sinh_real Y3))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se7788150548672797655nteger N))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ _let_1 A))))))
% 6.83/7.13 (assert (= tptp.tanh_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sinh_complex X)) (@ tptp.cosh_complex X)))))
% 6.83/7.13 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X)))))
% 6.83/7.13 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real X4)) (@ tptp.uminus_uminus_real (@ tptp.exp_real (@ tptp.uminus_uminus_real X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.sinh_complex X4)) (@ tptp.cosh_complex X4)) (@ tptp.uminus1482373934393186551omplex (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.cosh_real X4)) (@ tptp.sinh_real X4)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.cosh_complex X4)) (@ tptp.sinh_complex X4)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X4) Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y3))) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y3)) (@ _let_1 X4)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_complex (@ _let_1 X4)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sinh_complex X4))) (@ tptp.cosh_complex X4))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_real (@ _let_1 X4)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sinh_real X4))) (@ tptp.cosh_real X4))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int M))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat M))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) A))))))
% 6.83/7.13 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat M) N)) A))))))
% 6.83/7.13 (assert (= tptp.divide1717551699836669952omplex (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.times_times_complex X) (@ tptp.invers8013647133539491842omplex Y)))))
% 6.83/7.13 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y3)) (@ (@ tptp.ord_less_real X4) Y3)))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y3) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y3)) (@ (@ tptp.ord_less_real Y3) X4))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_1)) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_1)) tptp.one_one_complex)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_1)) tptp.one_one_complex)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_1)) tptp.one_one_real)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_1)) tptp.one_one_complex))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_1)) tptp.one_one_real))))
% 6.83/7.13 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A3) B4) (not (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (@ (@ tptp.ord_less_eq_set_nat B4) A3))))))
% 6.83/7.13 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B7) (not (= A6 B7))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A3) B4) (@ (@ tptp.ord_less_eq_set_nat A3) B4))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A3))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C5) (@ _let_1 C5))))))
% 6.83/7.13 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B7) (not (@ (@ tptp.ord_less_eq_set_nat B7) A6))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (=> (@ (@ tptp.ord_less_set_nat B4) C5) (@ (@ tptp.ord_less_set_nat A3) C5)))))
% 6.83/7.13 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A6) B7) (= A6 B7)))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C5) (= (@ (@ tptp.minus_minus_set_nat B4) (@ (@ tptp.minus_minus_set_nat C5) A3)) A3)))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) B4)) A3)))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (C5 tptp.set_nat) (D4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C5) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) B4)) (@ (@ tptp.minus_minus_set_nat C5) D4))))))
% 6.83/7.13 (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))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ tptp.arcosh_real (@ tptp.cosh_real X4)) X4))))
% 6.83/7.13 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int A4) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 6.83/7.13 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N2 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat A4) (@ (@ tptp.bit_se547839408752420682it_nat N2) tptp.one_one_nat)))))
% 6.83/7.13 (assert (forall ((X4 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)) X4)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_2)))))))
% 6.83/7.13 (assert (forall ((X4 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)) X4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_2)))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_2 (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int (@ _let_2 A)) _let_1))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_2 (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 A)) _let_1))))))
% 6.83/7.13 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N2 tptp.nat)) (not (= (@ (@ tptp.bit_se725231765392027082nd_int A4) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.83/7.13 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N2 tptp.nat)) (not (= (@ (@ tptp.bit_se727722235901077358nd_nat A4) (@ (@ tptp.bit_se547839408752420682it_nat N2) tptp.one_one_nat)) tptp.zero_zero_nat)))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.83/7.13 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (@ (@ tptp.times_times_int A4) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.83/7.13 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.times_times_nat A4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) A) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.bit_se7788150548672797655nteger N) B5))))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) A) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.bit_se545348938243370406it_int N) B5))))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) A) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.bit_se547839408752420682it_nat N) B5))))))))
% 6.83/7.13 (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)))))
% 6.83/7.13 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.tanh_complex Y3))) (let ((_let_2 (@ tptp.tanh_complex X4))) (=> (not (= (@ tptp.cosh_complex X4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cosh_complex Y3) tptp.zero_zero_complex)) (= (@ tptp.tanh_complex (@ (@ tptp.plus_plus_complex X4) Y3)) (@ (@ 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))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.tanh_real Y3))) (let ((_let_2 (@ tptp.tanh_real X4))) (=> (not (= (@ tptp.cosh_real X4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cosh_real Y3) tptp.zero_zero_real)) (= (@ tptp.tanh_real (@ (@ tptp.plus_plus_real X4) Y3)) (@ (@ 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))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (N tptp.nat) (Y3 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) X4) (=> (@ (@ tptp.ord_less_int X4) _let_1) (=> (@ (@ tptp.ord_less_int Y3) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X4) Y3)) _let_1)))))))
% 6.83/7.13 (assert (= tptp.cosh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (= tptp.cosh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 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 B2) _let_1)))) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.complex2 A) B2)) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real A) _let_2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real B2)) _let_2)))))))
% 6.83/7.13 (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)))))))))
% 6.83/7.13 (assert (= tptp.sinh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (assert (= tptp.sinh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.83/7.13 (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)))))))))))))
% 6.83/7.13 (assert (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)))
% 6.83/7.13 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M6)) (@ X6 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.83/7.13 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.83/7.13 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.83/7.13 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.83/7.13 (assert (forall ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X4) X4)))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) X4)))
% 6.83/7.13 (assert (forall ((X4 tptp.num)) (@ (@ tptp.ord_less_eq_num X4) X4)))
% 6.83/7.13 (assert (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) X4)))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_int X4) X4)))
% 6.83/7.13 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.83/7.13 (assert (forall ((C tptp.extended_enat) (A3 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.complex) (A3 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.extended_enat) (A3 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (= (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B4)) (and (@ _let_1 A3) (not (@ _let_1 B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.complex) (A3 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B4)) (and (@ _let_1 A3) (not (@ _let_1 B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) B4)) (and (@ _let_1 A3) (not (@ _let_1 B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B4)) (and (@ _let_1 A3) (not (@ _let_1 B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B4)) (and (@ _let_1 A3) (not (@ _let_1 B4)))))))
% 6.83/7.13 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A3) B4))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B4) _let_1))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (= (@ tptp.bit_ri7919022796975470100ot_int X4) (@ tptp.bit_ri7919022796975470100ot_int Y3)) (= X4 Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_ri7919022796975470100ot_int X4)) X4)))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int X4))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int Y3)) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X4)) Y3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int X4) Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X4) (@ tptp.bit_ri7919022796975470100ot_int X4)) tptp.zero_zero_int)))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int X4)) X4) tptp.zero_zero_int)))
% 6.83/7.13 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.83/7.13 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.83/7.13 (assert (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.83/7.13 (assert (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.83/7.13 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X4) (@ tptp.bit_ri7632146776885996613nteger X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X4) (@ tptp.bit_ri7919022796975470100ot_int X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X4) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X4) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.bit_ri7632146776885996613nteger X4)) X4) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X4)) X4) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.83/7.13 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X4) (@ tptp.bit_ri7632146776885996613nteger X4)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X4) (@ tptp.bit_ri7919022796975470100ot_int X4)) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.83/7.13 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.83/7.13 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_ri7919022796975470100ot_int K)) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.83/7.13 (assert (forall ((N tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ tptp.inc N)))))
% 6.83/7.13 (assert (forall ((N tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ tptp.inc N)))))
% 6.83/7.13 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7632146776885996613nteger A)) (not (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (not (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se7788150548672797655nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N)))))
% 6.83/7.13 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N)))))
% 6.83/7.13 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.83/7.13 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.83/7.13 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys))) (@ P Xs3))) (@ P Xs2))))
% 6.83/7.13 (assert (forall ((P (-> tptp.list_o Bool)) (Xs2 tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys)) (@ tptp.size_size_list_o Xs3)) (@ P Ys))) (@ P Xs3))) (@ P Xs2))))
% 6.83/7.13 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs2 tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys))) (@ P Xs3))) (@ P Xs2))))
% 6.83/7.13 (assert (forall ((P (-> tptp.list_int Bool)) (Xs2 tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys)) (@ tptp.size_size_list_int Xs3)) (@ P Ys))) (@ P Xs3))) (@ P Xs2))))
% 6.83/7.13 (assert (forall ((C tptp.extended_enat) (A3 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B4)) (not (=> (@ _let_1 A3) (@ _let_1 B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.complex) (A3 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B4)) (not (=> (@ _let_1 A3) (@ _let_1 B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) B4)) (not (=> (@ _let_1 A3) (@ _let_1 B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B4)) (not (=> (@ _let_1 A3) (@ _let_1 B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B4)) (not (=> (@ _let_1 A3) (@ _let_1 B4)))))))
% 6.83/7.13 (assert (forall ((C tptp.extended_enat) (A3 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B4)) (@ _let_1 A3)))))
% 6.83/7.13 (assert (forall ((C tptp.complex) (A3 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B4)) (@ _let_1 A3)))))
% 6.83/7.13 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) B4)) (@ _let_1 A3)))))
% 6.83/7.13 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B4)) (@ _let_1 A3)))))
% 6.83/7.13 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B4)) (@ _let_1 A3)))))
% 6.83/7.13 (assert (forall ((C tptp.extended_enat) (A3 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat C))) (=> (@ _let_1 (@ (@ tptp.minus_925952699566721837d_enat A3) B4)) (not (@ _let_1 B4))))))
% 6.83/7.13 (assert (forall ((C tptp.complex) (A3 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A3) B4)) (not (@ _let_1 B4))))))
% 6.83/7.13 (assert (forall ((C tptp.real) (A3 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A3) B4)) (not (@ _let_1 B4))))))
% 6.83/7.13 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B4)) (not (@ _let_1 B4))))))
% 6.83/7.13 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B4)) (not (@ _let_1 B4))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int B2))) (= (@ _let_1 A) (@ _let_1 B2))))))
% 6.83/7.13 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 A))) (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A))))))
% 6.83/7.13 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.83/7.13 (assert (forall ((K tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.bit_ri7919022796975470100ot_int K)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.ring_1_of_int_int K)))))
% 6.83/7.13 (assert (forall ((X4 tptp.list_VEBT_VEBT) (Y3 tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X4) (@ tptp.size_s6755466524823107622T_VEBT Y3))) (not (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.list_o) (Y3 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X4) (@ tptp.size_size_list_o Y3))) (not (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.list_nat) (Y3 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X4) (@ tptp.size_size_list_nat Y3))) (not (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.list_int) (Y3 tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X4) (@ tptp.size_size_list_int Y3))) (not (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (not (= (@ tptp.size_size_num X4) (@ tptp.size_size_num Y3))) (not (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.minus_minus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B2))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B2))))
% 6.83/7.13 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.bit_ri7632146776885996613nteger A4)) tptp.one_one_Code_integer))))
% 6.83/7.13 (assert (= tptp.uminus_uminus_int (lambda ((A4 tptp.int)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A4)) tptp.one_one_int))))
% 6.83/7.13 (assert (= tptp.bit_ri7632146776885996613nteger (lambda ((A4 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A4)) tptp.one_one_Code_integer))))
% 6.83/7.13 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((A4 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A4)) tptp.one_one_int))))
% 6.83/7.13 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A4 tptp.code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ (@ tptp.minus_8373710615458151222nteger A4) tptp.one_one_Code_integer)))))
% 6.83/7.13 (assert (= tptp.uminus_uminus_int (lambda ((A4 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A4) tptp.one_one_int)))))
% 6.83/7.13 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 6.83/7.13 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.bit_se1146084159140164899it_int B2) N4) (@ (@ tptp.bit_se1146084159140164899it_int A) N4))) (= (@ (@ tptp.minus_minus_int A) B2) (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.bit_ri7919022796975470100ot_int B2))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A) B2)) (and (@ (@ tptp.ord_less_eq_rat B2) A) (not (= B2 A))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A) B2)) (and (@ (@ tptp.ord_less_eq_num B2) A) (not (= B2 A))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B2)) (and (@ (@ tptp.ord_less_eq_nat B2) A) (not (= B2 A))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A) B2)) (and (@ (@ tptp.ord_less_eq_int B2) A) (not (= B2 A))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X4))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y3))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X4))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X4))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ tptp.ord_less_eq_num Y3))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X4))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X4))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y3))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X4))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X4))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ tptp.ord_less_eq_int Y3))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X4))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.set_nat) (Z4 tptp.set_nat)) (= Y6 Z4)) (lambda ((X tptp.set_nat) (Y tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat Y) X)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((X tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((X tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X)))))
% 6.83/7.13 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (=> (= A B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ (@ tptp.ord_less_eq_set_nat A) C)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (= A B2) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (@ (@ tptp.ord_less_eq_rat A) C)))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (=> (= A B2) (=> (@ (@ tptp.ord_less_eq_num B2) C) (@ (@ tptp.ord_less_eq_num A) C)))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (= A B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 6.83/7.13 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X4) Y3) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) X4) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) X4) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (=> (@ (@ tptp.ord_less_eq_num Y3) X4) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) X4) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) X4) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_num B2) C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) Z) (@ _let_1 Z))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) Z) (@ _let_1 Z))))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_num Y3) Z) (@ _let_1 Z))))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) Z) (@ _let_1 Z))))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) Z) (@ _let_1 Z))))))
% 6.83/7.13 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B2 tptp.rat)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B2)))))
% 6.83/7.13 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B2 tptp.num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B2)))))
% 6.83/7.13 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B2)))))
% 6.83/7.13 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B2 tptp.int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B2)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.set_nat) (Z4 tptp.set_nat)) (= Y6 Z4)) (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)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A4) (@ (@ tptp.ord_less_eq_rat A4) B3)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A4) (@ (@ tptp.ord_less_eq_num A4) B3)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A4) (@ (@ tptp.ord_less_eq_nat A4) B3)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A4) (@ (@ tptp.ord_less_eq_int A4) B3)))))
% 6.83/7.13 (assert (forall ((B2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (= A B2)))))
% 6.83/7.13 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B2) A) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (= A B2)))))
% 6.83/7.13 (assert (forall ((B2 tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B2) A) (=> (@ (@ tptp.ord_less_eq_num A) B2) (= A B2)))))
% 6.83/7.13 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (= A B2)))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ (@ tptp.ord_less_eq_int A) B2) (= A B2)))))
% 6.83/7.13 (assert (forall ((B2 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 B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((B2 tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ (@ tptp.ord_less_eq_num B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.13 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (= A B2)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat B2) A) (= A B2)))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_eq_num B2) A) (= A B2)))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (= A B2)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_eq_int B2) A) (= A B2)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.set_nat) (Z4 tptp.set_nat)) (= Y6 Z4)) (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)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B3) (@ (@ tptp.ord_less_eq_rat B3) A4)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B3) (@ (@ tptp.ord_less_eq_num B3) A4)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ tptp.ord_less_eq_nat B3) A4)))))
% 6.83/7.13 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B3) (@ (@ tptp.ord_less_eq_int B3) A4)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_int B2) C) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_eq_nat (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_eq_int (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_num (@ F B2)) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat)) (=> (= X4 Y3) (@ (@ tptp.ord_less_eq_set_nat X4) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (= X4 Y3) (@ (@ tptp.ord_less_eq_rat X4) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (= X4 Y3) (@ (@ tptp.ord_less_eq_num X4) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= X4 Y3) (@ (@ tptp.ord_less_eq_nat X4) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= X4 Y3) (@ (@ tptp.ord_less_eq_int X4) Y3))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat Y3) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num Y3) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X4) Y3) (@ (@ tptp.ord_less_eq_int Y3) X4))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C tptp.rat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B2 tptp.rat) (C tptp.rat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B2 tptp.rat) (C tptp.rat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B2 tptp.rat) (C tptp.rat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B2 tptp.num) (C tptp.num)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B2 tptp.num) (C tptp.num)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B2 tptp.num) (C tptp.num)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B2 tptp.num) (C tptp.num)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B2 tptp.nat) (C tptp.nat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X4) Y3)) (@ (@ tptp.ord_less_eq_rat Y3) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X4) Y3)) (@ (@ tptp.ord_less_eq_num Y3) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X4) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X4) Y3)) (@ (@ tptp.ord_less_eq_int Y3) X4))))
% 6.83/7.13 (assert (forall ((Y3 tptp.set_nat) (X4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) X4) (= (@ (@ tptp.ord_less_eq_set_nat X4) Y3) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X4) (= (@ (@ tptp.ord_less_eq_rat X4) Y3) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.num) (X4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y3) X4) (= (@ (@ tptp.ord_less_eq_num X4) Y3) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X4) (= (@ (@ tptp.ord_less_eq_nat X4) Y3) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X4) (= (@ (@ tptp.ord_less_eq_int X4) Y3) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (exists ((Y4 tptp.real)) (@ (@ tptp.ord_less_real Y4) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (exists ((Y4 tptp.rat)) (@ (@ tptp.ord_less_rat Y4) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (exists ((Y4 tptp.int)) (@ (@ tptp.ord_less_int Y4) X4))))
% 6.83/7.13 (assert (forall ((X4 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X4) X_1))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X4) X_1))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X4) X_1))))
% 6.83/7.13 (assert (forall ((X4 tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X4) X_1))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real X4) Z2) (@ (@ tptp.ord_less_real Z2) Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (exists ((Z2 tptp.rat)) (and (@ (@ tptp.ord_less_rat X4) Z2) (@ (@ tptp.ord_less_rat Z2) Y3))))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (not (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (not (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (not (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (not (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (not (@ (@ tptp.ord_less_real B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (not (@ (@ tptp.ord_less_rat B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A) B2) (not (@ (@ tptp.ord_less_num B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (not (@ (@ tptp.ord_less_nat B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (not (@ (@ tptp.ord_less_int B2) A)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (= A B2) (=> (@ (@ tptp.ord_less_real B2) C) (@ (@ tptp.ord_less_real A) C)))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (= A B2) (=> (@ (@ tptp.ord_less_rat B2) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (=> (= A B2) (=> (@ (@ tptp.ord_less_num B2) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (= A B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (= A B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B2) (=> (= B2 C) (@ _let_1 C))))))
% 6.83/7.13 (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))))
% 6.83/7.13 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y3) X4)) (= (not (@ (@ tptp.ord_less_real X4) Y3)) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y3) X4)) (= (not (@ (@ tptp.ord_less_rat X4) Y3)) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.num) (X4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y3) X4)) (= (not (@ (@ tptp.ord_less_num X4) Y3)) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.nat) (X4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y3) X4)) (= (not (@ (@ tptp.ord_less_nat X4) Y3)) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((Y3 tptp.int) (X4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y3) X4)) (= (not (@ (@ tptp.ord_less_int X4) Y3)) (= X4 Y3)))))
% 6.83/7.13 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X4) Y3)) (=> (not (= X4 Y3)) (@ (@ tptp.ord_less_real Y3) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X4) Y3)) (=> (not (= X4 Y3)) (@ (@ tptp.ord_less_rat Y3) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X4) Y3)) (=> (not (= X4 Y3)) (@ (@ tptp.ord_less_num Y3) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y3)) (=> (not (= X4 Y3)) (@ (@ tptp.ord_less_nat Y3) X4)))))
% 6.83/7.13 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X4) Y3)) (=> (not (= X4 Y3)) (@ (@ tptp.ord_less_int Y3) X4)))))
% 6.83/7.13 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (not (@ (@ tptp.ord_less_real A) B2)))))
% 6.83/7.13 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A) (not (@ (@ tptp.ord_less_rat A) B2)))))
% 6.83/7.13 (assert (forall ((B2 tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A) (not (@ (@ tptp.ord_less_num A) B2)))))
% 6.83/7.13 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (not (@ (@ tptp.ord_less_nat A) B2)))))
% 6.83/7.13 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (not (@ (@ tptp.ord_less_int A) B2)))))
% 6.83/7.13 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.83/7.13 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.83/7.13 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.83/7.13 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.83/7.13 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.83/7.13 (assert (= (lambda ((P5 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P5 X7))) (lambda ((P6 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P6 N2) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N2) (not (@ P6 M6)))))))))
% 6.83/7.13 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B2 tptp.real)) (=> (forall ((A5 tptp.real) (B5 tptp.real)) (=> (@ (@ tptp.ord_less_real A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.real)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.real) (B5 tptp.real)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B2))))))
% 6.83/7.13 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B2 tptp.rat)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.rat)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B2))))))
% 6.83/7.13 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B2 tptp.num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ tptp.ord_less_num A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.num)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B2))))))
% 6.83/7.13 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B2))))))
% 6.83/7.13 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B2 tptp.int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.int)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B2))))))
% 6.83/7.13 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_real B2) C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_rat B2) C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_num B2) C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ _let_1 C))))))
% 6.83/7.13 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ _let_1 C))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (not (@ (@ tptp.ord_less_real X4) Y3)) (or (@ (@ tptp.ord_less_real Y3) X4) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X4) Y3)) (or (@ (@ tptp.ord_less_rat Y3) X4) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (not (@ (@ tptp.ord_less_num X4) Y3)) (or (@ (@ tptp.ord_less_num Y3) X4) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X4) Y3)) (or (@ (@ tptp.ord_less_nat Y3) X4) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (not (@ (@ tptp.ord_less_int X4) Y3)) (or (@ (@ tptp.ord_less_int Y3) X4) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (not (= A B2)))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (not (= A B2)))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A) B2) (not (= A B2)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (not (= A B2)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (not (= A B2)))))
% 6.83/7.14 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (not (= A B2)))))
% 6.83/7.14 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A) (not (= A B2)))))
% 6.83/7.14 (assert (forall ((B2 tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A) (not (= A B2)))))
% 6.83/7.14 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (not (= A B2)))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (not (= A B2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_real X4) Y3)) (@ (@ tptp.ord_less_real Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_rat X4) Y3)) (@ (@ tptp.ord_less_rat Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_num X4) Y3)) (@ (@ tptp.ord_less_num Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_nat X4) Y3)) (@ (@ tptp.ord_less_nat Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_int X4) Y3)) (@ (@ tptp.ord_less_int Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (not (@ (@ tptp.ord_less_real Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (not (@ (@ tptp.ord_less_rat Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (not (@ (@ tptp.ord_less_num Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (@ (@ tptp.ord_less_nat Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (not (@ (@ tptp.ord_less_int Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (not (= X4 Y3)) (or (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (not (= X4 Y3)) (or (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (not (= X4 Y3)) (or (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_num Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (not (= X4 Y3)) (or (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (not (= X4 Y3)) (or (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_int Y3) X4)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (not (@ (@ tptp.ord_less_real B2) A)))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (not (@ (@ tptp.ord_less_rat B2) A)))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A) B2) (not (@ (@ tptp.ord_less_num B2) A)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (not (@ (@ tptp.ord_less_nat B2) A)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (not (@ (@ tptp.ord_less_int B2) A)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_real Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_rat Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_num Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_nat Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_int Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B2 tptp.real) (C tptp.real)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B2 tptp.rat) (C tptp.rat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C tptp.rat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B2 tptp.rat) (C tptp.rat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B2 tptp.rat) (C tptp.rat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B2 tptp.rat) (C tptp.rat)) (=> (= A (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (= (@ F B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (not (@ (@ tptp.ord_less_real X4) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat)) (not (@ (@ tptp.ord_less_rat X4) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.num)) (not (@ (@ tptp.ord_less_num X4) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat)) (not (@ (@ tptp.ord_less_nat X4) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.int)) (not (@ (@ tptp.ord_less_int X4) X4))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_rat (@ F B2)) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_num (@ F B2)) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_rat (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_num (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (not (@ (@ tptp.ord_less_real Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (not (@ (@ tptp.ord_less_rat Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (not (@ (@ tptp.ord_less_num Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (@ (@ tptp.ord_less_nat Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (not (@ (@ tptp.ord_less_int Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X4) Y3) (=> (@ (@ tptp.ord_less_real Y3) X4) P))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (=> (@ (@ tptp.ord_less_rat Y3) X4) P))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X4) Y3) (=> (@ (@ tptp.ord_less_num Y3) X4) P))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (=> (@ (@ tptp.ord_less_nat Y3) X4) P))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X4) Y3) (=> (@ (@ tptp.ord_less_int Y3) X4) P))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y3) (= X4 Y3) (@ (@ tptp.ord_less_real Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_rat X4) Y3) (= X4 Y3) (@ (@ tptp.ord_less_rat Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_num X4) Y3) (= X4 Y3) (@ (@ tptp.ord_less_num Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y3) (= X4 Y3) (@ (@ tptp.ord_less_nat Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_int X4) Y3) (= X4 Y3) (@ (@ tptp.ord_less_int Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (not (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (not (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (not (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (not (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (not (= Y3 X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (not (= Y3 X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (not (= Y3 X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (= Y3 X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (not (= Y3 X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (not (@ (@ tptp.ord_less_real Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (not (@ (@ tptp.ord_less_rat Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (not (@ (@ tptp.ord_less_num Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (@ (@ tptp.ord_less_nat Y3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (not (@ (@ tptp.ord_less_int Y3) X4)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (@ (@ tptp.minus_minus_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N)))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))))
% 6.83/7.14 (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)))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N))) tptp.zero_zero_int))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int M) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.plus_plus_nat N) M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int M))))))
% 6.83/7.14 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A4) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int A)) N) (and (not (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_int)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N))))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N)))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N)))))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.complex)) (E tptp.real)) (=> (@ tptp.topolo6517432010174082258omplex X8) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M9 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M5) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M5)) (@ X8 N6)))) E))))))))))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.real)) (E tptp.real)) (=> (@ tptp.topolo4055970368930404560y_real X8) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M9 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M5) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M5)) (@ X8 N6)))) E))))))))))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.complex))) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M10 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M4) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N4) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M4)) (@ X8 N4)))) E2)))))))) (@ tptp.topolo6517432010174082258omplex X8))))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M10 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M4) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N4) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M4)) (@ X8 N4)))) E2)))))))) (@ tptp.topolo4055970368930404560y_real X8))))
% 6.83/7.14 (assert (= tptp.topolo6517432010174082258omplex (lambda ((X6 (-> tptp.nat tptp.complex))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X6 M6)) (@ X6 N2)))) E3)))))))))))
% 6.83/7.14 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X6 M6)) (@ X6 N2)))) E3)))))))))))
% 6.83/7.14 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y3) X4) (not (@ (@ tptp.ord_less_real X4) Y3)))))
% 6.83/7.14 (assert (forall ((Y3 tptp.set_nat) (X4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) X4) (not (@ (@ tptp.ord_less_set_nat X4) Y3)))))
% 6.83/7.14 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X4) (not (@ (@ tptp.ord_less_rat X4) Y3)))))
% 6.83/7.14 (assert (forall ((Y3 tptp.num) (X4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y3) X4) (not (@ (@ tptp.ord_less_num X4) Y3)))))
% 6.83/7.14 (assert (forall ((Y3 tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X4) (not (@ (@ tptp.ord_less_nat X4) Y3)))))
% 6.83/7.14 (assert (forall ((Y3 tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X4) (not (@ (@ tptp.ord_less_int X4) Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X4) Y3)) (@ (@ tptp.ord_less_eq_real Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X4) Y3)) (@ (@ tptp.ord_less_eq_rat Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X4) Y3)) (@ (@ tptp.ord_less_eq_num Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X4) Y3)) (@ (@ tptp.ord_less_eq_int Y3) X4))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B2)) (or (not (@ (@ tptp.ord_less_eq_real A) B2)) (= A B2)))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A) B2)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B2)) (= A B2)))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A) B2)) (or (not (@ (@ tptp.ord_less_eq_rat A) B2)) (= A B2)))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num)) (= (not (@ (@ tptp.ord_less_num A) B2)) (or (not (@ (@ tptp.ord_less_eq_num A) B2)) (= A B2)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B2)) (or (not (@ (@ tptp.ord_less_eq_nat A) B2)) (= A B2)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B2)) (or (not (@ (@ tptp.ord_less_eq_int A) B2)) (= A B2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X4) Y3)) (= (@ (@ tptp.ord_less_eq_real X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X4) Y3)) (= (@ (@ tptp.ord_less_eq_set_nat X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X4) Y3)) (= (@ (@ tptp.ord_less_eq_rat X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X4) Y3)) (= (@ (@ tptp.ord_less_eq_num X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y3)) (= (@ (@ tptp.ord_less_eq_nat X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X4) Y3)) (= (@ (@ tptp.ord_less_eq_int X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (= (not (@ (@ tptp.ord_less_real X4) Y3)) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X4) Y3) (= (not (@ (@ tptp.ord_less_set_nat X4) Y3)) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (= (not (@ (@ tptp.ord_less_rat X4) Y3)) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (= (not (@ (@ tptp.ord_less_num X4) Y3)) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (= (not (@ (@ tptp.ord_less_nat X4) Y3)) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (= (not (@ (@ tptp.ord_less_int X4) Y3)) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((Z tptp.real) (Y3 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X3) (@ (@ tptp.ord_less_eq_real Y3) X3))) (@ (@ tptp.ord_less_eq_real Y3) Z))))
% 6.83/7.14 (assert (forall ((Z tptp.rat) (Y3 tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X3) (@ (@ tptp.ord_less_eq_rat Y3) X3))) (@ (@ tptp.ord_less_eq_rat Y3) Z))))
% 6.83/7.14 (assert (forall ((Y3 tptp.real) (Z tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y3) (@ (@ tptp.ord_less_eq_real X3) Z))) (@ (@ tptp.ord_less_eq_real Y3) Z))))
% 6.83/7.14 (assert (forall ((Y3 tptp.rat) (Z tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat X3) Z))) (@ (@ tptp.ord_less_eq_rat Y3) Z))))
% 6.83/7.14 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (@ (@ tptp.ord_less_eq_real Y) X))))))
% 6.83/7.14 (assert (= tptp.ord_less_set_nat (lambda ((X tptp.set_nat) (Y tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X) Y) (not (@ (@ tptp.ord_less_eq_set_nat Y) X))))))
% 6.83/7.14 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y) (not (@ (@ tptp.ord_less_eq_rat Y) X))))))
% 6.83/7.14 (assert (= tptp.ord_less_num (lambda ((X tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y) (not (@ (@ tptp.ord_less_eq_num Y) X))))))
% 6.83/7.14 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y) (not (@ (@ tptp.ord_less_eq_nat Y) X))))))
% 6.83/7.14 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (not (@ (@ tptp.ord_less_eq_int Y) X))))))
% 6.83/7.14 (assert (forall ((Y3 tptp.real) (X4 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y3) X4)) (@ (@ tptp.ord_less_real X4) Y3))))
% 6.83/7.14 (assert (forall ((Y3 tptp.rat) (X4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y3) X4)) (@ (@ tptp.ord_less_rat X4) Y3))))
% 6.83/7.14 (assert (forall ((Y3 tptp.num) (X4 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y3) X4)) (@ (@ tptp.ord_less_num X4) Y3))))
% 6.83/7.14 (assert (forall ((Y3 tptp.nat) (X4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y3) X4)) (@ (@ tptp.ord_less_nat X4) Y3))))
% 6.83/7.14 (assert (forall ((Y3 tptp.int) (X4 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y3) X4)) (@ (@ tptp.ord_less_int X4) Y3))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B3 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B3) (= A4 B3)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (or (@ (@ tptp.ord_less_rat A4) B3) (= A4 B3)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B3 tptp.num)) (or (@ (@ tptp.ord_less_num A4) B3) (= A4 B3)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A4) B3) (= A4 B3)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B3) (= A4 B3)))))
% 6.83/7.14 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B3) (not (= A4 B3))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B3) (not (= A4 B3))))))
% 6.83/7.14 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B3) (not (= A4 B3))))))
% 6.83/7.14 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B3) (not (= A4 B3))))))
% 6.83/7.14 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B3) (not (= A4 B3))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.ord_less_real B2) C) (@ (@ tptp.ord_less_real A) C)))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (=> (@ (@ tptp.ord_less_set_nat B2) C) (@ (@ tptp.ord_less_set_nat A) C)))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_rat B2) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_num B2) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat B2) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (@ (@ tptp.ord_less_int B2) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_real B2) C) (@ _let_1 C))))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_nat B2) C) (@ _let_1 C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (@ _let_1 C))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_num B2) C) (@ _let_1 C))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_nat B2) C) (@ _let_1 C))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_int B2) C) (@ _let_1 C))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (=> (forall ((W3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W3) (=> (@ (@ tptp.ord_less_real W3) X4) (@ (@ tptp.ord_less_eq_real Y3) W3)))) (@ (@ tptp.ord_less_eq_real Y3) Z)))))
% 6.83/7.14 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X4) (=> (forall ((W3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W3) (=> (@ (@ tptp.ord_less_rat W3) X4) (@ (@ tptp.ord_less_eq_rat Y3) W3)))) (@ (@ tptp.ord_less_eq_rat Y3) Z)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (=> (forall ((W3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) W3) (=> (@ (@ tptp.ord_less_real W3) Y3) (@ (@ tptp.ord_less_eq_real W3) Z)))) (@ (@ tptp.ord_less_eq_real Y3) Z)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (=> (forall ((W3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) W3) (=> (@ (@ tptp.ord_less_rat W3) Y3) (@ (@ tptp.ord_less_eq_rat W3) Z)))) (@ (@ tptp.ord_less_eq_rat Y3) Z)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B3) A4) (= A4 B3)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (or (@ (@ tptp.ord_less_rat B3) A4) (= A4 B3)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A4 tptp.num)) (or (@ (@ tptp.ord_less_num B3) A4) (= A4 B3)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A4) (= A4 B3)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B3) A4) (= A4 B3)))))
% 6.83/7.14 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A4) (not (= A4 B3))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A4) (not (= A4 B3))))))
% 6.83/7.14 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A4) (not (= A4 B3))))))
% 6.83/7.14 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A4) (not (= A4 B3))))))
% 6.83/7.14 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A4) (not (= A4 B3))))))
% 6.83/7.14 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 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 B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B2) A) (=> (@ _let_1 B2) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (=> (@ (@ tptp.ord_less_eq_real C) B2) (@ (@ tptp.ord_less_real C) A)))))
% 6.83/7.14 (assert (forall ((B2 tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A) (=> (@ (@ tptp.ord_less_eq_set_nat C) B2) (@ (@ tptp.ord_less_set_nat C) A)))))
% 6.83/7.14 (assert (forall ((B2 tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A) (=> (@ (@ tptp.ord_less_eq_rat C) B2) (@ (@ tptp.ord_less_rat C) A)))))
% 6.83/7.14 (assert (forall ((B2 tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A) (=> (@ (@ tptp.ord_less_eq_num C) B2) (@ (@ tptp.ord_less_num C) A)))))
% 6.83/7.14 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (=> (@ (@ tptp.ord_less_eq_nat C) B2) (@ (@ tptp.ord_less_nat C) A)))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (=> (@ (@ tptp.ord_less_eq_int C) B2) (@ (@ tptp.ord_less_int C) A)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.ord_less_eq_real A) B2))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B2) (@ (@ tptp.ord_less_eq_set_nat A) B2))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (@ (@ tptp.ord_less_eq_rat A) B2))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A) B2) (@ (@ tptp.ord_less_eq_num A) B2))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_eq_nat A) B2))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_eq_int A) B2))))
% 6.83/7.14 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (@ (@ tptp.ord_less_eq_real B2) A))))
% 6.83/7.14 (assert (forall ((B2 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B2) A) (@ (@ tptp.ord_less_eq_set_nat B2) A))))
% 6.83/7.14 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A) (@ (@ tptp.ord_less_eq_rat B2) A))))
% 6.83/7.14 (assert (forall ((B2 tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A) (@ (@ tptp.ord_less_eq_num B2) A))))
% 6.83/7.14 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (@ (@ tptp.ord_less_eq_nat B2) A))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (@ (@ tptp.ord_less_eq_int B2) A))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_set_nat (lambda ((X tptp.set_nat) (Y tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X) Y) (= X Y)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_num (lambda ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 6.83/7.14 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (= X Y))))))
% 6.83/7.14 (assert (= tptp.ord_less_set_nat (lambda ((X tptp.set_nat) (Y tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X) Y) (not (= X Y))))))
% 6.83/7.14 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y) (not (= X Y))))))
% 6.83/7.14 (assert (= tptp.ord_less_num (lambda ((X tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y) (not (= X Y))))))
% 6.83/7.14 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y) (not (= X Y))))))
% 6.83/7.14 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (not (= X Y))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X4) Y3)) (@ (@ tptp.ord_less_real Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X4) Y3)) (@ (@ tptp.ord_less_rat Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X4) Y3)) (@ (@ tptp.ord_less_num Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X4) Y3)) (@ (@ tptp.ord_less_nat Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X4) Y3)) (@ (@ tptp.ord_less_int Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (not (@ (@ tptp.ord_less_real X4) Y3)) (@ (@ tptp.ord_less_eq_real Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X4) Y3)) (@ (@ tptp.ord_less_eq_rat Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (not (@ (@ tptp.ord_less_num X4) Y3)) (@ (@ tptp.ord_less_eq_num Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X4) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (not (@ (@ tptp.ord_less_int X4) Y3)) (@ (@ tptp.ord_less_eq_int Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_eq_real X4) Y3))))
% 6.83/7.14 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X4) Y3) (@ (@ tptp.ord_less_eq_set_nat X4) Y3))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat X4) Y3))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_eq_num X4) Y3))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat X4) Y3))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_eq_int X4) Y3))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_real A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_set_nat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_rat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_num A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_nat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (=> (not (= A B2)) (@ (@ tptp.ord_less_int A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_real A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B2) (@ (@ tptp.ord_less_set_nat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (@ (@ tptp.ord_less_rat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (@ (@ tptp.ord_less_num A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (@ (@ tptp.ord_less_nat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (not (= A B2)) (=> (@ (@ tptp.ord_less_eq_int A) B2) (@ (@ tptp.ord_less_int A) B2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (=> (@ (@ tptp.ord_less_real Y3) Z) (@ (@ tptp.ord_less_real X4) Z)))))
% 6.83/7.14 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X4) Y3) (=> (@ (@ tptp.ord_less_set_nat Y3) Z) (@ (@ tptp.ord_less_set_nat X4) Z)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (=> (@ (@ tptp.ord_less_rat Y3) Z) (@ (@ tptp.ord_less_rat X4) Z)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (=> (@ (@ tptp.ord_less_num Y3) Z) (@ (@ tptp.ord_less_num X4) Z)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (=> (@ (@ tptp.ord_less_nat Y3) Z) (@ (@ tptp.ord_less_nat X4) Z)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (=> (@ (@ tptp.ord_less_int Y3) Z) (@ (@ tptp.ord_less_int X4) Z)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_real Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_rat Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_num Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_int Y3) Z) (@ _let_1 Z))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B2)) (=> (@ (@ tptp.ord_less_real B2) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B2)) (=> (@ (@ tptp.ord_less_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B2 tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B2)) (=> (@ (@ tptp.ord_less_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B2)) (=> (@ (@ tptp.ord_less_nat B2) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B2)) (=> (@ (@ tptp.ord_less_int B2) C) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_rat (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_num (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_real (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_rat (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_num (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_nat (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B2) (=> (@ (@ tptp.ord_less_int (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_rat B2) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B2 tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B2)) (=> (@ (@ tptp.ord_less_eq_num B2) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y4) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_num A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_eq_real (@ F B2)) C) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y4) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_eq_rat (@ F B2)) C) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_real Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_rat Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_num Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_nat Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X4) Y3) (@ (@ tptp.ord_less_int Y3) X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (or (@ (@ tptp.ord_less_real X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X4) Y3) (or (@ (@ tptp.ord_less_set_nat X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (or (@ (@ tptp.ord_less_rat X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (or (@ (@ tptp.ord_less_num X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (or (@ (@ tptp.ord_less_nat X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (or (@ (@ tptp.ord_less_int X4) Y3) (= X4 Y3)))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I4)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) tptp.na) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I4)) (@ (@ tptp.vEBT_VEBT_low X5) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X5) (@ (@ tptp.ord_less_eq_nat X5) tptp.ma)))))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= tptp.za tptp.ma) (@ (@ 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)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (not (exists ((U2 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))) U2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_1)) U2))))))
% 6.83/7.14 (assert (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.sc)) X_1)))
% 6.83/7.14 (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.za) _let_1))) (@ (@ tptp.vEBT_VEBT_low tptp.za) _let_1))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= tptp.za tptp.ma) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.za) _let_1))) (@ (@ tptp.vEBT_VEBT_low tptp.za) _let_1)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) (@ (@ tptp.nth_VEBT_VEBT Ys2) I3)))) (= Xs2 Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_o) (Ys2 tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) (@ (@ tptp.nth_o Ys2) I3)))) (= Xs2 Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_nat) (Ys2 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) (@ (@ tptp.nth_nat Ys2) I3)))) (= Xs2 Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_int) (Ys2 tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) (@ (@ tptp.nth_int Ys2) I3)))) (= Xs2 Ys2)))))
% 6.83/7.14 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X6 tptp.vEBT_VEBT)) (@ (@ P I2) X6)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_VEBT_VEBT Xs) I2)))))))))
% 6.83/7.14 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X6 Bool)) (@ (@ P I2) X6)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_o Xs) I2)))))))))
% 6.83/7.14 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X6 tptp.nat)) (@ (@ P I2) X6)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_nat Xs) I2)))))))))
% 6.83/7.14 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X6 tptp.int)) (@ (@ P I2) X6)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_int Xs) I2)))))))))
% 6.83/7.14 (assert (= (lambda ((Y6 tptp.list_VEBT_VEBT) (Z4 tptp.list_VEBT_VEBT)) (= Y6 Z4)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Ys3) I2))))))))
% 6.83/7.14 (assert (= (lambda ((Y6 tptp.list_o) (Z4 tptp.list_o)) (= Y6 Z4)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I2) (@ (@ tptp.nth_o Ys3) I2))))))))
% 6.83/7.14 (assert (= (lambda ((Y6 tptp.list_nat) (Z4 tptp.list_nat)) (= Y6 Z4)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I2) (@ (@ tptp.nth_nat Ys3) I2))))))))
% 6.83/7.14 (assert (= (lambda ((Y6 tptp.list_int) (Z4 tptp.list_int)) (= Y6 Z4)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I2) (@ (@ tptp.nth_int Ys3) I2))))))))
% 6.83/7.14 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.83/7.14 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) N2))) (@ (@ tptp.vEBT_VEBT_low X) N2)))))
% 6.83/7.14 (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))
% 6.83/7.14 (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))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.83/7.14 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X4) (@ (@ tptp.vEBT_vebt_member T) X4)))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X4) (@ (@ tptp.vEBT_vebt_member T) X4)))))
% 6.83/7.14 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) tptp.sc))
% 6.83/7.14 (assert (@ (@ tptp.vEBT_vebt_member tptp.summary) tptp.sc))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X4) (@ (@ tptp.member_nat X4) (@ tptp.vEBT_set_vebt T))))))
% 6.83/7.14 (assert (forall ((Tree tptp.vEBT_VEBT) (X4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X4) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.83/7.14 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.za) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.83/7.14 (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)))
% 6.83/7.14 (assert (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I4)))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat) (Y3 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 X4) _let_1) (=> (@ (@ tptp.ord_less_nat Y3) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X4)) Y3) (or (@ (@ tptp.vEBT_vebt_member T) Y3) (= X4 Y3)))))))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat) (Y3 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 X4) _let_1) (=> (@ (@ tptp.ord_less_nat Y3) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y3)) X4))))))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X4)) X4)))))
% 6.83/7.14 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X4 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 X4) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X4) _let_3))) (@ (@ tptp.vEBT_VEBT_low X4) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X4)))))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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) (S3 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList3) S3))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 6.83/7.14 (assert (@ (@ (@ tptp.vEBT_is_succ_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.sc))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_Extended_enat) (P (-> tptp.extended_enat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) (@ tptp.set_Extended_enat2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3941691890525107288d_enat Xs2)) (@ P (@ (@ tptp.nth_Extended_enat Xs2) N))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X4) Y3) (and (@ (@ tptp.vEBT_vebt_member T) Y3) (@ (@ tptp.ord_less_nat X4) Y3) (forall ((Z5 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z5) (@ (@ tptp.ord_less_nat X4) Z5)) (@ (@ tptp.ord_less_eq_nat Y3) Z5)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.extended_enat) (Xs2 tptp.list_Extended_enat)) (=> (@ (@ tptp.member_Extended_enat X4) (@ tptp.set_Extended_enat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3941691890525107288d_enat Xs2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 6.83/7.14 (assert (forall ((X4 Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_Extended_enat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3941691890525107288d_enat Xs2)) (@ (@ tptp.member_Extended_enat (@ (@ tptp.nth_Extended_enat Xs2) N)) (@ tptp.set_Extended_enat2 Xs2)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((X4 tptp.extended_enat) (Xs2 tptp.list_Extended_enat)) (= (@ (@ tptp.member_Extended_enat X4) (@ tptp.set_Extended_enat2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3941691890525107288d_enat Xs2)) (= (@ (@ tptp.nth_Extended_enat Xs2) I2) X4))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I2) X4))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I2) X4))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) X4))))))
% 6.83/7.14 (assert (forall ((X4 Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I2) X4))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I2) X4))))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I2) X4))))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_Extended_enat) (P (-> tptp.extended_enat Bool)) (X4 tptp.extended_enat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3941691890525107288d_enat Xs2)) (@ P (@ (@ tptp.nth_Extended_enat Xs2) I3)))) (=> (@ (@ tptp.member_Extended_enat X4) (@ tptp.set_Extended_enat2 Xs2)) (@ P X4)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (X4 tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) I3)))) (=> (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs2)) (@ P X4)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X4 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 X4) (@ tptp.set_real2 Xs2)) (@ P X4)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X4 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 X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X4)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X4 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 X4) (@ tptp.set_o2 Xs2)) (@ P X4)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X4 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 X4) (@ tptp.set_nat2 Xs2)) (@ P X4)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X4 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 X4) (@ tptp.set_int2 Xs2)) (@ P X4)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)))))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X Bool)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I2)))))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P X))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I2)))))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P X))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I2)))))))
% 6.83/7.14 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z5 tptp.nat)) (=> (@ (@ tptp.member_nat Z5) Xs) (=> (@ (@ tptp.ord_less_nat X) Z5) (@ (@ tptp.ord_less_eq_nat Y) Z5))))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (not (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.sc)) tptp.bot_bot_set_nat)))
% 6.83/7.14 (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.xa) tptp.za)))
% 6.83/7.14 (assert (= (@ (@ tptp.vEBT_vebt_succ 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.sc)))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X4) Y3) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X4)) (@ tptp.some_nat Y3)) (@ tptp.some_nat Z)))))
% 6.83/7.14 (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 ((Xa2 tptp.nat) (Xb2 tptp.nat)) (= (= (@ (@ tptp.vEBT_vebt_succ X5) Xa2) (@ tptp.some_nat Xb2)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt X5)) Xa2) Xb2)))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Sx tptp.nat)) (= (= (@ (@ tptp.vEBT_vebt_succ tptp.summary) X4) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt tptp.summary)) X4) Sx))))
% 6.83/7.14 (assert (forall ((I tptp.extended_enat) (L2 tptp.extended_enat) (U tptp.extended_enat)) (= (@ (@ tptp.member_Extended_enat I) (@ (@ tptp.set_or5403411693681687835d_enat L2) U)) (and (@ (@ tptp.ord_le2932123472753598470d_enat L2) I) (@ (@ tptp.ord_le2932123472753598470d_enat I) U)))))
% 6.83/7.14 (assert (forall ((I tptp.set_nat) (L2 tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ (@ tptp.set_or4548717258645045905et_nat L2) U)) (and (@ (@ tptp.ord_less_eq_set_nat L2) I) (@ (@ tptp.ord_less_eq_set_nat I) U)))))
% 6.83/7.14 (assert (forall ((I tptp.rat) (L2 tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I) (@ (@ tptp.set_or633870826150836451st_rat L2) U)) (and (@ (@ tptp.ord_less_eq_rat L2) I) (@ (@ tptp.ord_less_eq_rat I) U)))))
% 6.83/7.14 (assert (forall ((I tptp.num) (L2 tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I) (@ (@ tptp.set_or7049704709247886629st_num L2) U)) (and (@ (@ tptp.ord_less_eq_num L2) I) (@ (@ tptp.ord_less_eq_num I) U)))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I) (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (and (@ (@ tptp.ord_less_eq_nat L2) I) (@ (@ tptp.ord_less_eq_nat I) U)))))
% 6.83/7.14 (assert (forall ((I tptp.int) (L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I) (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (and (@ (@ tptp.ord_less_eq_int L2) I) (@ (@ tptp.ord_less_eq_int I) U)))))
% 6.83/7.14 (assert (forall ((I tptp.real) (L2 tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I) (@ (@ tptp.set_or1222579329274155063t_real L2) U)) (and (@ (@ tptp.ord_less_eq_real L2) I) (@ (@ tptp.ord_less_eq_real I) U)))))
% 6.83/7.14 (assert (forall ((L2 tptp.set_nat) (H2 tptp.set_nat) (L4 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L2) H2) (@ (@ tptp.set_or4548717258645045905et_nat L4) H3)) (or (and (= L2 L4) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_set_nat L4) H3)))))))
% 6.83/7.14 (assert (forall ((L2 tptp.rat) (H2 tptp.rat) (L4 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L2) H2) (@ (@ tptp.set_or633870826150836451st_rat L4) H3)) (or (and (= L2 L4) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_rat L2) H2)) (not (@ (@ tptp.ord_less_eq_rat L4) H3)))))))
% 6.83/7.14 (assert (forall ((L2 tptp.num) (H2 tptp.num) (L4 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L2) H2) (@ (@ tptp.set_or7049704709247886629st_num L4) H3)) (or (and (= L2 L4) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_num L2) H2)) (not (@ (@ tptp.ord_less_eq_num L4) H3)))))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (H2 tptp.nat) (L4 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L2) H2) (@ (@ tptp.set_or1269000886237332187st_nat L4) H3)) (or (and (= L2 L4) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_nat L4) H3)))))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (H2 tptp.int) (L4 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L2) H2) (@ (@ tptp.set_or1266510415728281911st_int L4) H3)) (or (and (= L2 L4) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L2) H2)) (not (@ (@ tptp.ord_less_eq_int L4) H3)))))))
% 6.83/7.14 (assert (forall ((L2 tptp.real) (H2 tptp.real) (L4 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L2) H2) (@ (@ tptp.set_or1222579329274155063t_real L4) H3)) (or (and (= L2 L4) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L2) H2)) (not (@ (@ tptp.ord_less_eq_real L4) H3)))))))
% 6.83/7.14 (assert (forall ((X4 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 (= X4 Mi) (= X4 Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X4) _let_1))))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat)) (= (@ (@ tptp.minus_925952699566721837d_enat A3) A3) tptp.bot_bo7653980558646680370d_enat)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A3) A3) tptp.bot_bot_set_real)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A3) A3) tptp.bot_bot_set_int)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A3) A3) tptp.bot_bot_set_nat)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat)) (= (@ (@ tptp.minus_925952699566721837d_enat tptp.bot_bo7653980558646680370d_enat) A3) tptp.bot_bo7653980558646680370d_enat)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real tptp.bot_bot_set_real) A3) tptp.bot_bot_set_real)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A3) tptp.bot_bot_set_int)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A3) tptp.bot_bot_set_nat)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat)) (= (@ (@ tptp.minus_925952699566721837d_enat A3) tptp.bot_bo7653980558646680370d_enat) A3)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A3) tptp.bot_bot_set_real) A3)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A3) tptp.bot_bot_set_int) A3)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A3) tptp.bot_bot_set_nat) A3)))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((Deg tptp.nat) (X4 tptp.nat) (Mi tptp.nat) (Ma 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 X4) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X4) (@ tptp.some_nat Mi))))))
% 6.83/7.14 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (= (@ (@ tptp.set_or5403411693681687835d_enat A) B2) tptp.bot_bo7653980558646680370d_enat) (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B2) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B2) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A) B2) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B2) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B2) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B2) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (= tptp.bot_bo7653980558646680370d_enat (@ (@ tptp.set_or5403411693681687835d_enat A) B2)) (not (@ (@ tptp.ord_le2932123472753598470d_enat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B2)) (not (@ (@ tptp.ord_less_eq_set_nat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B2)) (not (@ (@ tptp.ord_less_eq_rat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B2)) (not (@ (@ tptp.ord_less_eq_num A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (not (@ (@ tptp.ord_less_eq_nat A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B2)) (not (@ (@ tptp.ord_less_eq_int A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (not (@ (@ tptp.ord_less_eq_real A) B2)))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat) (B2 tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B2)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B2)) (and (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat B2) D))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 tptp.rat) (C tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B2)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B2)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B2) D))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 tptp.num) (C tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B2)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (or (not (@ (@ tptp.ord_less_eq_num A) B2)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B2) D))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B2)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B2) D))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B2)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B2)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B2) D))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B2)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B2) D))))))
% 6.83/7.14 (assert (forall ((B2 tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B2) A) (= (@ (@ tptp.set_or5403411693681687835d_enat A) B2) tptp.bot_bo7653980558646680370d_enat))))
% 6.83/7.14 (assert (forall ((B2 tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B2) A) (= (@ (@ tptp.set_or633870826150836451st_rat A) B2) tptp.bot_bot_set_rat))))
% 6.83/7.14 (assert (forall ((B2 tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B2) A) (= (@ (@ tptp.set_or7049704709247886629st_num A) B2) tptp.bot_bot_set_num))))
% 6.83/7.14 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B2) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B2) tptp.bot_bot_set_nat))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B2) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B2) tptp.bot_bot_set_int))))
% 6.83/7.14 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B2) tptp.bot_bot_set_real))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat) (B4 tptp.set_Extended_enat)) (= (= (@ (@ tptp.minus_925952699566721837d_enat A3) B4) tptp.bot_bo7653980558646680370d_enat) (@ (@ tptp.ord_le7203529160286727270d_enat A3) B4))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real) (B4 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A3) B4) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A3) B4))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A3) B4) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A3) B4))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A3) B4) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A3) B4))))
% 6.83/7.14 (assert (not (forall ((Sc tptp.nat)) (not (= (@ (@ tptp.vEBT_vebt_succ 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 Sc))))))
% 6.83/7.14 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X4 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)) X4) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X4) _let_1))) (@ (@ tptp.vEBT_VEBT_low X4) _let_1)) (= X4 Mi) (= X4 Ma)))))))
% 6.83/7.14 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X4 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 X4) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X4) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X4 Mi) (= X4 Ma) (and (@ (@ tptp.ord_less_nat X4) Ma) (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ 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 X4) _let_2)))))))))))
% 6.83/7.14 (assert (forall ((X4 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 X4) _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 X4) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X4))))))))
% 6.83/7.14 (assert (= (@ tptp.some_nat tptp.miny) (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.sc))))
% 6.83/7.14 (assert (= tptp.ord_less_nat (lambda ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 6.83/7.14 (assert (not (= (@ (@ tptp.vEBT_vebt_succ tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) tptp.none_nat)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat)) (not (@ (@ tptp.ord_le2529575680413868914d_enat A3) tptp.bot_bo7653980558646680370d_enat))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A3) tptp.bot_bot_set_real))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A3) tptp.bot_bot_set_nat))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A3) tptp.bot_bot_set_int))))
% 6.83/7.14 (assert (forall ((A tptp.set_Extended_enat)) (= (not (= A tptp.bot_bo7653980558646680370d_enat)) (@ (@ tptp.ord_le2529575680413868914d_enat tptp.bot_bo7653980558646680370d_enat) A))))
% 6.83/7.14 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.83/7.14 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.83/7.14 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.83/7.14 (assert (forall ((A tptp.set_Extended_enat)) (not (@ (@ tptp.ord_le2529575680413868914d_enat A) tptp.bot_bo7653980558646680370d_enat))))
% 6.83/7.14 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.83/7.14 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.83/7.14 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.83/7.14 (assert (forall ((A tptp.set_Extended_enat)) (@ (@ tptp.ord_le7203529160286727270d_enat tptp.bot_bo7653980558646680370d_enat) A)))
% 6.83/7.14 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 6.83/7.14 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 6.83/7.14 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 6.83/7.14 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 6.83/7.14 (assert (forall ((A tptp.set_Extended_enat)) (= (@ (@ tptp.ord_le7203529160286727270d_enat A) tptp.bot_bo7653980558646680370d_enat) (= A tptp.bot_bo7653980558646680370d_enat))))
% 6.83/7.14 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.83/7.14 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.83/7.14 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.83/7.14 (assert (forall ((A tptp.set_Extended_enat)) (=> (@ (@ tptp.ord_le7203529160286727270d_enat A) tptp.bot_bo7653980558646680370d_enat) (= A tptp.bot_bo7653980558646680370d_enat))))
% 6.83/7.14 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.83/7.14 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.83/7.14 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.83/7.14 (assert (forall ((X4 tptp.set_Extended_enat) (Y3 tptp.set_Extended_enat)) (= (= (@ (@ tptp.minus_925952699566721837d_enat X4) Y3) tptp.bot_bo7653980558646680370d_enat) (@ (@ tptp.ord_le7203529160286727270d_enat X4) Y3))))
% 6.83/7.14 (assert (forall ((X4 tptp.set_real) (Y3 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X4) Y3) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X4) Y3))))
% 6.83/7.14 (assert (forall ((X4 tptp.set_int) (Y3 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X4) Y3) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X4) Y3))))
% 6.83/7.14 (assert (forall ((X4 tptp.set_nat) (Y3 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X4) Y3) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X4) Y3))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.83/7.14 (assert (forall ((A tptp.set_nat) (B2 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) B2)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B2) D) (or (@ (@ tptp.ord_less_set_nat C) A) (@ (@ tptp.ord_less_set_nat B2) D)))) (@ _let_1 D))))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (B2 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) B2)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B2) D) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B2) D)))) (@ _let_1 D))))))
% 6.83/7.14 (assert (forall ((A tptp.num) (B2 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) B2)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B2) D) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B2) D)))) (@ _let_1 D))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 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) B2)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B2) D) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B2) D)))) (@ _let_1 D))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 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) B2)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B2) D) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B2) D)))) (@ _let_1 D))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 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) B2)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B2) D) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B2) D)))) (@ _let_1 D))))))
% 6.83/7.14 (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)))))))))))))))
% 6.83/7.14 (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)))))))))))))))
% 6.83/7.14 (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))))))))))))
% 6.83/7.14 (assert (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat (@ (@ tptp.vEBT_vebt_succ tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) tptp.miny))
% 6.83/7.14 (assert (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat (@ (@ tptp.vEBT_vebt_succ tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) tptp.miny))
% 6.83/7.14 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat (@ (@ tptp.vEBT_vebt_succ tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) tptp.na))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X4) (@ (@ tptp.ord_less_eq_nat Mini) X4))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X4) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X4))))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X4)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X4)))))
% 6.83/7.14 (assert (not (forall ((Miny tptp.nat)) (not (= (@ tptp.some_nat Miny) (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.sc)))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (= (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int) tptp.bot_bot_nat_o))
% 6.83/7.14 (assert (= (@ tptp.bit_se1148574629649215175it_nat tptp.zero_zero_nat) tptp.bot_bot_nat_o))
% 6.83/7.14 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X4 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Ma 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 Mi) X4) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_VEBT_high X4) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X4) tptp.none_nat)))))))
% 6.83/7.14 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va2) _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 Va2))) (=> (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)))))))))))
% 6.83/7.14 (assert (= (@ tptp.some_nat tptp.miny) (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat (@ (@ tptp.vEBT_vebt_succ tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.83/7.14 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 6.83/7.14 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.83/7.14 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (A3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ 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) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (A3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ 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) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D4))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D4))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.83/7.14 (assert (forall ((D tptp.int) (D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) D4)) T)))))))))
% 6.83/7.14 (assert (forall ((D tptp.int) (D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) D4)) T))))))))))
% 6.83/7.14 (assert (forall ((D tptp.int) (D4 tptp.int) (A3 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) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T))))))))))
% 6.83/7.14 (assert (forall ((D tptp.int) (D4 tptp.int) (A3 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) A3) (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)))))))))))
% 6.83/7.14 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd)) Ve) tptp.none_nat)))
% 6.83/7.14 (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 ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (A3 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) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.plus_plus_int X5) D4)))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (T tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A3) (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) A3) (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))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (T tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A3) (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) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.plus_plus_int X5) D4) T)))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (T tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A3) (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) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X5 T) (= (@ (@ tptp.plus_plus_int X5) D4) T))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B4) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D4))))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X5) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X5) D4)) T)))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B4) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.minus_minus_int X5) D4) T)))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B4) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X5 T) (= (@ (@ tptp.minus_minus_int X5) D4) T))))))))
% 6.83/7.14 (assert (forall ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi) tptp.none_nat)))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (A3 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) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.plus_plus_int X5) D4)))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (T tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A3) (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) A3) (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))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B4) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D4))))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X5) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X5) D4)) T)))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (@ P X3) (@ P4 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P4 X3) (@ P4 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X6 tptp.int)) (@ P X6)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P4 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) B4) (@ P (@ (@ tptp.plus_plus_int Y) X))))))))))))))
% 6.83/7.14 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (@ P X3) (@ P4 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P4 X3) (@ P4 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X6 tptp.int)) (@ P X6)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P4 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y tptp.int)) (and (@ (@ tptp.member_int Y) A3) (@ P (@ (@ tptp.minus_minus_int Y) X))))))))))))))
% 6.83/7.14 (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_succ 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_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat _let_3))))))))))
% 6.83/7.14 (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)))))))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X4) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X4))))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X4)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X4) Y3) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X4)) (@ tptp.some_nat Y3)) (@ tptp.some_nat Z)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X4) Y3) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X4)) (@ tptp.some_nat Y3)) (@ tptp.some_nat Z)))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (X4 tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X4))))
% 6.83/7.14 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 6.83/7.14 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X4) (@ (@ tptp.ord_less_eq_nat X4) Maxi))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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_succ tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_2)))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ 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_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat _let_3)))))))))
% 6.83/7.14 (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_succ tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_2)))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ 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))) (and (=> _let_5 (= _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_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat _let_3)))))))))))))
% 6.83/7.14 (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_succ tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_2)))) (@ (@ 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.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_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ tptp.the_nat _let_3))))))))))
% 6.83/7.14 (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_succ 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_succ (@ (@ (@ (@ 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_4 tptp.none_nat))) (let ((_let_9 (@ _let_5 _let_3))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_2))) (let ((_let_12 (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_11)) _let_10)))) (and (=> _let_12 (= _let_7 (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_11)))) (=> (not _let_12) (and (=> _let_8 (= _let_7 tptp.none_nat)) (=> (not _let_8) (= _let_7 (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4))))))))))))))))))))))
% 6.83/7.14 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1))))) (or (= _let_2 tptp.none_nat) (not (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat (@ (@ tptp.vEBT_VEBT_low tptp.xa) _let_1))) _let_2))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 6.83/7.14 (assert (forall ((X4 tptp.produc3368934014287244435at_num)) (not (forall ((F3 (-> tptp.nat tptp.num tptp.num)) (A5 tptp.nat) (B5 tptp.nat) (Acc2 tptp.num)) (not (= X4 (@ (@ tptp.produc851828971589881931at_num F3) (@ (@ tptp.produc1195630363706982562at_num A5) (@ (@ tptp.product_Pair_nat_num B5) Acc2)))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.produc4471711990508489141at_nat)) (not (forall ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat) (Acc2 tptp.nat)) (not (= X4 (@ (@ tptp.produc3209952032786966637at_nat F3) (@ (@ tptp.produc487386426758144856at_nat A5) (@ (@ tptp.product_Pair_nat_nat B5) Acc2)))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.product_prod_num_num)) (=> (not (= X4 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N4 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N4))))) (=> (forall ((N4 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N4))))) (=> (forall ((M4 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N4 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit0 N4))))) (=> (forall ((M4 tptp.num) (N4 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit1 N4))))) (=> (forall ((M4 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N4 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit0 N4))))) (not (forall ((M4 tptp.num) (N4 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit1 N4))))))))))))))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 6.83/7.14 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X4 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X4))))
% 6.83/7.14 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X4 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (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 X4) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ 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 X4) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X4) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X4) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (X4 tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X4)))))
% 6.83/7.14 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T3 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T3)))))
% 6.83/7.14 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X4 tptp.nat) (Ma 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 X4) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ 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 X4) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X4) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X4) (@ (@ (@ 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_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.83/7.14 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 6.83/7.14 (assert (= tptp.ord_le2529575680413868914d_enat (lambda ((A6 tptp.set_Extended_enat) (B7 tptp.set_Extended_enat)) (@ (@ tptp.ord_le8499522857272258027enat_o (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) A6))) (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) B7))))))
% 6.83/7.14 (assert (= tptp.ord_less_set_complex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ (@ tptp.ord_less_complex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A6))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) B7))))))
% 6.83/7.14 (assert (= tptp.ord_less_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ (@ tptp.ord_less_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B7))))))
% 6.83/7.14 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B7))))))
% 6.83/7.14 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B7))))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) A)))) (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) B2)))) (and (@ (@ tptp.dvd_dvd_complex A) B2) (not (@ (@ tptp.dvd_dvd_complex B2) A))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) A)))) (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) B2)))) (and (@ (@ tptp.dvd_dvd_real A) B2) (not (@ (@ tptp.dvd_dvd_real B2) A))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B2)))) (and (@ (@ tptp.dvd_dvd_nat A) B2) (not (@ (@ tptp.dvd_dvd_nat B2) A))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B2)))) (and (@ (@ tptp.dvd_dvd_int A) B2) (not (@ (@ tptp.dvd_dvd_int B2) A))))))
% 6.83/7.14 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B2)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B2) (not (@ (@ tptp.dvd_dvd_Code_integer B2) A))))))
% 6.83/7.14 (assert (= tptp.minus_925952699566721837d_enat (lambda ((A6 tptp.set_Extended_enat) (B7 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 6.83/7.14 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 6.83/7.14 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ tptp.collect_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 6.83/7.14 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B7 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 6.83/7.14 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ tptp.collect_int (lambda ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 6.83/7.14 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 6.83/7.14 (assert (= tptp.minus_925952699566721837d_enat (lambda ((A6 tptp.set_Extended_enat) (B7 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (@ (@ tptp.minus_2020553357622893040enat_o (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) A6))) (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) B7)))))))
% 6.83/7.14 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ tptp.collect_complex (@ (@ tptp.minus_8727706125548526216plex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A6))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) B7)))))))
% 6.83/7.14 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.minus_minus_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B7)))))))
% 6.83/7.14 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B7 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.minus_1139252259498527702_nat_o (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A6))) (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) B7)))))))
% 6.83/7.14 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B7)))))))
% 6.83/7.14 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B7)))))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.83/7.14 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.83/7.14 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.83/7.14 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.83/7.14 (assert (forall ((C tptp.real)) (= (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C)) (@ tptp.times_times_real C))))
% 6.83/7.14 (assert (forall ((C tptp.rat)) (= (lambda ((X tptp.rat)) (@ (@ tptp.times_times_rat X) C)) (@ tptp.times_times_rat C))))
% 6.83/7.14 (assert (forall ((C tptp.nat)) (= (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C)) (@ tptp.times_times_nat C))))
% 6.83/7.14 (assert (forall ((C tptp.int)) (= (lambda ((X tptp.int)) (@ (@ tptp.times_times_int X) C)) (@ tptp.times_times_int C))))
% 6.83/7.14 (assert (= (lambda ((X tptp.complex)) X) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.83/7.14 (assert (= (lambda ((X tptp.real)) X) (@ tptp.times_times_real tptp.one_one_real)))
% 6.83/7.14 (assert (= (lambda ((X tptp.rat)) X) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.83/7.14 (assert (= (lambda ((X tptp.nat)) X) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.83/7.14 (assert (= (lambda ((X tptp.int)) X) (@ tptp.times_times_int tptp.one_one_int)))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) A)))) (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) B2)))) (@ (@ tptp.dvd_dvd_complex A) B2))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) A)))) (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) B2)))) (@ (@ tptp.dvd_dvd_real A) B2))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B2)))) (@ (@ tptp.dvd_dvd_int A) B2))))
% 6.83/7.14 (assert (forall ((A tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B2)))) (@ (@ tptp.dvd_dvd_Code_integer A) B2))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B2)))) (@ (@ tptp.dvd_dvd_nat A) B2))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_complex _let_2) _let_2))))))
% 6.83/7.14 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 6.83/7.14 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 6.83/7.14 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 6.83/7.14 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z) _let_2)) _let_2))))))
% 6.83/7.14 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z) _let_2)) _let_2))))))
% 6.83/7.14 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z) _let_2)) _let_2))))))
% 6.83/7.14 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z) _let_2)) _let_2))))))
% 6.83/7.14 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z) _let_2)) _let_2))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (= tptp.set_complex2 (lambda ((Xs tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu tptp.complex)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_complex Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3451745648224563538omplex Xs)))))))))
% 6.83/7.14 (assert (= tptp.set_real2 (lambda ((Xs tptp.list_real)) (@ tptp.collect_real (lambda ((Uu tptp.real)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_real Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs)))))))))
% 6.83/7.14 (assert (= tptp.set_list_nat2 (lambda ((Xs tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu tptp.list_nat)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_list_nat Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3023201423986296836st_nat Xs)))))))))
% 6.83/7.14 (assert (= tptp.set_VEBT_VEBT2 (lambda ((Xs tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu tptp.vEBT_VEBT)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_VEBT_VEBT Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))))))
% 6.83/7.14 (assert (= tptp.set_o2 (lambda ((Xs tptp.list_o)) (@ tptp.collect_o (lambda ((Uu Bool)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_o Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)))))))))
% 6.83/7.14 (assert (= tptp.set_nat2 (lambda ((Xs tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu tptp.nat)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_nat Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)))))))))
% 6.83/7.14 (assert (= tptp.set_int2 (lambda ((Xs tptp.list_int)) (@ tptp.collect_int (lambda ((Uu tptp.int)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_int Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)))))))))
% 6.83/7.14 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z6))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z6)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z6) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 6.83/7.14 (assert (= tptp.nat_set_decode (lambda ((X 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 X) (@ (@ tptp.power_power_nat _let_1) N2))))))))))
% 6.83/7.14 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N2 tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger _let_1) A4))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) _let_2))))))
% 6.83/7.14 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int _let_1) A4))) (@ (@ (@ tptp.if_int (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)))) _let_2))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X4 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X4) _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) X4)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X4) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary)) X4) (=> (not (= X4 Mi)) (=> (not (= X4 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 X4) _let_2))) _let_4))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va2 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 Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X4) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ 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 X4) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList2) Summary)) X4))) (let ((_let_12 (@ (@ tptp.ord_less_nat X4) Mi))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Mi))) (=> (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_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (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)))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X4 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 X4) _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)) X4) (or (= X4 Mi) (= X4 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X4) _let_2))) _let_4)))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) 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 X4) _let_1))))))))
% 6.83/7.14 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X4 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 X4) _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) S)) X4) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X4) _let_2))) _let_4))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X4))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X4))))
% 6.83/7.14 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T3 tptp.vEBT_VEBT) (X tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T3) X) (@ (@ tptp.vEBT_VEBT_membermima T3) X)))))
% 6.83/7.14 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X4) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X4) (@ (@ tptp.vEBT_VEBT_membermima Tree) X4))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X4))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa Mi2) (= Xa Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V3)) TreeList3) Vc2))) (not (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))) (not (forall ((V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList3) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X4) Xa) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2))) (not (=> (not (= Xa Mi2)) (=> (not (= Xa 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 Xa) _let_1))) _let_3))))))))))))))))))))
% 6.83/7.14 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X4 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X4) _let_1))))
% 6.83/7.14 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.83/7.14 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.83/7.14 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 6.83/7.14 (assert (forall ((A Bool) (B2 Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B2)) tptp.zero_zero_nat))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5)))))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))))))))
% 6.83/7.14 (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))))))))))))
% 6.83/7.14 (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))))))))))))
% 6.83/7.14 (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))))))))))))
% 6.83/7.14 (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))))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A3 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I2)) A))) A3)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) A))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A3 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I2)) A))) A3)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A3)) A))))
% 6.83/7.14 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A3 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I2 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I2)) A))) A3)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A3)) A))))
% 6.83/7.14 (assert (forall ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3)) X3)))) (=> (forall ((V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V3))) TreeList3) Summary2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X3)))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (A Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X4))) (let ((_let_4 (= X4 tptp.one_one_nat))) (let ((_let_5 (= X4 tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B2))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I2) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I2) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.83/7.14 (assert (forall ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X3)))) (=> (forall ((Uu2 tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv) Uw)) X3)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz)) X3)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X3)))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B5 Bool)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B5)) tptp.zero_zero_nat)))) (=> (forall ((Uv Bool) (Uw Bool) (N4 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N4))))) (=> (forall ((Ux tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy2) Uz)) Va3)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve2 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vc2) Vd2)) Ve2)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2)) X3))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv Bool) (Uw tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv)) Uw)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2)) Uz)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V3)) TreeList3) Vc2)) X3)))) (not (forall ((V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList3) Vd2)) X3)))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X3)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv) Uw)) Ux)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList3) S3)) X3)))))))))
% 6.83/7.14 (assert (forall ((A Bool) (B2 Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B2)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.83/7.14 (assert (forall ((A Bool) (B2 Bool) (X4 tptp.nat)) (let ((_let_1 (= X4 tptp.one_one_nat))) (let ((_let_2 (= X4 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B2)) X4) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))
% 6.83/7.14 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.83/7.14 (assert (forall ((Uv2 Bool) (Uw2 Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N)) tptp.none_nat)))
% 6.83/7.14 (assert (forall ((A Bool) (B2 Bool) (X4 tptp.nat)) (let ((_let_1 (= X4 tptp.one_one_nat))) (let ((_let_2 (= X4 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B2)) X4) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I2)))) _let_1)))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I2)))) _let_1)))))
% 6.83/7.14 (assert (forall ((Ux2 tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy) Uz2)) Va2) tptp.none_nat)))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X4 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)) X4) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X4) X4))) _let_1) TreeList2) Summary)))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 6.83/7.14 (assert (= tptp.semiri5044797733671781792omplex (lambda ((N2 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.83/7.14 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.83/7.14 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.83/7.14 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.83/7.14 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A4)) __flatten_var_0))) A) B2) tptp.one_one_complex))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A4)) __flatten_var_0))) A) B2) tptp.one_one_real))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A4)) __flatten_var_0))) A) B2) tptp.one_one_rat))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A4)) __flatten_var_0))) A) B2) tptp.one_one_nat))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A4)) __flatten_var_0))) A) B2) tptp.one_one_int))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (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))))))))))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (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))))))))))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (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))))))))))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P2))) (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))))))))))))
% 6.83/7.14 (assert (forall ((B2 Bool) (Uu3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu3) B2)) tptp.zero_zero_nat))) (and (=> B2 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= _let_1 tptp.none_nat))))))
% 6.83/7.14 (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 ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N2 tptp.nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N2) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.83/7.14 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N2 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N2) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.83/7.14 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N2 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N2) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.83/7.14 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.83/7.14 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N2 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)))))
% 6.83/7.14 (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 ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) Y3) (=> (=> (exists ((Uu2 Bool) (Uv Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv))) Y3) (=> (=> (exists ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) Y3) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y3 (not (or (= Xa Mi2) (= Xa Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V3)) TreeList3) Vc2))) (= Y3 (not (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))) (not (forall ((V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList3) Vd2))) (= Y3 (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X4) Xa)) (=> (forall ((Uu2 Bool) (Uv Bool)) (not (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa Mi2) (= Xa Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V3)) TreeList3) Vc2))) (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))) (not (forall ((V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList3) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri5044797733671781792omplex _let_1))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X4) Xa) Y3) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y3 (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv) Uw))) Y3) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz))) Y3) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y3) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2))) (= Y3 (not (=> (not (= Xa Mi2)) (=> (not (= Xa 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 Xa) _let_1))) _let_3))))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv) Uw)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (not (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList3) Summary2))) (=> (not (= Xa Mi2)) (=> (not (= Xa 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 Xa) _let_1))) _let_3))))))))))))))))))))))
% 6.83/7.14 (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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 N2)) (= A22 (@ (@ tptp.plus_plus_nat N2) N2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ 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) I2)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I2)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X6)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N2) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) 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 ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ 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) I2)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I2)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X6)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N2) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))))))
% 6.83/7.14 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 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) N4))) (=> (@ (@ 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 N4) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) 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) (N4 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) N4))) (=> (@ (@ 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 N4)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) 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) (N4 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) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M4)) (=> (= M4 N4) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M4)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _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 ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N4))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N4))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 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) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M4)) (=> (= M4 (@ tptp.suc N4)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M4)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ 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) I4)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _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 ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N4))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N4))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2)))))))))))))))))))))))))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X4 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 X4) _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)) X4) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X4) _let_2))) _let_4))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.option_nat)) (let ((_let_1 (not (= Y3 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X4) Xa) Y3) (=> (forall ((Uu2 Bool) (B5 Bool)) (=> (= X4 (@ (@ tptp.vEBT_Leaf Uu2) B5)) (=> (= Xa tptp.zero_zero_nat) (not (and (=> B5 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y3 tptp.none_nat))))))) (=> (=> (exists ((Uv Bool) (Uw Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uv) Uw))) (=> (exists ((N4 tptp.nat)) (= Xa (@ tptp.suc N4))) _let_1)) (=> (=> (exists ((Ux tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy2) Uz))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va 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 Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ 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 Xa) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Xa) Mi2))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y3 (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y3 (@ (@ (@ 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_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv) Uw)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList3) S3))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList3) S3))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) Y3) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y3 (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv) Uw))) Y3) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList3) S3))) (= Y3 (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Y3 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X4) Y3) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> B5 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y3 tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv) Uw))) (not (= Y3 tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux) Uy2) Uz))) (not (= Y3 (@ tptp.some_nat Ma2)))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Y3 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X4) Y3) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> A5 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B5 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y3 tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv) Uw))) (not (= Y3 tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux) Uy2) Uz))) (not (= Y3 (@ tptp.some_nat Mi2)))))))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.extended_enat tptp.complex))) (= (@ (@ tptp.groups4622424608036095791omplex G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_complex)))
% 6.83/7.14 (assert (forall ((G (-> tptp.extended_enat tptp.real))) (= (@ (@ tptp.groups97031904164794029t_real G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_real)))
% 6.83/7.14 (assert (forall ((G (-> tptp.extended_enat tptp.rat))) (= (@ (@ tptp.groups2245840878043517529at_rat G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_rat)))
% 6.83/7.14 (assert (forall ((G (-> tptp.extended_enat tptp.nat))) (= (@ (@ tptp.groups2880970938130013265at_nat G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_nat)))
% 6.83/7.14 (assert (forall ((G (-> tptp.extended_enat tptp.int))) (= (@ (@ tptp.groups2878480467620962989at_int G) tptp.bot_bo7653980558646680370d_enat) tptp.one_one_int)))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups4061424788464935467al_rat G) tptp.bot_bot_set_real) tptp.one_one_rat)))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.nat))) (= (@ (@ tptp.groups4696554848551431203al_nat G) tptp.bot_bot_set_real) tptp.one_one_nat)))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.int))) (= (@ (@ tptp.groups4694064378042380927al_int G) tptp.bot_bot_set_real) tptp.one_one_int)))
% 6.83/7.14 (assert (forall ((B2 Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B2)))) (and (=> B2 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu tptp.nat)) tptp.one_one_nat)) A3) tptp.one_one_nat)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu tptp.nat)) tptp.one_one_int)) A3) tptp.one_one_int)))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu tptp.int)) tptp.one_one_int)) A3) tptp.one_one_int)))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J))))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.extended_enat tptp.complex)) (A3 tptp.set_Extended_enat)) (=> (not (= (@ (@ tptp.groups4622424608036095791omplex G) A3) tptp.one_one_complex)) (not (forall ((A5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A5) A3) (= (@ G A5) tptp.one_one_complex)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.complex tptp.complex)) (A3 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups3708469109370488835omplex G) A3) tptp.one_one_complex)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A3) (= (@ G A5) tptp.one_one_complex)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.complex)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A3) tptp.one_one_complex)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A3) (= (@ G A5) tptp.one_one_complex)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.nat tptp.complex)) (A3 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A3) tptp.one_one_complex)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A3) (= (@ G A5) tptp.one_one_complex)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.int tptp.complex)) (A3 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A3) tptp.one_one_complex)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A3) (= (@ G A5) tptp.one_one_complex)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.extended_enat tptp.real)) (A3 tptp.set_Extended_enat)) (=> (not (= (@ (@ tptp.groups97031904164794029t_real G) A3) tptp.one_one_real)) (not (forall ((A5 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat A5) A3) (= (@ G A5) tptp.one_one_real)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.complex tptp.real)) (A3 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups766887009212190081x_real G) A3) tptp.one_one_real)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A3) (= (@ G A5) tptp.one_one_real)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.real)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A3) tptp.one_one_real)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A3) (= (@ G A5) tptp.one_one_real)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.nat tptp.real)) (A3 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A3) tptp.one_one_real)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A3) (= (@ G A5) tptp.one_one_real)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.int tptp.real)) (A3 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A3) tptp.one_one_real)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A3) (= (@ G A5) tptp.one_one_real)))))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (= (@ G X3) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A3) tptp.one_one_nat))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (= (@ G X3) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G) A3) tptp.one_one_int))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (= (@ G X3) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) A3) tptp.one_one_int))))
% 6.83/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat (@ G X)) (@ H2 X)))) A3) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A3)) (@ (@ tptp.groups708209901874060359at_nat H2) A3)))))
% 6.83/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.times_times_int (@ G X)) (@ H2 X)))) A3) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A3)) (@ (@ tptp.groups705719431365010083at_int H2) A3)))))
% 6.83/7.14 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.times_times_int (@ G X)) (@ H2 X)))) A3) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A3)) (@ (@ tptp.groups1705073143266064639nt_int H2) A3)))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) N) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.power_power_nat (@ F X)) N))) A3))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A3)) N) (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.power_power_int (@ F X)) N))) A3))))
% 6.83/7.14 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A3)) N) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.power_power_int (@ F X)) N))) A3))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real)) (G (-> tptp.extended_enat tptp.real))) (=> (forall ((I3 tptp.extended_enat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Extended_enat I3) A3) (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.groups97031904164794029t_real F) A3)) (@ (@ tptp.groups97031904164794029t_real G) A3)))))
% 6.83/7.14 (assert (forall ((A3 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) A3) (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) A3)) (@ (@ tptp.groups766887009212190081x_real G) A3)))))
% 6.83/7.14 (assert (forall ((A3 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) A3) (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) A3)) (@ (@ tptp.groups1681761925125756287l_real G) A3)))))
% 6.83/7.14 (assert (forall ((A3 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) A3) (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) A3)) (@ (@ tptp.groups129246275422532515t_real G) A3)))))
% 6.83/7.14 (assert (forall ((A3 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) A3) (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) A3)) (@ (@ tptp.groups2316167850115554303t_real G) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat)) (G (-> tptp.extended_enat tptp.rat))) (=> (forall ((I3 tptp.extended_enat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Extended_enat I3) A3) (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.groups2245840878043517529at_rat F) A3)) (@ (@ tptp.groups2245840878043517529at_rat G) A3)))))
% 6.83/7.14 (assert (forall ((A3 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) A3) (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) A3)) (@ (@ tptp.groups225925009352817453ex_rat G) A3)))))
% 6.83/7.14 (assert (forall ((A3 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) A3) (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) A3)) (@ (@ tptp.groups4061424788464935467al_rat G) A3)))))
% 6.83/7.14 (assert (forall ((A3 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) A3) (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) A3)) (@ (@ tptp.groups73079841787564623at_rat G) A3)))))
% 6.83/7.14 (assert (forall ((A3 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) A3) (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) A3)) (@ (@ tptp.groups1072433553688619179nt_rat G) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups97031904164794029t_real F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (forall ((X3 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups2245840878043517529at_rat F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A3)))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.real))) (=> (forall ((X3 tptp.extended_enat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_Extended_enat X3) A3) (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.groups97031904164794029t_real F) A3)) tptp.one_one_real))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_complex X3) A3) (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) A3)) tptp.one_one_real))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) A3) (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) A3)) tptp.one_one_real))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A3) (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) A3)) tptp.one_one_real))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A3) (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) A3)) tptp.one_one_real))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_Extended_enat) (F (-> tptp.extended_enat tptp.rat))) (=> (forall ((X3 tptp.extended_enat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_Extended_enat X3) A3) (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.groups2245840878043517529at_rat F) A3)) tptp.one_one_rat))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_complex X3) A3) (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) A3)) tptp.one_one_rat))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_real X3) A3) (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) A3)) tptp.one_one_rat))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A3) (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) A3)) tptp.one_one_rat))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A3) (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) A3)) tptp.one_one_rat))))
% 6.83/7.14 (assert (forall ((A Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A) B2)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B2 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= _let_1 tptp.none_nat))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X4) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B5))) (=> (= X4 _let_1) (=> (= Xa tptp.zero_zero_nat) (=> (and (=> B5 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y3 tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv Bool) (Uw Bool)) (=> (= X4 (@ (@ tptp.vEBT_Leaf Uv) Uw)) (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.suc N4))) (=> (= Xa _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv) Uw)) _let_1))))))))) (=> (forall ((Ux tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy2) Uz))) (=> (= X4 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X4 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) (=> (= X4 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (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 Xa) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ 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 Xa) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Xa) Mi2))) (=> (= X4 _let_2) (=> (and (=> _let_12 (= Y3 (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y3 (@ (@ (@ 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_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X4) (@ 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 X4) tptp.one_one_real)) (@ tptp.suc N2))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ tptp.arctan X4) (@ 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 X4) _let_1))))))))))
% 6.83/7.14 (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)))))))))))))
% 6.83/7.14 (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)))))))))))))
% 6.83/7.14 (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)))))))))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.83/7.14 (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)))))))))))))
% 6.83/7.14 (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)))))))))))))
% 6.83/7.14 (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)))))))))))))
% 6.83/7.14 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.83/7.14 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.83/7.14 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.83/7.14 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.83/7.14 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.83/7.14 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N2) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N2)))))))
% 6.83/7.14 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N2) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N2)))))))
% 6.83/7.14 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N2) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N2)))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X4) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv) Uw))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (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 Xa) _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) Xa)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X4 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa)) (=> (not (= Xa Mi2)) (=> (not (= Xa 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 Xa) _let_2))) _let_4))))))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X4) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X4 _let_1) (=> (= Y3 (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))))) (=> (forall ((Uu2 tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv) Uw))) (=> (= X4 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz))) (=> (= X4 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X4 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (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 Xa) _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) Xa)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (=> (= X4 _let_2) (=> (= Y3 (=> (not (= Xa Mi2)) (=> (not (= Xa 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 Xa) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X4 _let_1) (=> (= Y3 (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv) Uw))) (=> (= X4 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X4 _let_2) (=> (= Y3 (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X4) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (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 Xa) _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) Xa)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X4 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa)) (not (=> (not (= Xa Mi2)) (=> (not (= Xa 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 Xa) _let_2))) _let_4))))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv) Uw))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv))) (=> (= X4 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) (=> (= X4 _let_1) (=> (not Y3) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X4 _let_1) (=> (= Y3 (or (= Xa Mi2) (= Xa Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) 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 Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X4 _let_2) (=> (= Y3 (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))) (not (forall ((V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (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 Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X4 _let_2) (=> (= Y3 (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X4) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (or (= Xa Mi2) (= Xa Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))) (not (forall ((V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (or (= Xa Mi2) (= Xa Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))) (not (forall ((V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))))))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 6.83/7.14 (assert (forall ((Q2 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R2)) (= R2 tptp.zero_zero_nat))))
% 6.83/7.14 (assert (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R2)) (= R2 tptp.zero_zero_int))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 6.83/7.14 (assert (forall ((B2 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 B2) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B2) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B2)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) 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 X4) _let_1)))))))))
% 6.83/7.14 (assert (forall ((B2 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) B2) (=> (@ (@ (@ tptp.eucl_rel_int A) B2) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B2)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_num) (Ys2 tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs2) Ys2)) N) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys2)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ 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) Ys2)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys2)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys2)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys2))) (=> (@ (@ 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) Ys2)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys2))) (=> (@ (@ 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) Ys2)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys2))) (=> (@ (@ 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) Ys2)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys2))) (=> (@ (@ 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) Ys2)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (Ys2 tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys2))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr8326237132889035090at_num (@ (@ tptp.product_nat_num Xs2) Ys2)) N) (@ (@ tptp.product_Pair_nat_num (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys2) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys2 tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_o Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys2 tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_nat Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys2 tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_int Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_o) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_o) (Ys2 tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs2) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_o Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_o) (Ys2 tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs2) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_nat Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_o) (Ys2 tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs2) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_int Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_nat) (Ys2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys2)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.list_nat) (Ys2 tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs2) Ys2)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_size_list_o Ys2)))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B2))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= Q2 Q5))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B2))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= R2 R4))))))
% 6.83/7.14 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N4))) (@ G N4))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I3)) tptp.one_one_real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ F I2)) (@ (@ tptp.power_power_real Z) I2))))))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 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) B2) (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (not (= B2 tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ 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 B2) R2))))))))))
% 6.83/7.14 (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)))))))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 tptp.zero_zero_int) (= A32 (@ (@ 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) (= A32 (@ (@ 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) (= A32 (@ (@ 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))))))))
% 6.83/7.14 (assert (forall ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A33) (=> (=> (= A23 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q3 tptp.int)) (=> (= A33 (@ (@ 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)) (=> (= A33 (@ (@ 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)))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Xa tptp.int) (Y3 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 X4)) (not (@ _let_2 Xa)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X4) _let_4) (@ (@ tptp.member_int Xa) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X4) Xa) Y3) (and (=> _let_5 (= Y3 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y3 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X4) _let_1)) (@ (@ tptp.divide_divide_int Xa) _let_1)))))))))))))))
% 6.83/7.14 (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))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y3 (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X4) Y3) (=> (=> (= X4 tptp.zero_zero_nat) _let_1) (=> (=> (= X4 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X4 _let_2) (not (and (=> _let_8 (= Y3 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y3 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 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 X4) _let_1))))) (@ tptp.sin_real X4))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I2)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I2) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J3))))))
% 6.83/7.14 (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))
% 6.83/7.14 (assert (forall ((G (-> tptp.nat tptp.real)) (X4 tptp.real)) (=> (@ (@ tptp.sums_real G) X4) (@ (@ 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)))))) X4))))
% 6.83/7.14 (assert (forall ((G (-> tptp.nat tptp.real)) (X4 tptp.real) (F (-> tptp.nat tptp.real)) (Y3 tptp.real)) (=> (@ (@ tptp.sums_real G) X4) (=> (@ (@ tptp.sums_real F) Y3) (@ (@ 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 X4) Y3))))))
% 6.83/7.14 (assert (forall ((X4 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 X4) _let_1))))) (@ tptp.cos_real X4))))
% 6.83/7.14 (assert (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Xa tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X4) Xa)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X4)) (not (@ _let_3 Xa)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X4) _let_5) (@ (@ tptp.member_int Xa) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X4) Xa) Y3) (=> _let_1 (not (=> (and (=> _let_6 (= Y3 (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y3 (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X4) _let_2)) (@ (@ tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))))
% 6.83/7.14 (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))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Z tptp.nat) (A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X4) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A3) Z) (=> (@ tptp.finite_finite_nat B4) (=> (= A3 B4) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A3) X4) X_1))))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_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 A) X5))))))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 6.83/7.14 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N8) (@ (@ tptp.ord_less_nat X) M6)))))))
% 6.83/7.14 (assert (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N3) (@ (@ tptp.ord_less_nat X3) N))) (@ tptp.finite_finite_nat N3))))
% 6.83/7.14 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N8) (@ (@ tptp.ord_less_eq_nat X) M6)))))))
% 6.83/7.14 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I)))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N4) (@ F N4))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) U)))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N3))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat N) _let_1))))))
% 6.83/7.14 (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) (L3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L3)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L3) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))) (@ (@ P K2) L3)))))) (@ (@ P A0) A12)))))
% 6.83/7.14 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) K))))))
% 6.83/7.14 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K))))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L2) U))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_int A) I2) (@ (@ tptp.ord_less_int I2) B2)))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_int A) I2) (@ (@ tptp.ord_less_eq_int I2) B2)))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I2) (@ (@ tptp.ord_less_int I2) B2)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (not (@ (@ tptp.member_nat N) A3)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A3)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A3)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ 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))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I2) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ 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))))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A3)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A3))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_real X4) T2) (@ (@ tptp.ord_less_real T2) tptp.zero_zero_real) (= (@ tptp.cos_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T2) (@ (@ 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 X4) N))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_real T2) X4) (= (@ tptp.cos_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T2) (@ (@ 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 X4) N))))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_real T2) X4) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T2) (@ (@ 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 X4) N))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_eq_real T2) X4) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T2) (@ (@ 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 X4) N)))))))))
% 6.83/7.14 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K))))
% 6.83/7.14 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 6.83/7.14 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))) tptp.zero_zero_complex))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.83/7.14 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B8 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)) (@ F I2)) (@ G I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)) tptp.one_one_nat)))) _let_1))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (N tptp.nat)) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T2)) (@ tptp.abs_abs_real X4)) (= (@ tptp.exp_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X4) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X4)) N)))))
% 6.83/7.14 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) X)) (@ (@ 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)))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (N tptp.nat)) (=> (not (= X4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T2 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T2))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X4)) (= (@ tptp.exp_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X4) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N)))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (N tptp.nat)) (exists ((T2 tptp.real)) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T2) (@ (@ 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 X4) N)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (N tptp.nat)) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T2)) (@ tptp.abs_abs_real X4)) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T2) (@ (@ 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 X4) N))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (N tptp.nat)) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T2)) (@ tptp.abs_abs_real X4)) (= (@ tptp.cos_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T2) (@ (@ 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 X4) N))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K3))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))))))
% 6.83/7.14 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K))))
% 6.83/7.14 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.83/7.14 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 6.83/7.14 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B2)) 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 B2) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B2 (-> tptp.nat tptp.nat)) (X4 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) (= (@ B2 J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I2)) (@ (@ tptp.power_power_nat X4) I2)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B2 J3)) (@ (@ tptp.power_power_nat X4) 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)) (@ B2 (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_nat I2) (@ (@ tptp.binomial N) I2)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.83/7.14 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) N2)))
% 6.83/7.14 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.83/7.14 (assert (forall ((R2 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.real_V2046097035970521341omplex R2) (@ (@ tptp.complex2 A) B2)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B2))))))
% 6.83/7.14 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C))))))))
% 6.83/7.14 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M6 tptp.int)) (exists ((N2 tptp.int)) (and (@ (@ tptp.ord_less_int M6) (@ tptp.abs_abs_int N2)) (@ (@ tptp.member_int N2) S2)))))))
% 6.83/7.14 (assert (= tptp.arg (lambda ((Z5 tptp.complex)) (@ (@ (@ tptp.if_real (= Z5 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z5) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X4) X4)))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X4) (@ _let_1 Y3)) (= X4 Y3))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X4) tptp.zero_zero_real)))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_real X4) Y3))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y3)) (@ (@ tptp.ord_less_eq_real X4) Y3))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X4) tptp.one_one_real) (= X4 tptp.one_one_real)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Y3 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) Y3)) (@ _let_1 Y3))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Y3 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) Y3)) (@ _let_1 Y3))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Y3 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) Y3)) (@ _let_1 Y3))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Y3 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) Y3)) (@ _let_1 Y3))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X4)) N) X4)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X4)) (@ tptp.uminus_uminus_real (@ _let_1 X4))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.inverse_inverse_real X4)) (@ tptp.inverse_inverse_real (@ _let_1 X4))))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N))) (= (@ _let_1 (@ _let_2 X4)) (@ _let_2 (@ _let_1 X4)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X4) Y3)) (@ (@ tptp.times_times_real (@ _let_1 X4)) (@ _let_1 Y3))))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat) (X4 tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X4) (@ (@ tptp.root M) (@ (@ tptp.root N) X4)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y3)) (@ (@ tptp.divide_divide_real (@ _let_1 X4)) (@ _let_1 Y3))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.root N) X4))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ _let_1 X4)) (@ _let_1 Y3)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y3)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 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 X4) K)) (@ (@ tptp.power_power_real (@ _let_1 X4)) K))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X4)) (@ tptp.abs_abs_real (@ _let_1 X4)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X4)) (@ tptp.sgn_sgn_real X4)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.root N) X4)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (N3 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real (@ (@ tptp.root N3) X4)) (@ (@ tptp.root N) X4)))))))
% 6.83/7.14 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y3) N))) (@ tptp.abs_abs_real Y3)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X4))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (N3 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X4)) (@ (@ tptp.root N3) X4))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (N3 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N3) X4)) (@ (@ tptp.root N) X4)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X4)) N) X4)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Y3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (=> (= (@ (@ tptp.power_power_real Y3) N) X4) (= (@ (@ tptp.root N) X4) Y3))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X4) N)) X4)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X4)) N) X4))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Y3 tptp.real) (X4 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y3) N) X4) (= (@ (@ tptp.root N) X4) Y3)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X4) N)) X4))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (N3 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X4)) (@ (@ tptp.root N3) X4))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X4))) (=> (@ (@ 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)) X4)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y3)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y3)) N))) Y3))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B2)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ tptp.log B2))) (=> (@ (@ 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))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (B2 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B2) (= (@ (@ tptp.log (@ (@ tptp.root N) B2)) X4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B2) X4)))))))
% 6.83/7.14 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X4 tptp.real)) (= (@ P (@ (@ tptp.root N) X4)) (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)) X4) (@ P Y))))))))
% 6.83/7.14 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M6 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (@ (@ tptp.member_nat N2) S2)))))))
% 6.83/7.14 (assert (forall ((K tptp.nat) (S2 tptp.set_nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M4) (exists ((N6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N6) (@ (@ tptp.member_nat N6) S2))))) (not (@ tptp.finite_finite_nat S2)))))
% 6.83/7.14 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M6 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.member_nat N2) S2)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.root N) X4) (@ (@ tptp.powr_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X4 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 X4) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X4 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X4) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X4) (@ (@ 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)))))))))))))
% 6.83/7.14 (assert (forall ((X4 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 X4) _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) X4) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X4 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X4) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X4) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X4) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 6.83/7.14 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B2)) (and (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 6.83/7.14 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B2 tptp.zero_zero_nat)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 6.83/7.14 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X4 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (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 X4) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X4))) (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) X4) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= X4 Mi) (= X4 Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X4) 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)))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X4) Xa) Y3) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa tptp.one_one_nat))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= X4 _let_2) (not (and (=> _let_4 (= Y3 (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y3 (@ _let_1 true))) (=> (not _let_3) (= Y3 _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) (=> (= X4 _let_1) (not (= Y3 _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (=> (= X4 _let_1) (not (= Y3 _let_1))))) (=> (forall ((V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V3)))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2)) (not (= Y3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa) Xa))) _let_1) TreeList3) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (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 Xa) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X4 _let_2) (not (= Y3 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa Mi2) (= Xa Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa) 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))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X4) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa tptp.one_one_nat))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= X4 _let_2) (=> (and (=> _let_4 (= Y3 (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y3 (@ _let_1 true))) (=> (not _let_3) (= Y3 _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3))) (=> (= X4 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3))) (=> (= X4 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((V3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (= X4 _let_2) (=> (= Y3 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa) Xa))) _let_1) TreeList3) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (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 Xa) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X4 _let_2) (=> (= Y3 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa Mi2) (= Xa Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa) 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) Xa))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 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 (= Y3 (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X4) Y3) (=> (@ _let_2 X4) (=> (=> (= X4 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X4 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X4 _let_1) (=> (and (=> _let_8 (= Y3 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y3 (@ (@ _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)))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 6.83/7.14 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2))))))
% 6.83/7.14 (assert (= tptp.arctan (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X 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)) X) (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.tan_real X) Y))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X4) (@ tptp.the_real (lambda ((X tptp.real)) false))))))
% 6.83/7.14 (assert (= tptp.arccos (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.cos_real X) Y)))))))
% 6.83/7.14 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N2)) (@ (@ tptp.modulo_modulo_nat M6) N2)))))
% 6.83/7.14 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real))))))
% 6.83/7.14 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real)))))))
% 6.83/7.14 (assert (= tptp.arcsin (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X 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)) X) (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.sin_real X) Y))))))))
% 6.83/7.14 (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))))))))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) (and (@ _let_1 K) (@ _let_1 L2))))))
% 6.83/7.14 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y3) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X4) Y3)))))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y3)) (@ (@ tptp.bit_se1409905431419307370or_int X4) Y3)) (@ (@ tptp.plus_plus_int X4) Y3))))
% 6.83/7.14 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L))))))
% 6.83/7.14 (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)))
% 6.83/7.14 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L)))))
% 6.83/7.14 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (N tptp.nat) (Y3 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) X4) (=> (@ (@ tptp.ord_less_int X4) _let_1) (=> (@ (@ tptp.ord_less_int Y3) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X4) Y3)) _let_1)))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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)))))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (forall ((Y3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.83/7.14 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.83/7.14 (assert (forall ((Y3 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y3))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.83/7.14 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.83/7.14 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.83/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y3 tptp.num)) (let ((_let_1 (= Xa tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y3 tptp.one))))) (let ((_let_3 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X4) Xa) Y3) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit0 M4)) (not (= Y3 (@ tptp.bit1 M4)))))) (=> (=> _let_3 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (not (= Y3 _let_1)))))) (=> (=> (exists ((N4 tptp.num)) (= X4 (@ tptp.bit0 N4))) (=> _let_1 (not (= Y3 (@ tptp.bit0 tptp.one))))) (=> (forall ((N4 tptp.num)) (=> (= X4 (@ tptp.bit0 N4)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit0 M4)) (not (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M4)))))))) (=> (forall ((N4 tptp.num)) (=> (= X4 (@ tptp.bit0 N4)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit1 M4)) (not (= Y3 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N4) M4)))))))) (=> (=> (exists ((N4 tptp.num)) (= X4 (@ tptp.bit1 N4))) _let_2) (=> (forall ((N4 tptp.num)) (=> (= X4 (@ tptp.bit1 N4)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit0 M4)) (not (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M4)))))))) (not (forall ((N4 tptp.num)) (=> (= X4 (@ tptp.bit1 N4)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit1 M4)) (not (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M4)))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N) M))))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.83/7.14 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ 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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L2) U))))
% 6.83/7.14 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L2) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 6.83/7.14 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 6.83/7.14 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N3))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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)))))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B2 (-> 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 (@ B2 J2)) (@ B2 I3))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I2)) (@ B2 I2)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B2) _let_1))))))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L2) U))))
% 6.83/7.14 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L2) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L2) U))))
% 6.83/7.14 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.83/7.14 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.83/7.14 (assert (forall ((Uu3 Bool) (Uv2 Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu3) Uv2)) D) (= D tptp.one_one_nat))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.csqrt Z)) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.83/7.14 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 6.83/7.14 (assert (forall ((Z tptp.complex) (N tptp.nat)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex) (R2 tptp.real)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R2))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) R2))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.numeral_numeral_real W)))))
% 6.83/7.14 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.83/7.14 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L2) L2)))
% 6.83/7.14 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.14 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L2) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.14 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) L2) (@ tptp.uminus1351360451143612070nteger L2))))
% 6.83/7.14 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.83/7.14 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X4)) (@ tptp.real_V1022390504157884413omplex X4))))
% 6.83/7.14 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X4) Y3)) (@ (@ tptp.plus_plus_real (@ tptp.re X4)) (@ tptp.re Y3)))))
% 6.83/7.14 (assert (forall ((R2 tptp.real) (X4 tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X4)) (@ (@ tptp.times_times_real R2) (@ tptp.re X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.re (@ (@ tptp.minus_minus_complex X4) Y3)) (@ (@ tptp.minus_minus_real (@ tptp.re X4)) (@ tptp.re Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X4))) (@ tptp.real_V1022390504157884413omplex X4))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 6.83/7.14 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.re Z))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real _let_1) _let_2)) tptp.zero_zero_real) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (= tptp.csqrt (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z5))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z5))) (let ((_let_4 (@ tptp.im Z5))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.im Z))) (= (@ tptp.im (@ tptp.csqrt Z)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_1 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_1))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.re Z))))
% 6.83/7.14 (assert (forall ((Z tptp.complex) (R2 tptp.real)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R2))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) R2))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X4) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X4) N)) (@ (@ tptp.power_power_real (@ tptp.re X4)) N)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.numeral_numeral_real W)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex) (N tptp.nat)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.re X4))) (=> (= (@ tptp.im X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X4) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.im X4))) (=> (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 X4)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X4)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.re X4))) (=> (= (@ tptp.im X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X4) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 6.83/7.14 (assert (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int Xa) X4)))))
% 6.83/7.14 (assert (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ tptp.code_integer_of_int (@ (@ tptp.modulo_modulo_int Xa) X4)))))
% 6.83/7.14 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.83/7.14 (assert (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ (@ tptp.ord_less_int Xa) X4))))
% 6.83/7.14 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K3)) K3))))
% 6.83/7.14 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 6.83/7.14 (assert (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int Xa) X4)))))
% 6.83/7.14 (assert (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa) X4)))))
% 6.83/7.14 (assert (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ tptp.code_integer_of_int (@ (@ tptp.minus_minus_int Xa) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X4) Y3)) (@ (@ tptp.plus_plus_real (@ tptp.im X4)) (@ tptp.im Y3)))))
% 6.83/7.14 (assert (forall ((R2 tptp.real) (X4 tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X4)) (@ (@ tptp.times_times_real R2) (@ tptp.im X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.im (@ (@ tptp.minus_minus_complex X4) Y3)) (@ (@ tptp.minus_minus_real (@ tptp.im X4)) (@ tptp.im Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X4))) (@ tptp.real_V1022390504157884413omplex X4))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X4) Y3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X4)) (@ tptp.im Y3))) (@ (@ tptp.times_times_real (@ tptp.im X4)) (@ tptp.re Y3))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (=> (= (@ tptp.re X4) (@ tptp.re Y3)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y3)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X4))) (@ tptp.abs_abs_real (@ tptp.im Y3)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (=> (= (@ tptp.im X4) (@ tptp.im Y3)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y3)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X4))) (@ tptp.abs_abs_real (@ tptp.re Y3)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X4) Y3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X4)) (@ tptp.re Y3))) (@ (@ tptp.times_times_real (@ tptp.im X4)) (@ tptp.im Y3))))))
% 6.83/7.14 (assert (= tptp.plus_plus_complex (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y))) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y))))))
% 6.83/7.14 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X))) (@ _let_1 (@ tptp.im X)))))))
% 6.83/7.14 (assert (= tptp.minus_minus_complex (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ tptp.re X)) (@ tptp.re Y))) (@ (@ tptp.minus_minus_real (@ tptp.im X)) (@ tptp.im Y))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.csqrt Z))) (let ((_let_2 (@ tptp.re _let_1))) (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (and (= _let_2 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im _let_1))))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.cos_real (@ tptp.im Z))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.sin_real (@ tptp.im Z))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (= tptp.times_times_complex (lambda ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.re Y))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X)))) (let ((_let_3 (@ tptp.im Y))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X)))) (@ (@ 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))))))))))
% 6.83/7.14 (assert (= tptp.exp_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z5)))) (@ tptp.cis (@ tptp.im Z5))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X4) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X4))) (@ tptp.im X4))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X4) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X4)) _let_1))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= Z tptp.zero_zero_complex) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)) tptp.zero_zero_real)))))
% 6.83/7.14 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z5)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z5)) _let_1)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X4))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X4)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X4)) _let_1))))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (= Z tptp.zero_zero_complex)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y3))) (let ((_let_3 (@ tptp.re Y3))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X4) Y3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X4)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X4)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.83/7.14 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.re W))) (=> (= (@ (@ tptp.power_power_complex W) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im W)))) (= (@ tptp.csqrt Z) W))))))
% 6.83/7.14 (assert (forall ((B2 tptp.complex)) (let ((_let_1 (@ tptp.re B2))) (=> (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 B2)))) (= (@ tptp.csqrt (@ (@ tptp.power_power_complex B2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) B2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X4))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X4)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y3))) (let ((_let_3 (@ tptp.re Y3))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X4) Y3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X4)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X4)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z)))) (@ (@ tptp.times_times_real (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.real_V1022390504157884413omplex Z))) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.re Z)) _let_2)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.im Z)) _let_2)) _let_1)) tptp.one_one_real))))))
% 6.83/7.14 (assert (= tptp.invers8013647133539491842omplex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (let ((_let_3 (@ tptp.re X))) (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)))))))))
% 6.83/7.14 (assert (= tptp.divide1717551699836669952omplex (lambda ((X 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 X)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X)))) (@ (@ 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)))))))))))
% 6.83/7.14 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R2))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.83/7.14 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R2)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.83/7.14 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) R2)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.re R2))))))
% 6.83/7.14 (assert (forall ((Y3 tptp.complex) (X4 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X4) tptp.real_V2521375963428798218omplex) (= (= X4 (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y3)) (and (= X4 tptp.zero_zero_complex) (= Y3 tptp.zero_zero_complex)))))))
% 6.83/7.14 (assert (forall ((Y3 tptp.complex) (X4 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X4) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y3) X4) (and (= X4 tptp.zero_zero_complex) (= Y3 tptp.zero_zero_complex)))))))
% 6.83/7.14 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) R2)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.re R2))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.minus_minus_complex Z) (@ tptp.cnj Z)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.im Z)))) tptp.imaginary_unit))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X4) Y3)) (@ (@ tptp.times_times_complex (@ tptp.cnj X4)) (@ tptp.cnj Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.divide1717551699836669952omplex X4) Y3)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cnj X4)) (@ tptp.cnj Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.plus_plus_complex X4) Y3)) (@ (@ tptp.plus_plus_complex (@ tptp.cnj X4)) (@ tptp.cnj Y3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.minus_minus_complex X4) Y3)) (@ (@ tptp.minus_minus_complex (@ tptp.cnj X4)) (@ tptp.cnj Y3)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B2)) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2))) tptp.zero_zero_real))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B2)) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2))) tptp.zero_zero_real))))
% 6.83/7.14 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z5 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z5) (@ tptp.cnj Z5)))))))
% 6.83/7.14 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B2))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2)))) tptp.zero_zero_real))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B2))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2))))))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B2))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2))))))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B2))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2)))) tptp.zero_zero_real))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B2))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2)))) tptp.zero_zero_real))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B2))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2))))))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B2))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2))))))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B2))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2)))) tptp.zero_zero_real))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.83/7.14 (assert (forall ((A tptp.complex) (B2 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex A) (@ tptp.cnj B2)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.divide1717551699836669952omplex A) B2))) (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)))))))))
% 6.83/7.14 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)))))
% 6.83/7.14 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re Z))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (assert (forall ((Z tptp.complex) (W tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex Z) (@ tptp.cnj W)))) (= (@ (@ tptp.plus_plus_complex _let_1) (@ (@ tptp.times_times_complex (@ tptp.cnj Z)) W)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re _let_1)))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K3) L)) (@ (@ tptp.modulo364778990260209775nteger K3) L)))))
% 6.83/7.14 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.ord_less_nat I2) N)))) N)))
% 6.83/7.14 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I2) N)))) (@ tptp.suc N))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L2))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L2)))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L2)) tptp.one_one_int)))))
% 6.83/7.14 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 6.83/7.14 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 6.83/7.14 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 6.83/7.14 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A3))))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) _let_1) (= A3 _let_1)))))
% 6.83/7.14 (assert (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N3)) N))))
% 6.83/7.14 (assert (forall ((S2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) S2))))
% 6.83/7.14 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))) N)))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) N))))
% 6.83/7.14 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S4))) (= S4 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L) S4)))))) _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) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L)) S4)))))) _let_1))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Y3 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X4) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X4) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_1) (=> (and (=> B5 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y3 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv) Uw))) (=> (= X4 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux) Uy2) Uz))) (=> (= X4 _let_1) (=> (= Y3 (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Y3 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X4) Y3) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X4) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_1) (=> (and (=> A5 (= Y3 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B5 (= Y3 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y3 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv) Uw))) (=> (= X4 _let_1) (=> (= Y3 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux) Uy2) Uz))) (=> (= X4 _let_1) (=> (= Y3 (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 6.83/7.14 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M6 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M6) K3)) (@ (@ tptp.product_Pair_nat_nat M6) (@ (@ tptp.minus_minus_nat K3) M6))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M6) _let_1)))))))
% 6.83/7.14 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu tptp.nat)) false)) Nat))))
% 6.83/7.14 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu tptp.nat)) true)) Nat))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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 ((M2 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M2) N)))) M)))))
% 6.83/7.14 (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 ((M2 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M2)))) M)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X4))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa) X4))) (=> (= (@ (@ tptp.nat_prod_decode_aux X4) Xa) Y3) (and (=> _let_2 (= Y3 (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X4) Xa)))) (=> (not _let_2) (= Y3 (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa) _let_1))))))))))
% 6.83/7.14 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X23 tptp.nat)) X23))))
% 6.83/7.14 (assert (= tptp.archim6058952711729229775r_real (lambda ((X tptp.real)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))
% 6.83/7.14 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X tptp.rat)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z5)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N) K)) (@ _let_1 K)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.modulo_modulo_nat M) N))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (not (forall ((S3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S3) (forall ((T2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T2) (not (= R2 (@ (@ tptp.plus_plus_rat S3) T2)))))))))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N) M)) K)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P2)) (@ (@ 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 P2)))))
% 6.83/7.14 (assert (forall ((Q2 tptp.int) (P2 tptp.int)) (=> (@ (@ tptp.ord_less_int Q2) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P2)) (@ tptp.uminus_uminus_int Q2)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_integer K) L2)) (@ (@ tptp.modulo364778990260209775nteger K) L2))))
% 6.83/7.14 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_abs K) L2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L2)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 6.83/7.14 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R2)))))
% 6.83/7.14 (assert (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R5)))))
% 6.83/7.14 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))
% 6.83/7.14 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P2) 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 P2)))))
% 6.83/7.14 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P2) 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 P2)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P2) 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 P2)))))
% 6.83/7.14 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P2) 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 P2)))))
% 6.83/7.14 (assert (forall ((R2 tptp.rat) (P2 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.83/7.14 (assert (forall ((R2 tptp.product_prod_int_int) (P2 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.83/7.14 (assert (forall ((Q2 tptp.int) (S tptp.int) (P2 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S))) (= (@ (@ tptp.times_times_int P2) S) (@ (@ tptp.times_times_int R2) Q2)))))))
% 6.83/7.14 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N))))))))
% 6.83/7.14 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc8508995932063986495nteger (@ (@ tptp.code_divmod_integer K) L2)) (@ (@ tptp.divide6298287555418463151nteger K) L2))))
% 6.83/7.14 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc8508995932063986495nteger (@ (@ tptp.code_divmod_abs K) L2)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L2)))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N)))))))
% 6.83/7.14 (assert (= tptp.adjust_mod (lambda ((L tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L) R5)))))
% 6.83/7.14 (assert (= tptp.bezw (lambda ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) 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 X) Y)))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X4) Xa) Y3) (and (=> _let_3 (= Y3 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y3 (@ (@ 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 X4) Xa))))))))))))))
% 6.83/7.14 (assert (forall ((Y3 tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y3) (@ (@ tptp.modulo_modulo_nat X4) Y3)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y3) (= (@ (@ tptp.bezw X4) Y3) (@ (@ 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 X4) Y3)))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X4) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X4) Xa) Y3) (=> _let_1 (not (=> (and (=> _let_4 (= Y3 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y3 (@ (@ 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 X4) Xa)))))))) (not _let_1)))))))))))
% 6.83/7.14 (assert (= tptp.normalize (lambda ((P3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P3))) (let ((_let_2 (@ tptp.product_fst_int_int P3))) (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)))))))))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M) N)) (or (not (= M tptp.zero_zero_int)) (not (= N tptp.zero_zero_int))))))
% 6.83/7.14 (assert (= tptp.gcd_gcd_int (lambda ((X tptp.int) (Y tptp.int)) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X) Y)))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (exists ((U3 tptp.int) (V3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U3) X4)) (@ (@ tptp.times_times_int V3) Y3)) (@ (@ tptp.gcd_gcd_int X4) Y3)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B2)) A))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B2)) B2))))
% 6.83/7.14 (assert (forall ((Y3 tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y3) (= (@ (@ tptp.gcd_gcd_int X4) Y3) (@ (@ tptp.gcd_gcd_int Y3) (@ (@ tptp.modulo_modulo_int X4) Y3))))))
% 6.83/7.14 (assert (= tptp.gcd_gcd_int (lambda ((K3 tptp.int) (L tptp.int)) (@ tptp.abs_abs_int (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K3) (@ (@ tptp.gcd_gcd_int L) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int K3)) (@ tptp.abs_abs_int L))))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X4) Xa)))) (let ((_let_2 (@ tptp.suc X4))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa) X4))) (=> (= (@ (@ tptp.nat_prod_decode_aux X4) Xa) Y3) (=> _let_1 (not (=> (and (=> _let_3 (= Y3 (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X4) Xa)))) (=> (not _let_3) (= Y3 (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa) _let_2))))) (not _let_1))))))))))
% 6.83/7.14 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S2))) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N6) (@ tptp.finite_card_nat S2)) (@ (@ tptp.member_nat (@ R3 N6)) S2))))))))
% 6.83/7.14 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 6.83/7.14 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (= tptp.gcd_gcd_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X) Y)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (=> (not (= B2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B2)) B2))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B2)) A))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((Y3 tptp.nat) (X4 tptp.nat)) (=> (not (= Y3 tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X4) Y3) (@ (@ tptp.gcd_gcd_nat Y3) (@ (@ tptp.modulo_modulo_nat X4) Y3))))))
% 6.83/7.14 (assert (= tptp.gcd_gcd_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ (@ tptp.if_nat (= Y tptp.zero_zero_nat)) X) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X) Y))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X4) Xa) Y3) (and (=> _let_1 (= Y3 X4)) (=> (not _let_1) (= Y3 (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa)))))))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B2) Y4)) (@ (@ tptp.gcd_gcd_nat A) B2)))))))
% 6.83/7.14 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (exists ((X3 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B2))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y4))) (let ((_let_4 (@ tptp.times_times_nat B2))) (let ((_let_5 (@ _let_4 X3))) (let ((_let_6 (@ _let_4 Y4))) (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)))))))))))))
% 6.83/7.14 (assert (= tptp.gcd_gcd_Code_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ tptp.abs_abs_Code_integer (@ (@ (@ tptp.if_Code_integer (= L tptp.zero_z3403309356797280102nteger)) K3) (@ (@ tptp.gcd_gcd_Code_integer L) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K3)) (@ tptp.abs_abs_Code_integer L))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X4) Y3))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X4) Y3)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X4))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y3)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I4) (@ P I4))) (@ P K2)))) (@ P M)))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X4) Xa)))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X4) Xa) Y3) (=> _let_1 (not (=> (and (=> _let_2 (= Y3 X4)) (=> (not _let_2) (= Y3 (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa))))) (not _let_1)))))))))
% 6.83/7.14 (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) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L)) S4)))))) _let_1))))))))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L2) tptp.one_one_int))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L2) U))))
% 6.83/7.14 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L2) U))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L2)))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X4)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 6.83/7.14 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) X))) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 6.83/7.14 (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)))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.plus_p5714425477246183910nteger X4) Xa)) (@ (@ tptp.plus_plus_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa)))))
% 6.83/7.14 (assert (forall ((X4 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X4) Xa)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa)))))
% 6.83/7.14 (assert (forall ((X4 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.minus_8373710615458151222nteger X4) Xa)) (@ (@ tptp.minus_minus_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa)))))
% 6.83/7.14 (assert (forall ((X4 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.divide6298287555418463151nteger X4) Xa)) (@ (@ tptp.divide_divide_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa)))))
% 6.83/7.14 (assert (forall ((X4 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.modulo364778990260209775nteger X4) Xa)) (@ (@ tptp.modulo_modulo_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa)))))
% 6.83/7.14 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))
% 6.83/7.14 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L)))))
% 6.83/7.14 (assert (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0))) Xa) X4)))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (forall ((N3 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N3) (= (@ tptp.gcd_Gcd_nat N3) tptp.one_one_nat))))
% 6.83/7.14 (assert (forall ((X4 tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X4)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X4))))
% 6.83/7.14 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.83/7.14 (assert (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0))) Xa) X4))))
% 6.83/7.14 (assert (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0))) Xa) X4))))
% 6.83/7.14 (assert (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U4)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))) Xa) X4)))))
% 6.83/7.14 (assert (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U4)))) __flatten_var_0))) Xa) X4)))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.83/7.14 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 6.83/7.14 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U4) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 6.83/7.14 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U4) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 6.83/7.14 (assert (= tptp.nat2 (lambda ((X tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 6.83/7.14 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N2))) M6)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (let ((_let_1 (@ tptp.pow X4))) (= (@ _let_1 (@ tptp.bit1 Y3)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y3))) X4)))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 6.83/7.14 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.83/7.14 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 6.83/7.14 (assert (= tptp.sqr (lambda ((X tptp.num)) (@ (@ tptp.times_times_num X) X))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B2)))))
% 6.83/7.14 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B2) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (let ((_let_1 (@ tptp.pow X4))) (= (@ _let_1 (@ tptp.bit0 Y3)) (@ tptp.sqr (@ _let_1 Y3))))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X4) Xa) Y3) (=> (=> (exists ((Uu2 Bool) (Uv Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv))) (= Y3 (not (= Xa 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)))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (= Y3 (not (and (= Deg2 Xa) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X4) Xa) (=> (=> (exists ((Uu2 Bool) (Uv Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv))) (not (= Xa 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)))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (not (and (= Deg2 Xa) (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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X4) Xa)) (=> (=> (exists ((Uu2 Bool) (Uv Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv))) (= Xa 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)))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (and (= Deg2 Xa) (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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L2) U))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L2)))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L2) U))))
% 6.83/7.14 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg3 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)) Deg3) (and (= Deg Deg3) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima2)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y3 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X4) Xa) Y3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv))) (=> (= X4 _let_1) (=> (= Y3 (= Xa tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (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)))) (=> (= X4 _let_1) (=> (= Y3 (and (= Deg2 Xa) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X4) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (= Xa tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (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))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (= Deg2 Xa) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X4) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (= Xa tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (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))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (= Deg2 Xa) (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 ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) 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 ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X6)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X6 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X6)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))))
% 6.83/7.14 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B2))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.83/7.14 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B2 tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B2))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.83/7.14 (assert (forall ((P (-> tptp.nat Bool)) (B2 tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B2))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B2))) (let ((_let_2 (@ (@ tptp.fract A) B2))) (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))))))))
% 6.83/7.14 (assert (forall ((C tptp.nat) (Y3 tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X4) Y3))) (let ((_let_2 (@ (@ tptp.ord_less_nat X4) Y3))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y3))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X4) C)) (@ (@ tptp.minus_minus_nat Y3) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.83/7.14 (assert (forall ((M7 tptp.set_nat) (N3 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N3) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N3))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.83/7.14 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I)) (@ tptp.suc J)))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I)) (@ tptp.suc J)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.fract A) B2)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B2) D)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A) B2)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int B2) C)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.fract A) B2)) (@ (@ tptp.divide_divide_int A) B2))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B2) D))) (=> (not (= B2 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B2)) (@ (@ 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) B2)) _let_1))))))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A) B2)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B2))) (@ (@ tptp.times_times_int B2) D)))))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B2) D))) (=> (not (= B2 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B2)) (@ (@ 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) B2)) _let_1))))))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A) B2)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B2))) (@ (@ tptp.times_times_int B2) D)))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.fract A) B2)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B2))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A3)))))
% 6.83/7.14 (assert (forall ((P (-> tptp.rat Bool)) (Q2 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (@ P (@ (@ tptp.fract A5) B5)))) (@ P Q2))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B2 tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (@ (@ tptp.fract A) B2) (@ (@ tptp.fract C) D)) (= (@ (@ tptp.times_times_int A) D) (@ (@ tptp.times_times_int C) B2)))))))
% 6.83/7.14 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.fract A) B2))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.gcd_gcd_int A) B2))) (= (@ (@ tptp.fract (@ (@ tptp.divide_divide_int A) _let_1)) (@ (@ tptp.divide_divide_int B2) _let_1)) (@ (@ tptp.fract A) B2)))))
% 6.83/7.14 (assert (= tptp.fract (lambda ((K3 tptp.int) (L tptp.int)) (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K3)) (@ tptp.ring_1_of_int_rat L)))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B2) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B2)) (@ _let_1 A))))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B2)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B2)))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B2)) (@ (@ tptp.ord_less_int B2) A)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B2)) (@ (@ tptp.ord_less_eq_int B2) A)))))
% 6.83/7.14 (assert (forall ((B2 tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B2)))))
% 6.83/7.14 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.83/7.14 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat A) B2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or4665077453230672383an_nat A) B2)) (@ (@ tptp.set_or4662586982721622107an_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.83/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) L2))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L2))) (@ (@ tptp.set_or4662586982721622107an_int L2) U))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) U) (= (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U) (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ tptp.set_ord_lessThan_nat (@ tptp.nat2 U)))))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N) M)))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A) B2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B2)))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ tptp.positive X4) (=> (@ tptp.positive Y3) (@ tptp.positive (@ (@ tptp.plus_plus_rat X4) Y3))))))
% 6.83/7.14 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ tptp.positive X4) (=> (@ tptp.positive Y3) (@ tptp.positive (@ (@ tptp.times_times_rat X4) Y3))))))
% 6.83/7.14 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y) X)))))
% 6.83/7.14 (assert (= tptp.positive (lambda ((X tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X))) (@ (@ 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)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y3 tptp.option_num)) (let ((_let_1 (not (= Y3 tptp.none_num)))) (let ((_let_2 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X4) Xa) Y3) (=> (=> _let_2 (=> (= Xa tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N4 tptp.num)) (= Xa (@ tptp.bit0 N4))) (not (= Y3 (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N4 tptp.num)) (= Xa (@ tptp.bit1 N4))) _let_1)) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (not (= Y3 (@ tptp.some_num _let_1))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit0 N4)) (not (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N4)))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit1 N4)) (not (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N4)))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit1 M4)) (=> (= Xa tptp.one) (not (= Y3 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit0 N4)) (not (= Y3 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_and_not_num M4) N4)))))))) (not (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit1 N4)) (not (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N4))))))))))))))))))))))
% 6.83/7.14 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A4 tptp.nat) (X 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 ((P3 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) P3)))) (lambda ((P3 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P3))))) X))) A4))) (@ (@ tptp.product_Pair_nat_num N2) M6)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y3 tptp.option_num)) (let ((_let_1 (not (= Y3 (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y3 tptp.none_num)))) (let ((_let_5 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X4) Xa) Y3) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N4 tptp.num)) (= Xa (@ tptp.bit0 N4))) _let_4)) (=> (=> _let_5 (=> (exists ((N4 tptp.num)) (= Xa (@ tptp.bit1 N4))) _let_1)) (=> (=> (exists ((M4 tptp.num)) (= X4 (@ tptp.bit0 M4))) (=> _let_2 _let_4)) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit0 N4)) (not (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N4)))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit1 N4)) (not (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N4)))))))) (=> (=> (exists ((M4 tptp.num)) (= X4 (@ tptp.bit1 M4))) _let_3) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit0 N4)) (not (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N4)))))))) (not (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit1 N4)) (not (= Y3 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N4)))))))))))))))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y3 tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X4) Xa) Y3) (=> (=> _let_1 (=> (= Xa tptp.one) (not (= Y3 tptp.none_num)))) (=> (=> _let_1 (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit0 N4)) (not (= Y3 (@ tptp.some_num (@ tptp.bit1 N4))))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit1 N4)) (not (= Y3 (@ tptp.some_num (@ tptp.bit0 N4))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit0 M4)) (=> (= Xa tptp.one) (not (= Y3 (@ tptp.some_num (@ tptp.bit1 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit0 N4)) (not (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N4)))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit1 N4)) (not (= Y3 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N4))))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit1 M4)) (=> (= Xa tptp.one) (not (= Y3 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit0 N4)) (not (= Y3 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N4))))))))) (not (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (=> (= Xa (@ tptp.bit1 N4)) (not (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N4)))))))))))))))))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.83/7.14 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num tptp.one))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)))
% 6.83/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.83/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num (@ tptp.bit0 N)))))
% 6.83/7.14 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num (@ tptp.bit1 N)))))
% 6.83/7.14 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 6.83/7.14 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I)) (@ (@ tptp.minus_minus_nat N) I)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N)) I))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int) (R2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) R2) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N)) L2) R2)))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) L2)))))
% 6.83/7.14 (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 ((M2 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M2)))) M))))
% 6.83/7.14 (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 ((M2 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M2) N)))) M))))
% 6.83/7.14 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S2)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S2))))))
% 6.83/7.14 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N2)) M6))))))))
% 6.83/7.14 (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))))))))))
% 6.83/7.14 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.83/7.14 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 6.83/7.14 (assert (= tptp.upto_aux (lambda ((I2 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I2)) Js) (@ (@ (@ tptp.upto_aux I2) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.83/7.14 (assert (forall ((X4 tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X4) Xs2)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs2)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.list_nat) (Y3 tptp.nat)) (=> (= (@ tptp.nat_list_encode X4) Y3) (=> (=> (= X4 tptp.nil_nat) (not (= Y3 tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X4 (@ (@ tptp.cons_nat X3) Xs3)) (not (= Y3 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.83/7.14 (assert (= tptp.quotient_of (lambda ((X tptp.rat)) (@ tptp.the_Pr4378521158711661632nt_int (lambda ((Pair tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Pair))) (let ((_let_2 (@ tptp.product_fst_int_int Pair))) (and (= X (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)))))))))
% 6.83/7.14 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.algebr932160517623751201me_int K))) (= (@ _let_1 (@ tptp.abs_abs_int L2)) (@ _let_1 L2)))))
% 6.83/7.14 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.algebr932160517623751201me_int (@ tptp.abs_abs_int K)) L2) (@ (@ tptp.algebr932160517623751201me_int K) L2))))
% 6.83/7.14 (assert (forall ((Q2 tptp.int) (P2 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P2) Q2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2) (=> (@ (@ tptp.algebr932160517623751201me_int P2) Q2) (= (@ tptp.normalize _let_1) _let_1))))))
% 6.83/7.14 (assert (forall ((A tptp.int) (D tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int D))) (let ((_let_2 (@ tptp.abs_abs_int C))) (let ((_let_3 (@ tptp.abs_abs_int B2))) (let ((_let_4 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.algebr932160517623751201me_int A) D) (=> (@ (@ tptp.algebr932160517623751201me_int B2) C) (= (= (@ (@ tptp.times_times_int _let_4) _let_2) (@ (@ tptp.times_times_int _let_3) _let_1)) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))))
% 6.83/7.14 (assert (forall ((Q2 tptp.rat)) (not (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= Q2 (@ (@ tptp.fract A5) B5)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (not (@ (@ tptp.algebr932160517623751201me_int A5) B5))))))))
% 6.83/7.14 (assert (forall ((P (-> tptp.rat Bool)) (Q2 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.algebr932160517623751201me_int A5) B5) (@ P (@ (@ tptp.fract A5) B5))))) (@ P Q2))))
% 6.83/7.14 (assert (forall ((A tptp.int) (B2 tptp.int) (X4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X4))) (=> (@ (@ tptp.algebr932160517623751201me_int A) B2) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= (@ tptp.abs_abs_int X4) tptp.one_one_int)))))))
% 6.83/7.14 (assert (forall ((Q2 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= Q2 (@ (@ tptp.fract A5) B5)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (not (= A5 tptp.zero_zero_int)) (not (@ (@ tptp.algebr932160517623751201me_int A5) B5)))))) (= Q2 tptp.zero_zero_rat))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N3 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) N3))))) (@ (@ 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) N3)))))) (@ 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) N3))))))))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N3 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) N3))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N3) M)) tptp.one_one_nat)) N3))))
% 6.83/7.14 (assert (forall ((R2 tptp.rat)) (exists ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X3))) (let ((_let_2 (@ tptp.product_fst_int_int X3))) (and (= R2 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1) (forall ((Y5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y5))) (let ((_let_2 (@ tptp.product_fst_int_int Y5))) (=> (and (= R2 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)) (= Y5 X3)))))))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.algebr932160517623751201me_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.algebr934650988132801477me_nat M) N))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ (@ tptp.algebr932160517623751201me_int (@ tptp.semiri1314217659103216013at_int N)) K))))
% 6.83/7.14 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N) (@ (@ tptp.algebr932160517623751201me_int K) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (B2 tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X4))) (=> (@ (@ tptp.algebr934650988132801477me_nat A) B2) (=> (@ _let_1 A) (=> (@ _let_1 B2) (= X4 tptp.one_one_nat)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc tptp.zero_zero_nat))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc N)) N)))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc N))))
% 6.83/7.14 (assert (forall ((A tptp.nat) (D tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.algebr934650988132801477me_nat A) D) (=> (@ (@ tptp.algebr934650988132801477me_nat B2) C) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B2) D)) (and (= A B2) (= C D)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 6.83/7.14 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 6.83/7.14 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 6.83/7.14 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 6.83/7.14 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 6.83/7.14 (assert (forall ((I tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I) J)) K) _let_1)))))
% 6.83/7.14 (assert (forall ((I tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I)) tptp.one_one_int)))))
% 6.83/7.14 (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)))))))))
% 6.83/7.14 (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)))))))))
% 6.83/7.14 (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)))))))))
% 6.83/7.14 (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)))))))))
% 6.83/7.14 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))))
% 6.83/7.14 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))))
% 6.83/7.14 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I2) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.83/7.14 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J3)))))
% 6.83/7.14 (assert (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ (@ tptp.upto I) J) (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J))))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Xa tptp.int) (Y3 tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X4) Xa))) (=> (= (@ (@ tptp.upto X4) Xa) Y3) (and (=> _let_1 (= Y3 (@ (@ tptp.cons_int X4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X4) tptp.one_one_int)) Xa)))) (=> (not _let_1) (= Y3 tptp.nil_int)))))))
% 6.83/7.14 (assert (= tptp.upto (lambda ((I2 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I2) J3)) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.83/7.14 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 6.83/7.14 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.83/7.14 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.int) (Xa tptp.int) (Y3 tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X4) Xa)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X4) Xa))) (=> (= (@ (@ tptp.upto X4) Xa) Y3) (=> _let_1 (not (=> (and (=> _let_2 (= Y3 (@ (@ tptp.cons_int X4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X4) tptp.one_one_int)) Xa)))) (=> (not _let_2) (= Y3 tptp.nil_int))) (not _let_1)))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.list_nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X4) Y3) (=> (@ _let_1 X4) (=> (=> (= X4 tptp.nil_nat) (=> (= Y3 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))) (=> (= X4 _let_1) (=> (= Y3 (@ 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)))))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X4)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X4) X3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X3) X4)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X4) X3) (@ (@ tptp.ord_less_real X3) Y3))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (not (forall ((M4 tptp.nat) (N4 tptp.nat)) (=> (not (= N4 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X4) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M4)) (@ tptp.semiri5074537144036343181t_real N4))) (not (@ (@ tptp.algebr934650988132801477me_nat M4) N4)))))))))
% 6.83/7.14 (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)))))))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) M)) J))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) M))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 6.83/7.14 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I)))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J)) K) _let_1)))))
% 6.83/7.14 (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 ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))
% 6.83/7.14 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M6))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M6))))))
% 6.83/7.14 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M6)))))
% 6.83/7.14 (assert (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat) (X4 tptp.nat) (Xs2 tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X4) Xs2)) (and (@ (@ tptp.ord_less_nat I) J) (= I X4) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs2)))))
% 6.83/7.14 (assert (= tptp.upt (lambda ((I2 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I2) J3)) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J3))) tptp.nil_nat))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 6.83/7.14 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 6.83/7.14 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 6.83/7.14 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M6)) M6))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 6.83/7.14 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat I2) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((Ns tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.nth_nat Ns) I))))))
% 6.83/7.14 (assert (forall ((I tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J))))
% 6.83/7.14 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu tptp.real)) (exists ((I2 tptp.int) (J3 tptp.int)) (and (= Uu (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I2)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 6.83/7.14 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu tptp.real)) (exists ((I2 tptp.int) (N2 tptp.nat)) (and (= Uu (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I2)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.83/7.14 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.83/7.14 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.83/7.14 (assert (= tptp.root (lambda ((N2 tptp.nat) (X 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)))) X)))))
% 6.83/7.14 (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)))))))))))
% 6.83/7.14 (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)))))))))))))
% 6.83/7.14 (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))))))))))))
% 6.83/7.14 (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))))))))))))
% 6.83/7.14 (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))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 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 X4) 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 X4)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 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 X4)) (@ (@ 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 (= X4 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X4) 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 X4) tptp.top_top_set_real)))))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 X4) H4))) (@ F X4)))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 X4)) (@ F (@ (@ tptp.plus_plus_real X4) H4))))))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B2))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y5) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B2)) (@ F A))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y5) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B2)) (@ F A))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y5)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B2))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X3)))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (@ (@ tptp.ord_less_eq_real (@ G A)) (@ G B2)))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (X4 tptp.real) (Y3 tptp.real)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ F X4) (@ F Y3)))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (Y3 tptp.real) (X4 tptp.real)) (= (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real (@ tptp.uminus_uminus_real X4)) tptp.top_top_set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ F (@ tptp.uminus_uminus_real X)))) (@ tptp.uminus_uminus_real Y3)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B2)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A))) (@ (@ tptp.minus_minus_real B2) A)) K)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B2)) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) K))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 (@ (@ tptp.minus_minus_real X4) H4))) (@ F X4)))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 X4)) (@ F (@ (@ tptp.minus_minus_real X4) H4))))))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (X4 tptp.real) (Y3 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B2))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.member_real X4) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (= (@ F X4) (@ F Y3)))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ 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.minus_minus_real X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X4)))))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ 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.minus_minus_real X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F _let_1)))))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ 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 X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F _let_1)))))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ 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 X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X4)))))))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X3) (=> (@ (@ tptp.ord_less_eq_real X3) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B2) (= (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) (@ F4 Z2)))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y4))) D) (= (@ F X4) (@ F Y4)))) (= L2 tptp.zero_zero_real))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (V (-> tptp.real tptp.real)) (K tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (not (= A B2)) (=> (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) B2)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A)) (@ V B2))) _let_1)))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y4))) D) (@ (@ tptp.ord_less_eq_real (@ F Y4)) (@ F X4)))) (= L2 tptp.zero_zero_real))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X4 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y4))) D) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y4)))) (= L2 tptp.zero_zero_real))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X4) S))))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X4 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ G X)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X4)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 6.83/7.14 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z5 tptp.real)) (@ (@ tptp.powr_real Z5) R2))) (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B2)) X4))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X4 tptp.real) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (let ((_let_2 (@ G X4))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) 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)))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X4 tptp.real) (F (-> tptp.real tptp.real)) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (let ((_let_2 (@ G X4))) (let ((_let_3 (@ F X4))) (=> (@ (@ (@ 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 ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) (@ F X)))) (@ (@ 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)))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X4))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F4 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B2 tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F4 X0))) (=> (forall ((N4 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ F X) N4))) (@ (@ F4 X0) N4)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B2)) (@ tptp.summable_real (@ F X3)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B2)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N4 tptp.nat) (X3 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B2))) (=> (@ (@ tptp.member_real X3) _let_1) (=> (@ (@ tptp.member_real Y4) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X3) N4)) (@ (@ F Y4) N4)))) (@ (@ tptp.times_times_real (@ L5 N4)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y4)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ tptp.suminf_real (@ F X)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (A3 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 X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X4) A3))))
% 6.83/7.14 (assert (forall ((X4 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 X4)))) (=> (not (= X4 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X4) 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 X4) tptp.top_top_set_real)))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ (@ 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 X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X4) A3)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) 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 X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) A3)))))
% 6.83/7.14 (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 ((X tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X) (@ 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)))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 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) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X4)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) 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 X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) 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 X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))))
% 6.83/7.14 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X4 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 ((T2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T2)) (@ tptp.abs_abs_real X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N)))))))))
% 6.83/7.14 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X4 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 ((T2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T2)) (@ tptp.abs_abs_real X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X4 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 X4)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))))
% 6.83/7.14 (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) (T2 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_eq_real T2) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T2)) (@ (@ tptp.topolo2177554685111907308n_real T2) tptp.top_top_set_real)))) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_real T2) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.83/7.14 (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) (T2 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_eq_real T2) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T2)) (@ (@ tptp.topolo2177554685111907308n_real T2) tptp.top_top_set_real)))) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_eq_real T2) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 6.83/7.14 (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) (T2 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real H2) T2) (@ (@ tptp.ord_less_eq_real T2) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T2)) (@ (@ tptp.topolo2177554685111907308n_real T2) tptp.top_top_set_real)))) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T2) (@ (@ tptp.ord_less_real T2) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.83/7.14 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X4 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X4 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 ((T2 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T2))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N)))))))))))))
% 6.83/7.14 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X4 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T2 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T2)) (@ tptp.abs_abs_real X4))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T2)) (@ (@ tptp.topolo2177554685111907308n_real T2) tptp.top_top_set_real)))) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T2)) (@ tptp.abs_abs_real X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B2 tptp.real) (C tptp.real) (X4 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) (T2 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T2) (@ (@ tptp.ord_less_eq_real T2) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T2)) (@ (@ tptp.topolo2177554685111907308n_real T2) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B2) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) B2) (=> (not (= X4 C)) (exists ((T2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T2))) (let ((_let_2 (@ tptp.ord_less_real X4))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T2) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T2) (@ _let_1 X4))) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) C)) N))))))))))))))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T2 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T2) (@ (@ tptp.ord_less_eq_real T2) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T2)) (@ (@ tptp.topolo2177554685111907308n_real T2) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B2) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_real C) T2) (@ (@ tptp.ord_less_real T2) B2) (= (@ F B2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B2) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B2) C)) N)))))))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T2 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T2) (@ (@ tptp.ord_less_eq_real T2) B2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T2)) (@ (@ tptp.topolo2177554685111907308n_real T2) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B2) (exists ((T2 tptp.real)) (and (@ (@ tptp.ord_less_real A) T2) (@ (@ tptp.ord_less_real T2) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M6)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T2)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 6.83/7.14 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B4 tptp.real)) (=> (forall ((M4 tptp.nat) (T2 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T2) (@ (@ tptp.ord_less_eq_real T2) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T2)) (@ (@ tptp.topolo2177554685111907308n_real T2) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M5 tptp.nat) (T4 tptp.real)) (let ((_let_1 (@ tptp.suc M5))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M5))) (@ (@ tptp.minus_minus_real (@ (@ Diff M5) U4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M5) P3)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P3))) (@ (@ tptp.power_power_real U4) P3)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B4) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U4) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M5)) P3)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P3))) (@ (@ tptp.power_power_real T4) P3)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B4) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T4) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) 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 X4) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B2)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) F))) (exists ((L6 tptp.real) (M9 tptp.real)) (and (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B2)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M9))))) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y5) (@ (@ tptp.ord_less_eq_real Y5) M9)) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B2) (= (@ F X3) Y5)))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (@ (@ tptp.ord_less_real (@ F X5)) tptp.zero_zero_real)))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L2 tptp.zero_zero_real)) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (not (= (@ F X5) tptp.zero_zero_real))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X5))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.sqrt)))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ tptp.root N))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (not (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.archim2898591450579166408c_real))))
% 6.83/7.14 (assert (forall ((A tptp.real) (X4 tptp.real) (B2 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B2) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B2) (= (@ G (@ F Z2)) Z2)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X4)) tptp.top_top_set_real)) G)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.83/7.14 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))) (@ 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)))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (not (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.comp_int_real_real tptp.ring_1_of_int_real) tptp.archim6058952711729229775r_real)))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G (-> tptp.real tptp.real)) (X4 tptp.real) (A tptp.real) (B2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G X4)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B2) (=> (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y4) (=> (@ (@ tptp.ord_less_real Y4) B2) (= (@ F (@ G Y4)) Y4)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D4)) _let_1))))))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.arccos)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.83/7.14 (assert (forall ((B2 tptp.real) (X4 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B2) X4) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real B2) X4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.83/7.14 (assert (forall ((D tptp.real) (X4 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X4))) D) (= (@ G (@ F Z2)) Z2))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X4))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X4)) tptp.top_top_set_real)) G))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 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) B2) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) G)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A))) (@ G2 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B2)) (@ G A))) (@ F4 C3))))))))))))
% 6.83/7.14 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.83/7.14 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I3)) B4)) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) L6))))))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X8 I3))) B4)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 6.83/7.14 (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))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N4))) (@ G N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ G N4))) (=> (@ (@ (@ 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 ((L3 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L3))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N6)) L3)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L3) (@ G N6))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ (@ tptp.ord_less_real R3) (@ X8 N4)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.83/7.14 (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))
% 6.83/7.14 (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))))
% 6.83/7.14 (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))
% 6.83/7.14 (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)))
% 6.83/7.14 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) L2)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.plus_plus_real (@ F N6)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L2)) tptp.at_top_nat))))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X4)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X4) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X4) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.83/7.14 (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)))
% 6.83/7.14 (assert (forall ((X4 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 X4) (@ tptp.semiri5074537144036343181t_real N2)))) N2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X4))) tptp.at_top_nat)))
% 6.83/7.14 (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)))
% 6.83/7.14 (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))))))))
% 6.83/7.14 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ 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)))))))))
% 6.83/7.14 (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)))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) 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 X4) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.83/7.14 (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 ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))))))))
% 6.83/7.14 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat))))))
% 6.83/7.14 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L3 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L3))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6)))) L3)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) _let_1) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.83/7.14 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat)))))
% 6.83/7.14 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat))))))
% 6.83/7.14 (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 ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 6.83/7.14 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I2 tptp.nat)) (@ P (@ tptp.suc I2)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I2 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I2) K)))) tptp.at_top_nat))))
% 6.83/7.14 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N8 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ P N2)))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N8)) F5)))))
% 6.83/7.14 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.83/7.14 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F2 (-> tptp.real tptp.real))) (exists ((C2 tptp.real)) (= F2 (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C2)))))))
% 6.83/7.14 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_top_real) _let_1)))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_top_real) _let_1)))))))))
% 6.83/7.14 (assert (forall ((B2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B2) A) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real B2) A)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.real)) (X4 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) (@ tptp.set_or5984915006950818249n_real X4)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y3))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) _let_2) _let_1))))))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (X4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X4))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) _let_1) tptp.at_top_real) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) _let_1) tptp.at_top_real)))))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.real)) (X4 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y3))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) _let_2) _let_1))))))))))
% 6.83/7.14 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 6.83/7.14 (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))))
% 6.83/7.14 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real))
% 6.83/7.14 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) K)) (@ tptp.exp_real X)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (X4 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) (@ tptp.set_or5984915006950818249n_real X4)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) F5) _let_1))))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (X4 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) F5) _let_1))))))))))))
% 6.83/7.14 (assert (forall ((X4 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 X4) Y))) Y))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X4))) tptp.at_top_real)))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((B2 tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B2) X3) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y5) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B2))))))
% 6.83/7.14 (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))
% 6.83/7.14 (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 ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N))) tptp.at_top_real) F5))))))
% 6.83/7.14 (assert (= tptp.real_V975177566351809787t_real (lambda ((X tptp.real) (Y tptp.real)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y)))))
% 6.83/7.14 (assert (= tptp.real_V3694042436643373181omplex (lambda ((X tptp.complex) (Y tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y)))))
% 6.83/7.14 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_bot_real) _let_1)))))))))
% 6.83/7.14 (assert (forall ((B2 tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X3) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B2))))))
% 6.83/7.14 (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 ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N))) tptp.at_bot_real) F5))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_bot_real) _let_1)))))))))
% 6.83/7.14 (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))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I3)) B4)) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.83/7.14 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X4)) tptp.at_top_nat)))))
% 6.83/7.14 (assert (forall ((X4 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 X4) Y))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X4))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (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 ((X tptp.real)) (@ P (@ (@ tptp.plus_plus_real X) A)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real A) B2)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))))))
% 6.83/7.14 (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))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_top_real) _let_1)))))))))
% 6.83/7.14 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F0) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G0) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G0 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F0) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G0) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X)) (@ G0 X)))) F5) _let_1))))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (X4 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) (@ tptp.set_or5849166863359141190n_real X4)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) F5) _let_1))))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) tptp.at_bot_real) _let_1)))))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.real)) (X4 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) (@ tptp.set_or5849166863359141190n_real X4)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y3))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) _let_2) _let_1))))))))))
% 6.83/7.14 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (X4 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real X4))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X)) (@ G2 X)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ F X)) (@ G X)))) _let_2) _let_1))))))))))
% 6.83/7.14 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 6.83/7.14 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real B4) (@ X8 I3))) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.83/7.14 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.83/7.14 (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))))))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real B4) (@ X8 I3))) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real L6) (@ X8 I4)))))))))))
% 6.83/7.14 (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)))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (forall ((X3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B2)) (@ (@ 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) B2)) (@ (@ 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) B2)) (@ (@ 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) B2)) (@ (@ 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) B2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B2)) (@ G A))) F_c))))))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (X4 tptp.real) (S tptp.set_real)) (=> (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) S)) (not (forall ((Df tptp.real)) (not (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Df) (@ (@ tptp.topolo2177554685111907308n_real X4) S))))))))
% 6.83/7.14 (assert (forall ((F (-> tptp.real tptp.real)) (X4 tptp.real) (S tptp.set_real)) (= (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) S)) (exists ((D6 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D6) (@ (@ tptp.topolo2177554685111907308n_real X4) S))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B2) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((L3 tptp.real) (Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L3) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B2) A)) L3)))))))))
% 6.83/7.14 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X8 I3))) (= (@ tptp.suminf_real X8) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X8) (@ tptp.set_ord_lessThan_nat I2)))) tptp.top_top_set_nat)))))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A3) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A3) tptp.arcosh_real))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A3))) (=> (@ _let_1 F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ _let_1 (lambda ((X tptp.real)) (@ tptp.arcosh_real (@ F X)))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B2) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) F) (exists ((C3 tptp.real) (D3 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A) B2)) (@ (@ tptp.set_or1222579329274155063t_real C3) D3)) (@ (@ tptp.ord_less_eq_real C3) D3)))))))
% 6.83/7.14 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 6.83/7.14 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A3) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A3) tptp.artanh_real))))
% 6.83/7.14 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A3))) (=> (@ _let_1 F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A3) (@ (@ tptp.member_real (@ F X3)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)))) (@ _let_1 (lambda ((X tptp.real)) (@ tptp.artanh_real (@ F X)))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (= (@ F A) (@ F B2)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B2) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B2) (= (@ F4 Z2) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B2) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi) (=> (@ (@ tptp.ord_less_real Xi) B2) (not (= (@ (@ tptp.minus_minus_real (@ F B2)) (@ F A)) (@ (@ F4 Xi) (@ (@ tptp.minus_minus_real B2) A)))))))))))))
% 6.83/7.14 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) F) (@ (@ tptp.ord_less_real (@ F A)) (@ F B2)))))))
% 6.83/7.15 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B2) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y5) tptp.zero_zero_real)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) F) (@ (@ tptp.ord_less_real (@ F B2)) (@ F A)))))))
% 6.83/7.15 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (= (@ F B2) (@ F A)))))))
% 6.83/7.15 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real)) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B2) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B2) (= (@ F X4) (@ F A)))))))))
% 6.83/7.15 (assert (forall ((A tptp.real) (B2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B2) (=> (= (@ F A) (@ F B2)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B2)) F) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X3) (=> (@ (@ tptp.ord_less_real X3) B2) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B2) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))))))))
% 6.83/7.15 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.83/7.15 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.83/7.15 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.83/7.15 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 6.83/7.15 (assert (= tptp.comple4887499456419720421f_real (lambda ((X6 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X6))))))
% 6.83/7.15 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 6.83/7.15 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.83/7.15 (assert (= tptp.ord_less_rat (lambda ((P3 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 P3)))))
% 6.83/7.15 (assert (= tptp.ord_less_eq_rat (lambda ((P3 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 P3)))))
% 6.83/7.15 (assert (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z5) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 6.83/7.15 (assert (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z7) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 6.83/7.15 (assert (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X) Y)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.83/7.15 (assert (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X) Y)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.83/7.15 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (=> (@ tptp.order_mono_nat_real F) (=> (@ tptp.order_5726023648592871131at_nat G) (= (@ (@ tptp.bfun_nat_real (lambda ((X tptp.nat)) (@ F (@ G X)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))))
% 6.83/7.15 (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))))
% 6.83/7.15 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 6.83/7.15 (assert (forall ((B2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B2) (@ (@ tptp.inj_on_real_real (@ tptp.log B2)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.83/7.15 (assert (forall ((N3 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N3)))
% 6.83/7.15 (assert (forall ((N3 tptp.set_nat) (K tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.member_nat N4) N3) (@ (@ tptp.ord_less_eq_nat K) N4))) (@ (@ tptp.inj_on_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) K))) N3))))
% 6.83/7.15 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (@ tptp.summable_real (@ (@ tptp.comp_nat_real_nat F) G)))))))
% 6.83/7.15 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G))) (@ tptp.suminf_real F)))))))
% 6.83/7.15 (assert (forall ((X4 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (or (not (= X4 tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X4) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X4) N))))))
% 6.83/7.15 (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))))))))))))
% 6.83/7.15 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3))) (=> (forall ((X3 tptp.nat)) (=> (not (@ (@ tptp.member_nat X3) (@ (@ tptp.image_nat_nat G) tptp.top_top_set_nat))) (= (@ F X3) tptp.zero_zero_real))) (= (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G)) (@ tptp.suminf_real F))))))))
% 6.83/7.15 (assert (forall ((F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F4 X3))) (@ tptp.order_7092887310737990675l_real F)))))
% 6.83/7.15 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M6)))))))
% 6.83/7.15 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 6.83/7.15 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.83/7.15 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.83/7.15 (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)))))
% 6.83/7.15 (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)))))
% 6.83/7.15 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) N))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (exists ((A7 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A7) (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N4))) A7)))) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N2)) (@ Y7 N2))))))))
% 6.83/7.15 (assert (forall ((C tptp.rat)) (= (@ tptp.vanishes (lambda ((N2 tptp.nat)) C)) (= C tptp.zero_zero_rat))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N2)))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N2)) (@ Y7 N2))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X8) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y7 N2))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.vanishes X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N6))) R2))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N4))) R3)))))) (@ tptp.vanishes X8))))
% 6.83/7.15 (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)))))))))
% 6.83/7.15 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y3 tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X4) Xa) Y3) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y3 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ 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 ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa _let_1) (=> (= Y3 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))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (=> (= Y3 (@ 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)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N4))) (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)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N4))) (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))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (=> (= Y3 (@ 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)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_and_not_num M4) N4))) (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)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.83/7.15 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y3 tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X4) Xa) Y3) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y3 (@ tptp.some_num tptp.one)) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa _let_1) (=> (= Y3 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ 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))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (=> (= Y3 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)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N4))) (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))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (=> (= Y3 (@ 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)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.83/7.15 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y3 tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X4) Xa) Y3) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y3 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.some_num (@ tptp.bit1 N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.some_num (@ tptp.bit0 N4))) (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))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (=> (= Y3 (@ 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)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit0 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N4)))) (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))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (=> (= Y3 (@ 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)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N4)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X4 (@ tptp.bit1 M4)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.83/7.15 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y3 tptp.num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X4) Xa) Y3) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y3 tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.bit1 M4)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (=> (= Y3 (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N4 tptp.num)) (=> (= X4 (@ tptp.bit0 N4)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N4)) _let_1))))))))) (=> (forall ((N4 tptp.num)) (=> (= X4 (@ tptp.bit0 N4)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N4) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N4)) _let_1))))))))) (=> (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (=> (= Y3 tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N4 tptp.num)) (=> (= X4 (@ tptp.bit1 N4)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N4)) _let_1))))))))) (not (forall ((N4 tptp.num)) (=> (= X4 (@ tptp.bit1 N4)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y3 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N4)) _let_1))))))))))))))))))))))))
% 6.83/7.15 (assert (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))
% 6.83/7.15 (assert (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))
% 6.83/7.15 (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)))))
% 6.83/7.15 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.re (@ (@ tptp.rcis R2) A)) (@ (@ tptp.times_times_real R2) (@ tptp.cos_real A)))))
% 6.83/7.15 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.im (@ (@ tptp.rcis R2) A)) (@ (@ tptp.times_times_real R2) (@ tptp.sin_real A)))))
% 6.83/7.15 (assert (= tptp.cis (@ tptp.rcis tptp.one_one_real)))
% 6.83/7.15 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B2)) (@ (@ tptp.rcis (@ (@ tptp.times_times_real R1) R22)) (@ (@ tptp.plus_plus_real A) B2)))))
% 6.83/7.15 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B2)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real R1) R22)) (@ (@ tptp.minus_minus_real A) B2)))))
% 6.83/7.15 (assert (= tptp.rcis (lambda ((R5 tptp.real) (A4 tptp.real)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R5)) (@ tptp.cis A4)))))
% 6.83/7.15 (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)))))
% 6.83/7.15 (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))))))))
% 6.83/7.15 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.83/7.15 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.83/7.15 (assert (= tptp.cauchy (lambda ((X6 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X6 M6)) (@ X6 N2)))) R5)))))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) M4) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M4)) (@ X8 N4)))) R3)))))))) (@ tptp.cauchy X8))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N2))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y7 N2))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N2)) (@ Y7 N2))))))))
% 6.83/7.15 (assert (forall ((X4 tptp.rat)) (@ tptp.cauchy (lambda ((N2 tptp.nat)) X4))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N2)))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N2)) (@ Y7 N2))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (exists ((B5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B5) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N6))) B5)))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (=> (@ tptp.cauchy Y7) (=> (not (@ tptp.vanishes Y7)) (=> (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y7 N2)))) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ tptp.inverse_inverse_rat (@ X8 N2))) (@ tptp.inverse_inverse_rat (@ Y7 N2))))))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (exists ((B5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B5) (exists ((K2 tptp.nat)) (or (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B5) (@ tptp.uminus_uminus_rat (@ X8 N6))))) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B5) (@ X8 N6))))))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (not (@ tptp.vanishes X8)) (exists ((B5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B5) (exists ((K2 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B5) (@ tptp.abs_abs_rat (@ X8 N6))))))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.cauchy X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) M5) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M5)) (@ X8 N6)))) R2))))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X8)) (@ 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 (@ X8 N2)) (@ (@ tptp.plus_plus_rat (@ Y7 N2)) R5))))))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.real2 X8)))) (let ((_let_2 (@ tptp.vanishes X8))) (=> (@ tptp.cauchy X8) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N2))))))))))))
% 6.83/7.15 (assert (forall ((P (-> tptp.real Bool)) (X4 tptp.real)) (=> (forall ((X10 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X10) (@ P (@ tptp.real2 X10)))) (@ P X4))))
% 6.83/7.15 (assert (= tptp.one_one_real (@ tptp.real2 (lambda ((N2 tptp.nat)) tptp.one_one_rat))))
% 6.83/7.15 (assert (= tptp.semiri5074537144036343181t_real (lambda ((X tptp.nat)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat X))))))
% 6.83/7.15 (assert (= tptp.zero_zero_real (@ tptp.real2 (lambda ((N2 tptp.nat)) tptp.zero_zero_rat))))
% 6.83/7.15 (assert (= tptp.ring_1_of_int_real (lambda ((X tptp.int)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.ring_1_of_int_rat X))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X8)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N2))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 X8)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N2)) (@ Y7 N2)))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.times_times_real (@ tptp.real2 X8)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N2)) (@ Y7 N2)))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.minus_minus_real (@ tptp.real2 X8)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y7 N2)))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (= (= (@ tptp.real2 X8) (@ tptp.real2 Y7)) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y7 N2)))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (not (@ tptp.positive2 (@ tptp.real2 X8))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_eq_rat (@ X8 N2)) R5))))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (= (@ tptp.positive2 (@ tptp.real2 X8)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat R5) (@ X8 N2)))))))))))
% 6.83/7.15 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ tptp.positive2 X4) (=> (@ tptp.positive2 Y3) (@ tptp.positive2 (@ (@ tptp.times_times_real X4) Y3))))))
% 6.83/7.15 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ tptp.positive2 X4) (=> (@ tptp.positive2 Y3) (@ tptp.positive2 (@ (@ tptp.plus_plus_real X4) Y3))))))
% 6.83/7.15 (assert (not (@ tptp.positive2 tptp.zero_zero_real)))
% 6.83/7.15 (assert (forall ((X4 tptp.real)) (=> (not (@ tptp.positive2 X4)) (=> (not (= X4 tptp.zero_zero_real)) (@ tptp.positive2 (@ tptp.uminus_uminus_real X4))))))
% 6.83/7.15 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (@ tptp.positive2 (@ (@ tptp.minus_minus_real Y) X)))))
% 6.83/7.15 (assert (= tptp.positive2 (lambda ((X 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 X) N2))))))))))
% 6.83/7.15 (assert (forall ((X4 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X4) X4) (= (@ tptp.inverse_inverse_real (@ tptp.real2 X4)) (@ tptp.real2 (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X4)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X4 N2)))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (@ (@ tptp.realrel X8) X8))))
% 6.83/7.15 (assert (@ (@ tptp.realrel (lambda ((N2 tptp.nat)) tptp.one_one_rat)) (lambda ((N2 tptp.nat)) tptp.one_one_rat)))
% 6.83/7.15 (assert (@ (@ tptp.realrel (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)))
% 6.83/7.15 (assert (forall ((P (-> tptp.real Bool)) (X4 tptp.real)) (=> (forall ((Y4 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Y4) Y4) (@ P (@ tptp.real2 Y4)))) (@ P X4))))
% 6.83/7.15 (assert (forall ((X4 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X4) X4) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X4)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X4 N2))))))))
% 6.83/7.15 (assert (forall ((Xa (-> tptp.nat tptp.rat)) (X4 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa) Xa) (=> (@ (@ tptp.realrel X4) X4) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 Xa)) (@ tptp.real2 X4)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ Xa N2)) (@ X4 N2)))))))))
% 6.83/7.15 (assert (forall ((Xa (-> tptp.nat tptp.rat)) (X4 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa) Xa) (=> (@ (@ tptp.realrel X4) X4) (= (@ (@ tptp.times_times_real (@ tptp.real2 Xa)) (@ tptp.real2 X4)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ Xa N2)) (@ X4 N2)))))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X8) (=> (@ tptp.cauchy Y7) (=> (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N2)) (@ Y7 N2)))) (@ (@ tptp.realrel X8) Y7))))))
% 6.83/7.15 (assert (= tptp.realrel (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat))) (and (@ tptp.cauchy X6) (@ tptp.cauchy Y8) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X6 N2)) (@ Y8 N2))))))))
% 6.83/7.15 (assert (forall ((X4 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X4) X4) (= (@ tptp.positive2 (@ tptp.real2 X4)) (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) (@ X4 N2)))))))))))
% 6.83/7.15 (assert (= tptp.inverse_inverse_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2) (lambda ((X6 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X6)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X6 N2)))) __flatten_var_0)))))
% 6.83/7.15 (assert (= tptp.cr_real (lambda ((X (-> tptp.nat tptp.rat)) (Y tptp.real)) (and (@ (@ tptp.realrel X) X) (= (@ tptp.real2 X) Y)))))
% 6.83/7.15 (assert (= tptp.uminus_uminus_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2) (lambda ((X6 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X6 N2))))))
% 6.83/7.15 (assert (= tptp.times_times_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y8 N2))))))
% 6.83/7.15 (assert (= tptp.plus_plus_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2)) (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X6 N2)) (@ Y8 N2))))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o tptp.realrel) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4))) (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))))))))))
% 6.83/7.15 (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)))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X6 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X6 N2)))) (lambda ((X6 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X6 N2)))))
% 6.83/7.15 (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)))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re8402795839162346335um_int (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4))) (@ (@ tptp.bNF_re1822329894187522285nt_int (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M6)) (@ tptp.numeral_numeral_int N2)))) (lambda ((M6 tptp.num) (N2 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M6)) (@ tptp.numeral_numeral_int N2)))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)))) tptp.times_times_nat) tptp.times_times_nat))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) tptp.times_times_int) tptp.times_times_int))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) tptp.minus_minus_int) tptp.minus_minus_int))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)))) tptp.minus_minus_nat) tptp.minus_minus_nat))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)))) tptp.divide_divide_nat) tptp.divide_divide_nat))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) tptp.divide_divide_int) tptp.divide_divide_int))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)))) tptp.modulo_modulo_nat) tptp.modulo_modulo_nat))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) tptp.modulo_modulo_int) tptp.modulo_modulo_int))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) tptp.suc) tptp.suc))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)))) tptp.plus_plus_nat) tptp.plus_plus_nat))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)))) tptp.plus_plus_int) tptp.plus_plus_int))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4))) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) tptp.ord_less_int) tptp.ord_less_int))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 6.83/7.15 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S2)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S2) N)))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X6 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X6)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X6 N2)))) __flatten_var_0))) (lambda ((X6 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X6)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X6 N2)))) __flatten_var_0))))
% 6.83/7.15 (assert (forall ((S2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S2)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S2) N))))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4))) (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))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X 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 X))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _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))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re4521903465945308077real_o tptp.pcr_real) (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) tptp.realrel) (lambda ((Y6 tptp.real) (Z4 tptp.real)) (= Y6 Z4))))
% 6.83/7.15 (assert (= tptp.pcr_real tptp.cr_real))
% 6.83/7.15 (assert (@ (@ tptp.pcr_real (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) tptp.zero_zero_real))
% 6.83/7.15 (assert (@ (@ tptp.pcr_real (lambda ((N2 tptp.nat)) tptp.one_one_rat)) tptp.one_one_real))
% 6.83/7.15 (assert (= tptp.pcr_real (lambda ((X (-> tptp.nat tptp.rat)) (Y tptp.real)) (and (@ tptp.cauchy X) (= (@ tptp.real2 X) Y)))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X6 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X6 N2)))) tptp.uminus_uminus_real))
% 6.83/7.15 (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))
% 6.83/7.15 (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))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X6 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X6)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X6 N2)))) __flatten_var_0))) tptp.inverse_inverse_real))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X 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 X)) (@ tptp.product_fst_int_int Y))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X)) (@ tptp.product_snd_int_int Y))))) tptp.times_times_rat))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4))) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X))))) tptp.positive))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))) tptp.times_times_int))
% 6.83/7.15 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 6.83/7.15 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M6 tptp.nat)) (@ P (@ tptp.suc M6))))))))))
% 6.83/7.15 (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)))))))))
% 6.83/7.15 (assert (= tptp.comple1385675409528146559p_real (lambda ((X6 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z5 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) X6) (@ (@ tptp.ord_less_eq_real X) Z5))))))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re4555766996558763186at_nat tptp.pcr_int) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat)) tptp.nat2))
% 6.83/7.15 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0)))) tptp.ord_less_int))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U4)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))) tptp.plus_plus_int))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U4)))) __flatten_var_0)))) tptp.minus_minus_int))
% 6.83/7.15 (assert (= tptp.field_7254667332652039916t_real (lambda ((X tptp.rat)) (@ tptp.real2 (lambda ((N2 tptp.nat)) X)))))
% 6.83/7.15 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (exists ((Q3 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q3))) (and (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real _let_1) Y3)))))))
% 6.83/7.15 (assert (forall ((Y7 (-> tptp.nat tptp.rat)) (X4 tptp.real)) (=> (@ tptp.cauchy Y7) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.real2 Y7)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real X4) (@ tptp.field_7254667332652039916t_real (@ Y7 N4))))))))
% 6.83/7.15 (assert (forall ((Y7 (-> tptp.nat tptp.rat)) (X4 tptp.real)) (=> (@ tptp.cauchy Y7) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.field_7254667332652039916t_real (@ Y7 N4)))) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.real2 Y7))))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y3 tptp.real)) (=> (@ tptp.cauchy X8) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.field_7254667332652039916t_real (@ X8 N4))) Y3)) (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X8)) Y3)))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0)))))
% 6.83/7.15 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (U tptp.nat) (V tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (@ (@ tptp.product_Pair_nat_nat U) V)) (= (@ (@ tptp.plus_plus_nat X4) V) (@ (@ tptp.plus_plus_nat U) Y3)))))
% 6.83/7.15 (assert (let ((_let_1 (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (@ (@ (@ (@ tptp.bNF_re8246922863344978751at_nat tptp.intrel) (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4))) _let_1) _let_1)))
% 6.83/7.15 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.83/7.15 (assert (= tptp.intrel (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X) V4) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0)))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0)))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0)))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U4)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U4)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U4)))) __flatten_var_0)))))
% 6.83/7.15 (assert (forall ((Net tptp.filter_real)) (@ (@ (@ tptp.has_ve631408500373753343e_real (lambda ((X tptp.real)) X)) tptp.one_one_real) Net)))
% 6.83/7.15 (assert (= tptp.has_fi5821293074295781190e_real tptp.has_ve631408500373753343e_real))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X 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 X))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) (lambda ((X 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 X))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))))
% 6.83/7.15 (assert (= tptp.ratrel (lambda ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X))) (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 X)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_1))))))))
% 6.83/7.15 (assert (= tptp.ratrel (lambda ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X))) (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 X)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_1))))))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X 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 X)) (@ tptp.product_fst_int_int Y))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X)) (@ tptp.product_snd_int_int Y))))) (lambda ((X 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 X)) (@ tptp.product_fst_int_int Y))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X)) (@ tptp.product_snd_int_int Y))))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y6 Bool) (Z4 Bool)) (= Y6 Z4))) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X))))) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X))))))
% 6.83/7.15 (assert (forall ((Xa tptp.product_prod_int_int) (X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X4))) (let ((_let_2 (@ tptp.product_snd_int_int Xa))) (=> (@ (@ tptp.ratrel Xa) Xa) (=> (@ (@ tptp.ratrel X4) X4) (= (@ (@ tptp.plus_plus_rat (@ tptp.abs_Rat Xa)) (@ tptp.abs_Rat X4)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))))
% 6.83/7.15 (assert (forall ((X4 tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X4) X4) (= (@ tptp.positive (@ tptp.abs_Rat X4)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_snd_int_int X4)))))))
% 6.83/7.15 (assert (forall ((Xa tptp.product_prod_int_int) (X4 tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel Xa) Xa) (=> (@ (@ tptp.ratrel X4) X4) (= (@ (@ tptp.times_times_rat (@ tptp.abs_Rat Xa)) (@ tptp.abs_Rat X4)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa)) (@ tptp.product_fst_int_int X4))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int Xa)) (@ tptp.product_snd_int_int X4)))))))))
% 6.83/7.15 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.last_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))))
% 6.83/7.15 (assert (forall ((F (-> tptp.nat tptp.real)) (M7 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) M7)))) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N4) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ F M4))))) (@ tptp.topolo7531315842566124627t_real F)))))
% 6.83/7.15 (assert (forall ((F (-> tptp.nat tptp.real)) (M7 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) M7)))) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N4) (@ (@ tptp.ord_less_eq_real (@ F M4)) (@ F N4))))) (@ tptp.topolo7531315842566124627t_real F)))))
% 6.83/7.15 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N4) (@ (@ tptp.ord_less_eq_real (@ X8 M4)) (@ X8 N4)))) (@ tptp.topolo7531315842566124627t_real X8)))))
% 6.83/7.15 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ tptp.topolo7531315842566124627t_real (@ tptp.power_power_real X4))))))
% 6.83/7.15 (assert (forall ((D tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) D))) (= (@ (@ tptp.filtermap_real_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real X) D))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1))))))
% 6.83/7.15 (assert (forall ((A tptp.real)) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real X) A))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.83/7.15 (assert (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_nat S) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_less)))))
% 6.83/7.15 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X4))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y3)) (@ _let_1 Z))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y3) Z)))))
% 6.83/7.15 (assert (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_less))))
% 6.83/7.15 (assert (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B2) (=> (@ (@ tptp.ord_less_eq_nat S) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_leq)))))
% 6.83/7.15 (assert (forall ((A tptp.nat) (B2 tptp.nat) (S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S)) (@ (@ tptp.product_Pair_nat_nat B2) T))) tptp.fun_pair_leq))))
% 6.83/7.15 (assert (@ (@ (@ tptp.ordering_top_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) X))) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_nat Y) X))) tptp.zero_zero_nat))
% 6.83/7.15 (assert (forall ((A3 tptp.set_nat)) (= (@ tptp.nat_set_encode (@ (@ tptp.vimage_nat_nat tptp.suc) A3)) (@ (@ tptp.divide_divide_nat (@ tptp.nat_set_encode A3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.83/7.15 (assert (= tptp.euclid4774559944035922753ze_int (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)))
% 6.83/7.15 (assert (forall ((F5 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F5)) (@ tptp.finite_finite_nat F5))))
% 6.83/7.15 (assert (forall ((N tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat (@ tptp.suc N)) A3)) (@ (@ tptp.insert_nat N) (@ _let_1 A3))))))
% 6.83/7.15 (assert (forall ((A3 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A3)) (@ _let_1 A3)))))
% 6.83/7.15 (assert (forall ((X4 tptp.nat)) (= (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vimage_nat_nat tptp.suc) (@ tptp.nat_set_decode X4)))))
% 6.83/7.15 (assert (forall ((K tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.euclid3395696857347342551nt_int K)) tptp.one_one_int)))
% 6.83/7.15 (assert (= tptp.euclid3398187327856392827nt_nat (lambda ((N2 tptp.nat)) tptp.one_one_nat)))
% 6.83/7.15 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (= (@ tptp.euclid3395696857347342551nt_int K) (@ tptp.sgn_sgn_int K)))))
% 6.83/7.15 (assert (= tptp.euclid3395696857347342551nt_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.83/7.15 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((M6 tptp.extended_enat) (__flatten_var_0 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((N1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M1) N1))) false) M6))) true) __flatten_var_0))))
% 6.83/7.15 (assert (@ tptp.transp_nat_rat tptp.realrel))
% 6.83/7.15 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((M6 tptp.extended_enat) (N2 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (@ tptp.ord_less_nat M1)) true) N2))) false) M6))))
% 6.83/7.15 (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))))))))
% 6.83/7.15 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P3 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P3)))))
% 6.83/7.15 (assert (forall ((K tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_decode (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M)) (@ (@ tptp.nat_prod_decode_aux K) M))))
% 6.83/7.15 (assert (forall ((A0 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (@ _let_1 A0) (=> (=> (@ _let_1 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (=> (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.suc N4))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (=> (forall ((X5 tptp.nat) (Y5 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X5) Y5) (@ tptp.nat_prod_decode N4)) (@ P Y5))) (@ P _let_1))))) (@ P A0)))))))
% 6.83/7.15 (assert (forall ((X4 tptp.nat) (Y3 tptp.list_nat)) (=> (= (@ tptp.nat_list_decode X4) Y3) (=> (=> (= X4 tptp.zero_zero_nat) (not (= Y3 tptp.nil_nat))) (not (forall ((N4 tptp.nat)) (=> (= X4 (@ tptp.suc N4)) (not (= Y3 (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.cons_nat X) (@ tptp.nat_list_decode Y)))) (@ tptp.nat_prod_decode N4)))))))))))
% 6.83/7.15 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1) (= (@ tptp.nat_list_decode _let_1) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.cons_nat X) (@ tptp.nat_list_decode Y)))) (@ tptp.nat_prod_decode N)))))))
% 6.83/7.15 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_list_decode (@ tptp.suc N)) (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.cons_nat X) (@ tptp.nat_list_decode Y)))) (@ tptp.nat_prod_decode N)))))
% 6.83/7.15 (assert (forall ((X4 tptp.nat) (Y3 tptp.list_nat)) (let ((_let_1 (@ tptp.accp_nat tptp.nat_list_decode_rel))) (=> (= (@ tptp.nat_list_decode X4) Y3) (=> (@ _let_1 X4) (=> (=> (= X4 tptp.zero_zero_nat) (=> (= Y3 tptp.nil_nat) (not (@ _let_1 tptp.zero_zero_nat)))) (not (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.suc N4))) (=> (= X4 _let_1) (=> (= Y3 (@ (@ tptp.produc2761476792215241774st_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.cons_nat X) (@ tptp.nat_list_decode Y)))) (@ tptp.nat_prod_decode N4))) (not (@ (@ tptp.accp_nat tptp.nat_list_decode_rel) _let_1)))))))))))))
% 6.83/7.15 (assert (= tptp.powr_real2 (lambda ((B3 tptp.real) (I2 tptp.real)) (let ((_let_1 (@ tptp.literal2 false))) (let ((_let_2 (@ _let_1 false))) (let ((_let_3 (@ _let_2 true))) (let ((_let_4 (@ (@ (@ (@ _let_3 false) true) true) true))) (let ((_let_5 (@ _let_1 true))) (let ((_let_6 (@ _let_5 true))) (let ((_let_7 (@ (@ (@ (@ _let_6 true) false) true) true))) (let ((_let_8 (@ tptp.literal2 true))) (let ((_let_9 (@ _let_8 false))) (let ((_let_10 (@ _let_9 true))) (let ((_let_11 (@ (@ (@ (@ _let_10 false) false) true) true))) (let ((_let_12 (@ _let_8 true))) (let ((_let_13 (@ _let_12 true))) (let ((_let_14 (@ _let_13 true))) (let ((_let_15 (@ (@ (@ _let_14 false) true) true))) (let ((_let_16 (@ _let_2 false))) (let ((_let_17 (@ _let_16 false))) (let ((_let_18 (@ (@ (@ _let_17 true) true) true))) (let ((_let_19 (@ _let_16 true))) (let ((_let_20 (@ (@ (@ _let_17 false) true) false))) (let ((_let_21 (@ (@ _let_5 false) false))) (let ((_let_22 (@ (@ (@ _let_21 true) true) true))) (let ((_let_23 (@ _let_13 false))) (let ((_let_24 (@ _let_9 false))) (let ((_let_25 (@ (@ (@ (@ _let_24 true) false) true) true))) (let ((_let_26 (@ (@ (@ _let_19 false) true) true))) (let ((_let_27 (@ (@ (@ _let_23 true) true) true))) (let ((_let_28 (@ (@ (@ (@ _let_3 true) false) true) true))) (let ((_let_29 (@ (@ (@ (@ _let_24 false) false) true) true))) (let ((_let_30 (@ (@ (@ _let_14 true) false) true))) (let ((_let_31 (@ tptp.power_power_real B3))) (let ((_let_32 (@ tptp.archim6058952711729229775r_real I2))) (let ((_let_33 (@ (@ (@ (@ (@ _let_12 false) false) true) true) true))) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real B3) tptp.zero_zero_real)) (@ (@ tptp.abort_real (@ _let_18 (@ _let_15 (@ _let_27 (@ _let_22 (@ _let_30 (@ _let_22 (@ _let_11 (@ _let_29 (@ _let_28 (@ _let_20 (@ _let_27 (@ _let_25 (@ _let_4 (@ _let_26 (@ _let_20 (@ _let_7 (@ _let_15 (@ _let_7 (@ _let_18 (@ _let_15 (@ _let_33 (@ _let_25 (@ _let_4 (@ _let_25 (@ (@ (@ (@ (@ _let_6 false) true) true) true) (@ _let_11 (@ _let_20 (@ (@ (@ (@ _let_21 false) true) true) (@ _let_29 (@ _let_33 (@ _let_11 tptp.zero_zero_literal)))))))))))))))))))))))))))))))) (lambda ((Uu tptp.product_unit)) (@ (@ tptp.powr_real2 B3) I2)))) (@ (@ (@ tptp.if_real (= (@ tptp.ring_1_of_int_real _let_32) I2)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) I2)) (@ _let_31 (@ tptp.nat2 _let_32))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_31 (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real I2))))))) (@ (@ tptp.abort_real (@ _let_18 (@ _let_15 (@ _let_27 (@ _let_22 (@ _let_30 (@ _let_22 (@ _let_11 (@ _let_29 (@ _let_28 (@ _let_20 (@ _let_27 (@ _let_25 (@ _let_4 (@ _let_26 (@ _let_20 (@ _let_7 (@ _let_15 (@ _let_7 (@ (@ (@ (@ (@ _let_10 true) false) true) false) (@ _let_25 (@ _let_7 (@ _let_4 (@ _let_11 (@ (@ (@ (@ _let_23 false) true) true) (@ _let_11 (@ _let_22 (@ _let_20 (@ _let_11 (@ (@ (@ (@ _let_19 true) true) true) (@ _let_18 (@ _let_15 (@ _let_7 (@ _let_11 (@ _let_7 (@ _let_4 tptp.zero_zero_literal)))))))))))))))))))))))))))))))))))) (lambda ((Uu tptp.product_unit)) (@ (@ tptp.powr_real2 B3) I2)))))))))))))))))))))))))))))))))))))))))
% 6.83/7.15 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I2 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))))
% 6.83/7.15 (assert (forall ((A3 tptp.set_nat) (M tptp.nat)) (let ((_let_1 (@ tptp.produc457027306803732586at_nat A3))) (= (@ _let_1 (lambda ((Uu tptp.nat)) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 (lambda ((I2 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) I2))))) (@ _let_1 (lambda ((I2 tptp.nat)) (@ (@ tptp.set_or6659071591806873216st_nat (@ (@ tptp.minus_minus_nat M) I2)) M))))))))
% 6.83/7.15 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.83/7.15 (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)))))))))))
% 6.83/7.15 (assert (= tptp.euclid4777050414544973029ze_nat tptp.id_nat))
% 6.83/7.15 (assert (= tptp.times_times_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X 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 X)) (@ tptp.product_fst_int_int Y))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X)) (@ tptp.product_snd_int_int Y)))))))
% 6.83/7.15 (assert (= tptp.plus_plus_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X 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 X))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))
% 6.83/7.15 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X)))))))
% 6.83/7.15 (assert (= tptp.nat2 (@ (@ (@ tptp.map_fu2345160673673942751at_nat tptp.rep_Integ) tptp.id_nat) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))))
% 6.83/7.15 (assert (= tptp.ord_less_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0))))))
% 6.83/7.15 (assert (= tptp.ord_less_eq_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0))))))
% 6.83/7.15 (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 ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U4)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))))))
% 6.83/7.15 (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 ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U4)))) __flatten_var_0))))))
% 6.83/7.15 (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 ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U4 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U4)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U4))))))) __flatten_var_0))))))
% 6.83/7.15 (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 ((N8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N2) (@ P (@ (@ tptp.product_Pair_nat_nat N2) M6))))))))))
% 6.83/7.15 (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))))
% 6.83/7.15 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.83/7.15 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.extended_enat2 Nat) (@ tptp.extended_enat2 Nat2)) (= Nat Nat2))))
% 6.83/7.15 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.83/7.15 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.83/7.15 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ (@ tptp.plus_plus_nat M) N)))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) (@ tptp.extended_enat2 tptp.zero_zero_nat)) N)))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (let ((_let_1 (@ tptp.extended_enat2 tptp.zero_zero_nat))) (= (@ (@ tptp.minus_3235023915231533773d_enat _let_1) N) _let_1))))
% 6.83/7.15 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_enat2 A)) (@ tptp.extended_enat2 B2)) (@ tptp.extended_enat2 (@ (@ tptp.minus_minus_nat A) B2)))))
% 6.83/7.15 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat M) N)))))
% 6.83/7.15 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ (@ tptp.ord_max_nat M) N)))))
% 6.83/7.15 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat (@ tptp.extended_enat2 M)) (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ (@ tptp.ord_min_nat M) N)))))
% 6.83/7.15 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.extended_enat2 N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) N))))
% 6.83/7.15 (assert (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 tptp.zero_zero_nat)))
% 6.83/7.15 (assert (forall ((X4 tptp.nat)) (= (= (@ tptp.extended_enat2 X4) tptp.zero_z5237406670263579293d_enat) (= X4 tptp.zero_zero_nat))))
% 6.83/7.15 (assert (forall ((X4 tptp.nat)) (= (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 X4)) (= X4 tptp.zero_zero_nat))))
% 6.83/7.15 (assert (= tptp.semiri4216267220026989637d_enat tptp.extended_enat2))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat) (M tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_enat2 M)) (exists ((K2 tptp.nat)) (= N (@ tptp.extended_enat2 K2))))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat) (M tptp.nat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_enat2 M)) (not (forall ((K2 tptp.nat)) (=> (= N (@ tptp.extended_enat2 K2)) (not (@ (@ tptp.ord_less_nat K2) M))))))))
% 6.83/7.15 (assert (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_enat2 tptp.one_one_nat)))
% 6.83/7.15 (assert (forall ((X4 tptp.nat)) (= (= (@ tptp.extended_enat2 X4) tptp.one_on7984719198319812577d_enat) (= X4 tptp.one_one_nat))))
% 6.83/7.15 (assert (forall ((X4 tptp.nat)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_enat2 X4)) (= X4 tptp.one_one_nat))))
% 6.83/7.15 (assert (= tptp.numera1916890842035813515d_enat (lambda ((K3 tptp.num)) (@ tptp.extended_enat2 (@ tptp.numeral_numeral_nat K3)))))
% 6.83/7.15 (assert (forall ((M tptp.nat) (N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_enat2 (@ tptp.suc M))) N) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M)) N))))
% 6.83/7.15 (assert (forall ((A3 tptp.set_Extended_enat) (N tptp.nat)) (=> (forall ((Y4 tptp.extended_enat)) (=> (@ (@ tptp.member_Extended_enat Y4) A3) (@ (@ tptp.ord_le2932123472753598470d_enat Y4) (@ tptp.extended_enat2 N)))) (@ tptp.finite4001608067531595151d_enat A3))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat) (M tptp.nat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat N) (@ tptp.extended_enat2 M)) (exists ((K2 tptp.nat)) (= N (@ tptp.extended_enat2 K2))))))
% 6.83/7.15 (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))))
% 6.83/7.15 (assert (forall ((X4 tptp.extended_enat) (Y3 tptp.extended_enat) (N tptp.nat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X4) Y3)) (@ tptp.extended_enat2 N)) (exists ((Y9 tptp.nat) (X9 tptp.nat)) (and (= X4 (@ tptp.extended_enat2 X9)) (= Y3 (@ tptp.extended_enat2 Y9)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X9) Y9)) N))))))
% 6.83/7.15 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1)))))
% 6.83/7.15 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (L2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat L2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))) (let ((_let_3 (@ (@ tptp.vEBT_Node Info) Deg))) (= (@ (@ tptp.vEBT_VEBT_elim_dead (@ (@ _let_3 TreeList2) Summary)) (@ tptp.extended_enat2 L2)) (@ (@ _let_3 (@ (@ tptp.take_VEBT_VEBT _let_2) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T3) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))))) TreeList2))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary) (@ tptp.extended_enat2 _let_2)))))))))
% 6.83/7.15 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.extended_enat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_elim_dead X4) Xa) Y3) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_1) (not (= Y3 _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info2) Deg2))) (=> (= X4 (@ (@ _let_1 TreeList3) Summary2)) (=> (= Xa tptp.extend5688581933313929465d_enat) (not (= Y3 (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T3) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList3)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) tptp.extend5688581933313929465d_enat)))))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList3) Summary2)) (forall ((L3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat L3) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))) (=> (= Xa (@ tptp.extended_enat2 L3)) (not (= Y3 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) (@ (@ tptp.take_VEBT_VEBT _let_2) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T3) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList3))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) (@ tptp.extended_enat2 _let_2)))))))))))))))))
% 6.83/7.15 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info) Deg))) (= (@ (@ tptp.vEBT_VEBT_elim_dead (@ (@ _let_1 TreeList2) Summary)) tptp.extend5688581933313929465d_enat) (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T3) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg) _let_1))))))) TreeList2)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary) tptp.extend5688581933313929465d_enat))))))
% 6.83/7.15 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (= (@ (@ tptp.vEBT_VEBT_elim_dead _let_1) tptp.extend5688581933313929465d_enat) _let_1)))))
% 6.83/7.15 (assert (forall ((X4 tptp.extended_enat)) (= (not (= X4 tptp.extend5688581933313929465d_enat)) (exists ((I2 tptp.nat)) (= X4 (@ tptp.extended_enat2 I2))))))
% 6.83/7.15 (assert (forall ((X4 tptp.extended_enat)) (= (forall ((Y tptp.nat)) (not (= X4 (@ tptp.extended_enat2 Y)))) (= X4 tptp.extend5688581933313929465d_enat))))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat Q2) tptp.extend5688581933313929465d_enat) (not (= Q2 tptp.extend5688581933313929465d_enat)))))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.extend5688581933313929465d_enat) Q2))))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.extend5688581933313929465d_enat) Q2) tptp.extend5688581933313929465d_enat)))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat Q2) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat)))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat Q2) tptp.extend5688581933313929465d_enat)))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) Q2) (= Q2 tptp.extend5688581933313929465d_enat))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.extend5688581933313929465d_enat) N) tptp.extend5688581933313929465d_enat)))
% 6.83/7.15 (assert (= (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat)))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.extend5688581933313929465d_enat) Q2) tptp.extend5688581933313929465d_enat)))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.extend5688581933313929465d_enat) Q2)))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.extend5688581933313929465d_enat) Q2) Q2)))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (=> (not (= N tptp.extend5688581933313929465d_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) N) tptp.zero_z5237406670263579293d_enat))))
% 6.83/7.15 (assert (forall ((X4 tptp.extended_enat) (Y3 tptp.extended_enat)) (=> (not (= X4 tptp.extend5688581933313929465d_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X4) Y3)) X4) Y3))))
% 6.83/7.15 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_enat2 A)) tptp.extend5688581933313929465d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.83/7.15 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 N)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 6.83/7.15 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_enat2 M)) tptp.extend5688581933313929465d_enat))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z5237406670263579293d_enat)) (=> (not _let_2) (= _let_1 tptp.extend5688581933313929465d_enat)))))))
% 6.83/7.15 (assert (= tptp.comple4398354569131411667d_enat (lambda ((A6 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A6 tptp.bot_bo7653980558646680370d_enat)) tptp.zero_z5237406670263579293d_enat) (@ (@ (@ tptp.if_Extended_enat (@ tptp.finite4001608067531595151d_enat A6)) (@ tptp.lattic921264341876707157d_enat A6)) tptp.extend5688581933313929465d_enat)))))
% 6.83/7.15 (assert (= tptp.comple2295165028678016749d_enat (lambda ((A6 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A6 tptp.bot_bo7653980558646680370d_enat)) tptp.extend5688581933313929465d_enat) (@ tptp.ord_Le1955565732374568822d_enat (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) A6)))))))
% 6.83/7.15 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat A) B2) tptp.extend5688581933313929465d_enat) (or (and (= A tptp.extend5688581933313929465d_enat) (not (= B2 tptp.zero_z5237406670263579293d_enat))) (and (= B2 tptp.extend5688581933313929465d_enat) (not (= A tptp.zero_z5237406670263579293d_enat)))))))
% 6.83/7.15 (assert (not (= tptp.extend5688581933313929465d_enat tptp.zero_z5237406670263579293d_enat)))
% 6.83/7.15 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ _let_1 B2)) (@ _let_1 C)) (and (not (= A tptp.extend5688581933313929465d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat B2) C))))))
% 6.83/7.15 (assert (not (= tptp.extend5688581933313929465d_enat tptp.one_on7984719198319812577d_enat)))
% 6.83/7.15 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N) tptp.extend5688581933313929465d_enat) (or (= M tptp.extend5688581933313929465d_enat) (= N tptp.extend5688581933313929465d_enat)))))
% 6.83/7.15 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (or (= A tptp.extend5688581933313929465d_enat) (= B2 C))))))
% 6.83/7.15 (assert (forall ((K tptp.num)) (not (= (@ tptp.numera1916890842035813515d_enat K) tptp.extend5688581933313929465d_enat))))
% 6.83/7.15 (assert (= tptp.top_to3028658606643905974d_enat tptp.extend5688581933313929465d_enat))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat Q2) tptp.extend5688581933313929465d_enat)))
% 6.83/7.15 (assert (forall ((A tptp.extended_enat) (B2 tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ _let_1 B2)) (@ _let_1 C)) (or (= A tptp.extend5688581933313929465d_enat) (@ (@ tptp.ord_le2932123472753598470d_enat B2) C))))))
% 6.83/7.15 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 N)))))
% 6.83/7.15 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 M)))))
% 6.83/7.15 (assert (= (lambda ((P5 (-> tptp.extended_enat Bool))) (exists ((X7 tptp.extended_enat)) (@ P5 X7))) (lambda ((P6 (-> tptp.extended_enat Bool))) (or (@ P6 tptp.extend5688581933313929465d_enat) (exists ((X tptp.nat)) (@ P6 (@ tptp.extended_enat2 X)))))))
% 6.83/7.15 (assert (forall ((Y3 tptp.extended_enat) (Ya tptp.extended_enat) (Yb tptp.extended_enat)) (let ((_let_1 (not (= Yb tptp.extend5688581933313929465d_enat)))) (let ((_let_2 (= Ya tptp.extend5688581933313929465d_enat))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (= Y3 tptp.extend5688581933313929465d_enat))) (=> (=> (exists ((Nat3 tptp.nat)) (= Y3 (@ tptp.extended_enat2 Nat3))) (=> (exists ((Nata tptp.nat)) (= Ya (@ tptp.extended_enat2 Nata))) (forall ((Natb tptp.nat)) (not (= Yb (@ tptp.extended_enat2 Natb)))))) (=> (=> (exists ((Nat3 tptp.nat)) (= Y3 (@ tptp.extended_enat2 Nat3))) (=> (exists ((Nata tptp.nat)) (= Ya (@ tptp.extended_enat2 Nata))) _let_1)) (=> (=> (exists ((Nat3 tptp.nat)) (= Y3 (@ tptp.extended_enat2 Nat3))) (=> _let_2 (forall ((Nata tptp.nat)) (not (= Yb (@ tptp.extended_enat2 Nata)))))) (=> (=> (exists ((Nat3 tptp.nat)) (= Y3 (@ tptp.extended_enat2 Nat3))) _let_3) (=> (=> _let_4 (=> (exists ((Nat3 tptp.nat)) (= Ya (@ tptp.extended_enat2 Nat3))) (forall ((Nata tptp.nat)) (not (= Yb (@ tptp.extended_enat2 Nata)))))) (=> (=> _let_4 (=> (exists ((Nat3 tptp.nat)) (= Ya (@ tptp.extended_enat2 Nat3))) _let_1)) (=> (=> _let_4 (=> _let_2 (forall ((Nat3 tptp.nat)) (not (= Yb (@ tptp.extended_enat2 Nat3)))))) (not (=> _let_4 _let_3)))))))))))))))
% 6.83/7.15 (assert (forall ((Y3 tptp.extended_enat) (Ya tptp.extended_enat)) (let ((_let_1 (not (= Ya tptp.extend5688581933313929465d_enat)))) (let ((_let_2 (= Y3 tptp.extend5688581933313929465d_enat))) (=> (=> (exists ((Nat3 tptp.nat)) (= Y3 (@ tptp.extended_enat2 Nat3))) (forall ((Nata tptp.nat)) (not (= Ya (@ tptp.extended_enat2 Nata))))) (=> (=> (exists ((Nat3 tptp.nat)) (= Y3 (@ tptp.extended_enat2 Nat3))) _let_1) (=> (=> _let_2 (forall ((Nat3 tptp.nat)) (not (= Ya (@ tptp.extended_enat2 Nat3))))) (not (=> _let_2 _let_1)))))))))
% 6.83/7.15 (assert (forall ((Y3 tptp.extended_enat)) (=> (forall ((Nat3 tptp.nat)) (not (= Y3 (@ tptp.extended_enat2 Nat3)))) (= Y3 tptp.extend5688581933313929465d_enat))))
% 6.83/7.15 (assert (forall ((Nat tptp.nat)) (not (= (@ tptp.extended_enat2 Nat) tptp.extend5688581933313929465d_enat))))
% 6.83/7.15 (assert (forall ((Nat tptp.nat)) (not (= tptp.extend5688581933313929465d_enat (@ tptp.extended_enat2 Nat)))))
% 6.83/7.15 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le72135733267957522d_enat tptp.extend5688581933313929465d_enat) (@ tptp.extended_enat2 M)))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.extend5688581933313929465d_enat) (not (forall ((K2 tptp.nat)) (not (= N (@ tptp.extended_enat2 K2))))))))
% 6.83/7.15 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_enat2 M)) tptp.extend5688581933313929465d_enat)))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (= (@ (@ tptp.times_7803423173614009249d_enat tptp.extend5688581933313929465d_enat) N) tptp.extend5688581933313929465d_enat))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (= (@ (@ tptp.times_7803423173614009249d_enat N) tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat))))
% 6.83/7.15 (assert (= tptp.plus_p3455044024723400733d_enat (lambda ((M6 tptp.extended_enat) (N2 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P3 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.plus_plus_nat O) P3)))) tptp.extend5688581933313929465d_enat) N2))) tptp.extend5688581933313929465d_enat) M6))))
% 6.83/7.15 (assert (= tptp.minus_3235023915231533773d_enat (lambda ((A4 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((X tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((Y tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.minus_minus_nat X) Y)))) tptp.zero_z5237406670263579293d_enat) B3))) tptp.extend5688581933313929465d_enat) A4))))
% 6.83/7.15 (assert (= tptp.times_7803423173614009249d_enat (lambda ((M6 tptp.extended_enat) (N2 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P3 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P3)))) (@ (@ (@ tptp.if_Extended_enat (= O tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N2))) (@ (@ (@ tptp.if_Extended_enat (= N2 tptp.zero_z5237406670263579293d_enat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M6))))
% 6.83/7.15 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.extended_enat) (Y3 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_VEBT_elim_dead X4) Xa) Y3) (=> (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_1) (=> (= Y3 _let_1) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat _let_1) Xa))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Node Info2) Deg2))) (let ((_let_2 (@ (@ _let_1 TreeList3) Summary2))) (=> (= X4 _let_2) (=> (= Xa tptp.extend5688581933313929465d_enat) (=> (= Y3 (@ (@ _let_1 (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T3) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList3)) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) tptp.extend5688581933313929465d_enat))) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat _let_2) tptp.extend5688581933313929465d_enat))))))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList3) Summary2)) (forall ((L3 tptp.nat)) (let ((_let_1 (@ tptp.extended_enat2 L3))) (let ((_let_2 (@ (@ tptp.vEBT_Node Info2) Deg2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat L3) (@ (@ tptp.power_power_nat _let_3) (@ (@ tptp.divide_divide_nat Deg2) _let_3))))) (=> (= Xa _let_1) (=> (= Y3 (@ (@ _let_2 (@ (@ tptp.take_VEBT_VEBT _let_4) (@ (@ tptp.map_VE8901447254227204932T_VEBT (lambda ((T3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vEBT_VEBT_elim_dead T3) (@ tptp.extended_enat2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat Deg2) _let_1))))))) TreeList3))) (@ (@ tptp.vEBT_VEBT_elim_dead Summary2) (@ tptp.extended_enat2 _let_4)))) (not (@ (@ tptp.accp_P6183159247885693666d_enat tptp.vEBT_V312737461966249ad_rel) (@ (@ tptp.produc581526299967858633d_enat (@ (@ _let_2 TreeList3) Summary2)) _let_1)))))))))))))))))))
% 6.83/7.15 (assert (forall ((N tptp.nat)) (= (@ tptp.extended_the_enat (@ tptp.extended_enat2 N)) N)))
% 6.83/7.15 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (@ tptp.finite4001608067531595151d_enat A3) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.lattic921264341876707157d_enat A3)) (@ tptp.lattic921264341876707157d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A3)))))))
% 6.83/7.15 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ tptp.extended_eSuc M) (@ tptp.extended_eSuc N)) (= M N))))
% 6.83/7.15 (assert (= (@ tptp.extended_eSuc tptp.extend5688581933313929465d_enat) tptp.extend5688581933313929465d_enat))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat) (M tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc M)) (@ (@ tptp.ord_le72135733267957522d_enat N) M))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat) (M tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc M)) (@ (@ tptp.ord_le2932123472753598470d_enat N) M))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat) (M tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc M)) (@ (@ tptp.minus_3235023915231533773d_enat N) M))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat N) (@ tptp.extended_eSuc tptp.zero_z5237406670263579293d_enat)) (= N tptp.zero_z5237406670263579293d_enat))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat (@ tptp.extended_eSuc N)) tptp.one_on7984719198319812577d_enat) N)))
% 6.83/7.15 (assert (forall ((K tptp.num)) (= (@ tptp.extended_eSuc (@ tptp.numera1916890842035813515d_enat K)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num K) tptp.one)))))
% 6.83/7.15 (assert (forall ((M tptp.nat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.extended_enat2 M))) (= (@ (@ tptp.ord_le72135733267957522d_enat _let_1) (@ tptp.extended_eSuc N)) (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) N)))))
% 6.83/7.15 (assert (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_eSuc tptp.zero_z5237406670263579293d_enat)))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.extended_eSuc N))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_eSuc N)))))
% 6.83/7.15 (assert (= tptp.extended_eSuc (lambda ((N2 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat N2) tptp.one_on7984719198319812577d_enat))))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) Q2) (@ tptp.extended_eSuc Q2))))
% 6.83/7.15 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat Q2) tptp.one_on7984719198319812577d_enat) (@ tptp.extended_eSuc Q2))))
% 6.83/7.15 (assert (@ tptp.order_4130057895858720880d_enat tptp.extended_eSuc))
% 6.83/7.15 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat M))) (= (@ _let_1 (@ tptp.extended_eSuc N)) (@ tptp.extended_eSuc (@ _let_1 N))))))
% 6.83/7.15 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.extended_eSuc M)) N) (@ tptp.extended_eSuc (@ (@ tptp.plus_p3455044024723400733d_enat M) N)))))
% 6.83/7.15 (assert (forall ((X4 tptp.extended_enat) (Y3 tptp.extended_enat)) (= (@ tptp.extended_eSuc (@ (@ tptp.ord_ma741700101516333627d_enat X4) Y3)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.extended_eSuc X4)) (@ tptp.extended_eSuc Y3)))))
% 6.83/7.15 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat M))) (= (@ _let_1 (@ tptp.extended_eSuc N)) (@ (@ tptp.plus_p3455044024723400733d_enat M) (@ _let_1 N))))))
% 6.83/7.15 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.extended_eSuc M)) N) (@ (@ tptp.plus_p3455044024723400733d_enat N) (@ (@ tptp.times_7803423173614009249d_enat M) N)))))
% 6.83/7.15 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M) N) (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc M)) N))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat N) (@ tptp.extended_eSuc N))))
% 6.83/7.15 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.extended_eSuc N)) tptp.zero_z5237406670263579293d_enat))))
% 6.83/7.15 (assert (forall ((N tptp.nat)) (= (@ tptp.extended_eSuc (@ tptp.extended_enat2 N)) (@ tptp.extended_enat2 (@ tptp.suc N)))))
% 6.83/7.15 (assert (forall ((X4 tptp.extended_enat) (Y3 tptp.nat)) (= (= (@ tptp.extended_eSuc X4) (@ tptp.extended_enat2 Y3)) (exists ((N2 tptp.nat)) (and (= Y3 (@ tptp.suc N2)) (= X4 (@ tptp.extended_enat2 N2)))))))
% 6.83/7.15 (assert (forall ((Y3 tptp.nat) (X4 tptp.extended_enat)) (= (= (@ tptp.extended_enat2 Y3) (@ tptp.extended_eSuc X4)) (exists ((N2 tptp.nat)) (and (= Y3 (@ tptp.suc N2)) (= (@ tptp.extended_enat2 N2) X4))))))
% 6.83/7.15 (assert (forall ((A3 tptp.set_Extended_enat)) (=> (not (= A3 tptp.bot_bo7653980558646680370d_enat)) (= (@ tptp.extended_eSuc (@ tptp.comple4398354569131411667d_enat A3)) (@ tptp.comple4398354569131411667d_enat (@ (@ tptp.image_80655429650038917d_enat tptp.extended_eSuc) A3))))))
% 6.83/7.15 (assert (= tptp.extended_eSuc (@ (@ tptp.extend3600170679010898289d_enat (lambda ((N2 tptp.nat)) (@ tptp.extended_enat2 (@ tptp.suc N2)))) tptp.extend5688581933313929465d_enat)))
% 6.83/7.15 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y3)) tptp.less_than) (@ (@ tptp.ord_less_nat X4) Y3))))
% 6.83/7.15 (assert (@ (@ (@ (@ tptp.quotie3684837364556693515t_real tptp.realrel) tptp.real2) tptp.rep_real) tptp.cr_real))
% 6.83/7.15 (assert (= tptp.gcd_lcm_Code_integer (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A4)) (@ tptp.abs_abs_Code_integer B3))) (@ (@ tptp.gcd_gcd_Code_integer A4) B3)))))
% 6.83/7.15 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.gcd_lcm_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))))
% 6.83/7.15 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int M)) (@ tptp.abs_abs_int N)) (@ (@ tptp.times_times_int (@ (@ tptp.gcd_gcd_int M) N)) (@ (@ tptp.gcd_lcm_int M) N)))))
% 6.83/7.15 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.gcd_gcd_nat M6) N2)) (@ (@ tptp.gcd_lcm_nat M6) N2)))))
% 6.83/7.15 (assert (= tptp.gcd_lcm_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat X) Y)) (@ (@ tptp.gcd_gcd_nat X) Y)))))
% 6.83/7.15 (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) (@ _let_1 (@ (@ tptp.gcd_lcm_nat M) N)))))))
% 6.83/7.15 (assert (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (=> (not (= N tptp.zero_zero_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_lcm_int M) N))))))
% 6.83/7.15 (assert (= tptp.gcd_lcm_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A4)) (@ tptp.abs_abs_int B3))) (@ (@ tptp.gcd_gcd_int A4) B3)))))
% 6.83/7.15 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ (@ tptp.if_int false) X4) Y3) Y3)))
% 6.83/7.15 (assert (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ (@ tptp.if_int true) X4) Y3) X4)))
% 6.83/7.15 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X4) Y3) Y3)))
% 6.83/7.15 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X4) Y3) X4)))
% 6.83/7.15 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ (@ tptp.if_num false) X4) Y3) Y3)))
% 6.83/7.15 (assert (forall ((X4 tptp.num) (Y3 tptp.num)) (= (@ (@ (@ tptp.if_num true) X4) Y3) X4)))
% 6.83/7.15 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X4) Y3) Y3)))
% 6.83/7.15 (assert (forall ((X4 tptp.rat) (Y3 tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X4) Y3) X4)))
% 6.83/7.15 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ (@ tptp.if_real false) X4) Y3) Y3)))
% 6.83/7.15 (assert (forall ((X4 tptp.real) (Y3 tptp.real)) (= (@ (@ (@ tptp.if_real true) X4) Y3) X4)))
% 6.83/7.15 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X6 tptp.real)) (@ P X6)))))
% 6.83/7.15 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X4) Y3) Y3)))
% 6.83/7.15 (assert (forall ((X4 tptp.complex) (Y3 tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X4) Y3) X4)))
% 6.83/7.15 (assert (forall ((X4 tptp.extended_enat) (Y3 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X4) Y3) Y3)))
% 6.83/7.15 (assert (forall ((X4 tptp.extended_enat) (Y3 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X4) Y3) X4)))
% 6.83/7.15 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X4) Y3) Y3)))
% 6.83/7.15 (assert (forall ((X4 tptp.code_integer) (Y3 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X4) Y3) X4)))
% 6.83/7.15 (assert (forall ((X4 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X4) Y3) Y3)))
% 6.83/7.15 (assert (forall ((X4 tptp.set_int) (Y3 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X4) Y3) X4)))
% 6.83/7.15 (assert (forall ((X4 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X4) Y3) Y3)))
% 6.83/7.15 (assert (forall ((X4 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 tptp.list_int) (Y3 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 tptp.list_int) (Y3 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 tptp.list_nat) (Y3 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 tptp.list_nat) (Y3 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 (-> tptp.int tptp.int)) (Y3 (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 (-> tptp.int tptp.int)) (Y3 (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 (-> tptp.nat tptp.rat)) (Y3 (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 (-> tptp.nat tptp.rat)) (Y3 (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 tptp.option_nat) (Y3 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 tptp.option_nat) (Y3 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 tptp.option_num) (Y3 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 tptp.option_num) (Y3 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 (-> tptp.nat tptp.int tptp.int)) (Y3 (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 (-> tptp.nat tptp.int tptp.int)) (Y3 (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 (-> tptp.nat tptp.nat tptp.nat)) (Y3 (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 (-> tptp.nat tptp.nat tptp.nat)) (Y3 (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((X4 tptp.produc6271795597528267376eger_o) (Y3 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 tptp.produc6271795597528267376eger_o) (Y3 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X4) Y3) X4)))
% 47.56/47.88 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 47.56/47.88 (assert (forall ((X4 tptp.produc8923325533196201883nteger) (Y3 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X4) Y3) Y3)))
% 47.56/47.88 (assert (forall ((X4 tptp.produc8923325533196201883nteger) (Y3 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X4) Y3) X4)))
% 47.56/47.88 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ (@ tptp.vEBT_VEBT_high tptp.xa) _let_1) (@ (@ tptp.vEBT_VEBT_high tptp.za) _let_1)))))
% 47.56/47.88 (set-info :filename cvc5---1.0.5_30919)
% 47.56/47.88 (check-sat-assuming ( true ))
% 47.56/47.88 ------- get file name : TPTP file name is ITP246^1
% 47.56/47.88 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30919.smt2...
% 47.56/47.88 --- Run --ho-elim --full-saturate-quant at 10...
% 47.56/47.88 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 47.56/47.88 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 47.56/47.88 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 47.56/47.88 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 47.56/47.88 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 171.19/171.54 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 171.19/171.54 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 171.19/171.54 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 171.19/171.54 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 171.19/171.54 % SZS status Theorem for ITP246^1
% 171.19/171.54 % SZS output start Proof for ITP246^1
% 171.19/171.54 (
% 171.19/171.54 (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_high tptp.za) _let_4))) (let ((_let_6 (@ tptp.vEBT_VEBT_high tptp.xa))) (let ((_let_7 (@ _let_6 _let_4))) (let ((_let_8 (not (= _let_7 _let_5)))) (let ((_let_9 (= tptp.gcd_lcm_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A4)) (@ tptp.abs_abs_int B3))) (@ (@ tptp.gcd_gcd_int A4) B3)))))) (let ((_let_10 (= tptp.gcd_lcm_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat X) Y)) (@ (@ tptp.gcd_gcd_nat X) Y)))))) (let ((_let_11 (= tptp.gcd_lcm_Code_integer (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A4)) (@ tptp.abs_abs_Code_integer B3))) (@ (@ tptp.gcd_gcd_Code_integer A4) B3)))))) (let ((_let_12 (= tptp.extended_eSuc (lambda ((N2 tptp.extended_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat N2) tptp.one_on7984719198319812577d_enat))))) (let ((_let_13 (= tptp.times_7803423173614009249d_enat (lambda ((M6 tptp.extended_enat) (N2 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P3 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P3)))) (@ (@ (@ tptp.if_Extended_enat (= O tptp.zero_zero_nat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N2))) (@ (@ (@ tptp.if_Extended_enat (= N2 tptp.zero_z5237406670263579293d_enat)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M6))))) (let ((_let_14 (= tptp.minus_3235023915231533773d_enat (lambda ((A4 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((X tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((Y tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.minus_minus_nat X) Y)))) tptp.zero_z5237406670263579293d_enat) B3))) tptp.extend5688581933313929465d_enat) A4))))) (let ((_let_15 (= tptp.plus_p3455044024723400733d_enat (lambda ((M6 tptp.extended_enat) (N2 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P3 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.plus_plus_nat O) P3)))) tptp.extend5688581933313929465d_enat) N2))) tptp.extend5688581933313929465d_enat) M6))))) (let ((_let_16 (= tptp.top_to3028658606643905974d_enat tptp.extend5688581933313929465d_enat))) (let ((_let_17 (= tptp.comple2295165028678016749d_enat (lambda ((A6 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A6 tptp.bot_bo7653980558646680370d_enat)) tptp.extend5688581933313929465d_enat) (@ tptp.ord_Le1955565732374568822d_enat (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) A6)))))))) (let ((_let_18 (= tptp.comple4398354569131411667d_enat (lambda ((A6 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= A6 tptp.bot_bo7653980558646680370d_enat)) tptp.zero_z5237406670263579293d_enat) (@ (@ (@ tptp.if_Extended_enat (@ tptp.finite4001608067531595151d_enat A6)) (@ tptp.lattic921264341876707157d_enat A6)) tptp.extend5688581933313929465d_enat)))))) (let ((_let_19 (= tptp.numera1916890842035813515d_enat (lambda ((K3 tptp.num)) (@ tptp.extended_enat2 (@ tptp.numeral_numeral_nat K3)))))) (let ((_let_20 (= tptp.one_on7984719198319812577d_enat (@ tptp.extended_enat2 tptp.one_one_nat)))) (let ((_let_21 (= tptp.semiri4216267220026989637d_enat tptp.extended_enat2))) (let ((_let_22 (= tptp.zero_z5237406670263579293d_enat (@ tptp.extended_enat2 tptp.zero_zero_nat)))) (let ((_let_23 (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)))) (let ((_let_24 (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)))) (let ((_let_25 (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (let ((_let_26 (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)))) (let ((_let_27 (= tptp.plus_plus_rat (@ _let_26 (lambda ((X 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 X))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))) (let ((_let_28 (= tptp.times_times_rat (@ _let_26 (lambda ((X 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 X)) (@ tptp.product_fst_int_int Y))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X)) (@ tptp.product_snd_int_int Y)))))))) (let ((_let_29 (= tptp.euclid4777050414544973029ze_nat tptp.id_nat))) (let ((_let_30 (= tptp.semiri1316708129612266289at_nat tptp.id_nat))) (let ((_let_31 (= 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_32 (= tptp.ord_le72135733267957522d_enat (lambda ((M6 tptp.extended_enat) (N2 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (@ tptp.ord_less_nat M1)) true) N2))) false) M6))))) (let ((_let_33 (= tptp.ord_le2932123472753598470d_enat (lambda ((M6 tptp.extended_enat) (__flatten_var_0 tptp.extended_enat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((N1 tptp.nat)) (@ (@ (@ tptp.extended_case_enat_o (lambda ((M1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M1) N1))) false) M6))) true) __flatten_var_0))))) (let ((_let_34 (= tptp.euclid3395696857347342551nt_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))))) (let ((_let_35 (= tptp.euclid3398187327856392827nt_nat (lambda ((N2 tptp.nat)) tptp.one_one_nat)))) (let ((_let_36 (= tptp.euclid4774559944035922753ze_int (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)))) (let ((_let_37 (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)))) (let ((_let_38 (= tptp.ratrel (lambda ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X))) (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 X)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_1))))))))) (let ((_let_39 (= tptp.has_fi5821293074295781190e_real tptp.has_ve631408500373753343e_real))) (let ((_let_40 (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)))) (let ((_let_41 (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel))) (let ((_let_42 (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel))) (let ((_let_43 (= tptp.intrel (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U4 tptp.nat) (V4 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X) V4) (@ (@ tptp.plus_plus_nat U4) Y)))) __flatten_var_0)))))) (let ((_let_44 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (let ((_let_45 (= tptp.field_7254667332652039916t_real (lambda ((X tptp.rat)) (@ tptp.real2 (lambda ((N2 tptp.nat)) X)))))) (let ((_let_46 (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)))) (let ((_let_47 (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int))) (let ((_let_48 (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int))) (let ((_let_49 (= tptp.comple1385675409528146559p_real (lambda ((X6 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z5 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) X6) (@ (@ tptp.ord_less_eq_real X) Z5))))))))) (let ((_let_50 (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)))) (let ((_let_51 (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real))) (let ((_let_52 (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) _let_51))) (let ((_let_53 (= tptp.pcr_real tptp.cr_real))) (let ((_let_54 (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real))) (let ((_let_55 (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel))) (let ((_let_56 (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) _let_55))) (let ((_let_57 (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2))) (let ((_let_58 (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) _let_57))) (let ((_let_59 (= tptp.plus_plus_real (@ _let_58 (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X6 N2)) (@ Y8 N2))))))) (let ((_let_60 (= tptp.times_times_real (@ _let_58 (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X6 N2)) (@ Y8 N2))))))) (let ((_let_61 (= tptp.uminus_uminus_real (@ _let_57 (lambda ((X6 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X6 N2))))))) (let ((_let_62 (= tptp.cr_real (lambda ((X (-> tptp.nat tptp.rat)) (Y tptp.real)) (and (@ (@ tptp.realrel X) X) (= (@ tptp.real2 X) Y)))))) (let ((_let_63 (= tptp.inverse_inverse_real (@ _let_57 (lambda ((X6 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X6)) (lambda ((N2 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X6 N2)))) __flatten_var_0)))))) (let ((_let_64 (= tptp.realrel (lambda ((X6 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat))) (and (@ tptp.cauchy X6) (@ tptp.cauchy Y8) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X6 N2)) (@ Y8 N2))))))))) (let ((_let_65 (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (@ tptp.positive2 (@ (@ tptp.minus_minus_real Y) X)))))) (let ((_let_66 (= tptp.semiri5074537144036343181t_real (lambda ((X tptp.nat)) (@ tptp.real2 (lambda ((N2 tptp.nat)) (@ tptp.semiri681578069525770553at_rat X))))))) (let ((_let_67 (= tptp.cauchy (lambda ((X6 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X6 M6)) (@ X6 N2)))) R5)))))))))))) (let ((_let_68 (= tptp.rcis (lambda ((R5 tptp.real) (A4 tptp.real)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R5)) (@ tptp.cis A4)))))) (let ((_let_69 (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))) (let ((_let_70 (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))) (let ((_let_71 (= 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_72 (= tptp.sup_sup_nat tptp.ord_max_nat))) (let ((_let_73 (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))) (let ((_let_74 (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M6)))))))) (let ((_let_75 (@ tptp.bit0 _let_1))) (let ((_let_76 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_75))))))))) (let ((_let_77 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_78 (@ _let_77 _let_76))) (let ((_let_79 (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (let ((_let_80 (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X) Y)) E3))))))) _let_79))))) (let ((_let_81 (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X) Y)) E3))))))) _let_79))))) (let ((_let_82 (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z7) (@ (@ tptp.ord_less_int Z7) Z5))))))))) (let ((_let_83 (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z5) (@ (@ tptp.ord_less_int Z7) Z5))))))))) (let ((_let_84 (= tptp.ord_less_eq_rat (lambda ((P3 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 P3)))))) (let ((_let_85 (= tptp.inf_inf_nat tptp.ord_min_nat))) (let ((_let_86 (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))) (let ((_let_87 (= tptp.comple4887499456419720421f_real (lambda ((X6 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X6))))))) (let ((_let_88 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_89 (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real _let_88) tptp.one_one_real)))) (let ((_let_90 (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))) (let ((_let_91 (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat))) (let ((_let_92 (= _let_91 tptp.top_top_set_nat))) (let ((_let_93 (@ tptp.filterlim_real_real tptp.artanh_real))) (let ((_let_94 (@ tptp.topolo2177554685111907308n_real tptp.one_one_real))) (let ((_let_95 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (let ((_let_96 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_97 (@ tptp.divide_divide_real tptp.pi))) (let ((_let_98 (@ _let_97 _let_96))) (let ((_let_99 (@ tptp.uminus_uminus_real _let_98))) (let ((_let_100 (@ tptp.filterlim_real_real tptp.tan_real))) (let ((_let_101 (@ tptp.filterlim_real_real tptp.arctan))) (let ((_let_102 (@ tptp.filterlim_real_real tptp.tanh_real))) (let ((_let_103 (= tptp.real_V3694042436643373181omplex (lambda ((X tptp.complex) (Y tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y)))))) (let ((_let_104 (= tptp.real_V975177566351809787t_real (lambda ((X tptp.real) (Y tptp.real)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y)))))) (let ((_let_105 (@ tptp.topolo2177554685111907308n_real _let_98))) (let ((_let_106 (@ tptp.topolo2815343760600316023s_real tptp.one_one_real))) (let ((_let_107 (= tptp.real_V5970128139526366754l_real (lambda ((F2 (-> tptp.real tptp.real))) (exists ((C2 tptp.real)) (= F2 (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C2)))))))) (let ((_let_108 (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) _let_78)))) (let ((_let_109 (= tptp.root (lambda ((N2 tptp.nat) (X 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)))) X)))))) (let ((_let_110 (@ tptp.insert_nat tptp.zero_zero_nat))) (let ((_let_111 (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu tptp.real)) (exists ((I2 tptp.int) (J3 tptp.int)) (and (= Uu (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I2)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))) (let ((_let_112 (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M6)))))) (let ((_let_113 (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M6))))))) (let ((_let_114 (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M6))))))) (let ((_let_115 (= tptp.set_or5832277885323065728an_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))) (let ((_let_116 (= tptp.set_or6656581121297822940st_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J3)))))) (let ((_let_117 (= tptp.set_or4662586982721622107an_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I2) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))) (let ((_let_118 (= tptp.quotient_of (lambda ((X tptp.rat)) (@ tptp.the_Pr4378521158711661632nt_int (lambda ((Pair tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Pair))) (let ((_let_2 (@ tptp.product_fst_int_int Pair))) (and (= X (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)))))))))) (let ((_let_119 (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))) (let ((_let_120 (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))) (let ((_let_121 (= tptp.positive (lambda ((X tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X))) (@ (@ 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_122 (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))) (let ((_let_123 (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))) (let ((_let_124 (= tptp.fract (lambda ((K3 tptp.int) (L tptp.int)) (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K3)) (@ tptp.ring_1_of_int_rat L)))))) (let ((_let_125 (= tptp.sqr (lambda ((X tptp.num)) (@ (@ tptp.times_times_num X) X))))) (let ((_let_126 (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N2))) M6)))))) (let ((_let_127 (= tptp.ord_le6747313008572928689nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))) (let ((_let_128 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (let ((_let_129 (= tptp.normalize (lambda ((P3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P3))) (let ((_let_2 (@ tptp.product_fst_int_int P3))) (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_130 (= tptp.adjust_mod (lambda ((L tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L) R5)))))) (let ((_let_131 (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_132 (= 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_133 (= tptp.archim3151403230148437115or_rat (lambda ((X tptp.rat)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z5)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))) (let ((_let_134 (= tptp.archim6058952711729229775r_real (lambda ((X tptp.real)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))) (let ((_let_135 (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X23 tptp.nat)) X23))))) (let ((_let_136 (= 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_137 (= 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_138 (= 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_139 (@ tptp.numera6620942414471956472nteger _let_1))) (let ((_let_140 (= tptp.invers8013647133539491842omplex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (let ((_let_3 (@ tptp.re X))) (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_141 (= tptp.real_V1022390504157884413omplex (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z5)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z5)) _let_1)))))))) (let ((_let_142 (= tptp.times_times_complex (lambda ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.re Y))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X)))) (let ((_let_3 (@ tptp.im Y))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X)))) (@ (@ 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_143 (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X))) (@ _let_1 (@ tptp.im X)))))))) (let ((_let_144 (= tptp.plus_plus_complex (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y))) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y))))))) (let ((_let_145 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_146 (= tptp.csqrt (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z5))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z5))) (let ((_let_4 (@ tptp.im Z5))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))) (let ((_let_147 (= 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_148 (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))) (let ((_let_149 (= tptp.set_ord_lessThan_nat _let_77))) (let ((_let_150 (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))) (let ((_let_151 (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))) (let ((_let_152 (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L)))))) (let ((_let_153 (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))) (let ((_let_154 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (let ((_let_155 (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L))))))) (let ((_let_156 (= tptp.arcsin (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X 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)) X) (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.sin_real X) Y))))))))) (let ((_let_157 (@ tptp.times_times_real _let_96))) (let ((_let_158 (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N2)) (@ (@ tptp.modulo_modulo_nat M6) N2)))))) (let ((_let_159 (= tptp.arctan (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X 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)) X) (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.tan_real X) Y))))))))) (let ((_let_160 (= 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_161 (= 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_162 (= tptp.sqrt (@ tptp.root _let_2)))) (let ((_let_163 (= tptp.arg (lambda ((Z5 tptp.complex)) (@ (@ (@ tptp.if_real (= Z5 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z5) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))))) (let ((_let_164 (= tptp.real_V1485227260804924795R_real tptp.times_times_real))) (let ((_let_165 (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) N2)))) (let ((_let_166 (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))) (let ((_let_167 (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat))) (let ((_let_168 (= _let_167 tptp.bot_bot_set_nat))) (let ((_let_169 (@ tptp.power_power_nat _let_2))) (let ((_let_170 (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat _let_169)))) (let ((_let_171 (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N8) (@ (@ tptp.ord_less_nat X) M6)))))))) (let ((_let_172 (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 tptp.zero_zero_int) (= A32 (@ (@ 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) (= A32 (@ (@ 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) (= A32 (@ (@ 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_173 (@ tptp.numeral_numeral_real _let_75))) (let ((_let_174 (@ _let_97 _let_173))) (let ((_let_175 (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_176 (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))) (let ((_let_177 (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))) (let ((_let_178 (forall ((B2 Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B2)))) (and (=> B2 (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))) (let ((_let_179 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_180 (= tptp.vEBT_V8194947554948674370ptions (lambda ((T3 tptp.vEBT_VEBT) (X tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T3) X) (@ (@ tptp.vEBT_VEBT_membermima T3) X)))))) (let ((_let_181 (= 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_182 (= 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_183 (= 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_184 (= 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_185 (= 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_186 (= tptp.bit_ri6519982836138164636nteger (lambda ((N2 tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger _let_1) A4))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) _let_2))))))) (let ((_let_187 (= tptp.nat_set_decode (lambda ((X 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 X) (@ (@ tptp.power_power_nat _let_1) N2))))))))))) (let ((_let_188 (= tptp.set_int2 (lambda ((Xs tptp.list_int)) (@ tptp.collect_int (lambda ((Uu tptp.int)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_int Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)))))))))) (let ((_let_189 (= tptp.set_nat2 (lambda ((Xs tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu tptp.nat)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_nat Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)))))))))) (let ((_let_190 (= tptp.set_o2 (lambda ((Xs tptp.list_o)) (@ tptp.collect_o (lambda ((Uu Bool)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_o Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)))))))))) (let ((_let_191 (= tptp.set_VEBT_VEBT2 (lambda ((Xs tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu tptp.vEBT_VEBT)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_VEBT_VEBT Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))))))) (let ((_let_192 (= tptp.set_list_nat2 (lambda ((Xs tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu tptp.list_nat)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_list_nat Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3023201423986296836st_nat Xs)))))))))) (let ((_let_193 (= tptp.set_real2 (lambda ((Xs tptp.list_real)) (@ tptp.collect_real (lambda ((Uu tptp.real)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_real Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs)))))))))) (let ((_let_194 (= tptp.set_complex2 (lambda ((Xs tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu tptp.complex)) (exists ((I2 tptp.nat)) (and (= Uu (@ (@ tptp.nth_complex Xs) I2)) (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3451745648224563538omplex Xs)))))))))) (let ((_let_195 (= 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_196 (= 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_197 (= 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_198 (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))) (let ((_let_199 (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ tptp.collect_int (lambda ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))) (let ((_let_200 (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B7 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))) (let ((_let_201 (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ tptp.collect_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))) (let ((_let_202 (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))) (let ((_let_203 (= tptp.minus_925952699566721837d_enat (lambda ((A6 tptp.set_Extended_enat) (B7 tptp.set_Extended_enat)) (@ tptp.collec4429806609662206161d_enat (lambda ((X tptp.extended_enat)) (let ((_let_1 (@ tptp.member_Extended_enat X))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))) (let ((_let_204 (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B7))))))) (let ((_let_205 (= tptp.ord_less_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ (@ tptp.ord_less_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B7))))))) (let ((_let_206 (= tptp.ord_less_set_complex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ (@ tptp.ord_less_complex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A6))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) B7))))))) (let ((_let_207 (= tptp.ord_le2529575680413868914d_enat (lambda ((A6 tptp.set_Extended_enat) (B7 tptp.set_Extended_enat)) (@ (@ tptp.ord_le8499522857272258027enat_o (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) A6))) (lambda ((X tptp.extended_enat)) (@ (@ tptp.member_Extended_enat X) B7))))))) (let ((_let_208 (= tptp.vEBT_VEBT_set_vebt (lambda ((T3 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T3)))))) (let ((_let_209 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_210 (@ _let_209 _let_7))) (let ((_let_211 (@ tptp.vEBT_vebt_maxt _let_210))) (let ((_let_212 (@ tptp.vEBT_VEBT_low tptp.xa))) (let ((_let_213 (@ _let_212 _let_4))) (let ((_let_214 (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_213)) _let_211))) (let ((_let_215 (= _let_211 tptp.none_nat))) (let ((_let_216 (@ (@ tptp.vEBT_vebt_succ tptp.summary) _let_7))) (let ((_let_217 (@ _let_209 (@ tptp.the_nat _let_216)))) (let ((_let_218 (@ tptp.vEBT_vebt_mint _let_217))) (let ((_let_219 (@ _let_169 _let_4))) (let ((_let_220 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat _let_219)))) (let ((_let_221 (@ (@ tptp.vEBT_VEBT_add (@ _let_220 _let_216)) _let_218))) (let ((_let_222 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary))) (let ((_let_223 (@ (@ tptp.vEBT_vebt_succ _let_222) tptp.xa))) (let ((_let_224 (= _let_223 _let_221))) (let ((_let_225 (= _let_216 tptp.none_nat))) (let ((_let_226 (not _let_225))) (let ((_let_227 (and (=> _let_225 (= _let_223 tptp.none_nat)) (=> _let_226 _let_224)))) (let ((_let_228 (and (not _let_215) _let_214))) (let ((_let_229 (@ tptp.the_nat _let_221))) (let ((_let_230 (@ tptp.vEBT_vebt_member _let_222))) (let ((_let_231 (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))) (let ((_let_232 (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))) (let ((_let_233 (= tptp.res _let_229))) (let ((_let_234 (= tptp.bot_bot_nat tptp.zero_zero_nat))) (let ((_let_235 (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))) (let ((_let_236 (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))) (let ((_let_237 (@ tptp.some_nat tptp.miny))) (let ((_let_238 (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int))) (let ((_let_239 (= _let_238 tptp.bot_bot_nat_o))) (let ((_let_240 (@ _let_209 tptp.sc))) (let ((_let_241 (@ tptp.ord_less_nat tptp.xa))) (let ((_let_242 (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z5 tptp.nat)) (=> (@ (@ tptp.member_nat Z5) Xs) (=> (@ (@ tptp.ord_less_nat X) Z5) (@ (@ tptp.ord_less_eq_nat Y) Z5))))))))) (let ((_let_243 (= tptp.mi tptp.ma))) (let ((_let_244 (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))) (let ((_let_245 (@ _let_169 tptp.m))) (let ((_let_246 (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList))) (let ((_let_247 (= _let_246 _let_245))) (let ((_let_248 (@ tptp.vEBT_V8194947554948674370ptions tptp.summary))) (let ((_let_249 (@ tptp.vEBT_vebt_member tptp.summary))) (let ((_let_250 (@ _let_209 _let_5))) (let ((_let_251 (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) N2))) (@ (@ tptp.vEBT_VEBT_low X) N2)))))) (let ((_let_252 (@ (@ tptp.vEBT_VEBT_low tptp.za) _let_4))) (let ((_let_253 (@ (@ tptp.vEBT_V8194947554948674370ptions _let_250) _let_252))) (let ((_let_254 (= tptp.za tptp.ma))) (let ((_let_255 (@ (@ tptp.vEBT_vebt_member _let_250) _let_252))) (let ((_let_256 (= _let_5 _let_7))) (let ((_let_257 (@ tptp.ord_less_nat _let_5))) (let ((_let_258 (= tptp.za tptp.mi))) (let ((_let_259 (not _let_243))) (let ((_let_260 (= tptp.ord_less_num (lambda ((X tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y) (not (@ (@ tptp.ord_less_eq_num Y) X))))))) (let ((_let_261 (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y) (not (@ (@ tptp.ord_less_eq_rat Y) X))))))) (let ((_let_262 (= tptp.topolo6517432010174082258omplex (lambda ((X6 (-> tptp.nat tptp.complex))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X6 M6)) (@ X6 N2)))) E3)))))))))))) (let ((_let_263 (= tptp.uminus_uminus_int (lambda ((A4 tptp.int)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A4)) tptp.one_one_int))))) (let ((_let_264 (= tptp.uminus1351360451143612070nteger (lambda ((A4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.bit_ri7632146776885996613nteger A4)) tptp.one_one_Code_integer))))) (let ((_let_265 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_266 (@ tptp.uminus_uminus_int _let_265))) (let ((_let_267 (@ tptp.uminus1351360451143612070nteger _let_139))) (let ((_let_268 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_269 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_270 (= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M6)) (@ X6 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))) (let ((_let_271 (= tptp.sinh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))) (let ((_let_272 (= tptp.sinh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (let ((_let_273 (= tptp.cosh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))) (let ((_let_274 (= tptp.cosh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (let ((_let_275 (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_276 (= 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_277 (= 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_278 (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B7) (not (= A6 B7))))))) (let ((_let_279 (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))) (let ((_let_280 (= 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_281 (= 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_282 (= 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_283 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_284 (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B3)) A4))))) (let ((_let_285 (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B3)) A4))))) (let ((_let_286 (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B3)) A4))))) (let ((_let_287 (@ tptp.numeral_numeral_rat tptp.one))) (let ((_let_288 (@ tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_289 (@ tptp.numeral_numeral_real tptp.one))) (let ((_let_290 (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_291 (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))) (let ((_let_292 (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_293 (= 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_294 (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 K3))))))) (let ((_let_295 (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 K3))))))) (let ((_let_296 (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 K3))))))) (let ((_let_297 (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 K3))))))) (let ((_let_298 (= tptp.cis (lambda ((B3 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B3))))))) (let ((_let_299 (@ tptp.suc _let_179))) (let ((_let_300 (@ tptp.nat2 _let_265))) (let ((_let_301 (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))) (let ((_let_302 (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N2))))))) (let ((_let_303 (@ tptp.nat2 tptp.one_one_int))) (let ((_let_304 (= tptp.numeral_numeral_nat (lambda ((I2 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I2)))))) (let ((_let_305 (@ _let_157 tptp.pi))) (let ((_let_306 (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit))) (let ((_let_307 (@ tptp.sqrt _let_96))) (let ((_let_308 (@ tptp.plus_plus_complex tptp.one_one_complex))) (let ((_let_309 (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))) (let ((_let_310 (= tptp.sgn_sgn_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex Z5) (@ tptp.real_V4546457046886955230omplex (@ tptp.real_V1022390504157884413omplex Z5))))))) (let ((_let_311 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_312 (@ tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_313 (@ tptp.times_times_complex _let_312))) (let ((_let_314 (@ tptp.times_times_complex tptp.imaginary_unit))) (let ((_let_315 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_316 (= 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_317 (= 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_318 (= tptp.sgn_sgn_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_rat (= X tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))) (let ((_let_319 (= tptp.sgn_sgn_Code_integer (lambda ((X tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))) (let ((_let_320 (= tptp.sgn_sgn_int (lambda ((X tptp.int)) (@ (@ (@ tptp.if_int (= X tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))) (let ((_let_321 (= tptp.sgn_sgn_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))) (let ((_let_322 (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))) (let ((_let_323 (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))) (let ((_let_324 (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))) (let ((_let_325 (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))) (let ((_let_326 (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))) (let ((_let_327 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_328 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_329 (@ tptp.arccos _let_88))) (let ((_let_330 (= _let_329 tptp.pi))) (let ((_let_331 (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))) (let ((_let_332 (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_333 (@ tptp.bit1 tptp.one))) (let ((_let_334 (@ tptp.numeral_numeral_real _let_333))) (let ((_let_335 (@ tptp.sqrt _let_334))) (let ((_let_336 (@ _let_97 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_333))))) (let ((_let_337 (= tptp.sin_complex (lambda ((X tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))))) (let ((_let_338 (= tptp.sin_real (lambda ((X tptp.real)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))))) (let ((_let_339 (@ _let_97 _let_334))) (let ((_let_340 (= tptp.tan_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X)) (@ tptp.cos_real X)))))) (let ((_let_341 (= tptp.tan_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex X)))))) (let ((_let_342 (@ (@ tptp.divide1717551699836669952omplex _let_312) _let_315))) (let ((_let_343 (@ tptp.real_V1803761363581548252l_real tptp.pi))) (let ((_let_344 (@ (@ tptp.divide_divide_real _let_343) _let_96))) (let ((_let_345 (= tptp.arcosh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))) (let ((_let_346 (@ (@ tptp.divide_divide_real _let_335) _let_96))) (let ((_let_347 (@ _let_283 _let_96))) (let ((_let_348 (= tptp.powr_real (lambda ((X tptp.real) (A4 tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A4) (@ tptp.ln_ln_real X)))))))) (let ((_let_349 (@ (@ tptp.divide_divide_real _let_307) _let_96))) (let ((_let_350 (@ tptp.cos_real _let_96))) (let ((_let_351 (= tptp.archimedean_frac_rat (lambda ((X tptp.rat)) (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X))))))) (let ((_let_352 (= tptp.archim2898591450579166408c_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X))))))) (let ((_let_353 (= tptp.cot_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))))) (let ((_let_354 (= tptp.cot_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X)) (@ tptp.sin_complex X)))))) (let ((_let_355 (@ tptp.divide_divide_real _let_334))) (let ((_let_356 (@ (@ tptp.times_times_real (@ _let_355 _let_96)) tptp.pi))) (let ((_let_357 (@ tptp.bit1 _let_333))) (let ((_let_358 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_1)))) (let ((_let_359 (= tptp.archim7778729529865785530nd_rat (lambda ((X tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))) (let ((_let_360 (= tptp.archim8280529875227126926d_real (lambda ((X tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))) (let ((_let_361 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_362 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_363 (@ tptp.ord_less_real tptp.pi))) (let ((_let_364 (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))) (let ((_let_365 (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))) (let ((_let_366 (= tptp.archim2889992004027027881ng_rat (lambda ((X tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (@ (@ (@ tptp.if_int (= X (@ tptp.ring_1_of_int_rat _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))) (let ((_let_367 (= tptp.archim7802044766580827645g_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (@ (@ (@ tptp.if_int (= X (@ tptp.ring_1_of_int_real _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))) (let ((_let_368 (= 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_369 (= 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_370 (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 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 A4) (@ (@ tptp.power_power_nat _let_1) N2))))))))) (let ((_let_371 (= tptp.bit_se1146084159140164899it_int (lambda ((A4 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 A4) (@ (@ tptp.power_power_int _let_1) N2))))))))) (let ((_let_372 (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A4) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))))) (let ((_let_373 (= tptp.bit_se2161824704523386999it_nat (lambda ((N2 tptp.nat) (A4 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A4) N2)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N2) A4))))) (let ((_let_374 (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A4) N2)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N2) A4))))) (let ((_let_375 (@ tptp.exp_real tptp.one_one_real))) (let ((_let_376 (= tptp.log (lambda ((A4 tptp.real) (X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real A4)))))) (let ((_let_377 (= 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_378 (= 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_379 (= 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_380 (= 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_381 (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_382 (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))) (let ((_let_383 (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_384 (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))) (let ((_let_385 (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_386 (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_387 (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_388 (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))) (let ((_let_389 (= tptp.arsinh_real (lambda ((X tptp.real)) (@ tptp.ln_ln_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)))))))) (let ((_let_390 (= tptp.artanh_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (let ((_let_391 (= tptp.tanh_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))) (let ((_let_2 (@ tptp.exp_complex X))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))) (let ((_let_392 (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))) (let ((_let_393 (= 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_394 (= 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_395 (= 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_396 (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A4 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A4) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_397 (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))))) (let ((_let_398 (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A4) (@ tptp.bit_se2002935070580805687sk_nat N2)))))) (let ((_let_399 (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A4) (@ tptp.bit_se2000444600071755411sk_int N2)))))) (let ((_let_400 (= tptp.neg_nu3811975205180677377ec_int (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))) (let ((_let_401 (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))) (let ((_let_402 (= tptp.neg_nu6075765906172075777c_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))) (let ((_let_403 (= tptp.neg_nu6511756317524482435omplex (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))) (let ((_let_404 (= tptp.neg_nu5851722552734809277nc_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))) (let ((_let_405 (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))) (let ((_let_406 (= tptp.neg_nu8295874005876285629c_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))) (let ((_let_407 (= tptp.neg_nu8557863876264182079omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))) (let ((_let_408 (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))) (let ((_let_409 (@ tptp.numeral_numeral_int _let_333))) (let ((_let_410 (@ tptp.numeral_numeral_rat _let_333))) (let ((_let_411 (@ tptp.numera6690914467698888265omplex _let_333))) (let ((_let_412 (= tptp.zero_n2684676970156552555ol_int (lambda ((P3 Bool)) (@ (@ (@ tptp.if_int P3) tptp.one_one_int) tptp.zero_zero_int))))) (let ((_let_413 (= tptp.zero_n2687167440665602831ol_nat (lambda ((P3 Bool)) (@ (@ (@ tptp.if_nat P3) tptp.one_one_nat) tptp.zero_zero_nat))))) (let ((_let_414 (= tptp.zero_n2052037380579107095ol_rat (lambda ((P3 Bool)) (@ (@ (@ tptp.if_rat P3) tptp.one_one_rat) tptp.zero_zero_rat))))) (let ((_let_415 (= tptp.zero_n3304061248610475627l_real (lambda ((P3 Bool)) (@ (@ (@ tptp.if_real P3) tptp.one_one_real) tptp.zero_zero_real))))) (let ((_let_416 (= tptp.zero_n1201886186963655149omplex (lambda ((P3 Bool)) (@ (@ (@ tptp.if_complex P3) tptp.one_one_complex) tptp.zero_zero_complex))))) (let ((_let_417 (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))) (let ((_let_418 (@ tptp.numeral_numeral_int tptp.one))) (let ((_let_419 (@ tptp.ord_less_rat _let_327))) (let ((_let_420 (@ tptp.ord_le6747313008572928689nteger _let_269))) (let ((_let_421 (@ tptp.ord_less_int _let_268))) (let ((_let_422 (@ tptp.ord_less_real _let_88))) (let ((_let_423 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_424 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_425 (@ tptp.ord_less_eq_int _let_268))) (let ((_let_426 (@ tptp.ord_less_eq_rat _let_327))) (let ((_let_427 (@ tptp.ord_le3102999989581377725nteger _let_269))) (let ((_let_428 (@ tptp.ord_less_eq_real _let_88))) (let ((_let_429 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_430 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_431 (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))) (let ((_let_432 (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))) (let ((_let_433 (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))) (let ((_let_434 (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))) (let ((_let_435 (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))) (let ((_let_436 (@ tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_437 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_438 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_439 (@ tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_440 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_441 (@ tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_442 (@ tptp.uminus_uminus_rat _let_328))) (let ((_let_443 (@ tptp.uminus1482373934393186551omplex _let_315))) (let ((_let_444 (@ tptp.uminus_uminus_real _let_96))) (let ((_let_445 (= (@ (@ tptp.modulo364778990260209775nteger _let_269) _let_139) tptp.one_one_Code_integer))) (let ((_let_446 (= (@ (@ tptp.modulo_modulo_int _let_268) _let_265) tptp.one_one_int))) (let ((_let_447 (@ tptp.minus_minus_rat _let_327))) (let ((_let_448 (@ tptp.minus_8373710615458151222nteger _let_269))) (let ((_let_449 (@ tptp.minus_minus_complex _let_311))) (let ((_let_450 (@ tptp.minus_minus_int _let_268))) (let ((_let_451 (@ tptp.minus_minus_real _let_88))) (let ((_let_452 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_453 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_454 (@ tptp.minus_minus_int tptp.one_one_int))) (let ((_let_455 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_456 (@ tptp.plus_plus_rat _let_327))) (let ((_let_457 (@ tptp.plus_p5714425477246183910nteger _let_269))) (let ((_let_458 (@ tptp.plus_plus_complex _let_311))) (let ((_let_459 (@ tptp.plus_plus_int _let_268))) (let ((_let_460 (@ tptp.plus_plus_real _let_88))) (let ((_let_461 (@ tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_462 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_463 (@ tptp.plus_plus_real tptp.one_one_real))) (let ((_let_464 (= (@ _let_457 tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (let ((_let_465 (= 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_466 (not (@ _let_424 tptp.zero_zero_int)))) (let ((_let_467 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_468 (@ tptp.dvd_dvd_int _let_265))) (let ((_let_469 (@ tptp.dvd_dvd_nat _let_2))) (let ((_let_470 (@ tptp.dvd_dvd_Code_integer _let_139))) (let ((_let_471 (@ tptp.numeral_numeral_nat tptp.one))) (let ((_let_472 (@ _let_462 tptp.one_one_int))) (let ((_let_473 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_474 (@ _let_473 tptp.one_one_nat))) (let ((_let_475 (@ _let_461 tptp.one_one_rat))) (let ((_let_476 (@ _let_463 tptp.one_one_real))) (let ((_let_477 (@ tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_478 (@ _let_424 tptp.one_one_int))) (let ((_let_479 (@ _let_467 tptp.one_one_nat))) (let ((_let_480 (@ _let_423 tptp.one_one_rat))) (let ((_let_481 (@ _let_362 tptp.one_one_real))) (let ((_let_482 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_483 (@ _let_429 tptp.one_one_int))) (let ((_let_484 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_485 (@ _let_484 tptp.one_one_nat))) (let ((_let_486 (@ _let_430 tptp.one_one_rat))) (let ((_let_487 (@ _let_361 tptp.one_one_real))) (let ((_let_488 (= tptp.neg_numeral_dbl_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) X))))) (let ((_let_489 (= tptp.neg_numeral_dbl_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat X) X))))) (let ((_let_490 (= tptp.neg_numeral_dbl_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real X) X))))) (let ((_let_491 (= tptp.dvd_dvd_Code_integer (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B3) A4) tptp.zero_z3403309356797280102nteger))))) (let ((_let_492 (= tptp.dvd_dvd_int (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B3) A4) tptp.zero_zero_int))))) (let ((_let_493 (= tptp.dvd_dvd_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B3) A4) tptp.zero_zero_nat))))) (let ((_let_494 (= tptp.dvd_dvd_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (=> (= A4 tptp.zero_zero_rat) (= B3 tptp.zero_zero_rat)))))) (let ((_let_495 (= tptp.dvd_dvd_real (lambda ((A4 tptp.real) (B3 tptp.real)) (=> (= A4 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))) (let ((_let_496 (= (@ (@ tptp.divide_divide_int tptp.one_one_int) _let_265) tptp.zero_zero_int))) (let ((_let_497 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) _let_2))) (let ((_let_498 (= _let_497 tptp.zero_zero_nat))) (let ((_let_499 (@ _let_454 tptp.one_one_int))) (let ((_let_500 (= _let_499 tptp.zero_zero_int))) (let ((_let_501 (@ _let_452 tptp.one_one_rat))) (let ((_let_502 (= _let_501 tptp.zero_zero_rat))) (let ((_let_503 (@ _let_455 tptp.one_one_real))) (let ((_let_504 (= _let_503 tptp.zero_zero_real))) (let ((_let_505 (@ _let_453 tptp.one_one_complex))) (let ((_let_506 (= _let_505 tptp.zero_zero_complex))) (let ((_let_507 (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N2)) N2)))))) (let ((_let_508 (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) _let_139) tptp.one_one_Code_integer))) (let ((_let_509 (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) _let_265) tptp.one_one_int))) (let ((_let_510 (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) _let_2) tptp.one_one_nat))) (let ((_let_511 (= tptp.vEBT_VEBT_low (lambda ((X tptp.nat) (N2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_512 (= tptp.ord_less_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A4) tptp.one_one_int)) __flatten_var_0))))) (let ((_let_513 (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))) (let ((_let_514 (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M6) K3))))))) (let ((_let_515 (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (let ((_let_516 (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))))) (let ((_let_517 (= 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_518 (= _let_471 tptp.one_one_nat))) (let ((_let_519 (= _let_418 tptp.one_one_int))) (let ((_let_520 (= _let_287 tptp.one_one_rat))) (let ((_let_521 (= _let_289 tptp.one_one_real))) (let ((_let_522 (= _let_288 tptp.one_one_complex))) (let ((_let_523 (= _let_474 _let_2))) (let ((_let_524 (= tptp.m (@ tptp.suc tptp.na)))) (let ((_let_525 (@ tptp.ord_less_eq_nat tptp.mi))) (let ((_let_526 (@ (@ tptp.vEBT_VEBT_high tptp.res) _let_4))) (let ((_let_527 (= _let_526 tptp.sc))) (let ((_let_528 (forall ((A tptp.nat) (B2 tptp.nat)) (or (= A B2) (not (@ (@ tptp.ord_less_eq_nat A) B2)) (not (@ (@ tptp.ord_less_eq_nat B2) A)))))) (let ((_let_529 (@ _let_169 tptp.deg))) (let ((_let_530 (= tptp.vEBT_VEBT_high (lambda ((X tptp.nat) (N2 tptp.nat)) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))) (let ((_let_531 (= _let_4 tptp.na))) (let ((_let_532 (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat)) (and (@ (@ tptp.member_nat X) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat X) Y)))))))) (let ((_let_533 (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat)) (and (@ (@ tptp.member_nat X) Xs) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_eq_nat Y) X)))))))) (let ((_let_534 (@ (@ tptp.ord_less_eq_nat _let_7) _let_5))) (let ((_let_535 (@ (@ tptp.ord_less_eq_nat _let_5) _let_7))) (let ((_let_536 (ho_15161 k_15160 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31762))) (let ((_let_537 (ho_15118 k_15117 (ho_15114 k_15113 (ho_15152 k_15151 tptp.one))))) (let ((_let_538 (ho_15593 (ho_15592 k_15591 _let_537) (ho_15593 (ho_15592 k_15599 tptp.deg) _let_537)))) (let ((_let_539 (ho_15593 (ho_15592 k_15599 tptp.xa) _let_538))) (let ((_let_540 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 _let_539)) (ho_15161 k_15160 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31764))))) (let ((_let_541 (= _let_539 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 _let_540)) _let_536))))) (let ((_let_542 (not _let_541))) (let ((_let_543 (= _let_539 _let_540))) (let ((_let_544 (or _let_543 _let_542))) (let ((_let_545 (forall ((A tptp.nat) (BOUND_VARIABLE_454200 tptp.nat) (BOUND_VARIABLE_454193 tptp.nat)) (let ((_let_1 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 A)) (ho_15161 k_15160 BOUND_VARIABLE_454193))))) (or (= A _let_1) (not (= A (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 _let_1)) (ho_15161 k_15160 BOUND_VARIABLE_454200)))))))))) (let ((_let_546 (EQ_RESOLVE (ASSUME :args (_let_533)) (MACRO_SR_EQ_INTRO :args (_let_533 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_547 (EQ_RESOLVE (ASSUME :args (_let_532)) (MACRO_SR_EQ_INTRO :args (_let_532 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_548 (SYMM (ASSUME :args (_let_531))))) (let ((_let_549 (ASSUME :args (_let_530)))) (let ((_let_550 (EQ_RESOLVE (SYMM (ASSUME :args (_let_527))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_549 _let_548 _let_547 _let_546) :args ((= tptp.sc _let_526) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_551 (EQ_RESOLVE (ASSUME :args (_let_524)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_524 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_552 (SYMM (ASSUME :args (_let_522))))) (let ((_let_553 (SYMM (ASSUME :args (_let_521))))) (let ((_let_554 (SYMM (ASSUME :args (_let_520))))) (let ((_let_555 (SYMM (ASSUME :args (_let_518))))) (let ((_let_556 (SYMM (ASSUME :args (_let_519))))) (let ((_let_557 (ASSUME :args (_let_517)))) (let ((_let_558 (ASSUME :args (_let_516)))) (let ((_let_559 (EQ_RESOLVE (ASSUME :args (_let_515)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_515 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_560 (EQ_RESOLVE (ASSUME :args (_let_514)) (MACRO_SR_EQ_INTRO :args (_let_514 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_561 (ASSUME :args (_let_513)))) (let ((_let_562 (EQ_RESOLVE (ASSUME :args (_let_512)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_512 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_563 (ASSUME :args (_let_511)))) (let ((_let_564 (ASSUME :args (_let_507)))) (let ((_let_565 (EQ_RESOLVE (SYMM (ASSUME :args (_let_506))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.zero_zero_complex _let_505) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_566 (EQ_RESOLVE (SYMM (ASSUME :args (_let_504))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.zero_zero_real _let_503) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_567 (EQ_RESOLVE (SYMM (ASSUME :args (_let_502))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.zero_zero_rat _let_501) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_568 (EQ_RESOLVE (SYMM (ASSUME :args (_let_500))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.zero_zero_int _let_499) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_569 (EQ_RESOLVE (SYMM (ASSUME :args (_let_498))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.zero_zero_nat _let_497) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_570 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_495)) (MACRO_SR_EQ_INTRO :args (_let_495 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.dvd_dvd_real (lambda ((A4 tptp.real) (B3 tptp.real)) (=> (= tptp.zero_zero_real A4) (= tptp.zero_zero_real B3)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_571 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_494)) (MACRO_SR_EQ_INTRO :args (_let_494 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.dvd_dvd_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (=> (= tptp.zero_zero_rat A4) (= tptp.zero_zero_rat B3)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_572 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_493)) (MACRO_SR_EQ_INTRO :args (_let_493 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.dvd_dvd_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= tptp.zero_zero_nat (@ (@ tptp.modulo_modulo_nat B3) A4)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_573 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_492)) (MACRO_SR_EQ_INTRO :args (_let_492 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.dvd_dvd_int (lambda ((A4 tptp.int) (B3 tptp.int)) (= tptp.zero_zero_int (@ (@ tptp.modulo_modulo_int B3) A4)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_574 (EQ_RESOLVE (ASSUME :args (_let_491)) (MACRO_SR_EQ_INTRO :args (_let_491 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_575 (ASSUME :args (_let_490)))) (let ((_let_576 (ASSUME :args (_let_489)))) (let ((_let_577 (ASSUME :args (_let_488)))) (let ((_let_578 (EQ_RESOLVE (ASSUME :args (_let_465)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_465 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_579 (SYMM (ASSUME :args (_let_464))))) (let ((_let_580 (ASSUME :args (_let_435)))) (let ((_let_581 (ASSUME :args (_let_434)))) (let ((_let_582 (ASSUME :args (_let_433)))) (let ((_let_583 (ASSUME :args (_let_432)))) (let ((_let_584 (ASSUME :args (_let_431)))) (let ((_let_585 (SYMM (ASSUME :args (_let_417))))) (let ((_let_586 (EQ_RESOLVE (ASSUME :args (_let_416)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_416 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_587 (EQ_RESOLVE (ASSUME :args (_let_415)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_415 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_588 (EQ_RESOLVE (ASSUME :args (_let_414)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_414 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_589 (EQ_RESOLVE (ASSUME :args (_let_413)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_413 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_590 (EQ_RESOLVE (ASSUME :args (_let_412)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_412 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_591 (EQ_RESOLVE (ASSUME :args (_let_408)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_408 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_592 (EQ_RESOLVE (ASSUME :args (_let_407)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_407 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_593 (EQ_RESOLVE (ASSUME :args (_let_406)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_406 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_594 (EQ_RESOLVE (ASSUME :args (_let_405)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_405 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_595 (EQ_RESOLVE (ASSUME :args (_let_404)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_404 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_596 (EQ_RESOLVE (ASSUME :args (_let_403)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_403 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_597 (EQ_RESOLVE (ASSUME :args (_let_402)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_402 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_598 (EQ_RESOLVE (ASSUME :args (_let_401)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_401 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_599 (EQ_RESOLVE (ASSUME :args (_let_400)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_400 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_600 (ASSUME :args (_let_399)))) (let ((_let_601 (ASSUME :args (_let_398)))) (let ((_let_602 (EQ_RESOLVE (ASSUME :args (_let_397)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_397 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_603 (ASSUME :args (_let_396)))) (let ((_let_604 (EQ_RESOLVE (ASSUME :args (_let_395)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_395 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_605 (EQ_RESOLVE (ASSUME :args (_let_394)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_394 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_606 (EQ_RESOLVE (ASSUME :args (_let_393)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_393 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_607 (EQ_RESOLVE (ASSUME :args (_let_392)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_392 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_608 (EQ_RESOLVE (ASSUME :args (_let_391)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_391 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_609 (EQ_RESOLVE (ASSUME :args (_let_390)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_390 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_610 (EQ_RESOLVE (ASSUME :args (_let_389)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_389 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_611 (EQ_RESOLVE (ASSUME :args (_let_380)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_380 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_612 (EQ_RESOLVE (ASSUME :args (_let_379)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_379 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_613 (EQ_RESOLVE (ASSUME :args (_let_378)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_378 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_614 (EQ_RESOLVE (ASSUME :args (_let_377)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_377 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_615 (ASSUME :args (_let_376)))) (let ((_let_616 (ASSUME :args (_let_374)))) (let ((_let_617 (ASSUME :args (_let_373)))) (let ((_let_618 (EQ_RESOLVE (ASSUME :args (_let_372)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_372 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_619 (EQ_RESOLVE (ASSUME :args (_let_371)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_371 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_620 (EQ_RESOLVE (ASSUME :args (_let_370)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_370 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_621 (EQ_RESOLVE (ASSUME :args (_let_369)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_369 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_622 (EQ_RESOLVE (ASSUME :args (_let_368)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_368 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_623 (EQ_RESOLVE (ASSUME :args (_let_367)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_367 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_624 (EQ_RESOLVE (ASSUME :args (_let_366)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_366 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_625 (EQ_RESOLVE (ASSUME :args (_let_360)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_360 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_626 (EQ_RESOLVE (ASSUME :args (_let_359)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_359 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_627 (ASSUME :args (_let_354)))) (let ((_let_628 (ASSUME :args (_let_353)))) (let ((_let_629 (EQ_RESOLVE (ASSUME :args (_let_352)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_352 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_630 (EQ_RESOLVE (ASSUME :args (_let_351)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_351 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_631 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_348)) (MACRO_SR_EQ_INTRO :args (_let_348 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.powr_real (lambda ((X tptp.real) (A4 tptp.real)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_real X)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A4) (@ tptp.ln_ln_real X)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_632 (EQ_RESOLVE (ASSUME :args (_let_345)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_345 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_633 (ASSUME :args (_let_341)))) (let ((_let_634 (ASSUME :args (_let_340)))) (let ((_let_635 (EQ_RESOLVE (ASSUME :args (_let_338)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_338 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_636 (EQ_RESOLVE (ASSUME :args (_let_337)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_337 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_637 (EQ_RESOLVE (SYMM (ASSUME :args (_let_330))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.pi _let_329) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_638 (EQ_RESOLVE (ASSUME :args (_let_326)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_326 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_639 (EQ_RESOLVE (ASSUME :args (_let_325)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_325 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_640 (EQ_RESOLVE (ASSUME :args (_let_324)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_324 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_641 (EQ_RESOLVE (ASSUME :args (_let_323)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_323 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_642 (EQ_RESOLVE (ASSUME :args (_let_322)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_322 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_643 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_321)) (MACRO_SR_EQ_INTRO :args (_let_321 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.sgn_sgn_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_real X)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_644 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_320)) (MACRO_SR_EQ_INTRO :args (_let_320 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.sgn_sgn_int (lambda ((X tptp.int)) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int X)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_645 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_319)) (MACRO_SR_EQ_INTRO :args (_let_319 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.sgn_sgn_Code_integer (lambda ((X tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= tptp.zero_z3403309356797280102nteger X)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_646 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_318)) (MACRO_SR_EQ_INTRO :args (_let_318 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.sgn_sgn_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_rat (= tptp.zero_zero_rat X)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_647 (EQ_RESOLVE (ASSUME :args (_let_317)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_317 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_648 (EQ_RESOLVE (ASSUME :args (_let_316)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_316 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_649 (ASSUME :args (_let_310)))) (let ((_let_650 (EQ_RESOLVE (ASSUME :args (_let_309)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_309 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_651 (ASSUME :args (_let_304)))) (let ((_let_652 (EQ_RESOLVE (ASSUME :args (_let_302)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_302 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_653 (ASSUME :args (_let_301)))) (let ((_let_654 (EQ_RESOLVE (ASSUME :args (_let_298)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_298 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_655 (EQ_RESOLVE (ASSUME :args (_let_297)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_297 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_656 (EQ_RESOLVE (ASSUME :args (_let_296)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_296 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_657 (EQ_RESOLVE (ASSUME :args (_let_295)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_295 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_658 (EQ_RESOLVE (ASSUME :args (_let_294)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_294 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_659 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_293)) (MACRO_SR_EQ_INTRO :args (_let_293 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.divide_divide_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int L)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L) K3))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_660 (ASSUME :args (_let_286)))) (let ((_let_661 (ASSUME :args (_let_285)))) (let ((_let_662 (ASSUME :args (_let_284)))) (let ((_let_663 (EQ_RESOLVE (ASSUME :args (_let_282)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_282 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_664 (EQ_RESOLVE (ASSUME :args (_let_281)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_281 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_665 (EQ_RESOLVE (ASSUME :args (_let_280)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_280 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_666 (ASSUME :args (_let_279)))) (let ((_let_667 (ASSUME :args (_let_278)))) (let ((_let_668 (EQ_RESOLVE (ASSUME :args (_let_277)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_277 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_669 (ASSUME :args (_let_276)))) (let ((_let_670 (EQ_RESOLVE (ASSUME :args (_let_275)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_275 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_671 (EQ_RESOLVE (ASSUME :args (_let_274)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_274 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_672 (EQ_RESOLVE (ASSUME :args (_let_273)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_273 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_673 (EQ_RESOLVE (ASSUME :args (_let_272)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_272 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_674 (EQ_RESOLVE (ASSUME :args (_let_271)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_271 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_675 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_270)) (MACRO_SR_EQ_INTRO :args (_let_270 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.topolo4055970368930404560y_real (lambda ((X6 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (not (forall ((M8 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_179270 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M8))) (or (not (@ _let_1 M6)) (not (@ _let_1 BOUND_VARIABLE_179270)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X6 M6)) (@ X6 BOUND_VARIABLE_179270)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3))))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_676 (EQ_RESOLVE (ASSUME :args (_let_264)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_264 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_677 (EQ_RESOLVE (ASSUME :args (_let_263)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_263 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_678 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_262)) (MACRO_SR_EQ_INTRO :args (_let_262 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.topolo6517432010174082258omplex (lambda ((X6 (-> tptp.nat tptp.complex))) (forall ((E3 tptp.real)) (or (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3)) (not (forall ((M8 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_183088 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M8))) (or (not (@ _let_1 M6)) (not (@ _let_1 BOUND_VARIABLE_183088)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X6 M6)) (@ X6 BOUND_VARIABLE_183088)))) E3))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_679 (ASSUME :args (_let_261)))) (let ((_let_680 (ASSUME :args (_let_260)))) (let ((_let_681 (EQ_RESOLVE (ASSUME :args (_let_251)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_251 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_682 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_242)) (MACRO_SR_EQ_INTRO :args (_let_242 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z5 tptp.nat)) (or (not (@ (@ tptp.member_nat Z5) Xs)) (not (@ (@ tptp.ord_less_nat X) Z5)) (@ (@ tptp.ord_less_eq_nat Y) Z5)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_683 (EQ_RESOLVE (SYMM (ASSUME :args (_let_239))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.bot_bot_nat_o _let_238) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_684 (ASSUME :args (_let_236)))) (let ((_let_685 (SYMM (ASSUME :args (_let_235))))) (let ((_let_686 (EQ_RESOLVE (SYMM (ASSUME :args (_let_234))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.zero_zero_nat tptp.bot_bot_nat) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_687 (EQ_RESOLVE (ASSUME :args (_let_233)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_233 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_688 (ASSUME :args (_let_232)))) (let ((_let_689 (ASSUME :args (_let_231)))) (let ((_let_690 (ASSUME :args (_let_208)))) (let ((_let_691 (ASSUME :args (_let_207)))) (let ((_let_692 (ASSUME :args (_let_206)))) (let ((_let_693 (ASSUME :args (_let_205)))) (let ((_let_694 (ASSUME :args (_let_204)))) (let ((_let_695 (ASSUME :args (_let_203)))) (let ((_let_696 (ASSUME :args (_let_202)))) (let ((_let_697 (ASSUME :args (_let_201)))) (let ((_let_698 (ASSUME :args (_let_200)))) (let ((_let_699 (ASSUME :args (_let_199)))) (let ((_let_700 (ASSUME :args (_let_198)))) (let ((_let_701 (ASSUME :args (_let_197)))) (let ((_let_702 (ASSUME :args (_let_196)))) (let ((_let_703 (EQ_RESOLVE (ASSUME :args (_let_195)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_195 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_704 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_194)) (MACRO_SR_EQ_INTRO :args (_let_194 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.set_complex2 (lambda ((Xs tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu tptp.complex)) (not (forall ((I2 tptp.nat)) (or (not (= Uu (@ (@ tptp.nth_complex Xs) I2))) (not (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3451745648224563538omplex Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_705 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_193)) (MACRO_SR_EQ_INTRO :args (_let_193 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.set_real2 (lambda ((Xs tptp.list_real)) (@ tptp.collect_real (lambda ((Uu tptp.real)) (not (forall ((I2 tptp.nat)) (or (not (= Uu (@ (@ tptp.nth_real Xs) I2))) (not (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_706 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_192)) (MACRO_SR_EQ_INTRO :args (_let_192 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.set_list_nat2 (lambda ((Xs tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu tptp.list_nat)) (not (forall ((I2 tptp.nat)) (or (not (= Uu (@ (@ tptp.nth_list_nat Xs) I2))) (not (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3023201423986296836st_nat Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_707 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_191)) (MACRO_SR_EQ_INTRO :args (_let_191 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.set_VEBT_VEBT2 (lambda ((Xs tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu tptp.vEBT_VEBT)) (not (forall ((I2 tptp.nat)) (or (not (= Uu (@ (@ tptp.nth_VEBT_VEBT Xs) I2))) (not (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_708 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_190)) (MACRO_SR_EQ_INTRO :args (_let_190 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.set_o2 (lambda ((Xs tptp.list_o)) (@ tptp.collect_o (lambda ((Uu Bool)) (not (forall ((I2 tptp.nat)) (or (= (@ (@ tptp.nth_o Xs) I2) (not Uu)) (not (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_709 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_189)) (MACRO_SR_EQ_INTRO :args (_let_189 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.set_nat2 (lambda ((Xs tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu tptp.nat)) (not (forall ((I2 tptp.nat)) (or (not (= Uu (@ (@ tptp.nth_nat Xs) I2))) (not (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_710 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_188)) (MACRO_SR_EQ_INTRO :args (_let_188 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.set_int2 (lambda ((Xs tptp.list_int)) (@ tptp.collect_int (lambda ((Uu tptp.int)) (not (forall ((I2 tptp.nat)) (or (not (= Uu (@ (@ tptp.nth_int Xs) I2))) (not (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_711 (EQ_RESOLVE (ASSUME :args (_let_187)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_187 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_712 (EQ_RESOLVE (ASSUME :args (_let_186)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_186 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_713 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_185)) (MACRO_SR_EQ_INTRO :args (_let_185 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= tptp.zero_zero_nat N2)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_complex)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_714 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_184)) (MACRO_SR_EQ_INTRO :args (_let_184 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N2 tptp.nat)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_nat N2)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_real)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_715 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_183)) (MACRO_SR_EQ_INTRO :args (_let_183 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= tptp.zero_zero_nat N2)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_rat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_716 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_182)) (MACRO_SR_EQ_INTRO :args (_let_182 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N2 tptp.nat)) (@ (@ (@ tptp.if_int (= tptp.zero_zero_nat N2)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_int)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_717 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_181)) (MACRO_SR_EQ_INTRO :args (_let_181 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= tptp.zero_zero_nat N2)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_nat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_718 (ASSUME :args (_let_180)))) (let ((_let_719 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_178)) (MACRO_SR_EQ_INTRO :args (_let_178 SB_DEFAULT SBA_FIXPOINT))) :args (2)))) (let ((_let_720 (EQ_RESOLVE (ASSUME :args (_let_177)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_177 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_721 (EQ_RESOLVE (ASSUME :args (_let_176)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_176 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_722 (ASSUME :args (_let_175)))) (let ((_let_723 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_172)) (MACRO_SR_EQ_INTRO :args (_let_172 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (let ((_let_1 (= tptp.zero_zero_int A22))) (or (not (or (not _let_1) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A1))))) (not (or _let_1 (forall ((Q4 tptp.int)) (or (not (= A32 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int))) (not (= A1 (@ (@ tptp.times_times_int Q4) A22))))))) (not (forall ((R5 tptp.int) (Q4 tptp.int)) (or (not (= A32 (@ (@ tptp.product_Pair_int_int Q4) R5))) (not (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int A22))) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int A22))) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) A22)) R5)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_724 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_171)) (MACRO_SR_EQ_INTRO :args (_let_171 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (not (forall ((M6 tptp.nat)) (not (forall ((X tptp.nat)) (or (not (@ (@ tptp.member_nat X) N8)) (@ (@ tptp.ord_less_nat X) M6)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_725 (EQ_RESOLVE (ASSUME :args (_let_170)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_170 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_726 (EQ_RESOLVE (SYMM (ASSUME :args (_let_168))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.bot_bot_set_nat _let_167) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_727 (EQ_RESOLVE (ASSUME :args (_let_166)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_166 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_728 (ASSUME :args (_let_165)))) (let ((_let_729 (SYMM (ASSUME :args (_let_164))))) (let ((_let_730 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_163)) (MACRO_SR_EQ_INTRO :args (_let_163 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.arg (lambda ((Z5 tptp.complex)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_complex Z5)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z5) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_731 (EQ_RESOLVE (ASSUME :args (_let_162)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_162 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_732 (EQ_RESOLVE (ASSUME :args (_let_161)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_161 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_733 (EQ_RESOLVE (ASSUME :args (_let_160)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_160 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_734 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_159)) (MACRO_SR_EQ_INTRO :args (_let_159 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.arctan (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X 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)) X) (@ (@ tptp.ord_less_real X) _let_1) (= Y (@ tptp.tan_real X)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_735 (EQ_RESOLVE (ASSUME :args (_let_158)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_158 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_736 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_156)) (MACRO_SR_EQ_INTRO :args (_let_156 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.arcsin (lambda ((Y tptp.real)) (@ tptp.the_real (lambda ((X 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)) X) (@ (@ tptp.ord_less_eq_real X) _let_1) (= Y (@ tptp.sin_real X)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_737 (ASSUME :args (_let_155)))) (let ((_let_738 (EQ_RESOLVE (ASSUME :args (_let_152)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_152 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_739 (EQ_RESOLVE (ASSUME :args (_let_151)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_151 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_740 (EQ_RESOLVE (ASSUME :args (_let_150)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_150 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_741 (EQ_RESOLVE (ASSUME :args (_let_149)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_149 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_742 (ASSUME :args (_let_148)))) (let ((_let_743 (EQ_RESOLVE (ASSUME :args (_let_147)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_147 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_744 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_146)) (MACRO_SR_EQ_INTRO :args (_let_146 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.csqrt (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z5))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z5))) (let ((_let_4 (@ tptp.im Z5))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= tptp.zero_zero_real _let_4)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_745 (ASSUME :args (_let_144)))) (let ((_let_746 (EQ_RESOLVE (ASSUME :args (_let_143)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_143 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_747 (EQ_RESOLVE (ASSUME :args (_let_142)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_142 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_748 (EQ_RESOLVE (ASSUME :args (_let_141)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_141 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_749 (EQ_RESOLVE (ASSUME :args (_let_140)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_140 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_750 (EQ_RESOLVE (ASSUME :args (_let_138)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_138 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_751 (ASSUME :args (_let_137)))) (let ((_let_752 (EQ_RESOLVE (ASSUME :args (_let_136)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_136 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_753 (EQ_RESOLVE (ASSUME :args (_let_135)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_135 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_754 (EQ_RESOLVE (ASSUME :args (_let_134)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_134 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_755 (EQ_RESOLVE (ASSUME :args (_let_133)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_133 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_756 (EQ_RESOLVE (ASSUME :args (_let_132)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_132 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_757 (EQ_RESOLVE (ASSUME :args (_let_131)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_131 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_758 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_130)) (MACRO_SR_EQ_INTRO :args (_let_130 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.adjust_mod (lambda ((L tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int R5)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L) R5)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_759 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_129)) (MACRO_SR_EQ_INTRO :args (_let_129 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.normalize (lambda ((P3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P3))) (let ((_let_2 (@ tptp.product_fst_int_int P3))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= tptp.zero_zero_int _let_1)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_760 (EQ_RESOLVE (ASSUME :args (_let_127)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_127 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_761 (EQ_RESOLVE (ASSUME :args (_let_126)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_126 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_762 (ASSUME :args (_let_125)))) (let ((_let_763 (EQ_RESOLVE (ASSUME :args (_let_124)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_124 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_764 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_123)) (MACRO_SR_EQ_INTRO :args (_let_123 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= tptp.zero_zero_nat _let_1)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_765 (SYMM (ASSUME :args (_let_122))))) (let ((_let_766 (EQ_RESOLVE (ASSUME :args (_let_121)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_121 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_767 (SYMM (ASSUME :args (_let_120))))) (let ((_let_768 (SYMM (ASSUME :args (_let_119))))) (let ((_let_769 (EQ_RESOLVE (ASSUME :args (_let_118)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_118 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_770 (EQ_RESOLVE (ASSUME :args (_let_117)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_117 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_771 (EQ_RESOLVE (ASSUME :args (_let_116)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_116 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_772 (EQ_RESOLVE (ASSUME :args (_let_115)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_115 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_773 (EQ_RESOLVE (ASSUME :args (_let_114)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_114 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_774 (EQ_RESOLVE (ASSUME :args (_let_113)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_113 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_775 (EQ_RESOLVE (ASSUME :args (_let_112)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_112 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_776 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_111)) (MACRO_SR_EQ_INTRO :args (_let_111 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu tptp.real)) (not (forall ((I2 tptp.int) (J3 tptp.int)) (or (not (= Uu (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I2)) (@ tptp.ring_1_of_int_real J3)))) (= tptp.zero_zero_int J3))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_777 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_109)) (MACRO_SR_EQ_INTRO :args (_let_109 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.root (lambda ((N2 tptp.nat) (X tptp.real)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_nat N2)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N2)))) X)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_778 (EQ_RESOLVE (ASSUME :args (_let_108)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_108 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_779 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_107)) (MACRO_SR_EQ_INTRO :args (_let_107 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.real_V5970128139526366754l_real (lambda ((F2 (-> tptp.real tptp.real))) (not (forall ((C2 tptp.real)) (not (= F2 (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C2)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_780 (EQ_RESOLVE (ASSUME :args (_let_104)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_104 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_781 (EQ_RESOLVE (ASSUME :args (_let_103)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_103 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_782 (EQ_RESOLVE (SYMM (ASSUME :args (_let_92))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.top_top_set_nat _let_91) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_783 (ASSUME :args (_let_87)))) (let ((_let_784 (ASSUME :args (_let_86)))) (let ((_let_785 (ASSUME :args (_let_85)))) (let ((_let_786 (EQ_RESOLVE (ASSUME :args (_let_84)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_84 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_787 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_788 (EQ_RESOLVE (ASSUME :args (_let_82)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_82 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_789 (EQ_RESOLVE (ASSUME :args (_let_81)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_81 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_790 (EQ_RESOLVE (ASSUME :args (_let_80)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_80 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_791 (EQ_RESOLVE (ASSUME :args (_let_74)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_74 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_792 (ASSUME :args (_let_73)))) (let ((_let_793 (ASSUME :args (_let_72)))) (let ((_let_794 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_71)) (MACRO_SR_EQ_INTRO :args (_let_71 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.vanishes (lambda ((X6 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (or (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5)) (not (forall ((K3 tptp.nat)) (not (forall ((N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat K3) N2)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X6 N2))) R5)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_795 (SYMM (ASSUME :args (_let_70))))) (let ((_let_796 (SYMM (ASSUME :args (_let_69))))) (let ((_let_797 (EQ_RESOLVE (ASSUME :args (_let_68)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_68 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_798 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_67)) (MACRO_SR_EQ_INTRO :args (_let_67 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.cauchy (lambda ((X6 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (or (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5)) (not (forall ((K3 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_203718 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K3))) (or (not (@ _let_1 M6)) (not (@ _let_1 BOUND_VARIABLE_203718)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X6 M6)) (@ X6 BOUND_VARIABLE_203718)))) R5))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_799 (ASSUME :args (_let_66)))) (let ((_let_800 (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_65 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_801 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_802 (EQ_RESOLVE (ASSUME :args (_let_63)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_63 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_803 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_62)) (MACRO_SR_EQ_INTRO :args (_let_62 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.cr_real (lambda ((X (-> tptp.nat tptp.rat)) (Y tptp.real)) (and (@ (@ tptp.realrel X) X) (= Y (@ tptp.real2 X))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_804 (ASSUME :args (_let_61)))) (let ((_let_805 (EQ_RESOLVE (ASSUME :args (_let_60)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_60 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_806 (ASSUME :args (_let_59)))) (let ((_let_807 (EQ_RESOLVE (SYMM (ASSUME :args (_let_53))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.cr_real tptp.pcr_real) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_808 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO :args (_let_49 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.comple1385675409528146559p_real (lambda ((X6 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z5 tptp.real)) (forall ((X tptp.real)) (or (not (@ (@ tptp.member_real X) X6)) (@ (@ tptp.ord_less_eq_real X) Z5))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_809 (ASSUME :args (_let_45)))) (let ((_let_810 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_811 (ASSUME :args (_let_39)))) (let ((_let_812 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.ratrel (lambda ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X))) (let ((_let_2 (@ tptp.product_snd_int_int Y))) (and (not (= tptp.zero_zero_int _let_1)) (not (= tptp.zero_zero_int _let_2)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y)) _let_1))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_813 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_814 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_815 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_816 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_817 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_818 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= tptp.zero_zero_int R5))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_819 (EQ_RESOLVE (SYMM (ASSUME :args (_let_30))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.id_nat tptp.semiri1316708129612266289at_nat) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_820 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_821 (ASSUME :args (_let_28)))) (let ((_let_822 (ASSUME :args (_let_27)))) (let ((_let_823 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_824 (SYMM (ASSUME :args (_let_21))))) (let ((_let_825 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_826 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_827 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.comple4398354569131411667d_enat (lambda ((A6 tptp.set_Extended_enat)) (@ (@ (@ tptp.if_Extended_enat (= tptp.bot_bo7653980558646680370d_enat A6)) tptp.zero_z5237406670263579293d_enat) (@ (@ (@ tptp.if_Extended_enat (@ tptp.finite4001608067531595151d_enat A6)) (@ tptp.lattic921264341876707157d_enat A6)) tptp.extend5688581933313929465d_enat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_828 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_829 (SYMM (ASSUME :args (_let_16))))) (let ((_let_830 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_829 _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_831 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_830 _let_829 _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_832 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_831 _let_830 _let_829 _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args ((= tptp.times_7803423173614009249d_enat (lambda ((M6 tptp.extended_enat) (N2 tptp.extended_enat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((O tptp.nat)) (@ (@ (@ tptp.extend3600170679010898289d_enat (lambda ((P3 tptp.nat)) (@ tptp.extended_enat2 (@ (@ tptp.times_times_nat O) P3)))) (@ (@ (@ tptp.if_Extended_enat (= tptp.zero_zero_nat O)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) N2))) (@ (@ (@ tptp.if_Extended_enat (= tptp.zero_z5237406670263579293d_enat N2)) tptp.zero_z5237406670263579293d_enat) tptp.extend5688581933313929465d_enat)) M6))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_833 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_832 _let_831 _let_830 _let_829 _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_834 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_833 _let_832 _let_831 _let_830 _let_829 _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_835 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_834 _let_833 _let_832 _let_831 _let_830 _let_829 _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_836 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_835 _let_834 _let_833 _let_832 _let_831 _let_830 _let_829 _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) _let_835 _let_834 _let_833 _let_832 _let_831 _let_830 _let_829 _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546))) (let ((_let_837 (EQ_RESOLVE (ASSUME :args (_let_528)) (TRANS (MACRO_SR_EQ_INTRO _let_836 :args (_let_528 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A tptp.nat) (BOUND_VARIABLE_454200 tptp.nat) (BOUND_VARIABLE_454193 tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int BOUND_VARIABLE_454193))))) (or (= A _let_1) (not (= A (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1314217659103216013at_int BOUND_VARIABLE_454200)))))))) _let_545))))))) (let ((_let_838 (ho_15593 (ho_15592 k_15599 tptp.za) _let_538))) (let ((_let_839 (= _let_838 _let_540))) (let ((_let_840 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 _let_838)) _let_536)))) (let ((_let_841 (= _let_539 _let_840))) (let ((_let_842 (forall ((K3 tptp.nat)) (let ((_let_1 (ho_15118 k_15117 (ho_15114 k_15113 (ho_15152 k_15151 tptp.one))))) (let ((_let_2 (ho_15593 (ho_15592 k_15591 _let_1) (ho_15593 (ho_15592 k_15599 tptp.deg) _let_1)))) (not (= (ho_15593 (ho_15592 k_15599 tptp.za) _let_2) (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 (ho_15593 (ho_15592 k_15599 tptp.xa) _let_2))) (ho_15161 k_15160 K3)))))))))) (let ((_let_843 (not _let_842))) (let ((_let_844 (EQ_RESOLVE (ASSUME :args (_let_534)) (TRANS (MACRO_SR_EQ_INTRO _let_836 :args (_let_534 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((K3 tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (not (= (@ (@ tptp.divide_divide_nat tptp.za) _let_2) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat tptp.xa) _let_2))) (@ tptp.semiri1314217659103216013at_int K3))))))))) _let_843))))))) (let ((_let_845 (or))) (let ((_let_846 (_let_839))) (let ((_let_847 (not _let_839))) (let ((_let_848 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_844) :args (_let_843)) (REWRITE :args ((=> _let_843 (not _let_847)))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_843) _let_842))) (REFL :args _let_846) :args _let_845)) _let_844 :args (_let_839 true _let_842)))) (let ((_let_849 (forall ((K3 tptp.nat)) (let ((_let_1 (ho_15118 k_15117 (ho_15114 k_15113 (ho_15152 k_15151 tptp.one))))) (let ((_let_2 (ho_15593 (ho_15592 k_15591 _let_1) (ho_15593 (ho_15592 k_15599 tptp.deg) _let_1)))) (not (= (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 (ho_15593 (ho_15592 k_15599 tptp.za) _let_2))) (ho_15161 k_15160 K3))) (ho_15593 (ho_15592 k_15599 tptp.xa) _let_2)))))))) (let ((_let_850 (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_25663 x z) (ho_25663 y z)))) (= x y))))) (let ((_let_851 (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_25661 x z) (ho_25661 y z)))) (= x y))))) (let ((_let_852 (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_31761 x z) (ho_31761 y z)))) (= x y))))) (let ((_let_853 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_25657 x z) (ho_25657 y z)))) (= x y))))) (let ((_let_854 (forall ((x |u_(-> tptp.set_list_nat tptp.set_list_nat tptp.set_list_nat)|) (y |u_(-> tptp.set_list_nat tptp.set_list_nat tptp.set_list_nat)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_25654 x z) (ho_25654 y z)))) (= x y))))) (let ((_let_855 (forall ((x |u_(-> tptp.list_num tptp.list_P3744719386663036955um_num)|) (y |u_(-> tptp.list_num tptp.list_P3744719386663036955um_num)|)) (or (not (forall ((z tptp.list_num)) (= (ho_31188 x z) (ho_31188 y z)))) (= x y))))) (let ((_let_856 (forall ((x |u_(-> tptp.set_list_nat tptp.set_list_nat)|) (y |u_(-> tptp.set_list_nat tptp.set_list_nat)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_25655 x z) (ho_25655 y z)))) (= x y))))) (let ((_let_857 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.int)_ tptp.set_Extended_enat tptp.int)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.int)_ tptp.set_Extended_enat tptp.int)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.int)|)) (= (ho_31141 x z) (ho_31141 y z)))) (= x y))))) (let ((_let_858 (forall ((x |u_(-> Bool tptp.produc334124729049499915VEBT_o)|) (y |u_(-> Bool tptp.produc334124729049499915VEBT_o)|)) (or (not (forall ((z Bool)) (= (ho_31203 x z) (ho_31203 y z)))) (= x y))))) (let ((_let_859 (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_25652 x z) (ho_25652 y z)))) (= x y))))) (let ((_let_860 (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_31647 x z) (ho_31647 y z)))) (= x y))))) (let ((_let_861 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_25648 x z) (ho_25648 y z)))) (= x y))))) (let ((_let_862 (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_31515 x z) (ho_31515 y z)))) (= x y))))) (let ((_let_863 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ _u_(-> tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_25642 x z) (ho_25642 y z)))) (= x y))))) (let ((_let_864 (forall ((x |u_(-> tptp.rat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_17074 x z) (ho_17074 y z)))) (= x y))))) (let ((_let_865 (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_25640 x z) (ho_25640 y z)))) (= x y))))) (let ((_let_866 (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_25562 x z) (ho_25562 y z)))) (= x y))))) (let ((_let_867 (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_18464 x z) (ho_18464 y z)))) (= x y))))) (let ((_let_868 (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_25560 x z) (ho_25560 y z)))) (= x y))))) (let ((_let_869 (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_25542 x z) (ho_25542 y z)))) (= x y))))) (let ((_let_870 (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_25502 x z) (ho_25502 y z)))) (= x y))))) (let ((_let_871 (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_24896 x z) (ho_24896 y z)))) (= x y))))) (let ((_let_872 (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_31597 x z) (ho_31597 y z)))) (= x y))))) (let ((_let_873 (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_25490 x z) (ho_25490 y z)))) (= x y))))) (let ((_let_874 (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_25454 x z) (ho_25454 y z)))) (= x y))))) (let ((_let_875 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_31707 x z) (ho_31707 y z)))) (= x y))))) (let ((_let_876 (forall ((x |u_(-> tptp.nat tptp.code_integer)|) (y |u_(-> tptp.nat tptp.code_integer)|)) (or (not (forall ((z tptp.nat)) (= (ho_25595 x z) (ho_25595 y z)))) (= x y))))) (let ((_let_877 (forall ((x |u_(-> tptp.nat tptp.nat tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_24331 x z) (ho_24331 y z)))) (= x y))))) (let ((_let_878 (forall ((x |u_(-> _u_(-> tptp.int tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.nat)|)) (= (ho_31617 x z) (ho_31617 y z)))) (= x y))))) (let ((_let_879 (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_25452 x z) (ho_25452 y z)))) (= x y))))) (let ((_let_880 (forall ((x |u_(-> Bool tptp.vEBT_VEBT)|) (y |u_(-> Bool tptp.vEBT_VEBT)|)) (or (not (forall ((z Bool)) (= (ho_25392 x z) (ho_25392 y z)))) (= x y))))) (let ((_let_881 (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_25387 x z) (ho_25387 y z)))) (= x y))))) (let ((_let_882 (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_25389 x z) (ho_25389 y z)))) (= x y))))) (let ((_let_883 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (= (ho_31705 x z) (ho_31705 y z)))) (= x y))))) (let ((_let_884 (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_25368 x z) (ho_25368 y z)))) (= x y))))) (let ((_let_885 (forall ((x |u_(-> Bool Bool tptp.vEBT_VEBT)|) (y |u_(-> Bool Bool tptp.vEBT_VEBT)|)) (or (not (forall ((z Bool)) (= (ho_25391 x z) (ho_25391 y z)))) (= x y))))) (let ((_let_886 (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_25327 x z) (ho_25327 y z)))) (= x y))))) (let ((_let_887 (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_25246 x z) (ho_25246 y z)))) (= x y))))) (let ((_let_888 (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_17741 x z) (ho_17741 y z)))) (= x y))))) (let ((_let_889 (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_25320 x z) (ho_25320 y z)))) (= x y))))) (let ((_let_890 (forall ((x |u_(-> tptp.extended_enat tptp.produc7272778201969148633d_enat)|) (y |u_(-> tptp.extended_enat tptp.produc7272778201969148633d_enat)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_31734 x z) (ho_31734 y z)))) (= x y))))) (let ((_let_891 (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_25304 x z) (ho_25304 y z)))) (= x y))))) (let ((_let_892 (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_18739 x z) (ho_18739 y z)))) (= x y))))) (let ((_let_893 (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_25258 x z) (ho_25258 y z)))) (= x y))))) (let ((_let_894 (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_18674 x z) (ho_18674 y z)))) (= x y))))) (let ((_let_895 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.int)|)) (= (ho_31533 x z) (ho_31533 y z)))) (= x y))))) (let ((_let_896 (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_31695 x z) (ho_31695 y z)))) (= x y))))) (let ((_let_897 (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_25299 x z) (ho_25299 y z)))) (= x y))))) (let ((_let_898 (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_25261 x z) (ho_25261 y z)))) (= x y))))) (let ((_let_899 (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_25249 x z) (ho_25249 y z)))) (= x y))))) (let ((_let_900 (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_31516 x z) (ho_31516 y z)))) (= x y))))) (let ((_let_901 (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_25245 x z) (ho_25245 y z)))) (= x y))))) (let ((_let_902 (forall ((x |u_(-> tptp.complex tptp.nat tptp.complex)|) (y |u_(-> tptp.complex tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_25005 x z) (ho_25005 y z)))) (= x y))))) (let ((_let_903 (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_25242 x z) (ho_25242 y z)))) (= x y))))) (let ((_let_904 (forall ((x |u_(-> tptp.int tptp.set_int)|) (y |u_(-> tptp.int tptp.set_int)|)) (or (not (forall ((z tptp.int)) (= (ho_25243 x z) (ho_25243 y z)))) (= x y))))) (let ((_let_905 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_15091 x z) (ho_15091 y z)))) (= x y))))) (let ((_let_906 (forall ((x |u_(-> tptp.nat tptp.int tptp.int tptp.int)|) (y |u_(-> tptp.nat tptp.int tptp.int tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_25057 x z) (ho_25057 y z)))) (= x y))))) (let ((_let_907 (forall ((x |u_(-> tptp.nat tptp.rat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_16697 x z) (ho_16697 y z)))) (= x y))))) (let ((_let_908 (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_25385 x z) (ho_25385 y z)))) (= x y))))) (let ((_let_909 (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_25046 x z) (ho_25046 y z)))) (= x y))))) (let ((_let_910 (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_25047 x z) (ho_25047 y z)))) (= x y))))) (let ((_let_911 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)|)) (= (ho_15090 x z) (ho_15090 y z)))) (= x y))))) (let ((_let_912 (forall ((x |u_(-> tptp.num tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_25040 x z) (ho_25040 y z)))) (= x y))))) (let ((_let_913 (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_31544 x z) (ho_31544 y z)))) (= x y))))) (let ((_let_914 (forall ((x |u_(-> tptp.int tptp.code_integer)|) (y |u_(-> tptp.int tptp.code_integer)|)) (or (not (forall ((z tptp.int)) (= (ho_25034 x z) (ho_25034 y z)))) (= x y))))) (let ((_let_915 (forall ((x |u_(-> Bool tptp.char)|) (y |u_(-> Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_31440 x z) (ho_31440 y z)))) (= x y))))) (let ((_let_916 (forall ((x |u_(-> tptp.complex tptp.complex tptp.complex)|) (y |u_(-> tptp.complex tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_25024 x z) (ho_25024 y z)))) (= x y))))) (let ((_let_917 (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_19698 x z) (ho_19698 y z)))) (= x y))))) (let ((_let_918 (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_31640 x z) (ho_31640 y z)))) (= x y))))) (let ((_let_919 (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_24998 x z) (ho_24998 y z)))) (= x y))))) (let ((_let_920 (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_31229 x z) (ho_31229 y z)))) (= x y))))) (let ((_let_921 (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_31542 x z) (ho_31542 y z)))) (= x y))))) (let ((_let_922 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc6271795597528267376eger_o)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_24996 x z) (ho_24996 y z)))) (= x y))))) (let ((_let_923 (forall ((x |u_(-> tptp.real tptp.nat tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.real tptp.nat tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_18028 x z) (ho_18028 y z)))) (= x y))))) (let ((_let_924 (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_31760 x z) (ho_31760 y z)))) (= x y))))) (let ((_let_925 (forall ((x |u_(-> tptp.int tptp.complex)|) (y |u_(-> tptp.int tptp.complex)|)) (or (not (forall ((z tptp.int)) (= (ho_25599 x z) (ho_25599 y z)))) (= x y))))) (let ((_let_926 (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_24951 x z) (ho_24951 y z)))) (= x y))))) (let ((_let_927 (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_24871 x z) (ho_24871 y z)))) (= x y))))) (let ((_let_928 (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_24945 x z) (ho_24945 y z)))) (= x y))))) (let ((_let_929 (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_24934 x z) (ho_24934 y z)))) (= x y))))) (let ((_let_930 (forall ((x |u_(-> tptp.num tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.num tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_21785 x z) (ho_21785 y z)))) (= x y))))) (let ((_let_931 (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_24926 x z) (ho_24926 y z)))) (= x y))))) (let ((_let_932 (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_20894 x z) (ho_20894 y z)))) (= x y))))) (let ((_let_933 (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_24901 x z) (ho_24901 y z)))) (= x y))))) (let ((_let_934 (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_24893 x z) (ho_24893 y z)))) (= x y))))) (let ((_let_935 (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_25388 x z) (ho_25388 y z)))) (= x y))))) (let ((_let_936 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.rat)_ tptp.extended_enat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.rat)_ tptp.extended_enat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.rat)|)) (= (ho_18650 x z) (ho_18650 y z)))) (= x y))))) (let ((_let_937 (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_25292 x z) (ho_25292 y z)))) (= x y))))) (let ((_let_938 (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_31581 x z) (ho_31581 y z)))) (= x y))))) (let ((_let_939 (forall ((x |u_(-> tptp.set_VEBT_VEBT Bool)|) (y |u_(-> tptp.set_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.set_VEBT_VEBT)) (= (ho_24869 x z) (ho_24869 y z)))) (= x y))))) (let ((_let_940 (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_24866 x z) (ho_24866 y z)))) (= x y))))) (let ((_let_941 (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_25879 x z) (ho_25879 y z)))) (= x y))))) (let ((_let_942 (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_24863 x z) (ho_24863 y z)))) (= x y))))) (let ((_let_943 (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_25438 x z) (ho_25438 y z)))) (= x y))))) (let ((_let_944 (forall ((x |u_(-> tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_24851 x z) (ho_24851 y z)))) (= x y))))) (let ((_let_945 (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_24523 x z) (ho_24523 y z)))) (= x y))))) (let ((_let_946 (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_24805 x z) (ho_24805 y z)))) (= x y))))) (let ((_let_947 (forall ((x |u_(-> tptp.list_int tptp.nat)|) (y |u_(-> tptp.list_int tptp.nat)|)) (or (not (forall ((z tptp.list_int)) (= (ho_24803 x z) (ho_24803 y z)))) (= x y))))) (let ((_let_948 (forall ((x |u_(-> tptp.list_o Bool)|) (y |u_(-> tptp.list_o Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_25880 x z) (ho_25880 y z)))) (= x y))))) (let ((_let_949 (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_24796 x z) (ho_24796 y z)))) (= x y))))) (let ((_let_950 (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_24797 x z) (ho_24797 y z)))) (= x y))))) (let ((_let_951 (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_24793 x z) (ho_24793 y z)))) (= x y))))) (let ((_let_952 (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_24786 x z) (ho_24786 y z)))) (= x y))))) (let ((_let_953 (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_24773 x z) (ho_24773 y z)))) (= x y))))) (let ((_let_954 (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_24766 x z) (ho_24766 y z)))) (= x y))))) (let ((_let_955 (forall ((x |u_(-> tptp.nat tptp.nat tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_18115 x z) (ho_18115 y z)))) (= x y))))) (let ((_let_956 (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_31639 x z) (ho_31639 y z)))) (= x y))))) (let ((_let_957 (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_24760 x z) (ho_24760 y z)))) (= x y))))) (let ((_let_958 (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_24761 x z) (ho_24761 y z)))) (= x y))))) (let ((_let_959 (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_24757 x z) (ho_24757 y z)))) (= x y))))) (let ((_let_960 (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_24508 x z) (ho_24508 y z)))) (= x y))))) (let ((_let_961 (forall ((x |u_(-> tptp.int tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.int tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_27262 x z) (ho_27262 y z)))) (= x y))))) (let ((_let_962 (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_31312 x z) (ho_31312 y z)))) (= x y))))) (let ((_let_963 (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_25361 x z) (ho_25361 y z)))) (= x y))))) (let ((_let_964 (forall ((x |u_(-> tptp.complex tptp.complex Bool)|) (y |u_(-> tptp.complex tptp.complex Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_18845 x z) (ho_18845 y z)))) (= x y))))) (let ((_let_965 (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_24754 x z) (ho_24754 y z)))) (= x y))))) (let ((_let_966 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.int)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.int)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_24915 x z) (ho_24915 y z)))) (= x y))))) (let ((_let_967 (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_24758 x z) (ho_24758 y z)))) (= x y))))) (let ((_let_968 (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_24932 x z) (ho_24932 y z)))) (= x y))))) (let ((_let_969 (forall ((x |u_(-> Bool _u_(-> tptp.nat tptp.int tptp.int)_ _u_(-> tptp.nat tptp.int tptp.int)_ tptp.nat tptp.int tptp.int)|) (y |u_(-> Bool _u_(-> tptp.nat tptp.int tptp.int)_ _u_(-> tptp.nat tptp.int tptp.int)_ tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_26844 x z) (ho_26844 y z)))) (= x y))))) (let ((_let_970 (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_24719 x z) (ho_24719 y z)))) (= x y))))) (let ((_let_971 (forall ((x |u_(-> tptp.list_Extended_enat tptp.set_Extended_enat)|) (y |u_(-> tptp.list_Extended_enat tptp.set_Extended_enat)|)) (or (not (forall ((z tptp.list_Extended_enat)) (= (ho_31054 x z) (ho_31054 y z)))) (= x y))))) (let ((_let_972 (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_25367 x z) (ho_25367 y z)))) (= x y))))) (let ((_let_973 (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_24717 x z) (ho_24717 y z)))) (= x y))))) (let ((_let_974 (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_24712 x z) (ho_24712 y z)))) (= x y))))) (let ((_let_975 (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_24683 x z) (ho_24683 y z)))) (= x y))))) (let ((_let_976 (forall ((x |u_(-> tptp.real tptp.int)|) (y |u_(-> tptp.real tptp.int)|)) (or (not (forall ((z tptp.real)) (= (ho_24678 x z) (ho_24678 y z)))) (= x y))))) (let ((_let_977 (forall ((x |u_(-> tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_15145 x z) (ho_15145 y z)))) (= x y))))) (let ((_let_978 (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_24650 x z) (ho_24650 y z)))) (= x y))))) (let ((_let_979 (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_24580 x z) (ho_24580 y z)))) (= x y))))) (let ((_let_980 (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_31122 x z) (ho_31122 y z)))) (= x y))))) (let ((_let_981 (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_25272 x z) (ho_25272 y z)))) (= x y))))) (let ((_let_982 (forall ((x |u_(-> tptp.real tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_15101 x z) (ho_15101 y z)))) (= x y))))) (let ((_let_983 (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_24570 x z) (ho_24570 y z)))) (= x y))))) (let ((_let_984 (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_24568 x z) (ho_24568 y z)))) (= x y))))) (let ((_let_985 (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_24535 x z) (ho_24535 y z)))) (= x y))))) (let ((_let_986 (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_18542 x z) (ho_18542 y z)))) (= x y))))) (let ((_let_987 (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_18622 x z) (ho_18622 y z)))) (= x y))))) (let ((_let_988 (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_25271 x z) (ho_25271 y z)))) (= x y))))) (let ((_let_989 (forall ((x |u_(-> tptp.real tptp.filter_real Bool)|) (y |u_(-> tptp.real tptp.filter_real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_24536 x z) (ho_24536 y z)))) (= x y))))) (let ((_let_990 (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_31452 x z) (ho_31452 y z)))) (= x y))))) (let ((_let_991 (forall ((x |u_(-> tptp.int tptp.list_int)|) (y |u_(-> tptp.int tptp.list_int)|)) (or (not (forall ((z tptp.int)) (= (ho_24755 x z) (ho_24755 y z)))) (= x y))))) (let ((_let_992 (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_31294 x z) (ho_31294 y z)))) (= x y))))) (let ((_let_993 (forall ((x |u_(-> _u_(-> tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat Bool)_ tptp.produc7272778201969148633d_enat Bool)|) (y |u_(-> _u_(-> tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat Bool)_ tptp.produc7272778201969148633d_enat Bool)|)) (or (not (forall ((z |u_(-> tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat Bool)|)) (= (ho_31738 x z) (ho_31738 y z)))) (= x y))))) (let ((_let_994 (forall ((x |u_(-> tptp.filter_real Bool)|) (y |u_(-> tptp.filter_real Bool)|)) (or (not (forall ((z tptp.filter_real)) (= (ho_24537 x z) (ho_24537 y z)))) (= x y))))) (let ((_let_995 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool tptp.extended_enat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool tptp.extended_enat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_23917 x z) (ho_23917 y z)))) (= x y))))) (let ((_let_996 (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_24524 x z) (ho_24524 y z)))) (= x y))))) (let ((_let_997 (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_24520 x z) (ho_24520 y z)))) (= x y))))) (let ((_let_998 (forall ((x |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num Bool)|)) (= (ho_31531 x z) (ho_31531 y z)))) (= x y))))) (let ((_let_999 (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_25545 x z) (ho_25545 y z)))) (= x y))))) (let ((_let_1000 (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_25498 x z) (ho_25498 y z)))) (= x y))))) (let ((_let_1001 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_16520 x z) (ho_16520 y z)))) (= x y))))) (let ((_let_1002 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_24411 x z) (ho_24411 y z)))) (= x y))))) (let ((_let_1003 (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_24332 x z) (ho_24332 y z)))) (= x y))))) (let ((_let_1004 (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_24868 x z) (ho_24868 y z)))) (= x y))))) (let ((_let_1005 (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_16509 x z) (ho_16509 y z)))) (= x y))))) (let ((_let_1006 (forall ((x |u_(-> tptp.set_complex Bool)|) (y |u_(-> tptp.set_complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_18828 x z) (ho_18828 y z)))) (= x y))))) (let ((_let_1007 (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_31627 x z) (ho_31627 y z)))) (= x y))))) (let ((_let_1008 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_24507 x z) (ho_24507 y z)))) (= x y))))) (let ((_let_1009 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_24220 x z) (ho_24220 y z)))) (= x y))))) (let ((_let_1010 (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_31645 x z) (ho_31645 y z)))) (= x y))))) (let ((_let_1011 (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_24198 x z) (ho_24198 y z)))) (= x y))))) (let ((_let_1012 (forall ((x |u_(-> tptp.num tptp.num tptp.int)|) (y |u_(-> tptp.num tptp.num tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_24189 x z) (ho_24189 y z)))) (= x y))))) (let ((_let_1013 (forall ((x |u_(-> Bool _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|) (y |u_(-> Bool _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (or (not (forall ((z Bool)) (= (ho_24119 x z) (ho_24119 y z)))) (= x y))))) (let ((_let_1014 (forall ((x |u_(-> tptp.set_real tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_real tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_18678 x z) (ho_18678 y z)))) (= x y))))) (let ((_let_1015 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat 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 tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_26812 x z) (ho_26812 y z)))) (= x y))))) (let ((_let_1016 (forall ((x |u_(-> tptp.set_o Bool)|) (y |u_(-> tptp.set_o Bool)|)) (or (not (forall ((z tptp.set_o)) (= (ho_31059 x z) (ho_31059 y z)))) (= x y))))) (let ((_let_1017 (forall ((x |u_(-> tptp.rat Bool)|) (y |u_(-> tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_24114 x z) (ho_24114 y z)))) (= x y))))) (let ((_let_1018 (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_25000 x z) (ho_25000 y z)))) (= x y))))) (let ((_let_1019 (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_31539 x z) (ho_31539 y z)))) (= x y))))) (let ((_let_1020 (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_24109 x z) (ho_24109 y z)))) (= x y))))) (let ((_let_1021 (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_31578 x z) (ho_31578 y z)))) (= x y))))) (let ((_let_1022 (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_24093 x z) (ho_24093 y z)))) (= x y))))) (let ((_let_1023 (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_18791 x z) (ho_18791 y z)))) (= x y))))) (let ((_let_1024 (forall ((x |u_(-> Bool Bool Bool)|) (y |u_(-> Bool Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_24064 x z) (ho_24064 y z)))) (= x y))))) (let ((_let_1025 (forall ((x |u_(-> Bool Bool)|) (y |u_(-> Bool Bool)|)) (or (not (forall ((z Bool)) (= (ho_24065 x z) (ho_24065 y z)))) (= x y))))) (let ((_let_1026 (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_31632 x z) (ho_31632 y z)))) (= x y))))) (let ((_let_1027 (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_25649 x z) (ho_25649 y z)))) (= x y))))) (let ((_let_1028 (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_24061 x z) (ho_24061 y z)))) (= x y))))) (let ((_let_1029 (forall ((x |u_(-> tptp.rat tptp.int)|) (y |u_(-> tptp.rat tptp.int)|)) (or (not (forall ((z tptp.rat)) (= (ho_24049 x z) (ho_24049 y z)))) (= x y))))) (let ((_let_1030 (forall ((x |u_(-> tptp.literal _u_(-> tptp.product_unit tptp.real)_ tptp.real)|) (y |u_(-> tptp.literal _u_(-> tptp.product_unit tptp.real)_ tptp.real)|)) (or (not (forall ((z tptp.literal)) (= (ho_24037 x z) (ho_24037 y z)))) (= x y))))) (let ((_let_1031 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.rat)_ tptp.extended_enat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.rat)_ tptp.extended_enat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.rat)|)) (= (ho_25309 x z) (ho_25309 y z)))) (= x y))))) (let ((_let_1032 (forall ((x |u_(-> tptp.int tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.int tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_17099 x z) (ho_17099 y z)))) (= x y))))) (let ((_let_1033 (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_31759 x z) (ho_31759 y z)))) (= x y))))) (let ((_let_1034 (forall ((x |u_(-> Bool Bool Bool Bool Bool Bool Bool tptp.literal tptp.literal)|) (y |u_(-> Bool Bool Bool Bool Bool Bool Bool tptp.literal tptp.literal)|)) (or (not (forall ((z Bool)) (= (ho_24028 x z) (ho_24028 y z)))) (= x y))))) (let ((_let_1035 (forall ((x |u_(-> Bool Bool Bool Bool Bool Bool tptp.literal tptp.literal)|) (y |u_(-> Bool Bool Bool Bool Bool Bool tptp.literal tptp.literal)|)) (or (not (forall ((z Bool)) (= (ho_24029 x z) (ho_24029 y z)))) (= x y))))) (let ((_let_1036 (forall ((x |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.code_integer tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_18536 x z) (ho_18536 y z)))) (= x y))))) (let ((_let_1037 (forall ((x |u_(-> Bool Bool Bool Bool Bool tptp.literal tptp.literal)|) (y |u_(-> Bool Bool Bool Bool Bool tptp.literal tptp.literal)|)) (or (not (forall ((z Bool)) (= (ho_24030 x z) (ho_24030 y z)))) (= x y))))) (let ((_let_1038 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_24330 x z) (ho_24330 y z)))) (= x y))))) (let ((_let_1039 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_15183 x z) (ho_15183 y z)))) (= x y))))) (let ((_let_1040 (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_18579 x z) (ho_18579 y z)))) (= x y))))) (let ((_let_1041 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)|)) (= (ho_31586 x z) (ho_31586 y z)))) (= x y))))) (let ((_let_1042 (forall ((x |u_(-> Bool Bool Bool Bool tptp.literal tptp.literal)|) (y |u_(-> Bool Bool Bool Bool tptp.literal tptp.literal)|)) (or (not (forall ((z Bool)) (= (ho_24031 x z) (ho_24031 y z)))) (= x y))))) (let ((_let_1043 (forall ((x |u_(-> Bool Bool Bool tptp.literal tptp.literal)|) (y |u_(-> Bool Bool Bool tptp.literal tptp.literal)|)) (or (not (forall ((z Bool)) (= (ho_24032 x z) (ho_24032 y z)))) (= x y))))) (let ((_let_1044 (forall ((x |u_(-> Bool tptp.literal tptp.literal)|) (y |u_(-> Bool tptp.literal tptp.literal)|)) (or (not (forall ((z Bool)) (= (ho_24034 x z) (ho_24034 y z)))) (= x y))))) (let ((_let_1045 (forall ((x |u_(-> tptp.nat tptp.vEBT_VEBT)|) (y |u_(-> tptp.nat tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_18506 x z) (ho_18506 y z)))) (= x y))))) (let ((_let_1046 (forall ((x |u_(-> tptp.literal tptp.literal)|) (y |u_(-> tptp.literal tptp.literal)|)) (or (not (forall ((z tptp.literal)) (= (ho_24035 x z) (ho_24035 y z)))) (= x y))))) (let ((_let_1047 (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_24020 x z) (ho_24020 y z)))) (= x y))))) (let ((_let_1048 (forall ((x |u_(-> tptp.num tptp.nat Bool)|) (y |u_(-> tptp.num tptp.nat Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_24004 x z) (ho_24004 y z)))) (= x y))))) (let ((_let_1049 (forall ((x |u_(-> _u_(-> tptp.extended_enat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.extended_enat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.extended_enat Bool)|)) (= (ho_23957 x z) (ho_23957 y z)))) (= x y))))) (let ((_let_1050 (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_25260 x z) (ho_25260 y z)))) (= x y))))) (let ((_let_1051 (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_18548 x z) (ho_18548 y z)))) (= x y))))) (let ((_let_1052 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.extended_enat tptp.vEBT_VEBT)|) (y |u_(-> tptp.vEBT_VEBT tptp.extended_enat tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_23949 x z) (ho_23949 y z)))) (= x y))))) (let ((_let_1053 (forall ((x |u_(-> tptp.extended_enat tptp.vEBT_VEBT)|) (y |u_(-> tptp.extended_enat tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_23950 x z) (ho_23950 y z)))) (= x y))))) (let ((_let_1054 (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_16517 x z) (ho_16517 y z)))) (= x y))))) (let ((_let_1055 (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_23947 x z) (ho_23947 y z)))) (= x y))))) (let ((_let_1056 (forall ((x |u_(-> tptp.extended_enat tptp.extended_enat tptp.nat tptp.extended_enat)|) (y |u_(-> tptp.extended_enat tptp.extended_enat tptp.nat tptp.extended_enat)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_23926 x z) (ho_23926 y z)))) (= x y))))) (let ((_let_1057 (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_31237 x z) (ho_31237 y z)))) (= x y))))) (let ((_let_1058 (forall ((x |u_(-> tptp.extended_enat tptp.nat Bool)|) (y |u_(-> tptp.extended_enat tptp.nat Bool)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_23920 x z) (ho_23920 y z)))) (= x y))))) (let ((_let_1059 (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_31283 x z) (ho_31283 y z)))) (= x y))))) (let ((_let_1060 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_24392 x z) (ho_24392 y z)))) (= x y))))) (let ((_let_1061 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.rat)_ tptp.set_Extended_enat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.rat)_ tptp.set_Extended_enat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.rat)|)) (= (ho_18695 x z) (ho_18695 y z)))) (= x y))))) (let ((_let_1062 (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_31305 x z) (ho_31305 y z)))) (= x y))))) (let ((_let_1063 (forall ((x |u_(-> Bool tptp.extended_enat Bool)|) (y |u_(-> Bool tptp.extended_enat Bool)|)) (or (not (forall ((z Bool)) (= (ho_23918 x z) (ho_23918 y z)))) (= x y))))) (let ((_let_1064 (forall ((x |u_(-> tptp.set_real Bool)|) (y |u_(-> tptp.set_real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_18819 x z) (ho_18819 y z)))) (= x y))))) (let ((_let_1065 (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_31551 x z) (ho_31551 y z)))) (= x y))))) (let ((_let_1066 (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_25275 x z) (ho_25275 y z)))) (= x y))))) (let ((_let_1067 (forall ((x |u_(-> tptp.rat tptp.nat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.nat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_22280 x z) (ho_22280 y z)))) (= x y))))) (let ((_let_1068 (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_24745 x z) (ho_24745 y z)))) (= x y))))) (let ((_let_1069 (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_31537 x z) (ho_31537 y z)))) (= x y))))) (let ((_let_1070 (forall ((x |u_(-> tptp.int tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.int tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_21710 x z) (ho_21710 y z)))) (= x y))))) (let ((_let_1071 (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_15142 x z) (ho_15142 y z)))) (= x y))))) (let ((_let_1072 (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_21347 x z) (ho_21347 y z)))) (= x y))))) (let ((_let_1073 (forall ((x |u_(-> tptp.int tptp.rat tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.rat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_20657 x z) (ho_20657 y z)))) (= x y))))) (let ((_let_1074 (forall ((x |u_(-> tptp.int tptp.real)|) (y |u_(-> tptp.int tptp.real)|)) (or (not (forall ((z tptp.int)) (= (ho_15081 x z) (ho_15081 y z)))) (= x y))))) (let ((_let_1075 (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_20626 x z) (ho_20626 y z)))) (= x y))))) (let ((_let_1076 (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_20101 x z) (ho_20101 y z)))) (= x y))))) (let ((_let_1077 (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_31505 x z) (ho_31505 y z)))) (= x y))))) (let ((_let_1078 (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_19873 x z) (ho_19873 y z)))) (= x y))))) (let ((_let_1079 (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_19818 x z) (ho_19818 y z)))) (= x y))))) (let ((_let_1080 (forall ((x |u_(-> tptp.literal tptp.literal tptp.literal)|) (y |u_(-> tptp.literal tptp.literal tptp.literal)|)) (or (not (forall ((z tptp.literal)) (= (ho_31000 x z) (ho_31000 y z)))) (= x y))))) (let ((_let_1081 (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_31522 x z) (ho_31522 y z)))) (= x y))))) (let ((_let_1082 (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_19815 x z) (ho_19815 y z)))) (= x y))))) (let ((_let_1083 (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_19812 x z) (ho_19812 y z)))) (= x y))))) (let ((_let_1084 (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_19705 x z) (ho_19705 y z)))) (= x y))))) (let ((_let_1085 (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_19700 x z) (ho_19700 y z)))) (= x y))))) (let ((_let_1086 (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_19701 x z) (ho_19701 y z)))) (= x y))))) (let ((_let_1087 (forall ((x |u_(-> _u_(-> tptp.num tptp.rat)_ tptp.num tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.num tptp.rat)_ tptp.num tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.rat)|)) (= (ho_18911 x z) (ho_18911 y z)))) (= x y))))) (let ((_let_1088 (forall ((x |u_(-> tptp.extended_enat tptp.set_Extended_enat Bool)|) (y |u_(-> tptp.extended_enat tptp.set_Extended_enat Bool)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_18836 x z) (ho_18836 y z)))) (= x y))))) (let ((_let_1089 (forall ((x |u_(-> tptp.set_Extended_enat Bool)|) (y |u_(-> tptp.set_Extended_enat Bool)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_18837 x z) (ho_18837 y z)))) (= x y))))) (let ((_let_1090 (forall ((x |u_(-> tptp.set_Extended_enat tptp.set_Extended_enat tptp.extended_enat Bool)|) (y |u_(-> tptp.set_Extended_enat tptp.set_Extended_enat tptp.extended_enat Bool)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_18832 x z) (ho_18832 y z)))) (= x y))))) (let ((_let_1091 (forall ((x |u_(-> tptp.set_Extended_enat tptp.extended_enat Bool)|) (y |u_(-> tptp.set_Extended_enat tptp.extended_enat Bool)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_18833 x z) (ho_18833 y z)))) (= x y))))) (let ((_let_1092 (forall ((x |u_(-> tptp.code_integer tptp.int)|) (y |u_(-> tptp.code_integer tptp.int)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_18529 x z) (ho_18529 y z)))) (= x y))))) (let ((_let_1093 (forall ((x |u_(-> Bool Bool tptp.char)|) (y |u_(-> Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_31439 x z) (ho_31439 y z)))) (= x y))))) (let ((_let_1094 (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_25364 x z) (ho_25364 y z)))) (= x y))))) (let ((_let_1095 (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_18656 x z) (ho_18656 y z)))) (= x y))))) (let ((_let_1096 (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_24528 x z) (ho_24528 y z)))) (= x y))))) (let ((_let_1097 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_15593 x z) (ho_15593 y z)))) (= x y))))) (let ((_let_1098 (forall ((x |u_(-> tptp.extended_enat Bool)|) (y |u_(-> tptp.extended_enat Bool)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_18834 x z) (ho_18834 y z)))) (= x y))))) (let ((_let_1099 (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_25664 x z) (ho_25664 y z)))) (= x y))))) (let ((_let_1100 (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_25323 x z) (ho_25323 y z)))) (= x y))))) (let ((_let_1101 (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_24953 x z) (ho_24953 y z)))) (= x y))))) (let ((_let_1102 (forall ((x |u_(-> tptp.complex tptp.set_complex Bool)|) (y |u_(-> tptp.complex tptp.set_complex Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_18827 x z) (ho_18827 y z)))) (= x y))))) (let ((_let_1103 (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_31662 x z) (ho_31662 y z)))) (= x y))))) (let ((_let_1104 (forall ((x |u_(-> tptp.set_complex tptp.set_complex tptp.complex Bool)|) (y |u_(-> tptp.set_complex tptp.set_complex tptp.complex Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_18823 x z) (ho_18823 y z)))) (= x y))))) (let ((_let_1105 (forall ((x |u_(-> tptp.complex Bool)|) (y |u_(-> tptp.complex Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_18825 x z) (ho_18825 y z)))) (= x y))))) (let ((_let_1106 (forall ((x |u_(-> tptp.real tptp.set_real Bool)|) (y |u_(-> tptp.real tptp.set_real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_18818 x z) (ho_18818 y z)))) (= x y))))) (let ((_let_1107 (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_31413 x z) (ho_31413 y z)))) (= x y))))) (let ((_let_1108 (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_25315 x z) (ho_25315 y z)))) (= x y))))) (let ((_let_1109 (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_18816 x z) (ho_18816 y z)))) (= x y))))) (let ((_let_1110 (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_28728 x z) (ho_28728 y z)))) (= x y))))) (let ((_let_1111 (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_18810 x z) (ho_18810 y z)))) (= x y))))) (let ((_let_1112 (forall ((x |u_(-> tptp.nat tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_18754 x z) (ho_18754 y z)))) (= x y))))) (let ((_let_1113 (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_31716 x z) (ho_31716 y z)))) (= x y))))) (let ((_let_1114 (forall ((x |u_(-> tptp.set_list_nat Bool)|) (y |u_(-> tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_18811 x z) (ho_18811 y z)))) (= x y))))) (let ((_let_1115 (forall ((x |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.int)|)) (= (ho_31758 x z) (ho_31758 y z)))) (= x y))))) (let ((_let_1116 (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_18807 x z) (ho_18807 y z)))) (= x y))))) (let ((_let_1117 (forall ((x |u_(-> tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_18808 x z) (ho_18808 y z)))) (= x y))))) (let ((_let_1118 (forall ((x |u_(-> tptp.int tptp.set_int Bool)|) (y |u_(-> tptp.int tptp.set_int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_18801 x z) (ho_18801 y z)))) (= x y))))) (let ((_let_1119 (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_31062 x z) (ho_31062 y z)))) (= x y))))) (let ((_let_1120 (forall ((x |u_(-> tptp.set_int Bool)|) (y |u_(-> tptp.set_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_18802 x z) (ho_18802 y z)))) (= x y))))) (let ((_let_1121 (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_24444 x z) (ho_24444 y z)))) (= x y))))) (let ((_let_1122 (forall ((x |u_(-> tptp.set_int tptp.set_int tptp.int Bool)|) (y |u_(-> tptp.set_int tptp.set_int tptp.int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_18798 x z) (ho_18798 y z)))) (= x y))))) (let ((_let_1123 (forall ((x |u_(-> tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_18793 x z) (ho_18793 y z)))) (= x y))))) (let ((_let_1124 (forall ((x |u_(-> tptp.set_o tptp.nat)|) (y |u_(-> tptp.set_o tptp.nat)|)) (or (not (forall ((z tptp.set_o)) (= (ho_31419 x z) (ho_31419 y z)))) (= x y))))) (let ((_let_1125 (forall ((x |u_(-> tptp.num tptp.complex)|) (y |u_(-> tptp.num tptp.complex)|)) (or (not (forall ((z tptp.num)) (= (ho_19703 x z) (ho_19703 y z)))) (= x y))))) (let ((_let_1126 (forall ((x |u_(-> tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18794 x z) (ho_18794 y z)))) (= x y))))) (let ((_let_1127 (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_25316 x z) (ho_25316 y z)))) (= x y))))) (let ((_let_1128 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18790 x z) (ho_18790 y z)))) (= x y))))) (let ((_let_1129 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.nat)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.nat)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_24445 x z) (ho_24445 y z)))) (= x y))))) (let ((_let_1130 (forall ((x |u_(-> tptp.rat tptp.nat tptp.rat)|) (y |u_(-> tptp.rat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_17072 x z) (ho_17072 y z)))) (= x y))))) (let ((_let_1131 (forall ((x |u_(-> tptp.real tptp.product_unit tptp.real)|) (y |u_(-> tptp.real tptp.product_unit tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_17834 x z) (ho_17834 y z)))) (= x y))))) (let ((_let_1132 (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_31540 x z) (ho_31540 y z)))) (= x y))))) (let ((_let_1133 (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_17817 x z) (ho_17817 y z)))) (= x y))))) (let ((_let_1134 (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_31168 x z) (ho_31168 y z)))) (= x y))))) (let ((_let_1135 (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_17818 x z) (ho_17818 y z)))) (= x y))))) (let ((_let_1136 (forall ((x |u_(-> tptp.set_list_nat tptp.set_list_nat tptp.list_nat Bool)|) (y |u_(-> tptp.set_list_nat tptp.set_list_nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_18806 x z) (ho_18806 y z)))) (= x y))))) (let ((_let_1137 (forall ((x |u_(-> Bool Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_31437 x z) (ho_31437 y z)))) (= x y))))) (let ((_let_1138 (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_18549 x z) (ho_18549 y z)))) (= x y))))) (let ((_let_1139 (forall ((x |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.set_Code_integer)|) (y |u_(-> _u_(-> tptp.code_integer Bool)_ tptp.set_Code_integer)|)) (or (not (forall ((z |u_(-> tptp.code_integer Bool)|)) (= (ho_31114 x z) (ho_31114 y z)))) (= x y))))) (let ((_let_1140 (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_24052 x z) (ho_24052 y z)))) (= x y))))) (let ((_let_1141 (forall ((x |u_(-> tptp.nat Bool Bool)|) (y |u_(-> tptp.nat Bool Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_31042 x z) (ho_31042 y z)))) (= x y))))) (let ((_let_1142 (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_18751 x z) (ho_18751 y z)))) (= x y))))) (let ((_let_1143 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.rat tptp.rat tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_17501 x z) (ho_17501 y z)))) (= x y))))) (let ((_let_1144 (forall ((x |u_(-> tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_15161 x z) (ho_15161 y z)))) (= x y))))) (let ((_let_1145 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.list_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.list_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_31679 x z) (ho_31679 y z)))) (= x y))))) (let ((_let_1146 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_15125 x z) (ho_15125 y z)))) (= x y))))) (let ((_let_1147 (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_25305 x z) (ho_25305 y z)))) (= x y))))) (let ((_let_1148 (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_25012 x z) (ho_25012 y z)))) (= x y))))) (let ((_let_1149 (forall ((x |u_(-> tptp.num tptp.num)|) (y |u_(-> tptp.num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_15152 x z) (ho_15152 y z)))) (= x y))))) (let ((_let_1150 (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_18302 x z) (ho_18302 y z)))) (= x y))))) (let ((_let_1151 (forall ((x |u_(-> tptp.rat tptp.rat tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.rat tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_17502 x z) (ho_17502 y z)))) (= x y))))) (let ((_let_1152 (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_24540 x z) (ho_24540 y z)))) (= x y))))) (let ((_let_1153 (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_16334 x z) (ho_16334 y z)))) (= x y))))) (let ((_let_1154 (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_18533 x z) (ho_18533 y z)))) (= x y))))) (let ((_let_1155 (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_26813 x z) (ho_26813 y z)))) (= x y))))) (let ((_let_1156 (forall ((x |u_(-> tptp.int tptp.produc4894624898956917775BT_int)|) (y |u_(-> tptp.int tptp.produc4894624898956917775BT_int)|)) (or (not (forall ((z tptp.int)) (= (ho_31217 x z) (ho_31217 y z)))) (= x y))))) (let ((_let_1157 (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_25328 x z) (ho_25328 y z)))) (= x y))))) (let ((_let_1158 (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_25365 x z) (ho_25365 y z)))) (= x y))))) (let ((_let_1159 (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_31165 x z) (ho_31165 y z)))) (= x y))))) (let ((_let_1160 (forall ((x |u_(-> tptp.nat tptp.int Bool)|) (y |u_(-> tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_24812 x z) (ho_24812 y z)))) (= x y))))) (let ((_let_1161 (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_31571 x z) (ho_31571 y z)))) (= x y))))) (let ((_let_1162 (forall ((x |u_(-> tptp.nat tptp.list_nat Bool)|) (y |u_(-> tptp.nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_24767 x z) (ho_24767 y z)))) (= x y))))) (let ((_let_1163 (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_31623 x z) (ho_31623 y z)))) (= x y))))) (let ((_let_1164 (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_24649 x z) (ho_24649 y z)))) (= x y))))) (let ((_let_1165 (forall ((x |u_(-> tptp.real tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_18406 x z) (ho_18406 y z)))) (= x y))))) (let ((_let_1166 (forall ((x |u_(-> tptp.nat tptp.complex tptp.complex)|) (y |u_(-> tptp.nat tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_18760 x z) (ho_18760 y z)))) (= x y))))) (let ((_let_1167 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_18540 x z) (ho_18540 y z)))) (= x y))))) (let ((_let_1168 (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_15110 x z) (ho_15110 y z)))) (= x y))))) (let ((_let_1169 (forall ((x |u_(-> tptp.set_nat tptp.int)|) (y |u_(-> tptp.set_nat tptp.int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25442 x z) (ho_25442 y z)))) (= x y))))) (let ((_let_1170 (forall ((x |u_(-> tptp.set_complex tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_complex tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_18687 x z) (ho_18687 y z)))) (= x y))))) (let ((_let_1171 (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_18583 x z) (ho_18583 y z)))) (= x y))))) (let ((_let_1172 (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_31591 x z) (ho_31591 y z)))) (= x y))))) (let ((_let_1173 (forall ((x |u_(-> tptp.rat tptp.rat tptp.int Bool)|) (y |u_(-> tptp.rat tptp.rat tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_16636 x z) (ho_16636 y z)))) (= x y))))) (let ((_let_1174 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat Bool)|)) (= (ho_31757 x z) (ho_31757 y z)))) (= x y))))) (let ((_let_1175 (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_24872 x z) (ho_24872 y z)))) (= x y))))) (let ((_let_1176 (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_31521 x z) (ho_31521 y z)))) (= x y))))) (let ((_let_1177 (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_24690 x z) (ho_24690 y z)))) (= x y))))) (let ((_let_1178 (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_20915 x z) (ho_20915 y z)))) (= x y))))) (let ((_let_1179 (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_15137 x z) (ho_15137 y z)))) (= x y))))) (let ((_let_1180 (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_20916 x z) (ho_20916 y z)))) (= x y))))) (let ((_let_1181 (forall ((x |u_(-> tptp.set_rat Bool)|) (y |u_(-> tptp.set_rat Bool)|)) (or (not (forall ((z tptp.set_rat)) (= (ho_31018 x z) (ho_31018 y z)))) (= x y))))) (let ((_let_1182 (forall ((x |u_(-> tptp.rat tptp.int Bool)|) (y |u_(-> tptp.rat tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_15783 x z) (ho_15783 y z)))) (= x y))))) (let ((_let_1183 (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_24723 x z) (ho_24723 y z)))) (= x y))))) (let ((_let_1184 (forall ((x |u_(-> tptp.real tptp.real Bool)|) (y |u_(-> tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_18443 x z) (ho_18443 y z)))) (= x y))))) (let ((_let_1185 (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_24010 x z) (ho_24010 y z)))) (= x y))))) (let ((_let_1186 (forall ((x |u_(-> tptp.produc8923325533196201883nteger Bool)|) (y |u_(-> tptp.produc8923325533196201883nteger Bool)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_31180 x z) (ho_31180 y z)))) (= x y))))) (let ((_let_1187 (forall ((x |u_(-> tptp.nat tptp.vEBT_VEBT tptp.vEBT_VEBT)|) (y |u_(-> tptp.nat tptp.vEBT_VEBT tptp.vEBT_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_23946 x z) (ho_23946 y z)))) (= x y))))) (let ((_let_1188 (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_31712 x z) (ho_31712 y z)))) (= x y))))) (let ((_let_1189 (forall ((x |u_(-> tptp.int tptp.rat)|) (y |u_(-> tptp.int tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_18632 x z) (ho_18632 y z)))) (= x y))))) (let ((_let_1190 (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_18736 x z) (ho_18736 y z)))) (= x y))))) (let ((_let_1191 (forall ((x |u_(-> tptp.list_nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_16541 x z) (ho_16541 y z)))) (= x y))))) (let ((_let_1192 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_15163 x z) (ho_15163 y z)))) (= x y))))) (let ((_let_1193 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ _u_(-> tptp.nat tptp.int tptp.int)_ tptp.nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ _u_(-> tptp.nat tptp.int tptp.int)_ tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.int)|)) (= (ho_26845 x z) (ho_26845 y z)))) (= x y))))) (let ((_let_1194 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_15592 x z) (ho_15592 y z)))) (= x y))))) (let ((_let_1195 (forall ((x |u_(-> tptp.set_nat tptp.set_real)|) (y |u_(-> tptp.set_nat tptp.set_real)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_24518 x z) (ho_24518 y z)))) (= x y))))) (let ((_let_1196 (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_31611 x z) (ho_31611 y z)))) (= x y))))) (let ((_let_1197 (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_15141 x z) (ho_15141 y z)))) (= x y))))) (let ((_let_1198 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_17879 x z) (ho_17879 y z)))) (= x y))))) (let ((_let_1199 (forall ((x |u_(-> tptp.num tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.num tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_17253 x z) (ho_17253 y z)))) (= x y))))) (let ((_let_1200 (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_26243 x z) (ho_26243 y z)))) (= x y))))) (let ((_let_1201 (forall ((x |u_(-> tptp.nat tptp.list_nat)|) (y |u_(-> tptp.nat tptp.list_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_16539 x z) (ho_16539 y z)))) (= x y))))) (let ((_let_1202 (forall ((x |u_(-> tptp.option_num tptp.num)|) (y |u_(-> tptp.option_num tptp.num)|)) (or (not (forall ((z tptp.option_num)) (= (ho_15614 x z) (ho_15614 y z)))) (= x y))))) (let ((_let_1203 (forall ((x |u_(-> tptp.set_real tptp.nat)|) (y |u_(-> tptp.set_real tptp.nat)|)) (or (not (forall ((z tptp.set_real)) (= (ho_31151 x z) (ho_31151 y z)))) (= x y))))) (let ((_let_1204 (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_31281 x z) (ho_31281 y z)))) (= x y))))) (let ((_let_1205 (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_16518 x z) (ho_16518 y z)))) (= x y))))) (let ((_let_1206 (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_24071 x z) (ho_24071 y z)))) (= x y))))) (let ((_let_1207 (forall ((x |u_(-> tptp.code_integer Bool)|) (y |u_(-> tptp.code_integer Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_18620 x z) (ho_18620 y z)))) (= x y))))) (let ((_let_1208 (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_25883 x z) (ho_25883 y z)))) (= x y))))) (let ((_let_1209 (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_18626 x z) (ho_18626 y z)))) (= x y))))) (let ((_let_1210 (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_25232 x z) (ho_25232 y z)))) (= x y))))) (let ((_let_1211 (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_24044 x z) (ho_24044 y z)))) (= x y))))) (let ((_let_1212 (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_31258 x z) (ho_31258 y z)))) (= x y))))) (let ((_let_1213 (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_17740 x z) (ho_17740 y z)))) (= x y))))) (let ((_let_1214 (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_27551 x z) (ho_27551 y z)))) (= x y))))) (let ((_let_1215 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_16519 x z) (ho_16519 y z)))) (= x y))))) (let ((_let_1216 (forall ((x |u_(-> Bool tptp.code_integer)|) (y |u_(-> Bool tptp.code_integer)|)) (or (not (forall ((z Bool)) (= (ho_18296 x z) (ho_18296 y z)))) (= x y))))) (let ((_let_1217 (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_24532 x z) (ho_24532 y z)))) (= x y))))) (let ((_let_1218 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_17878 x z) (ho_17878 y z)))) (= x y))))) (let ((_let_1219 (forall ((x |u_(-> tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_16503 x z) (ho_16503 y z)))) (= x y))))) (let ((_let_1220 (forall ((x |u_(-> tptp.nat tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.nat tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_31041 x z) (ho_31041 y z)))) (= x y))))) (let ((_let_1221 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_16347 x z) (ho_16347 y z)))) (= x y))))) (let ((_let_1222 (forall ((x |u_(-> tptp.set_nat tptp.complex)|) (y |u_(-> tptp.set_nat tptp.complex)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_25458 x z) (ho_25458 y z)))) (= x y))))) (let ((_let_1223 (forall ((x |u_(-> tptp.nat tptp.complex)|) (y |u_(-> tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_18757 x z) (ho_18757 y z)))) (= x y))))) (let ((_let_1224 (forall ((x |u_(-> tptp.real tptp.nat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.real tptp.nat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_16194 x z) (ho_16194 y z)))) (= x y))))) (let ((_let_1225 (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_31573 x z) (ho_31573 y z)))) (= x y))))) (let ((_let_1226 (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_16507 x z) (ho_16507 y z)))) (= x y))))) (let ((_let_1227 (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_24936 x z) (ho_24936 y z)))) (= x y))))) (let ((_let_1228 (forall ((x |u_(-> tptp.set_complex tptp.rat)|) (y |u_(-> tptp.set_complex tptp.rat)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_18684 x z) (ho_18684 y z)))) (= x y))))) (let ((_let_1229 (forall ((x |u_(-> tptp.nat tptp.nat tptp.extended_enat)|) (y |u_(-> tptp.nat tptp.nat tptp.extended_enat)|)) (or (not (forall ((z tptp.nat)) (= (ho_16011 x z) (ho_16011 y z)))) (= x y))))) (let ((_let_1230 (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_25359 x z) (ho_25359 y z)))) (= x y))))) (let ((_let_1231 (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_31435 x z) (ho_31435 y z)))) (= x y))))) (let ((_let_1232 (forall ((x |u_(-> tptp.real tptp.filter_real)|) (y |u_(-> tptp.real tptp.filter_real)|)) (or (not (forall ((z tptp.real)) (= (ho_31449 x z) (ho_31449 y z)))) (= x y))))) (let ((_let_1233 (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_16506 x z) (ho_16506 y z)))) (= x y))))) (let ((_let_1234 (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_31624 x z) (ho_31624 y z)))) (= x y))))) (let ((_let_1235 (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_18503 x z) (ho_18503 y z)))) (= x y))))) (let ((_let_1236 (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_17816 x z) (ho_17816 y z)))) (= x y))))) (let ((_let_1237 (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_31415 x z) (ho_31415 y z)))) (= x y))))) (let ((_let_1238 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)|)) (= (ho_31634 x z) (ho_31634 y z)))) (= x y))))) (let ((_let_1239 (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_15633 x z) (ho_15633 y z)))) (= x y))))) (let ((_let_1240 (forall ((x |u_(-> tptp.set_Extended_enat tptp.complex)|) (y |u_(-> tptp.set_Extended_enat tptp.complex)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_31130 x z) (ho_31130 y z)))) (= x y))))) (let ((_let_1241 (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_15139 x z) (ho_15139 y z)))) (= x y))))) (let ((_let_1242 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.complex)_ tptp.set_Extended_enat tptp.complex)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.complex)_ tptp.set_Extended_enat tptp.complex)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.complex)|)) (= (ho_31129 x z) (ho_31129 y z)))) (= x y))))) (let ((_let_1243 (forall ((x |u_(-> tptp.num tptp.num Bool)|) (y |u_(-> tptp.num tptp.num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_24184 x z) (ho_24184 y z)))) (= x y))))) (let ((_let_1244 (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_15601 x z) (ho_15601 y z)))) (= x y))))) (let ((_let_1245 (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_31541 x z) (ho_31541 y z)))) (= x y))))) (let ((_let_1246 (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_18762 x z) (ho_18762 y z)))) (= x y))))) (let ((_let_1247 (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_31485 x z) (ho_31485 y z)))) (= x y))))) (let ((_let_1248 (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_24746 x z) (ho_24746 y z)))) (= x y))))) (let ((_let_1249 (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_15602 x z) (ho_15602 y z)))) (= x y))))) (let ((_let_1250 (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_31288 x z) (ho_31288 y z)))) (= x y))))) (let ((_let_1251 (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_15613 x z) (ho_15613 y z)))) (= x y))))) (let ((_let_1252 (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_31277 x z) (ho_31277 y z)))) (= x y))))) (let ((_let_1253 (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_25495 x z) (ho_25495 y z)))) (= x y))))) (let ((_let_1254 (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_18518 x z) (ho_18518 y z)))) (= x y))))) (let ((_let_1255 (forall ((x |u_(-> Bool tptp.product_prod_int_int Bool)|) (y |u_(-> Bool tptp.product_prod_int_int Bool)|)) (or (not (forall ((z Bool)) (= (ho_21598 x z) (ho_21598 y z)))) (= x y))))) (let ((_let_1256 (forall ((x |u_(-> tptp.nat tptp.produc334124729049499915VEBT_o)|) (y |u_(-> tptp.nat tptp.produc334124729049499915VEBT_o)|)) (or (not (forall ((z tptp.nat)) (= (ho_31209 x z) (ho_31209 y z)))) (= x y))))) (let ((_let_1257 (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_24043 x z) (ho_24043 y z)))) (= x y))))) (let ((_let_1258 (forall ((x |u_(-> tptp.produc7272778201969148633d_enat Bool)|) (y |u_(-> tptp.produc7272778201969148633d_enat Bool)|)) (or (not (forall ((z tptp.produc7272778201969148633d_enat)) (= (ho_31739 x z) (ho_31739 y z)))) (= x y))))) (let ((_let_1259 (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_15603 x z) (ho_15603 y z)))) (= x y))))) (let ((_let_1260 (forall ((x |u_(-> tptp.list_nat tptp.list_num tptp.list_P1726324292696863441at_num)|) (y |u_(-> tptp.list_nat tptp.list_num tptp.list_P1726324292696863441at_num)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_31260 x z) (ho_31260 y z)))) (= x y))))) (let ((_let_1261 (forall ((x |u_(-> tptp.nat tptp.complex Bool)|) (y |u_(-> tptp.nat tptp.complex Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_25003 x z) (ho_25003 y z)))) (= x y))))) (let ((_let_1262 (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_31064 x z) (ho_31064 y z)))) (= x y))))) (let ((_let_1263 (forall ((x |u_(-> tptp.rat tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_15875 x z) (ho_15875 y z)))) (= x y))))) (let ((_let_1264 (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_15606 x z) (ho_15606 y z)))) (= x y))))) (let ((_let_1265 (forall ((x |u_(-> tptp.real tptp.nat tptp.int Bool)|) (y |u_(-> tptp.real tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_27830 x z) (ho_27830 y z)))) (= x y))))) (let ((_let_1266 (forall ((x |u_(-> tptp.extended_enat tptp.nat tptp.extended_enat)|) (y |u_(-> tptp.extended_enat tptp.nat tptp.extended_enat)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_17746 x z) (ho_17746 y z)))) (= x y))))) (let ((_let_1267 (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_15128 x z) (ho_15128 y z)))) (= x y))))) (let ((_let_1268 (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_25670 x z) (ho_25670 y z)))) (= x y))))) (let ((_let_1269 (forall ((x |u_(-> tptp.set_nat tptp.nat)|) (y |u_(-> tptp.set_nat tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18771 x z) (ho_18771 y z)))) (= x y))))) (let ((_let_1270 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_18539 x z) (ho_18539 y z)))) (= x y))))) (let ((_let_1271 (forall ((x |u_(-> tptp.rat tptp.set_rat Bool)|) (y |u_(-> tptp.rat tptp.set_rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_31017 x z) (ho_31017 y z)))) (= x y))))) (let ((_let_1272 (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_18531 x z) (ho_18531 y z)))) (= x y))))) (let ((_let_1273 (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_24009 x z) (ho_24009 y z)))) (= x y))))) (let ((_let_1274 (forall ((x |u_(-> tptp.rat tptp.rat)|) (y |u_(-> tptp.rat tptp.rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_15122 x z) (ho_15122 y z)))) (= x y))))) (let ((_let_1275 (forall ((x |u_(-> tptp.set_Extended_enat tptp.int tptp.int Bool)|) (y |u_(-> tptp.set_Extended_enat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_25332 x z) (ho_25332 y z)))) (= x y))))) (let ((_let_1276 (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_16538 x z) (ho_16538 y z)))) (= x y))))) (let ((_let_1277 (forall ((x |u_(-> tptp.real tptp.real tptp.product_unit tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.product_unit tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_17833 x z) (ho_17833 y z)))) (= x y))))) (let ((_let_1278 (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_18403 x z) (ho_18403 y z)))) (= x y))))) (let ((_let_1279 (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_25441 x z) (ho_25441 y z)))) (= x y))))) (let ((_let_1280 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.nat tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_24627 x z) (ho_24627 y z)))) (= x y))))) (let ((_let_1281 (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_31471 x z) (ho_31471 y z)))) (= x y))))) (let ((_let_1282 (forall ((x |u_(-> tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_15120 x z) (ho_15120 y z)))) (= x y))))) (let ((_let_1283 (forall ((x |u_(-> tptp.nat tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_18740 x z) (ho_18740 y z)))) (= x y))))) (let ((_let_1284 (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_15124 x z) (ho_15124 y z)))) (= x y))))) (let ((_let_1285 (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_31548 x z) (ho_31548 y z)))) (= x y))))) (let ((_let_1286 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.num)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.num)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_24787 x z) (ho_24787 y z)))) (= x y))))) (let ((_let_1287 (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_18627 x z) (ho_18627 y z)))) (= x y))))) (let ((_let_1288 (forall ((x |u_(-> tptp.int tptp.nat)|) (y |u_(-> tptp.int tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_15118 x z) (ho_15118 y z)))) (= x y))))) (let ((_let_1289 (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_24667 x z) (ho_24667 y z)))) (= x y))))) (let ((_let_1290 (forall ((x |u_(-> tptp.num tptp.option_num)|) (y |u_(-> tptp.num tptp.option_num)|)) (or (not (forall ((z tptp.num)) (= (ho_15195 x z) (ho_15195 y z)))) (= x y))))) (let ((_let_1291 (forall ((x |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_26804 x z) (ho_26804 y z)))) (= x y))))) (let ((_let_1292 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.rat)|)) (= (ho_15098 x z) (ho_15098 y z)))) (= x y))))) (let ((_let_1293 (forall ((x |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.set_nat tptp.set_real)|) (y |u_(-> _u_(-> tptp.nat tptp.real)_ tptp.set_nat tptp.set_real)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.real)|)) (= (ho_24517 x z) (ho_24517 y z)))) (= x y))))) (let ((_let_1294 (forall ((x |u_(-> tptp.option_nat Bool)|) (y |u_(-> tptp.option_nat Bool)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_25708 x z) (ho_25708 y z)))) (= x y))))) (let ((_let_1295 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.int Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.int Bool)|)) (= (ho_31614 x z) (ho_31614 y z)))) (= x y))))) (let ((_let_1296 (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_15598 x z) (ho_15598 y z)))) (= x y))))) (let ((_let_1297 (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_25437 x z) (ho_25437 y z)))) (= x y))))) (let ((_let_1298 (forall ((x |u_(-> tptp.real tptp.int Bool)|) (y |u_(-> tptp.real tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_16617 x z) (ho_16617 y z)))) (= x y))))) (let ((_let_1299 (forall ((x |u_(-> tptp.real tptp.rat)|) (y |u_(-> tptp.real tptp.rat)|)) (or (not (forall ((z tptp.real)) (= (ho_18638 x z) (ho_18638 y z)))) (= x y))))) (let ((_let_1300 (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_15105 x z) (ho_15105 y z)))) (= x y))))) (let ((_let_1301 (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_16910 x z) (ho_16910 y z)))) (= x y))))) (let ((_let_1302 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.nat tptp.int tptp.int)|) (y |u_(-> _u_(-> tptp.nat tptp.int tptp.int)_ tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int tptp.int)|)) (= (ho_26846 x z) (ho_26846 y z)))) (= x y))))) (let ((_let_1303 (forall ((x |u_(-> tptp.set_int tptp.int)|) (y |u_(-> tptp.set_int tptp.int)|)) (or (not (forall ((z tptp.set_int)) (= (ho_31123 x z) (ho_31123 y z)))) (= x y))))) (let ((_let_1304 (forall ((x |u_(-> tptp.num tptp.int)|) (y |u_(-> tptp.num tptp.int)|)) (or (not (forall ((z tptp.num)) (= (ho_15114 x z) (ho_15114 y z)))) (= x y))))) (let ((_let_1305 (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_26245 x z) (ho_26245 y z)))) (= x y))))) (let ((_let_1306 (forall ((x |u_(-> tptp.num tptp.rat)|) (y |u_(-> tptp.num tptp.rat)|)) (or (not (forall ((z tptp.num)) (= (ho_15150 x z) (ho_15150 y z)))) (= x y))))) (let ((_let_1307 (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_24573 x z) (ho_24573 y z)))) (= x y))))) (let ((_let_1308 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15350 x z) (ho_15350 y z)))) (= x y))))) (let ((_let_1309 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.nat)_ tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_25231 x z) (ho_25231 y z)))) (= x y))))) (let ((_let_1310 (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_24705 x z) (ho_24705 y z)))) (= x y))))) (let ((_let_1311 (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_31220 x z) (ho_31220 y z)))) (= x y))))) (let ((_let_1312 (forall ((x |u_(-> tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_15107 x z) (ho_15107 y z)))) (= x y))))) (let ((_let_1313 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_24410 x z) (ho_24410 y z)))) (= x y))))) (let ((_let_1314 (forall ((x |u_(-> tptp.real tptp.int tptp.real)|) (y |u_(-> tptp.real tptp.int tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_31493 x z) (ho_31493 y z)))) (= x y))))) (let ((_let_1315 (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_31710 x z) (ho_31710 y z)))) (= x y))))) (let ((_let_1316 (forall ((x |u_(-> tptp.int Bool)|) (y |u_(-> tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_15108 x z) (ho_15108 y z)))) (= x y))))) (let ((_let_1317 (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_18462 x z) (ho_18462 y z)))) (= x y))))) (let ((_let_1318 (forall ((x |u_(-> tptp.rat tptp.num tptp.int Bool)|) (y |u_(-> tptp.rat tptp.num tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_28009 x z) (ho_28009 y z)))) (= x y))))) (let ((_let_1319 (forall ((x |u_(-> tptp.vEBT_VEBT Bool)|) (y |u_(-> tptp.vEBT_VEBT Bool)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_18509 x z) (ho_18509 y z)))) (= x y))))) (let ((_let_1320 (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_31622 x z) (ho_31622 y z)))) (= x y))))) (let ((_let_1321 (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_15132 x z) (ho_15132 y z)))) (= x y))))) (let ((_let_1322 (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_24660 x z) (ho_24660 y z)))) (= x y))))) (let ((_let_1323 (forall ((x |u_(-> tptp.nat tptp.product_prod_num_num)|) (y |u_(-> tptp.nat tptp.product_prod_num_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_31191 x z) (ho_31191 y z)))) (= x y))))) (let ((_let_1324 (forall ((x |u_(-> tptp.nat tptp.option_num)|) (y |u_(-> tptp.nat tptp.option_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_16510 x z) (ho_16510 y z)))) (= x y))))) (let ((_let_1325 (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_15344 x z) (ho_15344 y z)))) (= x y))))) (let ((_let_1326 (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_24900 x z) (ho_24900 y z)))) (= x y))))) (let ((_let_1327 (forall ((x |u_(-> tptp.real tptp.real tptp.int tptp.int Bool)|) (y |u_(-> tptp.real tptp.real tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_26881 x z) (ho_26881 y z)))) (= x y))))) (let ((_let_1328 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_17872 x z) (ho_17872 y z)))) (= x y))))) (let ((_let_1329 (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_31653 x z) (ho_31653 y z)))) (= x y))))) (let ((_let_1330 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|) (y |u_(-> _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|)) (= (ho_15099 x z) (ho_15099 y z)))) (= x y))))) (let ((_let_1331 (forall ((x |u_(-> tptp.set_Extended_enat tptp.set_Extended_enat)|) (y |u_(-> tptp.set_Extended_enat tptp.set_Extended_enat)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_25682 x z) (ho_25682 y z)))) (= x y))))) (let ((_let_1332 (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_24530 x z) (ho_24530 y z)))) (= x y))))) (let ((_let_1333 (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_31590 x z) (ho_31590 y z)))) (= x y))))) (let ((_let_1334 (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_31600 x z) (ho_31600 y z)))) (= x y))))) (let ((_let_1335 (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_18600 x z) (ho_18600 y z)))) (= x y))))) (let ((_let_1336 (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_18628 x z) (ho_18628 y z)))) (= x y))))) (let ((_let_1337 (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_15106 x z) (ho_15106 y z)))) (= x y))))) (let ((_let_1338 (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_31583 x z) (ho_31583 y z)))) (= x y))))) (let ((_let_1339 (forall ((x |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int)|) (y |u_(-> _u_(-> tptp.product_prod_int_int Bool)_ tptp.product_prod_int_int)|)) (or (not (forall ((z |u_(-> tptp.product_prod_int_int Bool)|)) (= (ho_15260 x z) (ho_15260 y z)))) (= x y))))) (let ((_let_1340 (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_18420 x z) (ho_18420 y z)))) (= x y))))) (let ((_let_1341 (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_31226 x z) (ho_31226 y z)))) (= x y))))) (let ((_let_1342 (forall ((x |u_(-> tptp.set_nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18669 x z) (ho_18669 y z)))) (= x y))))) (let ((_let_1343 (forall ((x |u_(-> tptp.int tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_15078 x z) (ho_15078 y z)))) (= x y))))) (let ((_let_1344 (forall ((x |u_(-> _u_(-> tptp.rat tptp.rat)_ tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.rat tptp.rat)_ tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.rat tptp.rat)|)) (= (ho_18928 x z) (ho_18928 y z)))) (= x y))))) (let ((_let_1345 (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_31254 x z) (ho_31254 y z)))) (= x y))))) (let ((_let_1346 (forall ((x |u_(-> tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_15079 x z) (ho_15079 y z)))) (= x y))))) (let ((_let_1347 (forall ((x |u_(-> tptp.nat tptp.extended_enat)|) (y |u_(-> tptp.nat tptp.extended_enat)|)) (or (not (forall ((z tptp.nat)) (= (ho_16012 x z) (ho_16012 y z)))) (= x y))))) (let ((_let_1348 (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_18298 x z) (ho_18298 y z)))) (= x y))))) (let ((_let_1349 (forall ((x |u_(-> tptp.extended_enat tptp.extended_enat tptp.set_Extended_enat)|) (y |u_(-> tptp.extended_enat tptp.extended_enat tptp.set_Extended_enat)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_31061 x z) (ho_31061 y z)))) (= x y))))) (let ((_let_1350 (forall ((x |u_(-> _u_(-> tptp.nat tptp.extended_enat)_ tptp.extended_enat tptp.extended_enat tptp.extended_enat)|) (y |u_(-> _u_(-> tptp.nat tptp.extended_enat)_ tptp.extended_enat tptp.extended_enat tptp.extended_enat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.extended_enat)|)) (= (ho_17744 x z) (ho_17744 y z)))) (= x y))))) (let ((_let_1351 (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_24533 x z) (ho_24533 y z)))) (= x y))))) (let ((_let_1352 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_15100 x z) (ho_15100 y z)))) (= x y))))) (let ((_let_1353 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.rat)|)) (= (ho_15089 x z) (ho_15089 y z)))) (= x y))))) (let ((_let_1354 (forall ((x |u_(-> Bool tptp.int)|) (y |u_(-> Bool tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_25060 x z) (ho_25060 y z)))) (= x y))))) (let ((_let_1355 (forall ((x |u_(-> tptp.real Bool)|) (y |u_(-> tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_15103 x z) (ho_15103 y z)))) (= x y))))) (let ((_let_1356 (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_15605 x z) (ho_15605 y z)))) (= x y))))) (let ((_let_1357 (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_15134 x z) (ho_15134 y z)))) (= x y))))) (let ((_let_1358 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15502 x z) (ho_15502 y z)))) (= x y))))) (let ((_let_1359 (forall ((x |u_(-> Bool Bool tptp.literal tptp.literal)|) (y |u_(-> Bool Bool tptp.literal tptp.literal)|)) (or (not (forall ((z Bool)) (= (ho_24033 x z) (ho_24033 y z)))) (= x y))))) (let ((_let_1360 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.set_nat)|) (y |u_(-> tptp.vEBT_VEBT tptp.set_nat)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_31045 x z) (ho_31045 y z)))) (= x y))))) (let ((_let_1361 (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_18824 x z) (ho_18824 y z)))) (= x y))))) (let ((_let_1362 (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_18544 x z) (ho_18544 y z)))) (= x y))))) (let ((_let_1363 (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_18582 x z) (ho_18582 y z)))) (= x y))))) (let ((_let_1364 (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_31483 x z) (ho_31483 y z)))) (= x y))))) (let ((_let_1365 (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_31606 x z) (ho_31606 y z)))) (= x y))))) (let ((_let_1366 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_15495 x z) (ho_15495 y z)))) (= x y))))) (let ((_let_1367 (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_18460 x z) (ho_18460 y z)))) (= x y))))) (let ((_let_1368 (forall ((x |u_(-> tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_15092 x z) (ho_15092 y z)))) (= x y))))) (let ((_let_1369 (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_16543 x z) (ho_16543 y z)))) (= x y))))) (let ((_let_1370 (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_18535 x z) (ho_18535 y z)))) (= x y))))) (let ((_let_1371 (forall ((x |u_(-> tptp.nat tptp.complex tptp.complex tptp.complex)|) (y |u_(-> tptp.nat tptp.complex tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_25136 x z) (ho_25136 y z)))) (= x y))))) (let ((_let_1372 (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_31377 x z) (ho_31377 y z)))) (= x y))))) (let ((_let_1373 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_18634 x z) (ho_18634 y z)))) (= x y))))) (let ((_let_1374 (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_25248 x z) (ho_25248 y z)))) (= x y))))) (let ((_let_1375 (forall ((x |u_(-> tptp.nat tptp.set_nat)|) (y |u_(-> tptp.nat tptp.set_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_18401 x z) (ho_18401 y z)))) (= x y))))) (let ((_let_1376 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_15379 x z) (ho_15379 y z)))) (= x y))))) (let ((_let_1377 (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_18300 x z) (ho_18300 y z)))) (= x y))))) (let ((_let_1378 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_31615 x z) (ho_31615 y z)))) (= x y))))) (let ((_let_1379 (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_15083 x z) (ho_15083 y z)))) (= x y))))) (let ((_let_1380 (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_15266 x z) (ho_15266 y z)))) (= x y))))) (let ((_let_1381 (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_15138 x z) (ho_15138 y z)))) (= x y))))) (let ((_let_1382 (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_18683 x z) (ho_18683 y z)))) (= x y))))) (let ((_let_1383 (forall ((x |u_(-> tptp.product_unit tptp.real)|) (y |u_(-> tptp.product_unit tptp.real)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_17835 x z) (ho_17835 y z)))) (= x y))))) (let ((_let_1384 (forall ((x |u_(-> tptp.nat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15164 x z) (ho_15164 y z)))) (= x y))))) (let ((_let_1385 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.extended_enat tptp.produc7272778201969148633d_enat)|) (y |u_(-> tptp.vEBT_VEBT tptp.extended_enat tptp.produc7272778201969148633d_enat)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_31733 x z) (ho_31733 y z)))) (= x y))))) (let ((_let_1386 (forall ((x |u_(-> tptp.nat tptp.nat tptp.complex)|) (y |u_(-> tptp.nat tptp.nat tptp.complex)|)) (or (not (forall ((z tptp.nat)) (= (ho_18763 x z) (ho_18763 y z)))) (= x y))))) (let ((_let_1387 (forall ((x |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|) (y |u_(-> _u_(-> tptp.list_nat Bool)_ tptp.list_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.list_nat Bool)|)) (= (ho_25658 x z) (ho_25658 y z)))) (= x y))))) (let ((_let_1388 (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_24999 x z) (ho_24999 y z)))) (= x y))))) (let ((_let_1389 (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_31607 x z) (ho_31607 y z)))) (= x y))))) (let ((_let_1390 (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_18508 x z) (ho_18508 y z)))) (= x y))))) (let ((_let_1391 (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_17443 x z) (ho_17443 y z)))) (= x y))))) (let ((_let_1392 (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_24931 x z) (ho_24931 y z)))) (= x y))))) (let ((_let_1393 (forall ((x |u_(-> tptp.rat tptp.set_rat)|) (y |u_(-> tptp.rat tptp.set_rat)|)) (or (not (forall ((z tptp.rat)) (= (ho_31071 x z) (ho_31071 y z)))) (= x y))))) (let ((_let_1394 (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_16515 x z) (ho_16515 y z)))) (= x y))))) (let ((_let_1395 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_15343 x z) (ho_15343 y z)))) (= x y))))) (let ((_let_1396 (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_31651 x z) (ho_31651 y z)))) (= x y))))) (let ((_let_1397 (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_25152 x z) (ho_25152 y z)))) (= x y))))) (let ((_let_1398 (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_31159 x z) (ho_31159 y z)))) (= x y))))) (let ((_let_1399 (forall ((x |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.set_real tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.set_real tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.rat)|)) (= (ho_18677 x z) (ho_18677 y z)))) (= x y))))) (let ((_let_1400 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15168 x z) (ho_15168 y z)))) (= x y))))) (let ((_let_1401 (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_31083 x z) (ho_31083 y z)))) (= x y))))) (let ((_let_1402 (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_16505 x z) (ho_16505 y z)))) (= x y))))) (let ((_let_1403 (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_31564 x z) (ho_31564 y z)))) (= x y))))) (let ((_let_1404 (forall ((x |u_(-> tptp.num tptp.num tptp.produc8923325533196201883nteger)|) (y |u_(-> tptp.num tptp.num tptp.produc8923325533196201883nteger)|)) (or (not (forall ((z tptp.num)) (= (ho_25039 x z) (ho_25039 y z)))) (= x y))))) (let ((_let_1405 (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_18799 x z) (ho_18799 y z)))) (= x y))))) (let ((_let_1406 (forall ((x |u_(-> tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_15165 x z) (ho_15165 y z)))) (= x y))))) (let ((_let_1407 (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_16661 x z) (ho_16661 y z)))) (= x y))))) (let ((_let_1408 (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_31334 x z) (ho_31334 y z)))) (= x y))))) (let ((_let_1409 (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_15096 x z) (ho_15096 y z)))) (= x y))))) (let ((_let_1410 (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_18545 x z) (ho_18545 y z)))) (= x y))))) (let ((_let_1411 (forall ((x |u_(-> tptp.set_real tptp.real)|) (y |u_(-> tptp.set_real tptp.real)|)) (or (not (forall ((z tptp.set_real)) (= (ho_31148 x z) (ho_31148 y z)))) (= x y))))) (let ((_let_1412 (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_25300 x z) (ho_25300 y z)))) (= x y))))) (let ((_let_1413 (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_15608 x z) (ho_15608 y z)))) (= x y))))) (let ((_let_1414 (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_17742 x z) (ho_17742 y z)))) (= x y))))) (let ((_let_1415 (forall ((x |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.complex tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.complex tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.rat)|)) (= (ho_18645 x z) (ho_18645 y z)))) (= x y))))) (let ((_let_1416 (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_24946 x z) (ho_24946 y z)))) (= x y))))) (let ((_let_1417 (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_18304 x z) (ho_18304 y z)))) (= x y))))) (let ((_let_1418 (forall ((x |u_(-> tptp.num tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.num tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_17235 x z) (ho_17235 y z)))) (= x y))))) (let ((_let_1419 (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_31405 x z) (ho_31405 y z)))) (= x y))))) (let ((_let_1420 (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_15262 x z) (ho_15262 y z)))) (= x y))))) (let ((_let_1421 (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_24929 x z) (ho_24929 y z)))) (= x y))))) (let ((_let_1422 (forall ((x |u_(-> tptp.num tptp.real)|) (y |u_(-> tptp.num tptp.real)|)) (or (not (forall ((z tptp.num)) (= (ho_15094 x z) (ho_15094 y z)))) (= x y))))) (let ((_let_1423 (forall ((x |u_(-> tptp.rat tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_15209 x z) (ho_15209 y z)))) (= x y))))) (let ((_let_1424 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_16534 x z) (ho_16534 y z)))) (= x y))))) (let ((_let_1425 (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_24794 x z) (ho_24794 y z)))) (= x y))))) (let ((_let_1426 (forall ((x |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_17882 x z) (ho_17882 y z)))) (= x y))))) (let ((_let_1427 (forall ((x |u_(-> _u_(-> tptp.real tptp.real)_ _u_(-> tptp.real tptp.real)_ tptp.filter_real Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real)_ _u_(-> tptp.real tptp.real)_ tptp.filter_real Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real)|)) (= (ho_31481 x z) (ho_31481 y z)))) (= x y))))) (let ((_let_1428 (forall ((x |u_(-> tptp.nat tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.nat tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_17881 x z) (ho_17881 y z)))) (= x y))))) (let ((_let_1429 (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_25667 x z) (ho_25667 y z)))) (= x y))))) (let ((_let_1430 (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_25541 x z) (ho_25541 y z)))) (= x y))))) (let ((_let_1431 (forall ((x |u_(-> tptp.int tptp.nat tptp.rat)|) (y |u_(-> tptp.int tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.int)) (= (ho_18087 x z) (ho_18087 y z)))) (= x y))))) (let ((_let_1432 (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_21348 x z) (ho_21348 y z)))) (= x y))))) (let ((_let_1433 (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_31525 x z) (ho_31525 y z)))) (= x y))))) (let ((_let_1434 (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_18624 x z) (ho_18624 y z)))) (= x y))))) (let ((_let_1435 (forall ((x |u_(-> tptp.code_integer tptp.nat Bool)|) (y |u_(-> tptp.code_integer tptp.nat Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_28160 x z) (ho_28160 y z)))) (= x y))))) (let ((_let_1436 (forall ((x |u_(-> tptp.num Bool)|) (y |u_(-> tptp.num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_24185 x z) (ho_24185 y z)))) (= x y))))) (let ((_let_1437 (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_15345 x z) (ho_15345 y z)))) (= x y))))) (let ((_let_1438 (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_31206 x z) (ho_31206 y z)))) (= x y))))) (let ((_let_1439 (forall ((x |u_(-> tptp.nat tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.nat tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_18116 x z) (ho_18116 y z)))) (= x y))))) (let ((_let_1440 (forall ((x |u_(-> tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_18737 x z) (ho_18737 y z)))) (= x y))))) (let ((_let_1441 (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_25007 x z) (ho_25007 y z)))) (= x y))))) (let ((_let_1442 (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_25872 x z) (ho_25872 y z)))) (= x y))))) (let ((_let_1443 (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_15135 x z) (ho_15135 y z)))) (= x y))))) (let ((_let_1444 (forall ((x |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.real tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.real tptp.rat)_ tptp.real tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.rat)|)) (= (ho_18640 x z) (ho_18640 y z)))) (= x y))))) (let ((_let_1445 (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_31162 x z) (ho_31162 y z)))) (= x y))))) (let ((_let_1446 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.rat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.nat tptp.rat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_18114 x z) (ho_18114 y z)))) (= x y))))) (let ((_let_1447 (forall ((x |u_(-> tptp.code_integer tptp.nat)|) (y |u_(-> tptp.code_integer tptp.nat)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_18294 x z) (ho_18294 y z)))) (= x y))))) (let ((_let_1448 (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_26952 x z) (ho_26952 y z)))) (= x y))))) (let ((_let_1449 (forall ((x |u_(-> tptp.rat tptp.rat Bool)|) (y |u_(-> tptp.rat tptp.rat Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_24510 x z) (ho_24510 y z)))) (= x y))))) (let ((_let_1450 (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_31663 x z) (ho_31663 y z)))) (= x y))))) (let ((_let_1451 (forall ((x |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.set_nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.rat)|)) (= (ho_18668 x z) (ho_18668 y z)))) (= x y))))) (let ((_let_1452 (forall ((x |u_(-> tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_18396 x z) (ho_18396 y z)))) (= x y))))) (let ((_let_1453 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.int tptp.int)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.int tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_27738 x z) (ho_27738 y z)))) (= x y))))) (let ((_let_1454 (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_24007 x z) (ho_24007 y z)))) (= x y))))) (let ((_let_1455 (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_18665 x z) (ho_18665 y z)))) (= x y))))) (let ((_let_1456 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.rat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.nat)) (= (ho_20381 x z) (ho_20381 y z)))) (= x y))))) (let ((_let_1457 (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_18398 x z) (ho_18398 y z)))) (= x y))))) (let ((_let_1458 (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_18538 x z) (ho_18538 y z)))) (= x y))))) (let ((_let_1459 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.rat)_ tptp.set_Extended_enat tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.rat)_ tptp.set_Extended_enat tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.rat)|)) (= (ho_25331 x z) (ho_25331 y z)))) (= x y))))) (let ((_let_1460 (forall ((x |u_(-> _u_(-> tptp.product_unit tptp.real)_ tptp.real)|) (y |u_(-> _u_(-> tptp.product_unit tptp.real)_ tptp.real)|)) (or (not (forall ((z |u_(-> tptp.product_unit tptp.real)|)) (= (ho_24038 x z) (ho_24038 y z)))) (= x y))))) (let ((_let_1461 (forall ((x |u_(-> tptp.extended_enat tptp.extended_enat tptp.nat Bool)|) (y |u_(-> tptp.extended_enat tptp.extended_enat tptp.nat Bool)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_23961 x z) (ho_23961 y z)))) (= x y))))) (let ((_let_1462 (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_31275 x z) (ho_31275 y z)))) (= x y))))) (let ((_let_1463 (forall ((x |u_(-> tptp.real tptp.real tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.real tptp.real tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_19753 x z) (ho_19753 y z)))) (= x y))))) (let ((_let_1464 (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_18400 x z) (ho_18400 y z)))) (= x y))))) (let ((_let_1465 (forall ((x |u_(-> tptp.complex tptp.complex)|) (y |u_(-> tptp.complex tptp.complex)|)) (or (not (forall ((z tptp.complex)) (= (ho_18597 x z) (ho_18597 y z)))) (= x y))))) (let ((_let_1466 (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_31687 x z) (ho_31687 y z)))) (= x y))))) (let ((_let_1467 (forall ((x |u_(-> tptp.nat tptp.num)|) (y |u_(-> tptp.nat tptp.num)|)) (or (not (forall ((z tptp.nat)) (= (ho_15596 x z) (ho_15596 y z)))) (= x y))))) (let ((_let_1468 (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_25834 x z) (ho_25834 y z)))) (= x y))))) (let ((_let_1469 (forall ((x |u_(-> tptp.set_nat tptp.real)|) (y |u_(-> tptp.set_nat tptp.real)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18404 x z) (ho_18404 y z)))) (= x y))))) (let ((_let_1470 (forall ((x |u_(-> tptp.extended_enat tptp.rat)|) (y |u_(-> tptp.extended_enat tptp.rat)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_18648 x z) (ho_18648 y z)))) (= x y))))) (let ((_let_1471 (forall ((x |u_(-> tptp.nat tptp.real tptp.real)|) (y |u_(-> tptp.nat tptp.real tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_18422 x z) (ho_18422 y z)))) (= x y))))) (let ((_let_1472 (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_18434 x z) (ho_18434 y z)))) (= x y))))) (let ((_let_1473 (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_31569 x z) (ho_31569 y z)))) (= x y))))) (let ((_let_1474 (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_18433 x z) (ho_18433 y z)))) (= x y))))) (let ((_let_1475 (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_24995 x z) (ho_24995 y z)))) (= x y))))) (let ((_let_1476 (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_18437 x z) (ho_18437 y z)))) (= x y))))) (let ((_let_1477 (forall ((x |u_(-> tptp.set_int tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_int)) (= (ho_18660 x z) (ho_18660 y z)))) (= x y))))) (let ((_let_1478 (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_31246 x z) (ho_31246 y z)))) (= x y))))) (let ((_let_1479 (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_18436 x z) (ho_18436 y z)))) (= x y))))) (let ((_let_1480 (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_18447 x z) (ho_18447 y z)))) (= x y))))) (let ((_let_1481 (forall ((x |u_(-> tptp.num tptp.num tptp.num)|) (y |u_(-> tptp.num tptp.num tptp.num)|)) (or (not (forall ((z tptp.num)) (= (ho_18458 x z) (ho_18458 y z)))) (= x y))))) (let ((_let_1482 (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_18748 x z) (ho_18748 y z)))) (= x y))))) (let ((_let_1483 (forall ((x |u_(-> tptp.code_integer tptp.num)|) (y |u_(-> tptp.code_integer tptp.num)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_18456 x z) (ho_18456 y z)))) (= x y))))) (let ((_let_1484 (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_18743 x z) (ho_18743 y z)))) (= x y))))) (let ((_let_1485 (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_25324 x z) (ho_25324 y z)))) (= x y))))) (let ((_let_1486 (forall ((x |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> Bool Bool)|)) (= (ho_31703 x z) (ho_31703 y z)))) (= x y))))) (let ((_let_1487 (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_15130 x z) (ho_15130 y z)))) (= x y))))) (let ((_let_1488 (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_18465 x z) (ho_18465 y z)))) (= x y))))) (let ((_let_1489 (forall ((x |u_(-> tptp.set_int tptp.rat)|) (y |u_(-> tptp.set_int tptp.rat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_18657 x z) (ho_18657 y z)))) (= x y))))) (let ((_let_1490 (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_19706 x z) (ho_19706 y z)))) (= x y))))) (let ((_let_1491 (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_18498 x z) (ho_18498 y z)))) (= x y))))) (let ((_let_1492 (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_25319 x z) (ho_25319 y z)))) (= x y))))) (let ((_let_1493 (forall ((x |u_(-> tptp.complex tptp.real Bool)|) (y |u_(-> tptp.complex tptp.real Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_18603 x z) (ho_18603 y z)))) (= x y))))) (let ((_let_1494 (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_18505 x z) (ho_18505 y z)))) (= x y))))) (let ((_let_1495 (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_18521 x z) (ho_18521 y z)))) (= x y))))) (let ((_let_1496 (forall ((x |u_(-> tptp.complex tptp.real)|) (y |u_(-> tptp.complex tptp.real)|)) (or (not (forall ((z tptp.complex)) (= (ho_18592 x z) (ho_18592 y z)))) (= x y))))) (let ((_let_1497 (forall ((x |u_(-> tptp.rat tptp.num tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.rat tptp.num tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_17252 x z) (ho_17252 y z)))) (= x y))))) (let ((_let_1498 (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_18614 x z) (ho_18614 y z)))) (= x y))))) (let ((_let_1499 (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_17815 x z) (ho_17815 y z)))) (= x y))))) (let ((_let_1500 (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_18517 x z) (ho_18517 y z)))) (= x y))))) (let ((_let_1501 (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_18520 x z) (ho_18520 y z)))) (= x y))))) (let ((_let_1502 (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_24694 x z) (ho_24694 y z)))) (= x y))))) (let ((_let_1503 (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_16696 x z) (ho_16696 y z)))) (= x y))))) (let ((_let_1504 (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_18601 x z) (ho_18601 y z)))) (= x y))))) (let ((_let_1505 (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_18552 x z) (ho_18552 y z)))) (= x y))))) (let ((_let_1506 (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_18551 x z) (ho_18551 y z)))) (= x y))))) (let ((_let_1507 (forall ((x |u_(-> tptp.set_Extended_enat tptp.real)|) (y |u_(-> tptp.set_Extended_enat tptp.real)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_31134 x z) (ho_31134 y z)))) (= x y))))) (let ((_let_1508 (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_31293 x z) (ho_31293 y z)))) (= x y))))) (let ((_let_1509 (forall ((x |u_(-> tptp.real tptp.complex)|) (y |u_(-> tptp.real tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_18590 x z) (ho_18590 y z)))) (= x y))))) (let ((_let_1510 (forall ((x |u_(-> Bool tptp.produc6271795597528267376eger_o)|) (y |u_(-> Bool tptp.produc6271795597528267376eger_o)|)) (or (not (forall ((z Bool)) (= (ho_18580 x z) (ho_18580 y z)))) (= x y))))) (let ((_let_1511 (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_31284 x z) (ho_31284 y z)))) (= x y))))) (let ((_let_1512 (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_24687 x z) (ho_24687 y z)))) (= x y))))) (let ((_let_1513 (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_31252 x z) (ho_31252 y z)))) (= x y))))) (let ((_let_1514 (forall ((x |u_(-> tptp.filter1242075044329608583at_nat Bool)|) (y |u_(-> tptp.filter1242075044329608583at_nat Bool)|)) (or (not (forall ((z tptp.filter1242075044329608583at_nat)) (= (ho_31720 x z) (ho_31720 y z)))) (= x y))))) (let ((_let_1515 (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_18584 x z) (ho_18584 y z)))) (= x y))))) (let ((_let_1516 (forall ((x |u_(-> tptp.extended_enat tptp.int tptp.int Bool)|) (y |u_(-> tptp.extended_enat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_25310 x z) (ho_25310 y z)))) (= x y))))) (let ((_let_1517 (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_24811 x z) (ho_24811 y z)))) (= x y))))) (let ((_let_1518 (forall ((x |u_(-> tptp.real tptp.real tptp.complex)|) (y |u_(-> tptp.real tptp.real tptp.complex)|)) (or (not (forall ((z tptp.real)) (= (ho_18594 x z) (ho_18594 y z)))) (= x y))))) (let ((_let_1519 (forall ((x |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.set_complex tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.complex tptp.rat)_ tptp.set_complex tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.complex tptp.rat)|)) (= (ho_18686 x z) (ho_18686 y z)))) (= x y))))) (let ((_let_1520 (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_18605 x z) (ho_18605 y z)))) (= x y))))) (let ((_let_1521 (forall ((x |u_(-> tptp.real tptp.nat)|) (y |u_(-> tptp.real tptp.nat)|)) (or (not (forall ((z tptp.real)) (= (ho_31038 x z) (ho_31038 y z)))) (= x y))))) (let ((_let_1522 (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_24914 x z) (ho_24914 y z)))) (= x y))))) (let ((_let_1523 (forall ((x |u_(-> tptp.num tptp.code_integer)|) (y |u_(-> tptp.num tptp.code_integer)|)) (or (not (forall ((z tptp.num)) (= (ho_18616 x z) (ho_18616 y z)))) (= x y))))) (let ((_let_1524 (forall ((x |u_(-> tptp.real tptp.nat tptp.rat)|) (y |u_(-> tptp.real tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.real)) (= (ho_15087 x z) (ho_15087 y z)))) (= x y))))) (let ((_let_1525 (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_18619 x z) (ho_18619 y z)))) (= x y))))) (let ((_let_1526 (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_18753 x z) (ho_18753 y z)))) (= x y))))) (let ((_let_1527 (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_31347 x z) (ho_31347 y z)))) (= x y))))) (let ((_let_1528 (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_18606 x z) (ho_18606 y z)))) (= x y))))) (let ((_let_1529 (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_24127 x z) (ho_24127 y z)))) (= x y))))) (let ((_let_1530 (forall ((x |u_(-> tptp.real tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.real tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_18641 x z) (ho_18641 y z)))) (= x y))))) (let ((_let_1531 (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_24935 x z) (ho_24935 y z)))) (= x y))))) (let ((_let_1532 (forall ((x |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)_ tptp.int tptp.int Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|)) (= (ho_31706 x z) (ho_31706 y z)))) (= x y))))) (let ((_let_1533 (forall ((x |u_(-> tptp.complex tptp.rat)|) (y |u_(-> tptp.complex tptp.rat)|)) (or (not (forall ((z tptp.complex)) (= (ho_18643 x z) (ho_18643 y z)))) (= x y))))) (let ((_let_1534 (forall ((x |u_(-> tptp.complex tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.complex tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.complex)) (= (ho_18646 x z) (ho_18646 y z)))) (= x y))))) (let ((_let_1535 (forall ((x |u_(-> tptp.set_Code_integer Bool)|) (y |u_(-> tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_31022 x z) (ho_31022 y z)))) (= x y))))) (let ((_let_1536 (forall ((x |u_(-> tptp.extended_enat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.extended_enat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_18651 x z) (ho_18651 y z)))) (= x y))))) (let ((_let_1537 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_31636 x z) (ho_31636 y z)))) (= x y))))) (let ((_let_1538 (forall ((x |u_(-> tptp.set_real tptp.set_real tptp.real Bool)|) (y |u_(-> tptp.set_real tptp.set_real tptp.real Bool)|)) (or (not (forall ((z tptp.set_real)) (= (ho_18815 x z) (ho_18815 y z)))) (= x y))))) (let ((_let_1539 (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_31208 x z) (ho_31208 y z)))) (= x y))))) (let ((_let_1540 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_num)|) (y |u_(-> tptp.nat tptp.product_prod_nat_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_31264 x z) (ho_31264 y z)))) (= x y))))) (let ((_let_1541 (forall ((x |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.set_int tptp.product_prod_int_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.rat)_ tptp.set_int tptp.product_prod_int_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.rat)|)) (= (ho_18659 x z) (ho_18659 y z)))) (= x y))))) (let ((_let_1542 (forall ((x |u_(-> tptp.real tptp.set_real)|) (y |u_(-> tptp.real tptp.set_real)|)) (or (not (forall ((z tptp.real)) (= (ho_24571 x z) (ho_24571 y z)))) (= x y))))) (let ((_let_1543 (forall ((x |u_(-> tptp.nat tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.nat tptp.nat _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_24276 x z) (ho_24276 y z)))) (= x y))))) (let ((_let_1544 (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_31518 x z) (ho_31518 y z)))) (= x y))))) (let ((_let_1545 (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_15612 x z) (ho_15612 y z)))) (= x y))))) (let ((_let_1546 (forall ((x |u_(-> tptp.set_nat tptp.rat)|) (y |u_(-> tptp.set_nat tptp.rat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_18666 x z) (ho_18666 y z)))) (= x y))))) (let ((_let_1547 (forall ((x |u_(-> tptp.option4927543243414619207at_nat Bool)|) (y |u_(-> tptp.option4927543243414619207at_nat Bool)|)) (or (not (forall ((z tptp.option4927543243414619207at_nat)) (= (ho_31370 x z) (ho_31370 y z)))) (= x y))))) (let ((_let_1548 (forall ((x |u_(-> tptp.set_real tptp.rat)|) (y |u_(-> tptp.set_real tptp.rat)|)) (or (not (forall ((z tptp.set_real)) (= (ho_18675 x z) (ho_18675 y z)))) (= x y))))) (let ((_let_1549 (forall ((x |u_(-> tptp.set_Extended_enat tptp.rat)|) (y |u_(-> tptp.set_Extended_enat tptp.rat)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_18693 x z) (ho_18693 y z)))) (= x y))))) (let ((_let_1550 (forall ((x |u_(-> tptp.nat tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT)|) (y |u_(-> tptp.nat tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_31731 x z) (ho_31731 y z)))) (= x y))))) (let ((_let_1551 (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_15085 x z) (ho_15085 y z)))) (= x y))))) (let ((_let_1552 (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_18759 x z) (ho_18759 y z)))) (= x y))))) (let ((_let_1553 (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_31308 x z) (ho_31308 y z)))) (= x y))))) (let ((_let_1554 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.rat)_ tptp.set_Extended_enat tptp.rat)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.rat)_ tptp.set_Extended_enat tptp.rat)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.rat)|)) (= (ho_18692 x z) (ho_18692 y z)))) (= x y))))) (let ((_let_1555 (forall ((x |u_(-> tptp.set_Extended_enat tptp.product_prod_int_int Bool)|) (y |u_(-> tptp.set_Extended_enat tptp.product_prod_int_int Bool)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_18696 x z) (ho_18696 y z)))) (= x y))))) (let ((_let_1556 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_31637 x z) (ho_31637 y z)))) (= x y))))) (let ((_let_1557 (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_25457 x z) (ho_25457 y z)))) (= x y))))) (let ((_let_1558 (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_25274 x z) (ho_25274 y z)))) (= x y))))) (let ((_let_1559 (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_31047 x z) (ho_31047 y z)))) (= x y))))) (let ((_let_1560 (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_25645 x z) (ho_25645 y z)))) (= x y))))) (let ((_let_1561 (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_31655 x z) (ho_31655 y z)))) (= x y))))) (let ((_let_1562 (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_24897 x z) (ho_24897 y z)))) (= x y))))) (let ((_let_1563 (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_31375 x z) (ho_31375 y z)))) (= x y))))) (let ((_let_1564 (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_18768 x z) (ho_18768 y z)))) (= x y))))) (let ((_let_1565 (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_31575 x z) (ho_31575 y z)))) (= x y))))) (let ((_let_1566 (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_18770 x z) (ho_18770 y z)))) (= x y))))) (let ((_let_1567 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.nat tptp.rat)|)) (= (ho_31526 x z) (ho_31526 y z)))) (= x y))))) (let ((_let_1568 (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_25666 x z) (ho_25666 y z)))) (= x y))))) (let ((_let_1569 (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_25673 x z) (ho_25673 y z)))) (= x y))))) (let ((_let_1570 (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_25672 x z) (ho_25672 y z)))) (= x y))))) (let ((_let_1571 (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_31644 x z) (ho_31644 y z)))) (= x y))))) (let ((_let_1572 (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_25676 x z) (ho_25676 y z)))) (= x y))))) (let ((_let_1573 (forall ((x |u_(-> tptp.set_complex tptp.complex)|) (y |u_(-> tptp.set_complex tptp.complex)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_31157 x z) (ho_31157 y z)))) (= x y))))) (let ((_let_1574 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex Bool)_ tptp.complex Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex Bool)_ tptp.complex Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_25675 x z) (ho_25675 y z)))) (= x y))))) (let ((_let_1575 (forall ((x |u_(-> _u_(-> tptp.extended_enat Bool)_ tptp.set_Extended_enat)|) (y |u_(-> _u_(-> tptp.extended_enat Bool)_ tptp.set_Extended_enat)|)) (or (not (forall ((z |u_(-> tptp.extended_enat Bool)|)) (= (ho_25679 x z) (ho_25679 y z)))) (= x y))))) (let ((_let_1576 (forall ((x |u_(-> tptp.set_Extended_enat tptp.set_Extended_enat tptp.set_Extended_enat)|) (y |u_(-> tptp.set_Extended_enat tptp.set_Extended_enat tptp.set_Extended_enat)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_25681 x z) (ho_25681 y z)))) (= x y))))) (let ((_let_1577 (forall ((x |u_(-> _u_(-> tptp.extended_enat Bool)_ tptp.extended_enat Bool)|) (y |u_(-> _u_(-> tptp.extended_enat Bool)_ tptp.extended_enat Bool)|)) (or (not (forall ((z |u_(-> tptp.extended_enat Bool)|)) (= (ho_25685 x z) (ho_25685 y z)))) (= x y))))) (let ((_let_1578 (forall ((x |u_(-> _u_(-> tptp.extended_enat Bool)_ _u_(-> tptp.extended_enat Bool)_ tptp.extended_enat Bool)|) (y |u_(-> _u_(-> tptp.extended_enat Bool)_ _u_(-> tptp.extended_enat Bool)_ tptp.extended_enat Bool)|)) (or (not (forall ((z |u_(-> tptp.extended_enat Bool)|)) (= (ho_25684 x z) (ho_25684 y z)))) (= x y))))) (let ((_let_1579 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_25699 x z) (ho_25699 y z)))) (= x y))))) (let ((_let_1580 (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_25698 x z) (ho_25698 y z)))) (= x y))))) (let ((_let_1581 (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_31610 x z) (ho_31610 y z)))) (= x y))))) (let ((_let_1582 (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_25701 x z) (ho_25701 y z)))) (= x y))))) (let ((_let_1583 (forall ((x |u_(-> tptp.nat tptp.option_nat)|) (y |u_(-> tptp.nat tptp.option_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_25705 x z) (ho_25705 y z)))) (= x y))))) (let ((_let_1584 (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_25707 x z) (ho_25707 y z)))) (= x y))))) (let ((_let_1585 (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_25815 x z) (ho_25815 y z)))) (= x y))))) (let ((_let_1586 (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_25817 x z) (ho_25817 y z)))) (= x y))))) (let ((_let_1587 (forall ((x |u_(-> tptp.set_Extended_enat tptp.set_Extended_enat Bool)|) (y |u_(-> tptp.set_Extended_enat tptp.set_Extended_enat Bool)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_31089 x z) (ho_31089 y z)))) (= x y))))) (let ((_let_1588 (forall ((x |u_(-> tptp.list_o tptp.nat)|) (y |u_(-> tptp.list_o tptp.nat)|)) (or (not (forall ((z tptp.list_o)) (= (ho_25819 x z) (ho_25819 y z)))) (= x y))))) (let ((_let_1589 (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_25821 x z) (ho_25821 y z)))) (= x y))))) (let ((_let_1590 (forall ((x |u_(-> tptp.list_o Bool Bool)|) (y |u_(-> tptp.list_o Bool Bool)|)) (or (not (forall ((z tptp.list_o)) (= (ho_25823 x z) (ho_25823 y z)))) (= x y))))) (let ((_let_1591 (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_31373 x z) (ho_31373 y z)))) (= x y))))) (let ((_let_1592 (forall ((x |u_(-> tptp.list_real tptp.nat)|) (y |u_(-> tptp.list_real tptp.nat)|)) (or (not (forall ((z tptp.list_real)) (= (ho_25830 x z) (ho_25830 y z)))) (= x y))))) (let ((_let_1593 (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_25832 x z) (ho_25832 y z)))) (= x y))))) (let ((_let_1594 (forall ((x |u_(-> tptp.list_complex tptp.nat)|) (y |u_(-> tptp.list_complex tptp.nat)|)) (or (not (forall ((z tptp.list_complex)) (= (ho_25836 x z) (ho_25836 y z)))) (= x y))))) (let ((_let_1595 (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_25838 x z) (ho_25838 y z)))) (= x y))))) (let ((_let_1596 (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_25840 x z) (ho_25840 y z)))) (= x y))))) (let ((_let_1597 (forall ((x |u_(-> tptp.list_int Bool)|) (y |u_(-> tptp.list_int Bool)|)) (or (not (forall ((z tptp.list_int)) (= (ho_25873 x z) (ho_25873 y z)))) (= x y))))) (let ((_let_1598 (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_25915 x z) (ho_25915 y z)))) (= x y))))) (let ((_let_1599 (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_25876 x z) (ho_25876 y z)))) (= x y))))) (let ((_let_1600 (forall ((x |u_(-> tptp.list_VEBT_VEBT Bool)|) (y |u_(-> tptp.list_VEBT_VEBT Bool)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_25884 x z) (ho_25884 y z)))) (= x y))))) (let ((_let_1601 (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_25933 x z) (ho_25933 y z)))) (= x y))))) (let ((_let_1602 (forall ((x |u_(-> tptp.int tptp.nat Bool)|) (y |u_(-> tptp.int tptp.nat Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_26797 x z) (ho_26797 y z)))) (= x y))))) (let ((_let_1603 (forall ((x |u_(-> Bool _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|) (y |u_(-> Bool _u_(-> tptp.nat tptp.nat tptp.nat)_ _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z Bool)) (= (ho_26811 x z) (ho_26811 y z)))) (= x y))))) (let ((_let_1604 (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_26944 x z) (ho_26944 y z)))) (= x y))))) (let ((_let_1605 (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_26948 x z) (ho_26948 y z)))) (= x y))))) (let ((_let_1606 (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_31475 x z) (ho_31475 y z)))) (= x y))))) (let ((_let_1607 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat tptp.int Bool)|) (y |u_(-> tptp.nat tptp.nat tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_27605 x z) (ho_27605 y z)))) (= x y))))) (let ((_let_1608 (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_31458 x z) (ho_31458 y z)))) (= x y))))) (let ((_let_1609 (forall ((x |u_(-> tptp.int tptp.real tptp.int Bool)|) (y |u_(-> tptp.int tptp.real tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_27629 x z) (ho_27629 y z)))) (= x y))))) (let ((_let_1610 (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_31690 x z) (ho_31690 y z)))) (= x y))))) (let ((_let_1611 (forall ((x |u_(-> tptp.rat tptp.nat tptp.int Bool)|) (y |u_(-> tptp.rat tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_27827 x z) (ho_27827 y z)))) (= x y))))) (let ((_let_1612 (forall ((x |u_(-> tptp.int tptp.rat tptp.int Bool)|) (y |u_(-> tptp.int tptp.rat tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_27840 x z) (ho_27840 y z)))) (= x y))))) (let ((_let_1613 (forall ((x |u_(-> tptp.num tptp.int Bool)|) (y |u_(-> tptp.num tptp.int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_27916 x z) (ho_27916 y z)))) (= x y))))) (let ((_let_1614 (forall ((x |u_(-> tptp.num tptp.num tptp.int Bool)|) (y |u_(-> tptp.num tptp.num tptp.int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_27938 x z) (ho_27938 y z)))) (= x y))))) (let ((_let_1615 (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_31388 x z) (ho_31388 y z)))) (= x y))))) (let ((_let_1616 (forall ((x |u_(-> tptp.num tptp.nat tptp.int Bool)|) (y |u_(-> tptp.num tptp.nat tptp.int Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_28000 x z) (ho_28000 y z)))) (= x y))))) (let ((_let_1617 (forall ((x |u_(-> tptp.real tptp.num tptp.int Bool)|) (y |u_(-> tptp.real tptp.num tptp.int Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_28012 x z) (ho_28012 y z)))) (= x y))))) (let ((_let_1618 (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_28158 x z) (ho_28158 y z)))) (= x y))))) (let ((_let_1619 (forall ((x |u_(-> Bool tptp.nat tptp.rat)|) (y |u_(-> Bool tptp.nat tptp.rat)|)) (or (not (forall ((z Bool)) (= (ho_28339 x z) (ho_28339 y z)))) (= x y))))) (let ((_let_1620 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_31699 x z) (ho_31699 y z)))) (= x y))))) (let ((_let_1621 (forall ((x |u_(-> tptp.num tptp.nat tptp.rat)|) (y |u_(-> tptp.num tptp.nat tptp.rat)|)) (or (not (forall ((z tptp.num)) (= (ho_28364 x z) (ho_28364 y z)))) (= x y))))) (let ((_let_1622 (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_31446 x z) (ho_31446 y z)))) (= x y))))) (let ((_let_1623 (forall ((x |u_(-> Bool tptp.int tptp.int Bool)|) (y |u_(-> Bool tptp.int tptp.int Bool)|)) (or (not (forall ((z Bool)) (= (ho_28608 x z) (ho_28608 y z)))) (= x y))))) (let ((_let_1624 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.real)_ tptp.set_Extended_enat tptp.real)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.real)_ tptp.set_Extended_enat tptp.real)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.real)|)) (= (ho_31133 x z) (ho_31133 y z)))) (= x y))))) (let ((_let_1625 (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_28784 x z) (ho_28784 y z)))) (= x y))))) (let ((_let_1626 (forall ((x |u_(-> tptp.num tptp.nat)|) (y |u_(-> tptp.num tptp.nat)|)) (or (not (forall ((z tptp.num)) (= (ho_28787 x z) (ho_28787 y z)))) (= x y))))) (let ((_let_1627 (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_28822 x z) (ho_28822 y z)))) (= x y))))) (let ((_let_1628 (forall ((x |u_(-> tptp.product_prod_nat_num tptp.produc2963631642982155120at_num)|) (y |u_(-> tptp.product_prod_nat_num tptp.produc2963631642982155120at_num)|)) (or (not (forall ((z tptp.product_prod_nat_num)) (= (ho_31096 x z) (ho_31096 y z)))) (= x y))))) (let ((_let_1629 (forall ((x |u_(-> tptp.rat tptp.nat tptp.nat tptp.int tptp.int Bool)|) (y |u_(-> tptp.rat tptp.nat tptp.nat tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.rat)) (= (ho_29332 x z) (ho_29332 y z)))) (= x y))))) (let ((_let_1630 (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_30984 x z) (ho_30984 y z)))) (= x y))))) (let ((_let_1631 (forall ((x |u_(-> tptp.option_nat tptp.nat)|) (y |u_(-> tptp.option_nat tptp.nat)|)) (or (not (forall ((z tptp.option_nat)) (= (ho_30986 x z) (ho_30986 y z)))) (= x y))))) (let ((_let_1632 (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_30988 x z) (ho_30988 y z)))) (= x y))))) (let ((_let_1633 (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_30992 x z) (ho_30992 y z)))) (= x y))))) (let ((_let_1634 (forall ((x |u_(-> tptp.option_num tptp.int)|) (y |u_(-> tptp.option_num tptp.int)|)) (or (not (forall ((z tptp.option_num)) (= (ho_31379 x z) (ho_31379 y z)))) (= x y))))) (let ((_let_1635 (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_30991 x z) (ho_30991 y z)))) (= x y))))) (let ((_let_1636 (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_30990 x z) (ho_30990 y z)))) (= x y))))) (let ((_let_1637 (forall ((x |u_(-> Bool _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|) (y |u_(-> Bool _u_(-> tptp.int tptp.int)_ _u_(-> tptp.int tptp.int)_ tptp.int tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_31009 x z) (ho_31009 y z)))) (= x y))))) (let ((_let_1638 (forall ((x |u_(-> tptp.code_integer tptp.set_Code_integer Bool)|) (y |u_(-> tptp.code_integer tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.code_integer)) (= (ho_31021 x z) (ho_31021 y z)))) (= x y))))) (let ((_let_1639 (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_31451 x z) (ho_31451 y z)))) (= x y))))) (let ((_let_1640 (forall ((x |u_(-> _u_(-> tptp.extended_enat Bool)_ _u_(-> tptp.extended_enat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.extended_enat Bool)_ _u_(-> tptp.extended_enat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.extended_enat Bool)|)) (= (ho_31024 x z) (ho_31024 y z)))) (= x y))))) (let ((_let_1641 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_31027 x z) (ho_31027 y z)))) (= x y))))) (let ((_let_1642 (forall ((x |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.complex Bool)_ _u_(-> tptp.complex Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.complex Bool)|)) (= (ho_31026 x z) (ho_31026 y z)))) (= x y))))) (let ((_let_1643 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_31030 x z) (ho_31030 y z)))) (= x y))))) (let ((_let_1644 (forall ((x |u_(-> Bool tptp.product_prod_o_o)|) (y |u_(-> Bool tptp.product_prod_o_o)|)) (or (not (forall ((z Bool)) (= (ho_31235 x z) (ho_31235 y z)))) (= x y))))) (let ((_let_1645 (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_31355 x z) (ho_31355 y z)))) (= x y))))) (let ((_let_1646 (forall ((x |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.real Bool)_ _u_(-> tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real Bool)|)) (= (ho_31029 x z) (ho_31029 y z)))) (= x y))))) (let ((_let_1647 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_31033 x z) (ho_31033 y z)))) (= x y))))) (let ((_let_1648 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_31032 x z) (ho_31032 y z)))) (= x y))))) (let ((_let_1649 (forall ((x |u_(-> tptp.rat tptp.num)|) (y |u_(-> tptp.rat tptp.num)|)) (or (not (forall ((z tptp.rat)) (= (ho_31034 x z) (ho_31034 y z)))) (= x y))))) (let ((_let_1650 (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_31642 x z) (ho_31642 y z)))) (= x y))))) (let ((_let_1651 (forall ((x |u_(-> tptp.int tptp.num)|) (y |u_(-> tptp.int tptp.num)|)) (or (not (forall ((z tptp.int)) (= (ho_31035 x z) (ho_31035 y z)))) (= x y))))) (let ((_let_1652 (forall ((x |u_(-> tptp.rat tptp.nat)|) (y |u_(-> tptp.rat tptp.nat)|)) (or (not (forall ((z tptp.rat)) (= (ho_31036 x z) (ho_31036 y z)))) (= x y))))) (let ((_let_1653 (forall ((x |u_(-> tptp.real tptp.num)|) (y |u_(-> tptp.real tptp.num)|)) (or (not (forall ((z tptp.real)) (= (ho_31037 x z) (ho_31037 y z)))) (= x y))))) (let ((_let_1654 (forall ((x |u_(-> tptp.nat tptp.char)|) (y |u_(-> tptp.nat tptp.char)|)) (or (not (forall ((z tptp.nat)) (= (ho_31421 x z) (ho_31421 y z)))) (= x y))))) (let ((_let_1655 (forall ((x |u_(-> tptp.rat tptp.real)|) (y |u_(-> tptp.rat tptp.real)|)) (or (not (forall ((z tptp.rat)) (= (ho_31039 x z) (ho_31039 y z)))) (= x y))))) (let ((_let_1656 (forall ((x |u_(-> tptp.list_Extended_enat tptp.nat tptp.extended_enat)|) (y |u_(-> tptp.list_Extended_enat tptp.nat tptp.extended_enat)|)) (or (not (forall ((z tptp.list_Extended_enat)) (= (ho_31050 x z) (ho_31050 y z)))) (= x y))))) (let ((_let_1657 (forall ((x |u_(-> tptp.list_Extended_enat tptp.nat)|) (y |u_(-> tptp.list_Extended_enat tptp.nat)|)) (or (not (forall ((z tptp.list_Extended_enat)) (= (ho_31052 x z) (ho_31052 y z)))) (= x y))))) (let ((_let_1658 (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_31056 x z) (ho_31056 y z)))) (= x y))))) (let ((_let_1659 (forall ((x |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num Bool)|)) (= (ho_31528 x z) (ho_31528 y z)))) (= x y))))) (let ((_let_1660 (forall ((x |u_(-> Bool tptp.set_o Bool)|) (y |u_(-> Bool tptp.set_o Bool)|)) (or (not (forall ((z Bool)) (= (ho_31058 x z) (ho_31058 y z)))) (= x y))))) (let ((_let_1661 (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_31457 x z) (ho_31457 y z)))) (= x y))))) (let ((_let_1662 (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_31065 x z) (ho_31065 y z)))) (= x y))))) (let ((_let_1663 (forall ((x |u_(-> tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_31068 x z) (ho_31068 y z)))) (= x y))))) (let ((_let_1664 (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_31067 x z) (ho_31067 y z)))) (= x y))))) (let ((_let_1665 (forall ((x |u_(-> tptp.set_char tptp.nat)|) (y |u_(-> tptp.set_char tptp.nat)|)) (or (not (forall ((z tptp.set_char)) (= (ho_31426 x z) (ho_31426 y z)))) (= x y))))) (let ((_let_1666 (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_31630 x z) (ho_31630 y z)))) (= x y))))) (let ((_let_1667 (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_31070 x z) (ho_31070 y z)))) (= x y))))) (let ((_let_1668 (forall ((x |u_(-> tptp.num tptp.set_num)|) (y |u_(-> tptp.num tptp.set_num)|)) (or (not (forall ((z tptp.num)) (= (ho_31074 x z) (ho_31074 y z)))) (= x y))))) (let ((_let_1669 (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_31351 x z) (ho_31351 y z)))) (= x y))))) (let ((_let_1670 (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_31073 x z) (ho_31073 y z)))) (= x y))))) (let ((_let_1671 (forall ((x |u_(-> tptp.set_num Bool)|) (y |u_(-> tptp.set_num Bool)|)) (or (not (forall ((z tptp.set_num)) (= (ho_31077 x z) (ho_31077 y z)))) (= x y))))) (let ((_let_1672 (forall ((x |u_(-> tptp.num tptp.set_num Bool)|) (y |u_(-> tptp.num tptp.set_num Bool)|)) (or (not (forall ((z tptp.num)) (= (ho_31076 x z) (ho_31076 y z)))) (= x y))))) (let ((_let_1673 (forall ((x |u_(-> tptp.set_complex tptp.nat)|) (y |u_(-> tptp.set_complex tptp.nat)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_31330 x z) (ho_31330 y z)))) (= x y))))) (let ((_let_1674 (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_31079 x z) (ho_31079 y z)))) (= x y))))) (let ((_let_1675 (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_31081 x z) (ho_31081 y z)))) (= x y))))) (let ((_let_1676 (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_31085 x z) (ho_31085 y z)))) (= x y))))) (let ((_let_1677 (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_31087 x z) (ho_31087 y z)))) (= x y))))) (let ((_let_1678 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_num tptp.produc2963631642982155120at_num)|) (y |u_(-> tptp.nat tptp.product_prod_nat_num tptp.produc2963631642982155120at_num)|)) (or (not (forall ((z tptp.nat)) (= (ho_31095 x z) (ho_31095 y z)))) (= x y))))) (let ((_let_1679 (forall ((x |u_(-> _u_(-> tptp.real tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.real tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.real Bool)|)) (= (ho_31588 x z) (ho_31588 y z)))) (= x y))))) (let ((_let_1680 (forall ((x |u_(-> tptp.produc2963631642982155120at_num tptp.produc3368934014287244435at_num)|) (y |u_(-> tptp.produc2963631642982155120at_num tptp.produc3368934014287244435at_num)|)) (or (not (forall ((z tptp.produc2963631642982155120at_num)) (= (ho_31100 x z) (ho_31100 y z)))) (= x y))))) (let ((_let_1681 (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_31369 x z) (ho_31369 y z)))) (= x y))))) (let ((_let_1682 (forall ((x |u_(-> tptp.nat tptp.num tptp.num)|) (y |u_(-> tptp.nat tptp.num tptp.num)|)) (or (not (forall ((z tptp.nat)) (= (ho_31097 x z) (ho_31097 y z)))) (= x y))))) (let ((_let_1683 (forall ((x |u_(-> _u_(-> tptp.nat tptp.num tptp.num)_ tptp.produc2963631642982155120at_num tptp.produc3368934014287244435at_num)|) (y |u_(-> _u_(-> tptp.nat tptp.num tptp.num)_ tptp.produc2963631642982155120at_num tptp.produc3368934014287244435at_num)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.num tptp.num)|)) (= (ho_31099 x z) (ho_31099 y z)))) (= x y))))) (let ((_let_1684 (forall ((x |u_(-> tptp.set_complex tptp.real)|) (y |u_(-> tptp.set_complex tptp.real)|)) (or (not (forall ((z tptp.set_complex)) (= (ho_31163 x z) (ho_31163 y z)))) (= x y))))) (let ((_let_1685 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_31103 x z) (ho_31103 y z)))) (= x y))))) (let ((_let_1686 (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_31469 x z) (ho_31469 y z)))) (= x y))))) (let ((_let_1687 (forall ((x |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|) (y |u_(-> tptp.nat tptp.product_prod_nat_nat tptp.produc7248412053542808358at_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_31102 x z) (ho_31102 y z)))) (= x y))))) (let ((_let_1688 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_31587 x z) (ho_31587 y z)))) (= x y))))) (let ((_let_1689 (forall ((x |u_(-> tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|) (y |u_(-> tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|)) (or (not (forall ((z tptp.produc7248412053542808358at_nat)) (= (ho_31106 x z) (ho_31106 y z)))) (= x y))))) (let ((_let_1690 (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_31719 x z) (ho_31719 y z)))) (= x y))))) (let ((_let_1691 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.nat)_ tptp.produc7248412053542808358at_nat tptp.produc4471711990508489141at_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.nat)|)) (= (ho_31105 x z) (ho_31105 y z)))) (= x y))))) (let ((_let_1692 (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_31109 x z) (ho_31109 y z)))) (= x y))))) (let ((_let_1693 (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_31108 x z) (ho_31108 y z)))) (= x y))))) (let ((_let_1694 (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_31112 x z) (ho_31112 y z)))) (= x y))))) (let ((_let_1695 (forall ((x |u_(-> tptp.set_Code_integer tptp.set_Code_integer Bool)|) (y |u_(-> tptp.set_Code_integer tptp.set_Code_integer Bool)|)) (or (not (forall ((z tptp.set_Code_integer)) (= (ho_31116 x z) (ho_31116 y z)))) (= x y))))) (let ((_let_1696 (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_31118 x z) (ho_31118 y z)))) (= x y))))) (let ((_let_1697 (forall ((x |u_(-> tptp.nat tptp.produc9072475918466114483BT_nat)|) (y |u_(-> tptp.nat tptp.produc9072475918466114483BT_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_31126 x z) (ho_31126 y z)))) (= x y))))) (let ((_let_1698 (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_31125 x z) (ho_31125 y z)))) (= x y))))) (let ((_let_1699 (forall ((x |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.real tptp.nat tptp.rat)|)) (= (ho_31750 x z) (ho_31750 y z)))) (= x y))))) (let ((_let_1700 (forall ((x |u_(-> tptp.extended_enat tptp.complex)|) (y |u_(-> tptp.extended_enat tptp.complex)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_31127 x z) (ho_31127 y z)))) (= x y))))) (let ((_let_1701 (forall ((x |u_(-> tptp.extended_enat tptp.real)|) (y |u_(-> tptp.extended_enat tptp.real)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_31131 x z) (ho_31131 y z)))) (= x y))))) (let ((_let_1702 (forall ((x |u_(-> tptp.set_Extended_enat tptp.nat)|) (y |u_(-> tptp.set_Extended_enat tptp.nat)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_31138 x z) (ho_31138 y z)))) (= x y))))) (let ((_let_1703 (forall ((x |u_(-> tptp.extended_enat tptp.nat)|) (y |u_(-> tptp.extended_enat tptp.nat)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_31135 x z) (ho_31135 y z)))) (= x y))))) (let ((_let_1704 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.nat)_ tptp.set_Extended_enat tptp.nat)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.nat)_ tptp.set_Extended_enat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.nat)|)) (= (ho_31137 x z) (ho_31137 y z)))) (= x y))))) (let ((_let_1705 (forall ((x |u_(-> tptp.set_Extended_enat tptp.int)|) (y |u_(-> tptp.set_Extended_enat tptp.int)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_31142 x z) (ho_31142 y z)))) (= x y))))) (let ((_let_1706 (forall ((x |u_(-> tptp.extended_enat tptp.int)|) (y |u_(-> tptp.extended_enat tptp.int)|)) (or (not (forall ((z tptp.extended_enat)) (= (ho_31139 x z) (ho_31139 y z)))) (= x y))))) (let ((_let_1707 (forall ((x |u_(-> tptp.set_real tptp.complex)|) (y |u_(-> tptp.set_real tptp.complex)|)) (or (not (forall ((z tptp.set_real)) (= (ho_31145 x z) (ho_31145 y z)))) (= x y))))) (let ((_let_1708 (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_31144 x z) (ho_31144 y z)))) (= x y))))) (let ((_let_1709 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_31529 x z) (ho_31529 y z)))) (= x y))))) (let ((_let_1710 (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_31147 x z) (ho_31147 y z)))) (= x y))))) (let ((_let_1711 (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_31696 x z) (ho_31696 y z)))) (= x y))))) (let ((_let_1712 (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_31150 x z) (ho_31150 y z)))) (= x y))))) (let ((_let_1713 (forall ((x |u_(-> tptp.set_real tptp.int)|) (y |u_(-> tptp.set_real tptp.int)|)) (or (not (forall ((z tptp.set_real)) (= (ho_31154 x z) (ho_31154 y z)))) (= x y))))) (let ((_let_1714 (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_31153 x z) (ho_31153 y z)))) (= x y))))) (let ((_let_1715 (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_31156 x z) (ho_31156 y z)))) (= x y))))) (let ((_let_1716 (forall ((x |u_(-> tptp.set_int tptp.complex)|) (y |u_(-> tptp.set_int tptp.complex)|)) (or (not (forall ((z tptp.set_int)) (= (ho_31160 x z) (ho_31160 y z)))) (= x y))))) (let ((_let_1717 (forall ((x |u_(-> tptp.set_int tptp.real)|) (y |u_(-> tptp.set_int tptp.real)|)) (or (not (forall ((z tptp.set_int)) (= (ho_31166 x z) (ho_31166 y z)))) (= x y))))) (let ((_let_1718 (forall ((x |u_(-> tptp.produc9072475918466114483BT_nat Bool)|) (y |u_(-> tptp.produc9072475918466114483BT_nat Bool)|)) (or (not (forall ((z tptp.produc9072475918466114483BT_nat)) (= (ho_31171 x z) (ho_31171 y z)))) (= x y))))) (let ((_let_1719 (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_31170 x z) (ho_31170 y z)))) (= x y))))) (let ((_let_1720 (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_31173 x z) (ho_31173 y z)))) (= x y))))) (let ((_let_1721 (forall ((x |u_(-> tptp.list_num tptp.nat)|) (y |u_(-> tptp.list_num tptp.nat)|)) (or (not (forall ((z tptp.list_num)) (= (ho_31183 x z) (ho_31183 y z)))) (= x y))))) (let ((_let_1722 (forall ((x |u_(-> tptp.list_num tptp.nat tptp.num)|) (y |u_(-> tptp.list_num tptp.nat tptp.num)|)) (or (not (forall ((z tptp.list_num)) (= (ho_31185 x z) (ho_31185 y z)))) (= x y))))) (let ((_let_1723 (forall ((x |u_(-> tptp.list_num tptp.list_num tptp.list_P3744719386663036955um_num)|) (y |u_(-> tptp.list_num tptp.list_num tptp.list_P3744719386663036955um_num)|)) (or (not (forall ((z tptp.list_num)) (= (ho_31187 x z) (ho_31187 y z)))) (= x y))))) (let ((_let_1724 (forall ((x |u_(-> tptp.list_P3744719386663036955um_num tptp.nat tptp.product_prod_num_num)|) (y |u_(-> tptp.list_P3744719386663036955um_num tptp.nat tptp.product_prod_num_num)|)) (or (not (forall ((z tptp.list_P3744719386663036955um_num)) (= (ho_31190 x z) (ho_31190 y z)))) (= x y))))) (let ((_let_1725 (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_31194 x z) (ho_31194 y z)))) (= x y))))) (let ((_let_1726 (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_31193 x z) (ho_31193 y z)))) (= x y))))) (let ((_let_1727 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)|)) (= (ho_31751 x z) (ho_31751 y z)))) (= x y))))) (let ((_let_1728 (forall ((x |u_(-> tptp.nat tptp.produc8243902056947475879T_VEBT)|) (y |u_(-> tptp.nat tptp.produc8243902056947475879T_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_31200 x z) (ho_31200 y z)))) (= x y))))) (let ((_let_1729 (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_31197 x z) (ho_31197 y z)))) (= x y))))) (let ((_let_1730 (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_31196 x z) (ho_31196 y z)))) (= x y))))) (let ((_let_1731 (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_31199 x z) (ho_31199 y z)))) (= x y))))) (let ((_let_1732 (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_31202 x z) (ho_31202 y z)))) (= x y))))) (let ((_let_1733 (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_31205 x z) (ho_31205 y z)))) (= x y))))) (let ((_let_1734 (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_31658 x z) (ho_31658 y z)))) (= x y))))) (let ((_let_1735 (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_31212 x z) (ho_31212 y z)))) (= x y))))) (let ((_let_1736 (forall ((x |u_(-> _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)_ _u_(-> tptp.num tptp.num tptp.int)_ _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.num tptp.int)_ _u_(-> tptp.num tptp.int)_ Bool)|)) (= (ho_31532 x z) (ho_31532 y z)))) (= x y))))) (let ((_let_1737 (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_31211 x z) (ho_31211 y z)))) (= x y))))) (let ((_let_1738 (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_31214 x z) (ho_31214 y z)))) (= x y))))) (let ((_let_1739 (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_31216 x z) (ho_31216 y z)))) (= x y))))) (let ((_let_1740 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)|)) (= (ho_31749 x z) (ho_31749 y z)))) (= x y))))) (let ((_let_1741 (forall ((x |u_(-> tptp.nat tptp.produc4894624898956917775BT_int)|) (y |u_(-> tptp.nat tptp.produc4894624898956917775BT_int)|)) (or (not (forall ((z tptp.nat)) (= (ho_31223 x z) (ho_31223 y z)))) (= x y))))) (let ((_let_1742 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_31700 x z) (ho_31700 y z)))) (= x y))))) (let ((_let_1743 (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_31219 x z) (ho_31219 y z)))) (= x y))))) (let ((_let_1744 (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_31222 x z) (ho_31222 y z)))) (= x y))))) (let ((_let_1745 (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_31225 x z) (ho_31225 y z)))) (= x y))))) (let ((_let_1746 (forall ((x |u_(-> tptp.nat tptp.produc2504756804600209347T_VEBT)|) (y |u_(-> tptp.nat tptp.produc2504756804600209347T_VEBT)|)) (or (not (forall ((z tptp.nat)) (= (ho_31232 x z) (ho_31232 y z)))) (= x y))))) (let ((_let_1747 (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_31228 x z) (ho_31228 y z)))) (= x y))))) (let ((_let_1748 (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_31657 x z) (ho_31657 y z)))) (= x y))))) (let ((_let_1749 (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_31231 x z) (ho_31231 y z)))) (= x y))))) (let ((_let_1750 (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_31234 x z) (ho_31234 y z)))) (= x y))))) (let ((_let_1751 (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_31241 x z) (ho_31241 y z)))) (= x y))))) (let ((_let_1752 (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_31238 x z) (ho_31238 y z)))) (= x y))))) (let ((_let_1753 (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_31240 x z) (ho_31240 y z)))) (= x y))))) (let ((_let_1754 (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_31244 x z) (ho_31244 y z)))) (= x y))))) (let ((_let_1755 (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_31243 x z) (ho_31243 y z)))) (= x y))))) (let ((_let_1756 (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_31247 x z) (ho_31247 y z)))) (= x y))))) (let ((_let_1757 (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_31366 x z) (ho_31366 y z)))) (= x y))))) (let ((_let_1758 (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_31249 x z) (ho_31249 y z)))) (= x y))))) (let ((_let_1759 (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_31251 x z) (ho_31251 y z)))) (= x y))))) (let ((_let_1760 (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_31255 x z) (ho_31255 y z)))) (= x y))))) (let ((_let_1761 (forall ((x |u_(-> tptp.vEBT_VEBT tptp.nat)|) (y |u_(-> tptp.vEBT_VEBT tptp.nat)|)) (or (not (forall ((z tptp.vEBT_VEBT)) (= (ho_31499 x z) (ho_31499 y z)))) (= x y))))) (let ((_let_1762 (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_31257 x z) (ho_31257 y z)))) (= x y))))) (let ((_let_1763 (forall ((x |u_(-> tptp.list_num tptp.list_P1726324292696863441at_num)|) (y |u_(-> tptp.list_num tptp.list_P1726324292696863441at_num)|)) (or (not (forall ((z tptp.list_num)) (= (ho_31261 x z) (ho_31261 y z)))) (= x y))))) (let ((_let_1764 (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_31356 x z) (ho_31356 y z)))) (= x y))))) (let ((_let_1765 (forall ((x |u_(-> tptp.list_P1726324292696863441at_num tptp.nat tptp.product_prod_nat_num)|) (y |u_(-> tptp.list_P1726324292696863441at_num tptp.nat tptp.product_prod_nat_num)|)) (or (not (forall ((z tptp.list_P1726324292696863441at_num)) (= (ho_31263 x z) (ho_31263 y z)))) (= x y))))) (let ((_let_1766 (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_31267 x z) (ho_31267 y z)))) (= x y))))) (let ((_let_1767 (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_31269 x z) (ho_31269 y z)))) (= x y))))) (let ((_let_1768 (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_31271 x z) (ho_31271 y z)))) (= x y))))) (let ((_let_1769 (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_31273 x z) (ho_31273 y z)))) (= x y))))) (let ((_let_1770 (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_31279 x z) (ho_31279 y z)))) (= x y))))) (let ((_let_1771 (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_31286 x z) (ho_31286 y z)))) (= x y))))) (let ((_let_1772 (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_31289 x z) (ho_31289 y z)))) (= x y))))) (let ((_let_1773 (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_31291 x z) (ho_31291 y z)))) (= x y))))) (let ((_let_1774 (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_31298 x z) (ho_31298 y z)))) (= x y))))) (let ((_let_1775 (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_31306 x z) (ho_31306 y z)))) (= x y))))) (let ((_let_1776 (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_31311 x z) (ho_31311 y z)))) (= x y))))) (let ((_let_1777 (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_31314 x z) (ho_31314 y z)))) (= x y))))) (let ((_let_1778 (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_31318 x z) (ho_31318 y z)))) (= x y))))) (let ((_let_1779 (forall ((x |u_(-> tptp.list_o tptp.int)|) (y |u_(-> tptp.list_o tptp.int)|)) (or (not (forall ((z tptp.list_o)) (= (ho_31323 x z) (ho_31323 y z)))) (= x y))))) (let ((_let_1780 (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_31322 x z) (ho_31322 y z)))) (= x y))))) (let ((_let_1781 (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_31321 x z) (ho_31321 y z)))) (= x y))))) (let ((_let_1782 (forall ((x |u_(-> tptp.set_int tptp.nat)|) (y |u_(-> tptp.set_int tptp.nat)|)) (or (not (forall ((z tptp.set_int)) (= (ho_31328 x z) (ho_31328 y z)))) (= x y))))) (let ((_let_1783 (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_31723 x z) (ho_31723 y z)))) (= x y))))) (let ((_let_1784 (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_31332 x z) (ho_31332 y z)))) (= x y))))) (let ((_let_1785 (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_31337 x z) (ho_31337 y z)))) (= x y))))) (let ((_let_1786 (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_31339 x z) (ho_31339 y z)))) (= x y))))) (let ((_let_1787 (forall ((x |u_(-> tptp.produc8923325533196201883nteger tptp.code_integer)|) (y |u_(-> tptp.produc8923325533196201883nteger tptp.code_integer)|)) (or (not (forall ((z tptp.produc8923325533196201883nteger)) (= (ho_31343 x z) (ho_31343 y z)))) (= x y))))) (let ((_let_1788 (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_31358 x z) (ho_31358 y z)))) (= x y))))) (let ((_let_1789 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat Bool)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_31724 x z) (ho_31724 y z)))) (= x y))))) (let ((_let_1790 (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_31357 x z) (ho_31357 y z)))) (= x y))))) (let ((_let_1791 (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_31361 x z) (ho_31361 y z)))) (= x y))))) (let ((_let_1792 (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_31363 x z) (ho_31363 y z)))) (= x y))))) (let ((_let_1793 (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_31368 x z) (ho_31368 y z)))) (= x y))))) (let ((_let_1794 (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_31378 x z) (ho_31378 y z)))) (= x y))))) (let ((_let_1795 (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_31381 x z) (ho_31381 y z)))) (= x y))))) (let ((_let_1796 (forall ((x |u_(-> tptp.set_nat tptp.set_int)|) (y |u_(-> tptp.set_nat tptp.set_int)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_31384 x z) (ho_31384 y z)))) (= x y))))) (let ((_let_1797 (forall ((x |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.set_int)|) (y |u_(-> _u_(-> tptp.nat tptp.int)_ tptp.set_nat tptp.set_int)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.int)|)) (= (ho_31383 x z) (ho_31383 y z)))) (= x y))))) (let ((_let_1798 (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_31619 x z) (ho_31619 y z)))) (= x y))))) (let ((_let_1799 (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_31386 x z) (ho_31386 y z)))) (= x y))))) (let ((_let_1800 (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_31609 x z) (ho_31609 y z)))) (= x y))))) (let ((_let_1801 (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_31394 x z) (ho_31394 y z)))) (= x y))))) (let ((_let_1802 (forall ((x |u_(-> tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat Bool)|) (y |u_(-> tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat Bool)|)) (or (not (forall ((z tptp.produc859450856879609959at_nat)) (= (ho_31668 x z) (ho_31668 y z)))) (= x y))))) (let ((_let_1803 (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_31400 x z) (ho_31400 y z)))) (= x y))))) (let ((_let_1804 (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_31407 x z) (ho_31407 y z)))) (= x y))))) (let ((_let_1805 (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_31409 x z) (ho_31409 y z)))) (= x y))))) (let ((_let_1806 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.list_int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ tptp.list_int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_31411 x z) (ho_31411 y z)))) (= x y))))) (let ((_let_1807 (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_31417 x z) (ho_31417 y z)))) (= x y))))) (let ((_let_1808 (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_31424 x z) (ho_31424 y z)))) (= x y))))) (let ((_let_1809 (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_31423 x z) (ho_31423 y z)))) (= x y))))) (let ((_let_1810 (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_31756 x z) (ho_31756 y z)))) (= x y))))) (let ((_let_1811 (forall ((x |u_(-> tptp.char tptp.nat)|) (y |u_(-> tptp.char tptp.nat)|)) (or (not (forall ((z tptp.char)) (= (ho_31428 x z) (ho_31428 y z)))) (= x y))))) (let ((_let_1812 (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_31626 x z) (ho_31626 y z)))) (= x y))))) (let ((_let_1813 (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_31431 x z) (ho_31431 y z)))) (= x y))))) (let ((_let_1814 (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_31430 x z) (ho_31430 y z)))) (= x y))))) (let ((_let_1815 (forall ((x |u_(-> Bool Bool Bool tptp.char)|) (y |u_(-> Bool Bool Bool tptp.char)|)) (or (not (forall ((z Bool)) (= (ho_31438 x z) (ho_31438 y z)))) (= x y))))) (let ((_let_1816 (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_31436 x z) (ho_31436 y z)))) (= x y))))) (let ((_let_1817 (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_31434 x z) (ho_31434 y z)))) (= x y))))) (let ((_let_1818 (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_31433 x z) (ho_31433 y z)))) (= x y))))) (let ((_let_1819 (forall ((x |u_(-> tptp.char tptp.code_integer)|) (y |u_(-> tptp.char tptp.code_integer)|)) (or (not (forall ((z tptp.char)) (= (ho_31442 x z) (ho_31442 y z)))) (= x y))))) (let ((_let_1820 (forall ((x |u_(-> tptp.char tptp.char)|) (y |u_(-> tptp.char tptp.char)|)) (or (not (forall ((z tptp.char)) (= (ho_31444 x z) (ho_31444 y z)))) (= x y))))) (let ((_let_1821 (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_31447 x z) (ho_31447 y z)))) (= x y))))) (let ((_let_1822 (forall ((x |u_(-> _u_(-> tptp.real tptp.int)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.real tptp.int)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.real tptp.int)|)) (= (ho_31455 x z) (ho_31455 y z)))) (= x y))))) (let ((_let_1823 (forall ((x |u_(-> _u_(-> tptp.int tptp.real)_ _u_(-> tptp.real tptp.int)_ tptp.real tptp.real)|) (y |u_(-> _u_(-> tptp.int tptp.real)_ _u_(-> tptp.real tptp.int)_ tptp.real tptp.real)|)) (or (not (forall ((z |u_(-> tptp.int tptp.real)|)) (= (ho_31454 x z) (ho_31454 y z)))) (= x y))))) (let ((_let_1824 (forall ((x |u_(-> tptp.filter_nat Bool)|) (y |u_(-> tptp.filter_nat Bool)|)) (or (not (forall ((z tptp.filter_nat)) (= (ho_31459 x z) (ho_31459 y z)))) (= x y))))) (let ((_let_1825 (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_31463 x z) (ho_31463 y z)))) (= x y))))) (let ((_let_1826 (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_31462 x z) (ho_31462 y z)))) (= x y))))) (let ((_let_1827 (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_31465 x z) (ho_31465 y z)))) (= x y))))) (let ((_let_1828 (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_31477 x z) (ho_31477 y z)))) (= x y))))) (let ((_let_1829 (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_31489 x z) (ho_31489 y z)))) (= x y))))) (let ((_let_1830 (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_31495 x z) (ho_31495 y z)))) (= x y))))) (let ((_let_1831 (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_31501 x z) (ho_31501 y z)))) (= x y))))) (let ((_let_1832 (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_31508 x z) (ho_31508 y z)))) (= x y))))) (let ((_let_1833 (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_31507 x z) (ho_31507 y z)))) (= x y))))) (let ((_let_1834 (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_31514 x z) (ho_31514 y z)))) (= x y))))) (let ((_let_1835 (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_31513 x z) (ho_31513 y z)))) (= x y))))) (let ((_let_1836 (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_31524 x z) (ho_31524 y z)))) (= x y))))) (let ((_let_1837 (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_31523 x z) (ho_31523 y z)))) (= x y))))) (let ((_let_1838 (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_31519 x z) (ho_31519 y z)))) (= x y))))) (let ((_let_1839 (forall ((x |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ Bool)|) (y |u_(-> _u_(-> tptp.num tptp.num tptp.int)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.num tptp.num tptp.int)|)) (= (ho_31534 x z) (ho_31534 y z)))) (= x y))))) (let ((_let_1840 (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_31536 x z) (ho_31536 y z)))) (= x y))))) (let ((_let_1841 (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_31550 x z) (ho_31550 y z)))) (= x y))))) (let ((_let_1842 (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_31549 x z) (ho_31549 y z)))) (= x y))))) (let ((_let_1843 (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_31552 x z) (ho_31552 y z)))) (= x y))))) (let ((_let_1844 (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_31545 x z) (ho_31545 y z)))) (= x y))))) (let ((_let_1845 (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_31547 x z) (ho_31547 y z)))) (= x y))))) (let ((_let_1846 (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_31553 x z) (ho_31553 y z)))) (= x y))))) (let ((_let_1847 (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_31561 x z) (ho_31561 y z)))) (= x y))))) (let ((_let_1848 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_31560 x z) (ho_31560 y z)))) (= x y))))) (let ((_let_1849 (forall ((x |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> Bool Bool Bool)|)) (= (ho_31556 x z) (ho_31556 y z)))) (= x y))))) (let ((_let_1850 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> Bool Bool Bool)_ _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_31555 x z) (ho_31555 y z)))) (= x y))))) (let ((_let_1851 (forall ((x |u_(-> _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)|)) (= (ho_31559 x z) (ho_31559 y z)))) (= x y))))) (let ((_let_1852 (forall ((x |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int tptp.int Bool)_ _u_(-> _u_(-> tptp.int Bool)_ _u_(-> tptp.int Bool)_ Bool)_ _u_(-> tptp.int tptp.int Bool)_ _u_(-> tptp.int tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.int Bool)|)) (= (ho_31558 x z) (ho_31558 y z)))) (= x y))))) (let ((_let_1853 (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_31601 x z) (ho_31601 y z)))) (= x y))))) (let ((_let_1854 (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_31563 x z) (ho_31563 y z)))) (= x y))))) (let ((_let_1855 (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_31567 x z) (ho_31567 y z)))) (= x y))))) (let ((_let_1856 (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_31566 x z) (ho_31566 y z)))) (= x y))))) (let ((_let_1857 (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_31572 x z) (ho_31572 y z)))) (= x y))))) (let ((_let_1858 (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_31582 x z) (ho_31582 y z)))) (= x y))))) (let ((_let_1859 (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_31755 x z) (ho_31755 y z)))) (= x y))))) (let ((_let_1860 (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_31577 x z) (ho_31577 y z)))) (= x y))))) (let ((_let_1861 (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_31580 x z) (ho_31580 y z)))) (= x y))))) (let ((_let_1862 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ _u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real Bool)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> tptp.real tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)|)) (= (ho_31585 x z) (ho_31585 y z)))) (= x y))))) (let ((_let_1863 (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_31592 x z) (ho_31592 y z)))) (= x y))))) (let ((_let_1864 (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_31596 x z) (ho_31596 y z)))) (= x y))))) (let ((_let_1865 (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_31595 x z) (ho_31595 y z)))) (= x y))))) (let ((_let_1866 (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_31594 x z) (ho_31594 y z)))) (= x y))))) (let ((_let_1867 (forall ((x |u_(-> _u_(-> tptp.rat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.rat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.rat Bool)|)) (= (ho_31602 x z) (ho_31602 y z)))) (= x y))))) (let ((_let_1868 (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_31599 x z) (ho_31599 y z)))) (= x y))))) (let ((_let_1869 (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_31754 x z) (ho_31754 y z)))) (= x y))))) (let ((_let_1870 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.extended_enat)_ tptp.set_Extended_enat tptp.set_Extended_enat)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.extended_enat)_ tptp.set_Extended_enat tptp.set_Extended_enat)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.extended_enat)|)) (= (ho_31742 x z) (ho_31742 y z)))) (= x y))))) (let ((_let_1871 (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_31604 x z) (ho_31604 y z)))) (= x y))))) (let ((_let_1872 (forall ((x |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.int tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.product_prod_nat_nat tptp.nat)|)) (= (ho_31616 x z) (ho_31616 y z)))) (= x y))))) (let ((_let_1873 (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_31620 x z) (ho_31620 y z)))) (= x y))))) (let ((_let_1874 (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_31631 x z) (ho_31631 y z)))) (= x y))))) (let ((_let_1875 (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_31753 x z) (ho_31753 y z)))) (= x y))))) (let ((_let_1876 (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_31629 x z) (ho_31629 y z)))) (= x y))))) (let ((_let_1877 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_31635 x z) (ho_31635 y z)))) (= x y))))) (let ((_let_1878 (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_31643 x z) (ho_31643 y z)))) (= x y))))) (let ((_let_1879 (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_31652 x z) (ho_31652 y z)))) (= x y))))) (let ((_let_1880 (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_31713 x z) (ho_31713 y z)))) (= x y))))) (let ((_let_1881 (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_31648 x z) (ho_31648 y z)))) (= x y))))) (let ((_let_1882 (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_31650 x z) (ho_31650 y z)))) (= x y))))) (let ((_let_1883 (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_31656 x z) (ho_31656 y z)))) (= x y))))) (let ((_let_1884 (forall ((x |u_(-> tptp.set_Pr8693737435421807431at_nat Bool)|) (y |u_(-> tptp.set_Pr8693737435421807431at_nat Bool)|)) (or (not (forall ((z tptp.set_Pr8693737435421807431at_nat)) (= (ho_31669 x z) (ho_31669 y z)))) (= x y))))) (let ((_let_1885 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.produc859450856879609959at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.produc859450856879609959at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_31666 x z) (ho_31666 y z)))) (= x y))))) (let ((_let_1886 (forall ((x |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.produc859450856879609959at_nat)|) (y |u_(-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.produc859450856879609959at_nat)|)) (or (not (forall ((z tptp.product_prod_nat_nat)) (= (ho_31665 x z) (ho_31665 y z)))) (= x y))))) (let ((_let_1887 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat Bool)_ _u_(-> tptp.nat tptp.nat Bool)_ tptp.nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat Bool)|)) (= (ho_31671 x z) (ho_31671 y z)))) (= x y))))) (let ((_let_1888 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_31674 x z) (ho_31674 y z)))) (= x y))))) (let ((_let_1889 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat tptp.list_nat)_ tptp.product_prod_nat_nat tptp.list_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat tptp.list_nat)_ tptp.product_prod_nat_nat tptp.list_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat tptp.list_nat)|)) (= (ho_31678 x z) (ho_31678 y z)))) (= x y))))) (let ((_let_1890 (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_31681 x z) (ho_31681 y z)))) (= x y))))) (let ((_let_1891 (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_31684 x z) (ho_31684 y z)))) (= x y))))) (let ((_let_1892 (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_31683 x z) (ho_31683 y z)))) (= x y))))) (let ((_let_1893 (forall ((x |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|) (y |u_(-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)|)) (or (not (forall ((z tptp.set_Pr1261947904930325089at_nat)) (= (ho_31686 x z) (ho_31686 y z)))) (= x y))))) (let ((_let_1894 (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_31692 x z) (ho_31692 y z)))) (= x y))))) (let ((_let_1895 (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_31691 x z) (ho_31691 y z)))) (= x y))))) (let ((_let_1896 (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_31694 x z) (ho_31694 y z)))) (= x y))))) (let ((_let_1897 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> tptp.nat tptp.nat)_ _u_(-> tptp.product_prod_nat_nat tptp.nat)_ tptp.int tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (= (ho_31698 x z) (ho_31698 y z)))) (= x y))))) (let ((_let_1898 (forall ((x |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int tptp.product_prod_nat_nat)_ _u_(-> Bool Bool)_ _u_(-> tptp.product_prod_nat_nat Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int tptp.product_prod_nat_nat)|)) (= (ho_31702 x z) (ho_31702 y z)))) (= x y))))) (let ((_let_1899 (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_31714 x z) (ho_31714 y z)))) (= x y))))) (let ((_let_1900 (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_31752 x z) (ho_31752 y z)))) (= x y))))) (let ((_let_1901 (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_31709 x z) (ho_31709 y z)))) (= x y))))) (let ((_let_1902 (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_31717 x z) (ho_31717 y z)))) (= x y))))) (let ((_let_1903 (forall ((x |u_(-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT)|) (y |u_(-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT)|)) (or (not (forall ((z tptp.list_VEBT_VEBT)) (= (ho_31729 x z) (ho_31729 y z)))) (= x y))))) (let ((_let_1904 (forall ((x |u_(-> _u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT)_ tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT)|) (y |u_(-> _u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT)_ tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT)|)) (or (not (forall ((z |u_(-> tptp.vEBT_VEBT tptp.vEBT_VEBT)|)) (= (ho_31728 x z) (ho_31728 y z)))) (= x y))))) (let ((_let_1905 (forall ((x |u_(-> tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat Bool)|) (y |u_(-> tptp.produc7272778201969148633d_enat tptp.produc7272778201969148633d_enat Bool)|)) (or (not (forall ((z tptp.produc7272778201969148633d_enat)) (= (ho_31736 x z) (ho_31736 y z)))) (= x y))))) (let ((_let_1906 (forall ((x |u_(-> tptp.set_Extended_enat tptp.extended_enat)|) (y |u_(-> tptp.set_Extended_enat tptp.extended_enat)|)) (or (not (forall ((z tptp.set_Extended_enat)) (= (ho_31744 x z) (ho_31744 y z)))) (= x y))))) (let ((_let_1907 (forall ((x |u_(-> _u_(-> tptp.extended_enat tptp.extended_enat)_ Bool)|) (y |u_(-> _u_(-> tptp.extended_enat tptp.extended_enat)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.extended_enat tptp.extended_enat)|)) (= (ho_31746 x z) (ho_31746 y z)))) (= x y))))) (let ((_let_1908 (forall ((x |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real)_ _u_(-> tptp.real tptp.nat tptp.rat)_ _u_(-> _u_(-> tptp.nat tptp.rat)_ tptp.real Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> tptp.nat tptp.rat)_ _u_(-> tptp.nat tptp.rat)_ Bool)|)) (= (ho_31748 x z) (ho_31748 y z)))) (= x y))))) (let ((_let_1909 (forall ((BOUND_VARIABLE_2177615 tptp.int) (BOUND_VARIABLE_2177616 tptp.int) (BOUND_VARIABLE_2177617 tptp.int) (BOUND_VARIABLE_2177618 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177615) BOUND_VARIABLE_2177617))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177616) BOUND_VARIABLE_2177618))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15104 BOUND_VARIABLE_2177615) BOUND_VARIABLE_2177616) BOUND_VARIABLE_2177617) BOUND_VARIABLE_2177618))))))) (let ((_let_1910 (forall ((BOUND_VARIABLE_2177511 tptp.int) (BOUND_VARIABLE_2177512 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2177512))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2177512))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2177511) _let_3))) (= (ho_15142 (ho_15141 k_15140 BOUND_VARIABLE_2177511) BOUND_VARIABLE_2177512) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1911 (forall ((BOUND_VARIABLE_2177483 tptp.int) (BOUND_VARIABLE_2177484 tptp.int) (BOUND_VARIABLE_2177485 tptp.int) (BOUND_VARIABLE_2177486 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177483) BOUND_VARIABLE_2177485))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177484) BOUND_VARIABLE_2177486))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15143 BOUND_VARIABLE_2177483) BOUND_VARIABLE_2177484) BOUND_VARIABLE_2177485) BOUND_VARIABLE_2177486))))))) (let ((_let_1912 (forall ((BOUND_VARIABLE_2177404 tptp.rat) (BOUND_VARIABLE_2177405 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2177405))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2177405))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2177404 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15144 BOUND_VARIABLE_2177404) BOUND_VARIABLE_2177405)))))))))))))) (let ((_let_1913 (forall ((BOUND_VARIABLE_2177376 tptp.int) (BOUND_VARIABLE_2177377 tptp.int) (BOUND_VARIABLE_2177378 tptp.int) (BOUND_VARIABLE_2177379 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177376) BOUND_VARIABLE_2177378))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177377) BOUND_VARIABLE_2177379))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15146 BOUND_VARIABLE_2177376) BOUND_VARIABLE_2177377) BOUND_VARIABLE_2177378) BOUND_VARIABLE_2177379))))))) (let ((_let_1914 (forall ((BOUND_VARIABLE_2177272 tptp.int) (BOUND_VARIABLE_2177273 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2177273))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2177273))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2177272) _let_3))) (= (ho_15142 (ho_15141 k_15147 BOUND_VARIABLE_2177272) BOUND_VARIABLE_2177273) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1915 (forall ((BOUND_VARIABLE_2177244 tptp.int) (BOUND_VARIABLE_2177245 tptp.int) (BOUND_VARIABLE_2177246 tptp.int) (BOUND_VARIABLE_2177247 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177244) BOUND_VARIABLE_2177246))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177245) BOUND_VARIABLE_2177247))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15148 BOUND_VARIABLE_2177244) BOUND_VARIABLE_2177245) BOUND_VARIABLE_2177246) BOUND_VARIABLE_2177247))))))) (let ((_let_1916 (forall ((BOUND_VARIABLE_2177161 tptp.rat) (BOUND_VARIABLE_2177162 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2177162))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2177162))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15154 BOUND_VARIABLE_2177161) BOUND_VARIABLE_2177162) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2177161) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_1917 (forall ((BOUND_VARIABLE_2177133 tptp.int) (BOUND_VARIABLE_2177134 tptp.int) (BOUND_VARIABLE_2177135 tptp.int) (BOUND_VARIABLE_2177136 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177133) BOUND_VARIABLE_2177135))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177134) BOUND_VARIABLE_2177136))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15155 BOUND_VARIABLE_2177133) BOUND_VARIABLE_2177134) BOUND_VARIABLE_2177135) BOUND_VARIABLE_2177136))))))) (let ((_let_1918 (forall ((BOUND_VARIABLE_2177029 tptp.int) (BOUND_VARIABLE_2177030 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2177030))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2177030))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2177029) _let_3))) (= (ho_15142 (ho_15141 k_15156 BOUND_VARIABLE_2177029) BOUND_VARIABLE_2177030) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1919 (forall ((BOUND_VARIABLE_2177001 tptp.int) (BOUND_VARIABLE_2177002 tptp.int) (BOUND_VARIABLE_2177003 tptp.int) (BOUND_VARIABLE_2177004 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177001) BOUND_VARIABLE_2177003))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2177002) BOUND_VARIABLE_2177004))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15157 BOUND_VARIABLE_2177001) BOUND_VARIABLE_2177002) BOUND_VARIABLE_2177003) BOUND_VARIABLE_2177004))))))) (let ((_let_1920 (forall ((BOUND_VARIABLE_2176918 tptp.rat) (BOUND_VARIABLE_2176919 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2176919))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2176919))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15158 BOUND_VARIABLE_2176918) BOUND_VARIABLE_2176919) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2176918) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_1921 (forall ((BOUND_VARIABLE_2176890 tptp.int) (BOUND_VARIABLE_2176891 tptp.int) (BOUND_VARIABLE_2176892 tptp.int) (BOUND_VARIABLE_2176893 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176890) BOUND_VARIABLE_2176892))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176891) BOUND_VARIABLE_2176893))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15159 BOUND_VARIABLE_2176890) BOUND_VARIABLE_2176891) BOUND_VARIABLE_2176892) BOUND_VARIABLE_2176893))))))) (let ((_let_1922 (forall ((BOUND_VARIABLE_2196462 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2176804 tptp.nat) (BOUND_VARIABLE_2176805 tptp.nat) (BOUND_VARIABLE_2176806 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2176806))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2176806))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15162 BOUND_VARIABLE_2196462) BOUND_VARIABLE_2176804) BOUND_VARIABLE_2176805) BOUND_VARIABLE_2176806) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2196462 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2176804)) (ho_15161 k_15160 BOUND_VARIABLE_2176805))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_1923 (forall ((BOUND_VARIABLE_2176775 tptp.int) (BOUND_VARIABLE_2176776 tptp.int) (BOUND_VARIABLE_2176777 tptp.int) (BOUND_VARIABLE_2176778 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176775) BOUND_VARIABLE_2176777))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176776) BOUND_VARIABLE_2176778))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15166 BOUND_VARIABLE_2176775) BOUND_VARIABLE_2176776) BOUND_VARIABLE_2176777) BOUND_VARIABLE_2176778))))))) (let ((_let_1924 (forall ((BOUND_VARIABLE_2176678 tptp.nat) (BOUND_VARIABLE_2196563 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2176680 tptp.nat) (BOUND_VARIABLE_2176681 tptp.nat) (BOUND_VARIABLE_2176682 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2176682))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2176682))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2176680)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15167 BOUND_VARIABLE_2176678) BOUND_VARIABLE_2196563) BOUND_VARIABLE_2176680) BOUND_VARIABLE_2176681) BOUND_VARIABLE_2176682) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2196563 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2176678))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2196563 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2176681))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_1925 (forall ((BOUND_VARIABLE_2176650 tptp.int) (BOUND_VARIABLE_2176651 tptp.int) (BOUND_VARIABLE_2176652 tptp.int) (BOUND_VARIABLE_2176653 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176650) BOUND_VARIABLE_2176652))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176651) BOUND_VARIABLE_2176653))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15169 BOUND_VARIABLE_2176650) BOUND_VARIABLE_2176651) BOUND_VARIABLE_2176652) BOUND_VARIABLE_2176653))))))) (let ((_let_1926 (forall ((BOUND_VARIABLE_2176553 tptp.nat) (BOUND_VARIABLE_2196630 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2176555 tptp.nat) (BOUND_VARIABLE_2176556 tptp.nat) (BOUND_VARIABLE_2176557 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2176557))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2176557))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2176555)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15170 BOUND_VARIABLE_2176553) BOUND_VARIABLE_2196630) BOUND_VARIABLE_2176555) BOUND_VARIABLE_2176556) BOUND_VARIABLE_2176557) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2196630 (ho_15118 k_15117 (ho_15079 _let_11 (ho_15161 k_15160 BOUND_VARIABLE_2176553))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2196630 (ho_15118 k_15117 (ho_15079 _let_11 (ho_15161 k_15160 BOUND_VARIABLE_2176556)))))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_1927 (forall ((BOUND_VARIABLE_2176525 tptp.int) (BOUND_VARIABLE_2176526 tptp.int) (BOUND_VARIABLE_2176527 tptp.int) (BOUND_VARIABLE_2176528 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176525) BOUND_VARIABLE_2176527))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176526) BOUND_VARIABLE_2176528))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15171 BOUND_VARIABLE_2176525) BOUND_VARIABLE_2176526) BOUND_VARIABLE_2176527) BOUND_VARIABLE_2176528))))))) (let ((_let_1928 (forall ((BOUND_VARIABLE_2196730 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2176434 tptp.nat) (BOUND_VARIABLE_2176435 tptp.nat) (BOUND_VARIABLE_2176436 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2176436))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2176436))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15120 BOUND_VARIABLE_2196730 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2176434)) (ho_15161 k_15160 BOUND_VARIABLE_2176435)))))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15172 BOUND_VARIABLE_2196730) BOUND_VARIABLE_2176434) BOUND_VARIABLE_2176435) BOUND_VARIABLE_2176436) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_11) (ho_15122 k_15121 _let_11)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_1929 (forall ((BOUND_VARIABLE_2176405 tptp.int) (BOUND_VARIABLE_2176406 tptp.int) (BOUND_VARIABLE_2176407 tptp.int) (BOUND_VARIABLE_2176408 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176405) BOUND_VARIABLE_2176407))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176406) BOUND_VARIABLE_2176408))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15173 BOUND_VARIABLE_2176405) BOUND_VARIABLE_2176406) BOUND_VARIABLE_2176407) BOUND_VARIABLE_2176408))))))) (let ((_let_1930 (forall ((BOUND_VARIABLE_2196861 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2176319 tptp.nat) (BOUND_VARIABLE_2176320 tptp.nat) (BOUND_VARIABLE_2176321 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2176321))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2176321))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15174 BOUND_VARIABLE_2196861) BOUND_VARIABLE_2176319) BOUND_VARIABLE_2176320) BOUND_VARIABLE_2176321) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2196861 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2176319)) (ho_15161 k_15160 BOUND_VARIABLE_2176320))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_1931 (forall ((BOUND_VARIABLE_2176290 tptp.int) (BOUND_VARIABLE_2176291 tptp.int) (BOUND_VARIABLE_2176292 tptp.int) (BOUND_VARIABLE_2176293 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176290) BOUND_VARIABLE_2176292))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176291) BOUND_VARIABLE_2176293))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15175 BOUND_VARIABLE_2176290) BOUND_VARIABLE_2176291) BOUND_VARIABLE_2176292) BOUND_VARIABLE_2176293))))))) (let ((_let_1932 (forall ((BOUND_VARIABLE_2196952 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2176204 tptp.nat) (BOUND_VARIABLE_2176205 tptp.nat) (BOUND_VARIABLE_2176206 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2176206))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2176206))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15176 BOUND_VARIABLE_2196952) BOUND_VARIABLE_2176204) BOUND_VARIABLE_2176205) BOUND_VARIABLE_2176206) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2196952 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2176204)) (ho_15161 k_15160 BOUND_VARIABLE_2176205))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_1933 (forall ((BOUND_VARIABLE_2176175 tptp.int) (BOUND_VARIABLE_2176176 tptp.int) (BOUND_VARIABLE_2176177 tptp.int) (BOUND_VARIABLE_2176178 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176175) BOUND_VARIABLE_2176177))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176176) BOUND_VARIABLE_2176178))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15177 BOUND_VARIABLE_2176175) BOUND_VARIABLE_2176176) BOUND_VARIABLE_2176177) BOUND_VARIABLE_2176178))))))) (let ((_let_1934 (forall ((BOUND_VARIABLE_2176078 tptp.nat) (BOUND_VARIABLE_2197043 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2176080 tptp.nat) (BOUND_VARIABLE_2176081 tptp.nat) (BOUND_VARIABLE_2176082 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2176082))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2176082))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2176080)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15178 BOUND_VARIABLE_2176078) BOUND_VARIABLE_2197043) BOUND_VARIABLE_2176080) BOUND_VARIABLE_2176081) BOUND_VARIABLE_2176082) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2197043 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2176078))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2197043 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2176081))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_1935 (forall ((BOUND_VARIABLE_2176050 tptp.int) (BOUND_VARIABLE_2176051 tptp.int) (BOUND_VARIABLE_2176052 tptp.int) (BOUND_VARIABLE_2176053 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176050) BOUND_VARIABLE_2176052))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2176051) BOUND_VARIABLE_2176053))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15179 BOUND_VARIABLE_2176050) BOUND_VARIABLE_2176051) BOUND_VARIABLE_2176052) BOUND_VARIABLE_2176053))))))) (let ((_let_1936 (forall ((BOUND_VARIABLE_2175953 tptp.nat) (BOUND_VARIABLE_2197143 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2175955 tptp.nat) (BOUND_VARIABLE_2175956 tptp.nat) (BOUND_VARIABLE_2175957 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2175957))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2175957))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2175955)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15180 BOUND_VARIABLE_2175953) BOUND_VARIABLE_2197143) BOUND_VARIABLE_2175955) BOUND_VARIABLE_2175956) BOUND_VARIABLE_2175957) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2197143 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2175953))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2197143 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2175956))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_1937 (forall ((BOUND_VARIABLE_2175925 tptp.int) (BOUND_VARIABLE_2175926 tptp.int) (BOUND_VARIABLE_2175927 tptp.int) (BOUND_VARIABLE_2175928 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175925) BOUND_VARIABLE_2175927))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175926) BOUND_VARIABLE_2175928))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15181 BOUND_VARIABLE_2175925) BOUND_VARIABLE_2175926) BOUND_VARIABLE_2175927) BOUND_VARIABLE_2175928))))))) (let ((_let_1938 (forall ((BOUND_VARIABLE_2197246 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2197243 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2175833 tptp.nat) (BOUND_VARIABLE_2175834 tptp.nat) (BOUND_VARIABLE_2175835 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2175835))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2175835))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2175833)) (ho_15161 k_15160 BOUND_VARIABLE_2175834))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15182 BOUND_VARIABLE_2197246) BOUND_VARIABLE_2197243) BOUND_VARIABLE_2175833) BOUND_VARIABLE_2175834) BOUND_VARIABLE_2175835) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2197246 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2197243 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_1939 (forall ((BOUND_VARIABLE_2175803 tptp.int) (BOUND_VARIABLE_2175804 tptp.int) (BOUND_VARIABLE_2175805 tptp.int) (BOUND_VARIABLE_2175806 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175803) BOUND_VARIABLE_2175805))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175804) BOUND_VARIABLE_2175806))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15184 BOUND_VARIABLE_2175803) BOUND_VARIABLE_2175804) BOUND_VARIABLE_2175805) BOUND_VARIABLE_2175806))))))) (let ((_let_1940 (forall ((BOUND_VARIABLE_2175706 tptp.nat) (BOUND_VARIABLE_2197345 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2175708 tptp.nat) (BOUND_VARIABLE_2175709 tptp.nat) (BOUND_VARIABLE_2175710 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2175710))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2175710))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2175708)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15185 BOUND_VARIABLE_2175706) BOUND_VARIABLE_2197345) BOUND_VARIABLE_2175708) BOUND_VARIABLE_2175709) BOUND_VARIABLE_2175710) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2197345 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2175706))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2197345 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2175709))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_1941 (forall ((BOUND_VARIABLE_2175678 tptp.int) (BOUND_VARIABLE_2175679 tptp.int) (BOUND_VARIABLE_2175680 tptp.int) (BOUND_VARIABLE_2175681 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175678) BOUND_VARIABLE_2175680))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175679) BOUND_VARIABLE_2175681))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15186 BOUND_VARIABLE_2175678) BOUND_VARIABLE_2175679) BOUND_VARIABLE_2175680) BOUND_VARIABLE_2175681))))))) (let ((_let_1942 (forall ((BOUND_VARIABLE_2175650 tptp.int) (BOUND_VARIABLE_2175651 tptp.int) (BOUND_VARIABLE_2175652 tptp.int) (BOUND_VARIABLE_2175653 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175650) BOUND_VARIABLE_2175652))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175651) BOUND_VARIABLE_2175653))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15187 BOUND_VARIABLE_2175650) BOUND_VARIABLE_2175651) BOUND_VARIABLE_2175652) BOUND_VARIABLE_2175653))))))) (let ((_let_1943 (forall ((BOUND_VARIABLE_2175553 tptp.nat) (BOUND_VARIABLE_2197468 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2175555 tptp.nat) (BOUND_VARIABLE_2175556 tptp.nat) (BOUND_VARIABLE_2175557 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2175557))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2175557))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2175555)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15188 BOUND_VARIABLE_2175553) BOUND_VARIABLE_2197468) BOUND_VARIABLE_2175555) BOUND_VARIABLE_2175556) BOUND_VARIABLE_2175557) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2197468 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2175553))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2197468 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2175556))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_1944 (forall ((BOUND_VARIABLE_2175525 tptp.int) (BOUND_VARIABLE_2175526 tptp.int) (BOUND_VARIABLE_2175527 tptp.int) (BOUND_VARIABLE_2175528 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175525) BOUND_VARIABLE_2175527))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175526) BOUND_VARIABLE_2175528))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15189 BOUND_VARIABLE_2175525) BOUND_VARIABLE_2175526) BOUND_VARIABLE_2175527) BOUND_VARIABLE_2175528))))))) (let ((_let_1945 (forall ((BOUND_VARIABLE_2197568 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2175439 tptp.nat) (BOUND_VARIABLE_2175440 tptp.nat) (BOUND_VARIABLE_2175441 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2175441))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2175441))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15190 BOUND_VARIABLE_2197568) BOUND_VARIABLE_2175439) BOUND_VARIABLE_2175440) BOUND_VARIABLE_2175441) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2197568 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2175439)) (ho_15161 k_15160 BOUND_VARIABLE_2175440))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_1946 (forall ((BOUND_VARIABLE_2175410 tptp.int) (BOUND_VARIABLE_2175411 tptp.int) (BOUND_VARIABLE_2175412 tptp.int) (BOUND_VARIABLE_2175413 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175410) BOUND_VARIABLE_2175412))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175411) BOUND_VARIABLE_2175413))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15191 BOUND_VARIABLE_2175410) BOUND_VARIABLE_2175411) BOUND_VARIABLE_2175412) BOUND_VARIABLE_2175413))))))) (let ((_let_1947 (forall ((BOUND_VARIABLE_2175382 tptp.int) (BOUND_VARIABLE_2175383 tptp.int) (BOUND_VARIABLE_2175384 tptp.int) (BOUND_VARIABLE_2175385 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175382) BOUND_VARIABLE_2175384))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175383) BOUND_VARIABLE_2175385))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15192 BOUND_VARIABLE_2175382) BOUND_VARIABLE_2175383) BOUND_VARIABLE_2175384) BOUND_VARIABLE_2175385))))))) (let ((_let_1948 (forall ((BOUND_VARIABLE_2197682 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2175296 tptp.nat) (BOUND_VARIABLE_2175297 tptp.nat) (BOUND_VARIABLE_2175298 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2175298))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2175298))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15193 BOUND_VARIABLE_2197682) BOUND_VARIABLE_2175296) BOUND_VARIABLE_2175297) BOUND_VARIABLE_2175298) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2197682 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2175296)) (ho_15161 k_15160 BOUND_VARIABLE_2175297))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_1949 (forall ((BOUND_VARIABLE_2175288 tptp.num)) (= (ho_15195 k_15194 BOUND_VARIABLE_2175288) (ho_15195 k_15196 (ho_15152 k_15151 BOUND_VARIABLE_2175288)))))) (let ((_let_1950 (forall ((BOUND_VARIABLE_2175260 tptp.int) (BOUND_VARIABLE_2175261 tptp.int) (BOUND_VARIABLE_2175262 tptp.int) (BOUND_VARIABLE_2175263 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175260) BOUND_VARIABLE_2175262))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175261) BOUND_VARIABLE_2175263))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15197 BOUND_VARIABLE_2175260) BOUND_VARIABLE_2175261) BOUND_VARIABLE_2175262) BOUND_VARIABLE_2175263))))))) (let ((_let_1951 (forall ((BOUND_VARIABLE_2175156 tptp.int) (BOUND_VARIABLE_2175157 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2175157))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2175157))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2175156) _let_3))) (= (ho_15142 (ho_15141 k_15198 BOUND_VARIABLE_2175156) BOUND_VARIABLE_2175157) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1952 (forall ((BOUND_VARIABLE_2175128 tptp.int) (BOUND_VARIABLE_2175129 tptp.int) (BOUND_VARIABLE_2175130 tptp.int) (BOUND_VARIABLE_2175131 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175128) BOUND_VARIABLE_2175130))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175129) BOUND_VARIABLE_2175131))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15199 BOUND_VARIABLE_2175128) BOUND_VARIABLE_2175129) BOUND_VARIABLE_2175130) BOUND_VARIABLE_2175131))))))) (let ((_let_1953 (forall ((BOUND_VARIABLE_2175049 tptp.rat) (BOUND_VARIABLE_2175050 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2175050))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2175050))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2175049 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15200 BOUND_VARIABLE_2175049) BOUND_VARIABLE_2175050)))))))))))))) (let ((_let_1954 (forall ((BOUND_VARIABLE_2175021 tptp.int) (BOUND_VARIABLE_2175022 tptp.int) (BOUND_VARIABLE_2175023 tptp.int) (BOUND_VARIABLE_2175024 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175021) BOUND_VARIABLE_2175023))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2175022) BOUND_VARIABLE_2175024))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15201 BOUND_VARIABLE_2175021) BOUND_VARIABLE_2175022) BOUND_VARIABLE_2175023) BOUND_VARIABLE_2175024))))))) (let ((_let_1955 (forall ((BOUND_VARIABLE_2174917 tptp.int) (BOUND_VARIABLE_2174918 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2174918))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2174918))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2174917) _let_3))) (= (ho_15142 (ho_15141 k_15202 BOUND_VARIABLE_2174917) BOUND_VARIABLE_2174918) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1956 (forall ((BOUND_VARIABLE_2174889 tptp.int) (BOUND_VARIABLE_2174890 tptp.int) (BOUND_VARIABLE_2174891 tptp.int) (BOUND_VARIABLE_2174892 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174889) BOUND_VARIABLE_2174891))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174890) BOUND_VARIABLE_2174892))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15203 BOUND_VARIABLE_2174889) BOUND_VARIABLE_2174890) BOUND_VARIABLE_2174891) BOUND_VARIABLE_2174892))))))) (let ((_let_1957 (forall ((BOUND_VARIABLE_2174810 tptp.rat) (BOUND_VARIABLE_2174811 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2174811))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2174811))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2174810 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15204 BOUND_VARIABLE_2174810) BOUND_VARIABLE_2174811)))))))))))))) (let ((_let_1958 (forall ((BOUND_VARIABLE_2174782 tptp.int) (BOUND_VARIABLE_2174783 tptp.int) (BOUND_VARIABLE_2174784 tptp.int) (BOUND_VARIABLE_2174785 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174782) BOUND_VARIABLE_2174784))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174783) BOUND_VARIABLE_2174785))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15205 BOUND_VARIABLE_2174782) BOUND_VARIABLE_2174783) BOUND_VARIABLE_2174784) BOUND_VARIABLE_2174785))))))) (let ((_let_1959 (forall ((BOUND_VARIABLE_2174678 tptp.int) (BOUND_VARIABLE_2174679 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2174679))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2174679))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2174678) _let_3))) (= (ho_15142 (ho_15141 k_15206 BOUND_VARIABLE_2174678) BOUND_VARIABLE_2174679) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1960 (forall ((BOUND_VARIABLE_2174650 tptp.int) (BOUND_VARIABLE_2174651 tptp.int) (BOUND_VARIABLE_2174652 tptp.int) (BOUND_VARIABLE_2174653 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174650) BOUND_VARIABLE_2174652))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174651) BOUND_VARIABLE_2174653))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15207 BOUND_VARIABLE_2174650) BOUND_VARIABLE_2174651) BOUND_VARIABLE_2174652) BOUND_VARIABLE_2174653))))))) (let ((_let_1961 (forall ((BOUND_VARIABLE_2174566 tptp.rat) (BOUND_VARIABLE_2174567 tptp.rat) (BOUND_VARIABLE_2174568 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2174568))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2174568))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15208 BOUND_VARIABLE_2174566) BOUND_VARIABLE_2174567) BOUND_VARIABLE_2174568) (and (= (ho_15122 (ho_15125 _let_10 BOUND_VARIABLE_2174566) BOUND_VARIABLE_2174567) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1962 (forall ((BOUND_VARIABLE_2174538 tptp.int) (BOUND_VARIABLE_2174539 tptp.int) (BOUND_VARIABLE_2174540 tptp.int) (BOUND_VARIABLE_2174541 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174538) BOUND_VARIABLE_2174540))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174539) BOUND_VARIABLE_2174541))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15210 BOUND_VARIABLE_2174538) BOUND_VARIABLE_2174539) BOUND_VARIABLE_2174540) BOUND_VARIABLE_2174541))))))) (let ((_let_1963 (forall ((BOUND_VARIABLE_2174434 tptp.int) (BOUND_VARIABLE_2174435 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2174435))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2174435))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2174434) _let_3))) (= (ho_15142 (ho_15141 k_15211 BOUND_VARIABLE_2174434) BOUND_VARIABLE_2174435) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1964 (forall ((BOUND_VARIABLE_2174406 tptp.int) (BOUND_VARIABLE_2174407 tptp.int) (BOUND_VARIABLE_2174408 tptp.int) (BOUND_VARIABLE_2174409 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174406) BOUND_VARIABLE_2174408))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174407) BOUND_VARIABLE_2174409))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15212 BOUND_VARIABLE_2174406) BOUND_VARIABLE_2174407) BOUND_VARIABLE_2174408) BOUND_VARIABLE_2174409))))))) (let ((_let_1965 (forall ((BOUND_VARIABLE_2174327 tptp.rat) (BOUND_VARIABLE_2174328 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2174328))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2174328))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2174327 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15213 BOUND_VARIABLE_2174327) BOUND_VARIABLE_2174328)))))))))))))) (let ((_let_1966 (forall ((BOUND_VARIABLE_2174299 tptp.int) (BOUND_VARIABLE_2174300 tptp.int) (BOUND_VARIABLE_2174301 tptp.int) (BOUND_VARIABLE_2174302 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174299) BOUND_VARIABLE_2174301))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174300) BOUND_VARIABLE_2174302))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15214 BOUND_VARIABLE_2174299) BOUND_VARIABLE_2174300) BOUND_VARIABLE_2174301) BOUND_VARIABLE_2174302))))))) (let ((_let_1967 (forall ((BOUND_VARIABLE_2174195 tptp.int) (BOUND_VARIABLE_2174196 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2174196))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2174196))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2174195) _let_3))) (= (ho_15142 (ho_15141 k_15215 BOUND_VARIABLE_2174195) BOUND_VARIABLE_2174196) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1968 (forall ((BOUND_VARIABLE_2174167 tptp.int) (BOUND_VARIABLE_2174168 tptp.int) (BOUND_VARIABLE_2174169 tptp.int) (BOUND_VARIABLE_2174170 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174167) BOUND_VARIABLE_2174169))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174168) BOUND_VARIABLE_2174170))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15216 BOUND_VARIABLE_2174167) BOUND_VARIABLE_2174168) BOUND_VARIABLE_2174169) BOUND_VARIABLE_2174170))))))) (let ((_let_1969 (forall ((BOUND_VARIABLE_2174088 tptp.rat) (BOUND_VARIABLE_2174089 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2174089))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2174089))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2174088 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15217 BOUND_VARIABLE_2174088) BOUND_VARIABLE_2174089)))))))))))))) (let ((_let_1970 (forall ((BOUND_VARIABLE_2174060 tptp.int) (BOUND_VARIABLE_2174061 tptp.int) (BOUND_VARIABLE_2174062 tptp.int) (BOUND_VARIABLE_2174063 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174060) BOUND_VARIABLE_2174062))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2174061) BOUND_VARIABLE_2174063))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15218 BOUND_VARIABLE_2174060) BOUND_VARIABLE_2174061) BOUND_VARIABLE_2174062) BOUND_VARIABLE_2174063))))))) (let ((_let_1971 (forall ((BOUND_VARIABLE_2173956 tptp.int) (BOUND_VARIABLE_2173957 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2173957))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2173957))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2173956) _let_3))) (= (ho_15142 (ho_15141 k_15219 BOUND_VARIABLE_2173956) BOUND_VARIABLE_2173957) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1972 (forall ((BOUND_VARIABLE_2173928 tptp.int) (BOUND_VARIABLE_2173929 tptp.int) (BOUND_VARIABLE_2173930 tptp.int) (BOUND_VARIABLE_2173931 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173928) BOUND_VARIABLE_2173930))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173929) BOUND_VARIABLE_2173931))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15220 BOUND_VARIABLE_2173928) BOUND_VARIABLE_2173929) BOUND_VARIABLE_2173930) BOUND_VARIABLE_2173931))))))) (let ((_let_1973 (forall ((BOUND_VARIABLE_2173849 tptp.rat) (BOUND_VARIABLE_2173850 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2173850))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2173850))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2173849 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15221 BOUND_VARIABLE_2173849) BOUND_VARIABLE_2173850)))))))))))))) (let ((_let_1974 (forall ((BOUND_VARIABLE_2173821 tptp.int) (BOUND_VARIABLE_2173822 tptp.int) (BOUND_VARIABLE_2173823 tptp.int) (BOUND_VARIABLE_2173824 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173821) BOUND_VARIABLE_2173823))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173822) BOUND_VARIABLE_2173824))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15222 BOUND_VARIABLE_2173821) BOUND_VARIABLE_2173822) BOUND_VARIABLE_2173823) BOUND_VARIABLE_2173824))))))) (let ((_let_1975 (forall ((BOUND_VARIABLE_2173717 tptp.int) (BOUND_VARIABLE_2173718 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2173718))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2173718))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2173717) _let_3))) (= (ho_15142 (ho_15141 k_15223 BOUND_VARIABLE_2173717) BOUND_VARIABLE_2173718) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1976 (forall ((BOUND_VARIABLE_2173689 tptp.int) (BOUND_VARIABLE_2173690 tptp.int) (BOUND_VARIABLE_2173691 tptp.int) (BOUND_VARIABLE_2173692 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 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k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2173610 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15225 BOUND_VARIABLE_2173610) BOUND_VARIABLE_2173611)))))))))))))) (let ((_let_1978 (forall ((BOUND_VARIABLE_2173582 tptp.int) (BOUND_VARIABLE_2173583 tptp.int) (BOUND_VARIABLE_2173584 tptp.int) (BOUND_VARIABLE_2173585 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173582) BOUND_VARIABLE_2173584))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173583) BOUND_VARIABLE_2173585))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15226 BOUND_VARIABLE_2173582) BOUND_VARIABLE_2173583) BOUND_VARIABLE_2173584) BOUND_VARIABLE_2173585))))))) (let ((_let_1979 (forall ((BOUND_VARIABLE_2173478 tptp.int) (BOUND_VARIABLE_2173479 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2173479))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2173479))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2173478) _let_3))) (= (ho_15142 (ho_15141 k_15227 BOUND_VARIABLE_2173478) BOUND_VARIABLE_2173479) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1980 (forall ((BOUND_VARIABLE_2173450 tptp.int) (BOUND_VARIABLE_2173451 tptp.int) (BOUND_VARIABLE_2173452 tptp.int) (BOUND_VARIABLE_2173453 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173450) BOUND_VARIABLE_2173452))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173451) BOUND_VARIABLE_2173453))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15228 BOUND_VARIABLE_2173450) BOUND_VARIABLE_2173451) BOUND_VARIABLE_2173452) BOUND_VARIABLE_2173453))))))) (let ((_let_1981 (forall ((BOUND_VARIABLE_2173371 tptp.rat) (BOUND_VARIABLE_2173372 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2173372))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2173372))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2173371 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15229 BOUND_VARIABLE_2173371) BOUND_VARIABLE_2173372)))))))))))))) (let ((_let_1982 (forall ((BOUND_VARIABLE_2173343 tptp.int) (BOUND_VARIABLE_2173344 tptp.int) (BOUND_VARIABLE_2173345 tptp.int) (BOUND_VARIABLE_2173346 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173343) BOUND_VARIABLE_2173345))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173344) BOUND_VARIABLE_2173346))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15230 BOUND_VARIABLE_2173343) BOUND_VARIABLE_2173344) BOUND_VARIABLE_2173345) BOUND_VARIABLE_2173346))))))) (let ((_let_1983 (forall ((BOUND_VARIABLE_2173239 tptp.int) (BOUND_VARIABLE_2173240 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2173240))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2173240))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2173239) _let_3))) (= (ho_15142 (ho_15141 k_15231 BOUND_VARIABLE_2173239) BOUND_VARIABLE_2173240) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1984 (forall ((BOUND_VARIABLE_2173211 tptp.int) (BOUND_VARIABLE_2173212 tptp.int) (BOUND_VARIABLE_2173213 tptp.int) (BOUND_VARIABLE_2173214 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173211) BOUND_VARIABLE_2173213))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173212) BOUND_VARIABLE_2173214))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15232 BOUND_VARIABLE_2173211) BOUND_VARIABLE_2173212) BOUND_VARIABLE_2173213) BOUND_VARIABLE_2173214))))))) (let ((_let_1985 (forall ((BOUND_VARIABLE_2173132 tptp.rat) (BOUND_VARIABLE_2173133 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2173133))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2173133))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2173132 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15233 BOUND_VARIABLE_2173132) BOUND_VARIABLE_2173133)))))))))))))) (let ((_let_1986 (forall ((BOUND_VARIABLE_2173104 tptp.int) (BOUND_VARIABLE_2173105 tptp.int) (BOUND_VARIABLE_2173106 tptp.int) (BOUND_VARIABLE_2173107 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173104) BOUND_VARIABLE_2173106))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2173105) BOUND_VARIABLE_2173107))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15234 BOUND_VARIABLE_2173104) BOUND_VARIABLE_2173105) BOUND_VARIABLE_2173106) BOUND_VARIABLE_2173107))))))) (let ((_let_1987 (forall ((BOUND_VARIABLE_2173000 tptp.int) (BOUND_VARIABLE_2173001 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2173001))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2173001))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2173000) _let_3))) (= (ho_15142 (ho_15141 k_15235 BOUND_VARIABLE_2173000) BOUND_VARIABLE_2173001) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1988 (forall ((BOUND_VARIABLE_2172972 tptp.int) (BOUND_VARIABLE_2172973 tptp.int) (BOUND_VARIABLE_2172974 tptp.int) (BOUND_VARIABLE_2172975 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172972) BOUND_VARIABLE_2172974))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172973) BOUND_VARIABLE_2172975))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15236 BOUND_VARIABLE_2172972) BOUND_VARIABLE_2172973) BOUND_VARIABLE_2172974) BOUND_VARIABLE_2172975))))))) (let ((_let_1989 (forall ((BOUND_VARIABLE_2172893 tptp.rat) (BOUND_VARIABLE_2172894 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2172894))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2172894))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2172893 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15237 BOUND_VARIABLE_2172893) BOUND_VARIABLE_2172894)))))))))))))) (let ((_let_1990 (forall ((BOUND_VARIABLE_2172865 tptp.int) (BOUND_VARIABLE_2172866 tptp.int) (BOUND_VARIABLE_2172867 tptp.int) (BOUND_VARIABLE_2172868 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172865) BOUND_VARIABLE_2172867))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172866) BOUND_VARIABLE_2172868))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15238 BOUND_VARIABLE_2172865) BOUND_VARIABLE_2172866) BOUND_VARIABLE_2172867) BOUND_VARIABLE_2172868))))))) (let ((_let_1991 (forall ((BOUND_VARIABLE_2172761 tptp.int) (BOUND_VARIABLE_2172762 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2172762))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2172762))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2172761) _let_3))) (= (ho_15142 (ho_15141 k_15239 BOUND_VARIABLE_2172761) BOUND_VARIABLE_2172762) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1992 (forall ((BOUND_VARIABLE_2172733 tptp.int) (BOUND_VARIABLE_2172734 tptp.int) (BOUND_VARIABLE_2172735 tptp.int) (BOUND_VARIABLE_2172736 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172733) BOUND_VARIABLE_2172735))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172734) BOUND_VARIABLE_2172736))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15240 BOUND_VARIABLE_2172733) BOUND_VARIABLE_2172734) BOUND_VARIABLE_2172735) BOUND_VARIABLE_2172736))))))) (let ((_let_1993 (forall ((BOUND_VARIABLE_2172654 tptp.rat) (BOUND_VARIABLE_2172655 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2172655))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2172655))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2172654 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15241 BOUND_VARIABLE_2172654) BOUND_VARIABLE_2172655)))))))))))))) (let ((_let_1994 (forall ((BOUND_VARIABLE_2172626 tptp.int) (BOUND_VARIABLE_2172627 tptp.int) (BOUND_VARIABLE_2172628 tptp.int) (BOUND_VARIABLE_2172629 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172626) BOUND_VARIABLE_2172628))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172627) BOUND_VARIABLE_2172629))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15242 BOUND_VARIABLE_2172626) BOUND_VARIABLE_2172627) BOUND_VARIABLE_2172628) BOUND_VARIABLE_2172629))))))) (let ((_let_1995 (forall ((BOUND_VARIABLE_2172522 tptp.int) (BOUND_VARIABLE_2172523 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2172523))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2172523))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2172522) _let_3))) (= (ho_15142 (ho_15141 k_15243 BOUND_VARIABLE_2172522) BOUND_VARIABLE_2172523) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_1996 (forall ((BOUND_VARIABLE_2172494 tptp.int) (BOUND_VARIABLE_2172495 tptp.int) (BOUND_VARIABLE_2172496 tptp.int) (BOUND_VARIABLE_2172497 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172494) BOUND_VARIABLE_2172496))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172495) BOUND_VARIABLE_2172497))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15244 BOUND_VARIABLE_2172494) BOUND_VARIABLE_2172495) BOUND_VARIABLE_2172496) BOUND_VARIABLE_2172497))))))) (let ((_let_1997 (forall ((BOUND_VARIABLE_2172415 tptp.rat) (BOUND_VARIABLE_2172416 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2172416))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2172416))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2172415 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15245 BOUND_VARIABLE_2172415) BOUND_VARIABLE_2172416)))))))))))))) (let ((_let_1998 (forall ((BOUND_VARIABLE_2172387 tptp.int) (BOUND_VARIABLE_2172388 tptp.int) (BOUND_VARIABLE_2172389 tptp.int) (BOUND_VARIABLE_2172390 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172387) BOUND_VARIABLE_2172389))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172388) BOUND_VARIABLE_2172390))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15246 BOUND_VARIABLE_2172387) BOUND_VARIABLE_2172388) BOUND_VARIABLE_2172389) BOUND_VARIABLE_2172390))))))) (let ((_let_1999 (forall ((BOUND_VARIABLE_2172283 tptp.int) (BOUND_VARIABLE_2172284 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2172284))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2172284))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2172283) _let_3))) (= (ho_15142 (ho_15141 k_15247 BOUND_VARIABLE_2172283) BOUND_VARIABLE_2172284) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2000 (forall ((BOUND_VARIABLE_2172255 tptp.int) (BOUND_VARIABLE_2172256 tptp.int) (BOUND_VARIABLE_2172257 tptp.int) (BOUND_VARIABLE_2172258 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172255) BOUND_VARIABLE_2172257))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172256) BOUND_VARIABLE_2172258))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15248 BOUND_VARIABLE_2172255) BOUND_VARIABLE_2172256) BOUND_VARIABLE_2172257) BOUND_VARIABLE_2172258))))))) (let ((_let_2001 (forall ((BOUND_VARIABLE_2172176 tptp.rat) (BOUND_VARIABLE_2172177 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2172177))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2172177))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2172176 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15249 BOUND_VARIABLE_2172176) BOUND_VARIABLE_2172177)))))))))))))) (let ((_let_2002 (forall ((BOUND_VARIABLE_2172148 tptp.int) (BOUND_VARIABLE_2172149 tptp.int) (BOUND_VARIABLE_2172150 tptp.int) (BOUND_VARIABLE_2172151 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172148) BOUND_VARIABLE_2172150))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172149) BOUND_VARIABLE_2172151))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15250 BOUND_VARIABLE_2172148) BOUND_VARIABLE_2172149) BOUND_VARIABLE_2172150) BOUND_VARIABLE_2172151))))))) (let ((_let_2003 (forall ((BOUND_VARIABLE_2172044 tptp.int) (BOUND_VARIABLE_2172045 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2172045))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2172045))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2172044) _let_3))) (= (ho_15142 (ho_15141 k_15251 BOUND_VARIABLE_2172044) BOUND_VARIABLE_2172045) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2004 (forall ((BOUND_VARIABLE_2172016 tptp.int) (BOUND_VARIABLE_2172017 tptp.int) (BOUND_VARIABLE_2172018 tptp.int) (BOUND_VARIABLE_2172019 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172016) BOUND_VARIABLE_2172018))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2172017) BOUND_VARIABLE_2172019))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15252 BOUND_VARIABLE_2172016) BOUND_VARIABLE_2172017) BOUND_VARIABLE_2172018) BOUND_VARIABLE_2172019))))))) (let ((_let_2005 (forall ((BOUND_VARIABLE_2171937 tptp.rat) (BOUND_VARIABLE_2171938 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2171938))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2171938))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2171937 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15253 BOUND_VARIABLE_2171937) BOUND_VARIABLE_2171938)))))))))))))) (let ((_let_2006 (forall ((BOUND_VARIABLE_2171909 tptp.int) (BOUND_VARIABLE_2171910 tptp.int) (BOUND_VARIABLE_2171911 tptp.int) (BOUND_VARIABLE_2171912 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2171909) BOUND_VARIABLE_2171911))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2171910) BOUND_VARIABLE_2171912))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15254 BOUND_VARIABLE_2171909) BOUND_VARIABLE_2171910) BOUND_VARIABLE_2171911) BOUND_VARIABLE_2171912))))))) (let ((_let_2007 (forall ((BOUND_VARIABLE_2171805 tptp.int) (BOUND_VARIABLE_2171806 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2171806))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2171806))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2171805) _let_3))) (= (ho_15142 (ho_15141 k_15255 BOUND_VARIABLE_2171805) BOUND_VARIABLE_2171806) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2008 (forall ((BOUND_VARIABLE_2171777 tptp.int) (BOUND_VARIABLE_2171778 tptp.int) (BOUND_VARIABLE_2171779 tptp.int) (BOUND_VARIABLE_2171780 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2171777) BOUND_VARIABLE_2171779))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2171778) BOUND_VARIABLE_2171780))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15256 BOUND_VARIABLE_2171777) BOUND_VARIABLE_2171778) BOUND_VARIABLE_2171779) BOUND_VARIABLE_2171780))))))) (let ((_let_2009 (forall ((BOUND_VARIABLE_2171698 tptp.rat) (BOUND_VARIABLE_2171699 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2171699))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2171699))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2171698 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15257 BOUND_VARIABLE_2171698) BOUND_VARIABLE_2171699)))))))))))))) (let ((_let_2010 (forall ((BOUND_VARIABLE_2171596 tptp.int) (BOUND_VARIABLE_2171597 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2171597))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2171597))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15258 BOUND_VARIABLE_2171596) BOUND_VARIABLE_2171597) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2171596) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2171596)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2171596))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2011 (forall ((BOUND_VARIABLE_2171501 tptp.int) (BOUND_VARIABLE_2171502 tptp.int) (BOUND_VARIABLE_2171503 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15104 BOUND_VARIABLE_2171503) BOUND_VARIABLE_2171502)) (ho_15260 k_15259 (ho_15141 k_15140 BOUND_VARIABLE_2171501))) (ho_15108 (ho_15107 (ho_15106 k_15263 BOUND_VARIABLE_2171501) BOUND_VARIABLE_2171502) BOUND_VARIABLE_2171503))))) (let ((_let_2012 (forall ((BOUND_VARIABLE_2171422 tptp.rat) (BOUND_VARIABLE_2171423 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2171423))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2171423))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2171422 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15264 BOUND_VARIABLE_2171422) BOUND_VARIABLE_2171423)))))))))))))) (let ((_let_2013 (forall ((BOUND_VARIABLE_2171365 tptp.rat) (BOUND_VARIABLE_2171366 tptp.int) (BOUND_VARIABLE_2171367 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15143 BOUND_VARIABLE_2171367) BOUND_VARIABLE_2171366)) (ho_15260 k_15259 (ho_15145 k_15144 BOUND_VARIABLE_2171365))) (ho_15108 (ho_15107 (ho_15266 k_15265 BOUND_VARIABLE_2171365) BOUND_VARIABLE_2171366) BOUND_VARIABLE_2171367))))) (let ((_let_2014 (forall ((BOUND_VARIABLE_2171261 tptp.int) (BOUND_VARIABLE_2171262 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2171262))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2171262))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2171261) _let_3))) (= (ho_15142 (ho_15141 k_15267 BOUND_VARIABLE_2171261) BOUND_VARIABLE_2171262) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2015 (forall ((BOUND_VARIABLE_2171233 tptp.int) (BOUND_VARIABLE_2171234 tptp.int) (BOUND_VARIABLE_2171235 tptp.int) (BOUND_VARIABLE_2171236 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2171233) BOUND_VARIABLE_2171235))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2171234) BOUND_VARIABLE_2171236))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15268 BOUND_VARIABLE_2171233) BOUND_VARIABLE_2171234) BOUND_VARIABLE_2171235) BOUND_VARIABLE_2171236))))))) (let ((_let_2016 (forall ((BOUND_VARIABLE_2171129 tptp.int) (BOUND_VARIABLE_2171130 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2171130))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2171130))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2171129) _let_3))) (= (ho_15142 (ho_15141 k_15269 BOUND_VARIABLE_2171129) BOUND_VARIABLE_2171130) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2017 (forall ((BOUND_VARIABLE_2171101 tptp.int) (BOUND_VARIABLE_2171102 tptp.int) (BOUND_VARIABLE_2171103 tptp.int) (BOUND_VARIABLE_2171104 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2171101) BOUND_VARIABLE_2171103))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2171102) BOUND_VARIABLE_2171104))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15270 BOUND_VARIABLE_2171101) BOUND_VARIABLE_2171102) BOUND_VARIABLE_2171103) BOUND_VARIABLE_2171104))))))) (let ((_let_2018 (forall ((BOUND_VARIABLE_2171016 tptp.rat) (BOUND_VARIABLE_2171017 tptp.rat) (BOUND_VARIABLE_2171018 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2171018))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2171018))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15271 BOUND_VARIABLE_2171016) BOUND_VARIABLE_2171017) BOUND_VARIABLE_2171018) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 BOUND_VARIABLE_2171016)) BOUND_VARIABLE_2171017) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2019 (forall ((BOUND_VARIABLE_2170988 tptp.int) (BOUND_VARIABLE_2170989 tptp.int) (BOUND_VARIABLE_2170990 tptp.int) (BOUND_VARIABLE_2170991 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170988) BOUND_VARIABLE_2170990))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170989) BOUND_VARIABLE_2170991))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15272 BOUND_VARIABLE_2170988) BOUND_VARIABLE_2170989) BOUND_VARIABLE_2170990) BOUND_VARIABLE_2170991))))))) (let ((_let_2020 (forall ((BOUND_VARIABLE_2170884 tptp.int) (BOUND_VARIABLE_2170885 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2170885))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2170885))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2170884) _let_3))) (= (ho_15142 (ho_15141 k_15273 BOUND_VARIABLE_2170884) BOUND_VARIABLE_2170885) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2021 (forall ((BOUND_VARIABLE_2170856 tptp.int) (BOUND_VARIABLE_2170857 tptp.int) (BOUND_VARIABLE_2170858 tptp.int) (BOUND_VARIABLE_2170859 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170856) BOUND_VARIABLE_2170858))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170857) BOUND_VARIABLE_2170859))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15274 BOUND_VARIABLE_2170856) BOUND_VARIABLE_2170857) BOUND_VARIABLE_2170858) BOUND_VARIABLE_2170859))))))) (let ((_let_2022 (forall ((BOUND_VARIABLE_2170771 tptp.rat) (BOUND_VARIABLE_2170772 tptp.rat) (BOUND_VARIABLE_2170773 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2170773))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2170773))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15275 BOUND_VARIABLE_2170771) BOUND_VARIABLE_2170772) BOUND_VARIABLE_2170773) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 BOUND_VARIABLE_2170771)) BOUND_VARIABLE_2170772) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2023 (forall ((BOUND_VARIABLE_2170743 tptp.int) (BOUND_VARIABLE_2170744 tptp.int) (BOUND_VARIABLE_2170745 tptp.int) (BOUND_VARIABLE_2170746 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170743) BOUND_VARIABLE_2170745))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170744) BOUND_VARIABLE_2170746))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15276 BOUND_VARIABLE_2170743) BOUND_VARIABLE_2170744) BOUND_VARIABLE_2170745) BOUND_VARIABLE_2170746))))))) (let ((_let_2024 (forall ((BOUND_VARIABLE_2170639 tptp.int) (BOUND_VARIABLE_2170640 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2170640))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2170640))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2170639) _let_3))) (= (ho_15142 (ho_15141 k_15277 BOUND_VARIABLE_2170639) BOUND_VARIABLE_2170640) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2025 (forall ((BOUND_VARIABLE_2170611 tptp.int) (BOUND_VARIABLE_2170612 tptp.int) (BOUND_VARIABLE_2170613 tptp.int) (BOUND_VARIABLE_2170614 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170611) BOUND_VARIABLE_2170613))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170612) BOUND_VARIABLE_2170614))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15278 BOUND_VARIABLE_2170611) BOUND_VARIABLE_2170612) BOUND_VARIABLE_2170613) BOUND_VARIABLE_2170614))))))) (let ((_let_2026 (forall ((BOUND_VARIABLE_2170526 tptp.rat) (BOUND_VARIABLE_2170527 tptp.rat) (BOUND_VARIABLE_2170528 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2170528))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2170528))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15279 BOUND_VARIABLE_2170526) BOUND_VARIABLE_2170527) BOUND_VARIABLE_2170528) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 BOUND_VARIABLE_2170526)) BOUND_VARIABLE_2170527) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2027 (forall ((BOUND_VARIABLE_2170498 tptp.int) (BOUND_VARIABLE_2170499 tptp.int) (BOUND_VARIABLE_2170500 tptp.int) (BOUND_VARIABLE_2170501 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170498) BOUND_VARIABLE_2170500))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170499) BOUND_VARIABLE_2170501))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15280 BOUND_VARIABLE_2170498) BOUND_VARIABLE_2170499) BOUND_VARIABLE_2170500) BOUND_VARIABLE_2170501))))))) (let ((_let_2028 (forall ((BOUND_VARIABLE_2170394 tptp.int) (BOUND_VARIABLE_2170395 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2170395))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2170395))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2170394) _let_3))) (= (ho_15142 (ho_15141 k_15281 BOUND_VARIABLE_2170394) BOUND_VARIABLE_2170395) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2029 (forall ((BOUND_VARIABLE_2170366 tptp.int) (BOUND_VARIABLE_2170367 tptp.int) (BOUND_VARIABLE_2170368 tptp.int) (BOUND_VARIABLE_2170369 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170366) BOUND_VARIABLE_2170368))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170367) BOUND_VARIABLE_2170369))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15282 BOUND_VARIABLE_2170366) BOUND_VARIABLE_2170367) BOUND_VARIABLE_2170368) BOUND_VARIABLE_2170369))))))) (let ((_let_2030 (forall ((BOUND_VARIABLE_2170287 tptp.rat) (BOUND_VARIABLE_2170288 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2170288))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2170288))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2170287 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15283 BOUND_VARIABLE_2170287) BOUND_VARIABLE_2170288)))))))))))))) (let ((_let_2031 (forall ((BOUND_VARIABLE_2170259 tptp.int) (BOUND_VARIABLE_2170260 tptp.int) (BOUND_VARIABLE_2170261 tptp.int) (BOUND_VARIABLE_2170262 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170259) BOUND_VARIABLE_2170261))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170260) BOUND_VARIABLE_2170262))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15284 BOUND_VARIABLE_2170259) BOUND_VARIABLE_2170260) BOUND_VARIABLE_2170261) BOUND_VARIABLE_2170262))))))) (let ((_let_2032 (forall ((BOUND_VARIABLE_2170155 tptp.int) (BOUND_VARIABLE_2170156 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2170156))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2170156))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2170155) _let_3))) (= (ho_15142 (ho_15141 k_15285 BOUND_VARIABLE_2170155) BOUND_VARIABLE_2170156) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2033 (forall ((BOUND_VARIABLE_2170127 tptp.int) (BOUND_VARIABLE_2170128 tptp.int) (BOUND_VARIABLE_2170129 tptp.int) (BOUND_VARIABLE_2170130 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170127) BOUND_VARIABLE_2170129))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170128) BOUND_VARIABLE_2170130))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15286 BOUND_VARIABLE_2170127) BOUND_VARIABLE_2170128) BOUND_VARIABLE_2170129) BOUND_VARIABLE_2170130))))))) (let ((_let_2034 (forall ((BOUND_VARIABLE_2170048 tptp.rat) (BOUND_VARIABLE_2170049 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2170049))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2170049))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2170048 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15287 BOUND_VARIABLE_2170048) BOUND_VARIABLE_2170049)))))))))))))) (let ((_let_2035 (forall ((BOUND_VARIABLE_2170020 tptp.int) (BOUND_VARIABLE_2170021 tptp.int) (BOUND_VARIABLE_2170022 tptp.int) (BOUND_VARIABLE_2170023 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170020) BOUND_VARIABLE_2170022))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2170021) BOUND_VARIABLE_2170023))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15288 BOUND_VARIABLE_2170020) BOUND_VARIABLE_2170021) BOUND_VARIABLE_2170022) BOUND_VARIABLE_2170023))))))) (let ((_let_2036 (forall ((BOUND_VARIABLE_2169916 tptp.int) (BOUND_VARIABLE_2169917 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2169917))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2169917))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2169916) _let_3))) (= (ho_15142 (ho_15141 k_15289 BOUND_VARIABLE_2169916) BOUND_VARIABLE_2169917) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2037 (forall ((BOUND_VARIABLE_2169888 tptp.int) (BOUND_VARIABLE_2169889 tptp.int) (BOUND_VARIABLE_2169890 tptp.int) (BOUND_VARIABLE_2169891 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2169888) BOUND_VARIABLE_2169890))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2169889) BOUND_VARIABLE_2169891))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15290 BOUND_VARIABLE_2169888) BOUND_VARIABLE_2169889) BOUND_VARIABLE_2169890) BOUND_VARIABLE_2169891))))))) (let ((_let_2038 (forall ((BOUND_VARIABLE_2169809 tptp.rat) (BOUND_VARIABLE_2169810 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2169810))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2169810))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2169809 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15291 BOUND_VARIABLE_2169809) BOUND_VARIABLE_2169810)))))))))))))) (let ((_let_2039 (forall ((BOUND_VARIABLE_2169781 tptp.int) (BOUND_VARIABLE_2169782 tptp.int) (BOUND_VARIABLE_2169783 tptp.int) (BOUND_VARIABLE_2169784 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2169781) BOUND_VARIABLE_2169783))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2169782) BOUND_VARIABLE_2169784))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15292 BOUND_VARIABLE_2169781) BOUND_VARIABLE_2169782) BOUND_VARIABLE_2169783) BOUND_VARIABLE_2169784))))))) (let ((_let_2040 (forall ((BOUND_VARIABLE_2169677 tptp.int) (BOUND_VARIABLE_2169678 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2169678))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2169678))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2169677) _let_3))) (= (ho_15142 (ho_15141 k_15293 BOUND_VARIABLE_2169677) BOUND_VARIABLE_2169678) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2041 (forall ((BOUND_VARIABLE_2169649 tptp.int) (BOUND_VARIABLE_2169650 tptp.int) (BOUND_VARIABLE_2169651 tptp.int) (BOUND_VARIABLE_2169652 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2169649) BOUND_VARIABLE_2169651))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2169650) BOUND_VARIABLE_2169652))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15294 BOUND_VARIABLE_2169649) BOUND_VARIABLE_2169650) BOUND_VARIABLE_2169651) BOUND_VARIABLE_2169652))))))) (let ((_let_2042 (forall ((BOUND_VARIABLE_2169570 tptp.rat) (BOUND_VARIABLE_2169571 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2169571))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2169571))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2169570 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15295 BOUND_VARIABLE_2169570) BOUND_VARIABLE_2169571)))))))))))))) (let ((_let_2043 (forall ((BOUND_VARIABLE_2169542 tptp.int) (BOUND_VARIABLE_2169543 tptp.int) (BOUND_VARIABLE_2169544 tptp.int) (BOUND_VARIABLE_2169545 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2169542) BOUND_VARIABLE_2169544))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2169543) BOUND_VARIABLE_2169545))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15296 BOUND_VARIABLE_2169542) BOUND_VARIABLE_2169543) BOUND_VARIABLE_2169544) BOUND_VARIABLE_2169545))))))) (let ((_let_2044 (forall ((BOUND_VARIABLE_2169438 tptp.int) (BOUND_VARIABLE_2169439 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2169439))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2169439))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2169438) _let_3))) (= (ho_15142 (ho_15141 k_15297 BOUND_VARIABLE_2169438) BOUND_VARIABLE_2169439) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 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(BOUND_VARIABLE_2169413 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2169410) BOUND_VARIABLE_2169412))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2169411) BOUND_VARIABLE_2169413))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15298 BOUND_VARIABLE_2169410) BOUND_VARIABLE_2169411) BOUND_VARIABLE_2169412) BOUND_VARIABLE_2169413))))))) (let ((_let_2046 (forall ((BOUND_VARIABLE_2169327 tptp.rat) (BOUND_VARIABLE_2169328 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2169328))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2169328))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15299 BOUND_VARIABLE_2169327) BOUND_VARIABLE_2169328) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2169327) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2047 (forall ((BOUND_VARIABLE_2169225 tptp.int) (BOUND_VARIABLE_2169226 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2169226))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2169226))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15300 BOUND_VARIABLE_2169225) BOUND_VARIABLE_2169226) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2169225) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2169225)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2169225))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) 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((BOUND_VARIABLE_2169130 tptp.int) (BOUND_VARIABLE_2169131 tptp.int) (BOUND_VARIABLE_2169132 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15146 BOUND_VARIABLE_2169132) BOUND_VARIABLE_2169131)) (ho_15260 k_15259 (ho_15141 k_15147 BOUND_VARIABLE_2169130))) (ho_15108 (ho_15107 (ho_15106 k_15301 BOUND_VARIABLE_2169130) BOUND_VARIABLE_2169131) BOUND_VARIABLE_2169132))))) (let ((_let_2049 (forall ((BOUND_VARIABLE_2169047 tptp.rat) (BOUND_VARIABLE_2169048 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2169048))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2169048))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15302 BOUND_VARIABLE_2169047) BOUND_VARIABLE_2169048) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2169047) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2050 (forall ((BOUND_VARIABLE_2168986 tptp.rat) (BOUND_VARIABLE_2168987 tptp.int) (BOUND_VARIABLE_2168988 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15148 BOUND_VARIABLE_2168988) BOUND_VARIABLE_2168987)) (ho_15260 k_15259 (ho_15145 k_15154 BOUND_VARIABLE_2168986))) (ho_15108 (ho_15107 (ho_15266 k_15303 BOUND_VARIABLE_2168986) BOUND_VARIABLE_2168987) BOUND_VARIABLE_2168988))))) (let ((_let_2051 (forall ((BOUND_VARIABLE_2168882 tptp.int) (BOUND_VARIABLE_2168883 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2168883))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2168883))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2168882) _let_3))) (= (ho_15142 (ho_15141 k_15304 BOUND_VARIABLE_2168882) BOUND_VARIABLE_2168883) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2052 (forall ((BOUND_VARIABLE_2168854 tptp.int) (BOUND_VARIABLE_2168855 tptp.int) (BOUND_VARIABLE_2168856 tptp.int) (BOUND_VARIABLE_2168857 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2168854) BOUND_VARIABLE_2168856))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2168855) BOUND_VARIABLE_2168857))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15305 BOUND_VARIABLE_2168854) BOUND_VARIABLE_2168855) BOUND_VARIABLE_2168856) BOUND_VARIABLE_2168857))))))) (let ((_let_2053 (forall ((BOUND_VARIABLE_2168775 tptp.rat) (BOUND_VARIABLE_2168776 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2168776))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2168776))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2168775 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15306 BOUND_VARIABLE_2168775) BOUND_VARIABLE_2168776)))))))))))))) (let ((_let_2054 (forall ((BOUND_VARIABLE_2168747 tptp.int) (BOUND_VARIABLE_2168748 tptp.int) (BOUND_VARIABLE_2168749 tptp.int) (BOUND_VARIABLE_2168750 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2168747) BOUND_VARIABLE_2168749))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2168748) BOUND_VARIABLE_2168750))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15307 BOUND_VARIABLE_2168747) BOUND_VARIABLE_2168748) BOUND_VARIABLE_2168749) BOUND_VARIABLE_2168750))))))) (let ((_let_2055 (forall ((BOUND_VARIABLE_2168719 tptp.int) (BOUND_VARIABLE_2168720 tptp.int) (BOUND_VARIABLE_2168721 tptp.int) (BOUND_VARIABLE_2168722 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2168719) BOUND_VARIABLE_2168721))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2168720) BOUND_VARIABLE_2168722))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15308 BOUND_VARIABLE_2168719) BOUND_VARIABLE_2168720) BOUND_VARIABLE_2168721) BOUND_VARIABLE_2168722))))))) (let ((_let_2056 (forall ((BOUND_VARIABLE_2168640 tptp.rat) (BOUND_VARIABLE_2168641 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2168641))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2168641))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2168640 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15309 BOUND_VARIABLE_2168640) BOUND_VARIABLE_2168641)))))))))))))) (let ((_let_2057 (forall ((BOUND_VARIABLE_2168612 tptp.int) (BOUND_VARIABLE_2168613 tptp.int) (BOUND_VARIABLE_2168614 tptp.int) (BOUND_VARIABLE_2168615 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2168612) BOUND_VARIABLE_2168614))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2168613) BOUND_VARIABLE_2168615))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15310 BOUND_VARIABLE_2168612) BOUND_VARIABLE_2168613) BOUND_VARIABLE_2168614) BOUND_VARIABLE_2168615))))))) (let ((_let_2058 (forall ((BOUND_VARIABLE_2168508 tptp.int) (BOUND_VARIABLE_2168509 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2168509))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2168509))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2168508) _let_3))) (= (ho_15142 (ho_15141 k_15311 BOUND_VARIABLE_2168508) BOUND_VARIABLE_2168509) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2059 (forall ((BOUND_VARIABLE_2168480 tptp.int) (BOUND_VARIABLE_2168481 tptp.int) (BOUND_VARIABLE_2168482 tptp.int) (BOUND_VARIABLE_2168483 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2168480) BOUND_VARIABLE_2168482))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2168481) BOUND_VARIABLE_2168483))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15312 BOUND_VARIABLE_2168480) BOUND_VARIABLE_2168481) BOUND_VARIABLE_2168482) BOUND_VARIABLE_2168483))))))) (let ((_let_2060 (forall ((BOUND_VARIABLE_2168397 tptp.rat) (BOUND_VARIABLE_2168398 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2168398))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2168398))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15313 BOUND_VARIABLE_2168397) BOUND_VARIABLE_2168398) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2168397) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2061 (forall ((BOUND_VARIABLE_2168295 tptp.int) (BOUND_VARIABLE_2168296 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2168296))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2168296))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15314 BOUND_VARIABLE_2168295) BOUND_VARIABLE_2168296) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2168295) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2168295)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2168295))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2062 (forall ((BOUND_VARIABLE_2168200 tptp.int) (BOUND_VARIABLE_2168201 tptp.int) (BOUND_VARIABLE_2168202 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15155 BOUND_VARIABLE_2168202) BOUND_VARIABLE_2168201)) (ho_15260 k_15259 (ho_15141 k_15156 BOUND_VARIABLE_2168200))) (ho_15108 (ho_15107 (ho_15106 k_15315 BOUND_VARIABLE_2168200) BOUND_VARIABLE_2168201) BOUND_VARIABLE_2168202))))) (let ((_let_2063 (forall ((BOUND_VARIABLE_2168117 tptp.rat) (BOUND_VARIABLE_2168118 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2168118))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2168118))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15316 BOUND_VARIABLE_2168117) BOUND_VARIABLE_2168118) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2168117) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) 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k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2167952) _let_3))) (= (ho_15142 (ho_15141 k_15318 BOUND_VARIABLE_2167952) BOUND_VARIABLE_2167953) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 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(ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167924) BOUND_VARIABLE_2167926))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167925) BOUND_VARIABLE_2167927))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15319 BOUND_VARIABLE_2167924) BOUND_VARIABLE_2167925) BOUND_VARIABLE_2167926) BOUND_VARIABLE_2167927))))))) (let ((_let_2067 (forall ((BOUND_VARIABLE_2167820 tptp.int) (BOUND_VARIABLE_2167821 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2167821))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2167821))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2167820) _let_3))) (= (ho_15142 (ho_15141 k_15320 BOUND_VARIABLE_2167820) BOUND_VARIABLE_2167821) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2068 (forall ((BOUND_VARIABLE_2167792 tptp.int) (BOUND_VARIABLE_2167793 tptp.int) (BOUND_VARIABLE_2167794 tptp.int) (BOUND_VARIABLE_2167795 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167792) BOUND_VARIABLE_2167794))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167793) BOUND_VARIABLE_2167795))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15321 BOUND_VARIABLE_2167792) BOUND_VARIABLE_2167793) BOUND_VARIABLE_2167794) BOUND_VARIABLE_2167795))))))) (let ((_let_2069 (forall ((BOUND_VARIABLE_2167709 tptp.rat) (BOUND_VARIABLE_2167710 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2167710))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2167710))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15322 BOUND_VARIABLE_2167709) BOUND_VARIABLE_2167710) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2167709) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2070 (forall ((BOUND_VARIABLE_2167681 tptp.int) (BOUND_VARIABLE_2167682 tptp.int) (BOUND_VARIABLE_2167683 tptp.int) (BOUND_VARIABLE_2167684 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 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((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2167577) _let_3))) (= (ho_15142 (ho_15141 k_15324 BOUND_VARIABLE_2167577) BOUND_VARIABLE_2167578) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2072 (forall ((BOUND_VARIABLE_2167549 tptp.int) (BOUND_VARIABLE_2167550 tptp.int) (BOUND_VARIABLE_2167551 tptp.int) (BOUND_VARIABLE_2167552 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167549) BOUND_VARIABLE_2167551))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167550) BOUND_VARIABLE_2167552))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15325 BOUND_VARIABLE_2167549) BOUND_VARIABLE_2167550) BOUND_VARIABLE_2167551) BOUND_VARIABLE_2167552))))))) (let ((_let_2073 (forall ((BOUND_VARIABLE_2167466 tptp.rat) (BOUND_VARIABLE_2167467 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2167467))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2167467))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15139 _let_9 k_15127))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 k_15326 BOUND_VARIABLE_2167466) BOUND_VARIABLE_2167467) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2167466) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2074 (forall ((BOUND_VARIABLE_2167438 tptp.int) (BOUND_VARIABLE_2167439 tptp.int) (BOUND_VARIABLE_2167440 tptp.int) (BOUND_VARIABLE_2167441 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167438) BOUND_VARIABLE_2167440))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167439) BOUND_VARIABLE_2167441))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15327 BOUND_VARIABLE_2167438) BOUND_VARIABLE_2167439) BOUND_VARIABLE_2167440) BOUND_VARIABLE_2167441))))))) (let ((_let_2075 (forall ((BOUND_VARIABLE_2203316 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2167352 tptp.nat) (BOUND_VARIABLE_2167353 tptp.nat) (BOUND_VARIABLE_2167354 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2167354))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2167354))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15328 BOUND_VARIABLE_2203316) BOUND_VARIABLE_2167352) BOUND_VARIABLE_2167353) BOUND_VARIABLE_2167354) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2203316 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2167352)) (ho_15161 k_15160 BOUND_VARIABLE_2167353))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2076 (forall ((BOUND_VARIABLE_2167323 tptp.int) (BOUND_VARIABLE_2167324 tptp.int) (BOUND_VARIABLE_2167325 tptp.int) (BOUND_VARIABLE_2167326 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167323) BOUND_VARIABLE_2167325))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167324) BOUND_VARIABLE_2167326))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15329 BOUND_VARIABLE_2167323) BOUND_VARIABLE_2167324) BOUND_VARIABLE_2167325) BOUND_VARIABLE_2167326))))))) (let ((_let_2077 (forall ((BOUND_VARIABLE_2167219 tptp.int) (BOUND_VARIABLE_2167220 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2167220))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2167220))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2167219) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15330 BOUND_VARIABLE_2167219) BOUND_VARIABLE_2167220) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2078 (forall ((BOUND_VARIABLE_2167191 tptp.int) (BOUND_VARIABLE_2167192 tptp.int) (BOUND_VARIABLE_2167193 tptp.int) (BOUND_VARIABLE_2167194 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167191) BOUND_VARIABLE_2167193))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167192) BOUND_VARIABLE_2167194))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15331 BOUND_VARIABLE_2167191) BOUND_VARIABLE_2167192) BOUND_VARIABLE_2167193) BOUND_VARIABLE_2167194))))))) (let ((_let_2079 (forall ((BOUND_VARIABLE_2167112 tptp.rat) (BOUND_VARIABLE_2167113 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2167113))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2167113))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2167112 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15332 BOUND_VARIABLE_2167112) BOUND_VARIABLE_2167113)))))))))))))) (let ((_let_2080 (forall ((BOUND_VARIABLE_2167084 tptp.int) (BOUND_VARIABLE_2167085 tptp.int) (BOUND_VARIABLE_2167086 tptp.int) (BOUND_VARIABLE_2167087 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167084) BOUND_VARIABLE_2167086))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2167085) BOUND_VARIABLE_2167087))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15333 BOUND_VARIABLE_2167084) BOUND_VARIABLE_2167085) BOUND_VARIABLE_2167086) BOUND_VARIABLE_2167087))))))) (let ((_let_2081 (forall ((BOUND_VARIABLE_2166987 tptp.nat) (BOUND_VARIABLE_2203584 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2166989 tptp.nat) (BOUND_VARIABLE_2166990 tptp.nat) (BOUND_VARIABLE_2166991 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2166991))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2166991))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2166989)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15334 BOUND_VARIABLE_2166987) BOUND_VARIABLE_2203584) BOUND_VARIABLE_2166989) BOUND_VARIABLE_2166990) BOUND_VARIABLE_2166991) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2203584 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166987))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2203584 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166990))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2082 (forall ((BOUND_VARIABLE_2166959 tptp.int) (BOUND_VARIABLE_2166960 tptp.int) (BOUND_VARIABLE_2166961 tptp.int) (BOUND_VARIABLE_2166962 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2166959) BOUND_VARIABLE_2166961))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2166960) BOUND_VARIABLE_2166962))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15335 BOUND_VARIABLE_2166959) BOUND_VARIABLE_2166960) BOUND_VARIABLE_2166961) BOUND_VARIABLE_2166962))))))) (let ((_let_2083 (forall ((BOUND_VARIABLE_2166862 tptp.nat) (BOUND_VARIABLE_2203684 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2166864 tptp.nat) (BOUND_VARIABLE_2166865 tptp.nat) (BOUND_VARIABLE_2166866 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2166866))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2166866))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2166864)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15336 BOUND_VARIABLE_2166862) BOUND_VARIABLE_2203684) BOUND_VARIABLE_2166864) BOUND_VARIABLE_2166865) BOUND_VARIABLE_2166866) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2203684 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166862))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2203684 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166865))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2084 (forall ((BOUND_VARIABLE_2166834 tptp.int) (BOUND_VARIABLE_2166835 tptp.int) (BOUND_VARIABLE_2166836 tptp.int) (BOUND_VARIABLE_2166837 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2166834) BOUND_VARIABLE_2166836))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2166835) BOUND_VARIABLE_2166837))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15337 BOUND_VARIABLE_2166834) BOUND_VARIABLE_2166835) BOUND_VARIABLE_2166836) BOUND_VARIABLE_2166837))))))) (let ((_let_2085 (forall ((BOUND_VARIABLE_2166737 tptp.nat) (BOUND_VARIABLE_2203784 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2166739 tptp.nat) (BOUND_VARIABLE_2166740 tptp.nat) (BOUND_VARIABLE_2166741 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2166741))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2166741))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2166739)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15338 BOUND_VARIABLE_2166737) BOUND_VARIABLE_2203784) BOUND_VARIABLE_2166739) BOUND_VARIABLE_2166740) BOUND_VARIABLE_2166741) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2203784 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166737))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2203784 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166740))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2086 (forall ((BOUND_VARIABLE_2166709 tptp.int) (BOUND_VARIABLE_2166710 tptp.int) (BOUND_VARIABLE_2166711 tptp.int) (BOUND_VARIABLE_2166712 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2166709) BOUND_VARIABLE_2166711))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2166710) BOUND_VARIABLE_2166712))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15339 BOUND_VARIABLE_2166709) BOUND_VARIABLE_2166710) BOUND_VARIABLE_2166711) BOUND_VARIABLE_2166712))))))) (let ((_let_2087 (forall ((BOUND_VARIABLE_2203884 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2166623 tptp.nat) (BOUND_VARIABLE_2166624 tptp.nat) (BOUND_VARIABLE_2166625 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2166625))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2166625))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15340 BOUND_VARIABLE_2203884) BOUND_VARIABLE_2166623) BOUND_VARIABLE_2166624) BOUND_VARIABLE_2166625) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2203884 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2166623)) (ho_15161 k_15160 BOUND_VARIABLE_2166624))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2088 (forall ((BOUND_VARIABLE_2203952 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2166536 tptp.nat) (BOUND_VARIABLE_2166537 tptp.nat) (BOUND_VARIABLE_2166538 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2166538))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2166538))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15341 BOUND_VARIABLE_2203952) BOUND_VARIABLE_2166536) BOUND_VARIABLE_2166537) BOUND_VARIABLE_2166538) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2203952 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2166536)) (ho_15161 k_15160 BOUND_VARIABLE_2166537))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2089 (forall ((BOUND_VARIABLE_2203968 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2166461 tptp.nat) (BOUND_VARIABLE_2166462 tptp.nat) (BOUND_VARIABLE_2166463 tptp.int) (BOUND_VARIABLE_2166464 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15159 BOUND_VARIABLE_2166464) BOUND_VARIABLE_2166463)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15162 BOUND_VARIABLE_2203968) BOUND_VARIABLE_2166461) BOUND_VARIABLE_2166462))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_15342 BOUND_VARIABLE_2203968) BOUND_VARIABLE_2166461) BOUND_VARIABLE_2166462) BOUND_VARIABLE_2166463) BOUND_VARIABLE_2166464))))) (let ((_let_2090 (forall ((BOUND_VARIABLE_2166432 tptp.int) (BOUND_VARIABLE_2166433 tptp.int) (BOUND_VARIABLE_2166434 tptp.int) (BOUND_VARIABLE_2166435 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2166432) BOUND_VARIABLE_2166434))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2166433) BOUND_VARIABLE_2166435))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15346 BOUND_VARIABLE_2166432) BOUND_VARIABLE_2166433) BOUND_VARIABLE_2166434) BOUND_VARIABLE_2166435))))))) (let ((_let_2091 (forall ((BOUND_VARIABLE_2166335 tptp.nat) (BOUND_VARIABLE_2204076 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2166337 tptp.nat) (BOUND_VARIABLE_2166338 tptp.nat) (BOUND_VARIABLE_2166339 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2166339))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2166339))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2166337)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15347 BOUND_VARIABLE_2166335) BOUND_VARIABLE_2204076) BOUND_VARIABLE_2166337) BOUND_VARIABLE_2166338) BOUND_VARIABLE_2166339) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2204076 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166335))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2204076 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166338))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2092 (forall ((BOUND_VARIABLE_2166238 tptp.nat) (BOUND_VARIABLE_2204153 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2166240 tptp.nat) (BOUND_VARIABLE_2166241 tptp.nat) (BOUND_VARIABLE_2166242 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2166242))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2166242))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2166240)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15348 BOUND_VARIABLE_2166238) BOUND_VARIABLE_2204153) BOUND_VARIABLE_2166240) BOUND_VARIABLE_2166241) BOUND_VARIABLE_2166242) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2204153 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166238))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2204153 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166241))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2093 (forall ((BOUND_VARIABLE_2166146 tptp.nat) (BOUND_VARIABLE_2204178 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2166148 tptp.nat) (BOUND_VARIABLE_2166149 tptp.nat) (BOUND_VARIABLE_2166150 tptp.int) (BOUND_VARIABLE_2166151 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15166 BOUND_VARIABLE_2166151) BOUND_VARIABLE_2166150)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15167 BOUND_VARIABLE_2166146) BOUND_VARIABLE_2204178) BOUND_VARIABLE_2166148) BOUND_VARIABLE_2166149))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15349 BOUND_VARIABLE_2166146) BOUND_VARIABLE_2204178) BOUND_VARIABLE_2166148) BOUND_VARIABLE_2166149) BOUND_VARIABLE_2166150) BOUND_VARIABLE_2166151))))) (let ((_let_2094 (forall ((BOUND_VARIABLE_2166118 tptp.int) (BOUND_VARIABLE_2166119 tptp.int) (BOUND_VARIABLE_2166120 tptp.int) (BOUND_VARIABLE_2166121 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2166118) BOUND_VARIABLE_2166120))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2166119) BOUND_VARIABLE_2166121))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15351 BOUND_VARIABLE_2166118) BOUND_VARIABLE_2166119) BOUND_VARIABLE_2166120) BOUND_VARIABLE_2166121))))))) (let ((_let_2095 (forall ((BOUND_VARIABLE_2166021 tptp.nat) (BOUND_VARIABLE_2204283 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2166023 tptp.nat) (BOUND_VARIABLE_2166024 tptp.nat) (BOUND_VARIABLE_2166025 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2166025))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2166025))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2166023)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15352 BOUND_VARIABLE_2166021) BOUND_VARIABLE_2204283) BOUND_VARIABLE_2166023) BOUND_VARIABLE_2166024) BOUND_VARIABLE_2166025) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2204283 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166021))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2204283 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2166024))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2096 (forall ((BOUND_VARIABLE_2165924 tptp.nat) (BOUND_VARIABLE_2204323 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2165926 tptp.nat) (BOUND_VARIABLE_2165927 tptp.nat) (BOUND_VARIABLE_2165928 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2165928))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2165928))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2165926)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15353 BOUND_VARIABLE_2165924) BOUND_VARIABLE_2204323) BOUND_VARIABLE_2165926) BOUND_VARIABLE_2165927) BOUND_VARIABLE_2165928) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2204323 (ho_15118 k_15117 (ho_15079 _let_11 (ho_15161 k_15160 BOUND_VARIABLE_2165924))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2204323 (ho_15118 k_15117 (ho_15079 _let_11 (ho_15161 k_15160 BOUND_VARIABLE_2165927)))))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2097 (forall ((BOUND_VARIABLE_2165832 tptp.nat) (BOUND_VARIABLE_2204385 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2165834 tptp.nat) (BOUND_VARIABLE_2165835 tptp.nat) (BOUND_VARIABLE_2165836 tptp.int) (BOUND_VARIABLE_2165837 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15169 BOUND_VARIABLE_2165837) BOUND_VARIABLE_2165836)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15170 BOUND_VARIABLE_2165832) BOUND_VARIABLE_2204385) BOUND_VARIABLE_2165834) BOUND_VARIABLE_2165835))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15354 BOUND_VARIABLE_2165832) BOUND_VARIABLE_2204385) BOUND_VARIABLE_2165834) BOUND_VARIABLE_2165835) BOUND_VARIABLE_2165836) BOUND_VARIABLE_2165837))))) (let ((_let_2098 (forall ((BOUND_VARIABLE_2165804 tptp.int) (BOUND_VARIABLE_2165805 tptp.int) (BOUND_VARIABLE_2165806 tptp.int) (BOUND_VARIABLE_2165807 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2165804) BOUND_VARIABLE_2165806))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2165805) BOUND_VARIABLE_2165807))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15355 BOUND_VARIABLE_2165804) BOUND_VARIABLE_2165805) BOUND_VARIABLE_2165806) BOUND_VARIABLE_2165807))))))) (let ((_let_2099 (forall ((BOUND_VARIABLE_2204486 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2165713 tptp.nat) (BOUND_VARIABLE_2165714 tptp.nat) (BOUND_VARIABLE_2165715 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2165715))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2165715))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2204486 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2165713)) (ho_15161 k_15160 BOUND_VARIABLE_2165714)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15356 BOUND_VARIABLE_2204486) BOUND_VARIABLE_2165713) BOUND_VARIABLE_2165714) BOUND_VARIABLE_2165715) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2100 (forall ((BOUND_VARIABLE_2204520 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2165621 tptp.nat) (BOUND_VARIABLE_2165622 tptp.nat) (BOUND_VARIABLE_2165623 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2165623))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2165623))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15120 BOUND_VARIABLE_2204520 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2165621)) (ho_15161 k_15160 BOUND_VARIABLE_2165622)))))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15357 BOUND_VARIABLE_2204520) BOUND_VARIABLE_2165621) BOUND_VARIABLE_2165622) BOUND_VARIABLE_2165623) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_11) (ho_15122 k_15121 _let_11)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2101 (forall ((BOUND_VARIABLE_2204576 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2165540 tptp.nat) (BOUND_VARIABLE_2165541 tptp.nat) (BOUND_VARIABLE_2165542 tptp.int) (BOUND_VARIABLE_2165543 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15171 BOUND_VARIABLE_2165543) BOUND_VARIABLE_2165542)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15172 BOUND_VARIABLE_2204576) BOUND_VARIABLE_2165540) BOUND_VARIABLE_2165541))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_15358 BOUND_VARIABLE_2204576) BOUND_VARIABLE_2165540) BOUND_VARIABLE_2165541) BOUND_VARIABLE_2165542) BOUND_VARIABLE_2165543))))) (let ((_let_2102 (forall ((BOUND_VARIABLE_2165511 tptp.int) (BOUND_VARIABLE_2165512 tptp.int) (BOUND_VARIABLE_2165513 tptp.int) (BOUND_VARIABLE_2165514 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2165511) BOUND_VARIABLE_2165513))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2165512) BOUND_VARIABLE_2165514))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15359 BOUND_VARIABLE_2165511) BOUND_VARIABLE_2165512) BOUND_VARIABLE_2165513) BOUND_VARIABLE_2165514))))))) (let ((_let_2103 (forall ((BOUND_VARIABLE_2204674 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2165425 tptp.nat) (BOUND_VARIABLE_2165426 tptp.nat) (BOUND_VARIABLE_2165427 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2165427))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2165427))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15360 BOUND_VARIABLE_2204674) BOUND_VARIABLE_2165425) BOUND_VARIABLE_2165426) BOUND_VARIABLE_2165427) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2204674 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2165425)) (ho_15161 k_15160 BOUND_VARIABLE_2165426))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2104 (forall ((BOUND_VARIABLE_2204742 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2165338 tptp.nat) (BOUND_VARIABLE_2165339 tptp.nat) (BOUND_VARIABLE_2165340 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2165340))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2165340))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15361 BOUND_VARIABLE_2204742) BOUND_VARIABLE_2165338) BOUND_VARIABLE_2165339) BOUND_VARIABLE_2165340) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2204742 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2165338)) (ho_15161 k_15160 BOUND_VARIABLE_2165339))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2105 (forall ((BOUND_VARIABLE_2204758 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2165263 tptp.nat) (BOUND_VARIABLE_2165264 tptp.nat) (BOUND_VARIABLE_2165265 tptp.int) (BOUND_VARIABLE_2165266 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15173 BOUND_VARIABLE_2165266) BOUND_VARIABLE_2165265)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15174 BOUND_VARIABLE_2204758) BOUND_VARIABLE_2165263) BOUND_VARIABLE_2165264))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_15362 BOUND_VARIABLE_2204758) BOUND_VARIABLE_2165263) BOUND_VARIABLE_2165264) BOUND_VARIABLE_2165265) BOUND_VARIABLE_2165266))))) (let ((_let_2106 (forall ((BOUND_VARIABLE_2165234 tptp.int) (BOUND_VARIABLE_2165235 tptp.int) (BOUND_VARIABLE_2165236 tptp.int) (BOUND_VARIABLE_2165237 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2165234) BOUND_VARIABLE_2165236))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2165235) BOUND_VARIABLE_2165237))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15363 BOUND_VARIABLE_2165234) BOUND_VARIABLE_2165235) BOUND_VARIABLE_2165236) BOUND_VARIABLE_2165237))))))) (let ((_let_2107 (forall ((BOUND_VARIABLE_2204856 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2165148 tptp.nat) (BOUND_VARIABLE_2165149 tptp.nat) (BOUND_VARIABLE_2165150 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2165150))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2165150))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15364 BOUND_VARIABLE_2204856) BOUND_VARIABLE_2165148) BOUND_VARIABLE_2165149) BOUND_VARIABLE_2165150) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2204856 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2165148)) (ho_15161 k_15160 BOUND_VARIABLE_2165149))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2108 (forall ((BOUND_VARIABLE_2204924 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2165061 tptp.nat) (BOUND_VARIABLE_2165062 tptp.nat) (BOUND_VARIABLE_2165063 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2165063))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2165063))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15365 BOUND_VARIABLE_2204924) BOUND_VARIABLE_2165061) BOUND_VARIABLE_2165062) BOUND_VARIABLE_2165063) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2204924 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2165061)) (ho_15161 k_15160 BOUND_VARIABLE_2165062))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2109 (forall ((BOUND_VARIABLE_2204940 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2164986 tptp.nat) (BOUND_VARIABLE_2164987 tptp.nat) (BOUND_VARIABLE_2164988 tptp.int) (BOUND_VARIABLE_2164989 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15175 BOUND_VARIABLE_2164989) BOUND_VARIABLE_2164988)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15176 BOUND_VARIABLE_2204940) BOUND_VARIABLE_2164986) BOUND_VARIABLE_2164987))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_15366 BOUND_VARIABLE_2204940) BOUND_VARIABLE_2164986) BOUND_VARIABLE_2164987) BOUND_VARIABLE_2164988) BOUND_VARIABLE_2164989))))) (let ((_let_2110 (forall ((BOUND_VARIABLE_2164957 tptp.int) (BOUND_VARIABLE_2164958 tptp.int) (BOUND_VARIABLE_2164959 tptp.int) (BOUND_VARIABLE_2164960 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2164957) BOUND_VARIABLE_2164959))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2164958) BOUND_VARIABLE_2164960))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15367 BOUND_VARIABLE_2164957) BOUND_VARIABLE_2164958) BOUND_VARIABLE_2164959) BOUND_VARIABLE_2164960))))))) (let ((_let_2111 (forall ((BOUND_VARIABLE_2164860 tptp.nat) (BOUND_VARIABLE_2205038 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2164862 tptp.nat) (BOUND_VARIABLE_2164863 tptp.nat) (BOUND_VARIABLE_2164864 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2164864))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2164864))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2164862)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15368 BOUND_VARIABLE_2164860) BOUND_VARIABLE_2205038) BOUND_VARIABLE_2164862) BOUND_VARIABLE_2164863) BOUND_VARIABLE_2164864) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2205038 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2164860))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2205038 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2164863))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2112 (forall ((BOUND_VARIABLE_2164763 tptp.nat) (BOUND_VARIABLE_2205115 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2164765 tptp.nat) (BOUND_VARIABLE_2164766 tptp.nat) (BOUND_VARIABLE_2164767 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2164767))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2164767))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2164765)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15369 BOUND_VARIABLE_2164763) BOUND_VARIABLE_2205115) BOUND_VARIABLE_2164765) BOUND_VARIABLE_2164766) BOUND_VARIABLE_2164767) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2205115 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2164763))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2205115 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2164766))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2113 (forall ((BOUND_VARIABLE_2164671 tptp.nat) (BOUND_VARIABLE_2205140 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2164673 tptp.nat) (BOUND_VARIABLE_2164674 tptp.nat) (BOUND_VARIABLE_2164675 tptp.int) (BOUND_VARIABLE_2164676 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15177 BOUND_VARIABLE_2164676) BOUND_VARIABLE_2164675)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15178 BOUND_VARIABLE_2164671) BOUND_VARIABLE_2205140) BOUND_VARIABLE_2164673) BOUND_VARIABLE_2164674))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15370 BOUND_VARIABLE_2164671) BOUND_VARIABLE_2205140) BOUND_VARIABLE_2164673) BOUND_VARIABLE_2164674) BOUND_VARIABLE_2164675) BOUND_VARIABLE_2164676))))) (let ((_let_2114 (forall ((BOUND_VARIABLE_2164643 tptp.int) (BOUND_VARIABLE_2164644 tptp.int) (BOUND_VARIABLE_2164645 tptp.int) (BOUND_VARIABLE_2164646 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2164643) BOUND_VARIABLE_2164645))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2164644) BOUND_VARIABLE_2164646))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15371 BOUND_VARIABLE_2164643) BOUND_VARIABLE_2164644) BOUND_VARIABLE_2164645) BOUND_VARIABLE_2164646))))))) (let ((_let_2115 (forall ((BOUND_VARIABLE_2164546 tptp.nat) (BOUND_VARIABLE_2205241 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2164548 tptp.nat) (BOUND_VARIABLE_2164549 tptp.nat) (BOUND_VARIABLE_2164550 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2164550))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2164550))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2164548)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15372 BOUND_VARIABLE_2164546) BOUND_VARIABLE_2205241) BOUND_VARIABLE_2164548) BOUND_VARIABLE_2164549) BOUND_VARIABLE_2164550) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2205241 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2164546))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2205241 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2164549))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2116 (forall ((BOUND_VARIABLE_2164449 tptp.nat) (BOUND_VARIABLE_2205318 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2164451 tptp.nat) (BOUND_VARIABLE_2164452 tptp.nat) (BOUND_VARIABLE_2164453 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2164453))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2164453))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2164451)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15373 BOUND_VARIABLE_2164449) BOUND_VARIABLE_2205318) BOUND_VARIABLE_2164451) BOUND_VARIABLE_2164452) BOUND_VARIABLE_2164453) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2205318 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2164449))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2205318 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2164452))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2117 (forall ((BOUND_VARIABLE_2164357 tptp.nat) (BOUND_VARIABLE_2205343 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2164359 tptp.nat) (BOUND_VARIABLE_2164360 tptp.nat) (BOUND_VARIABLE_2164361 tptp.int) (BOUND_VARIABLE_2164362 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15179 BOUND_VARIABLE_2164362) BOUND_VARIABLE_2164361)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15180 BOUND_VARIABLE_2164357) BOUND_VARIABLE_2205343) BOUND_VARIABLE_2164359) BOUND_VARIABLE_2164360))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15374 BOUND_VARIABLE_2164357) BOUND_VARIABLE_2205343) BOUND_VARIABLE_2164359) BOUND_VARIABLE_2164360) BOUND_VARIABLE_2164361) BOUND_VARIABLE_2164362))))) (let ((_let_2118 (forall ((BOUND_VARIABLE_2164329 tptp.int) (BOUND_VARIABLE_2164330 tptp.int) (BOUND_VARIABLE_2164331 tptp.int) (BOUND_VARIABLE_2164332 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2164329) BOUND_VARIABLE_2164331))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2164330) BOUND_VARIABLE_2164332))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15375 BOUND_VARIABLE_2164329) BOUND_VARIABLE_2164330) BOUND_VARIABLE_2164331) BOUND_VARIABLE_2164332))))))) (let ((_let_2119 (forall ((BOUND_VARIABLE_2205447 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2205444 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2164237 tptp.nat) (BOUND_VARIABLE_2164238 tptp.nat) (BOUND_VARIABLE_2164239 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2164239))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2164239))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2164237)) (ho_15161 k_15160 BOUND_VARIABLE_2164238))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15376 BOUND_VARIABLE_2205447) BOUND_VARIABLE_2205444) BOUND_VARIABLE_2164237) BOUND_VARIABLE_2164238) BOUND_VARIABLE_2164239) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2205447 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2205444 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2120 (forall ((BOUND_VARIABLE_2205522 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2205519 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2164143 tptp.nat) (BOUND_VARIABLE_2164144 tptp.nat) (BOUND_VARIABLE_2164145 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2164145))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2164145))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2164143)) (ho_15161 k_15160 BOUND_VARIABLE_2164144))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15377 BOUND_VARIABLE_2205522) BOUND_VARIABLE_2205519) BOUND_VARIABLE_2164143) BOUND_VARIABLE_2164144) BOUND_VARIABLE_2164145) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2205522 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2205519 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2121 (forall ((BOUND_VARIABLE_2205543 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2205542 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2164057 tptp.nat) (BOUND_VARIABLE_2164058 tptp.nat) (BOUND_VARIABLE_2164059 tptp.int) (BOUND_VARIABLE_2164060 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15181 BOUND_VARIABLE_2164060) BOUND_VARIABLE_2164059)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15182 BOUND_VARIABLE_2205543) BOUND_VARIABLE_2205542) BOUND_VARIABLE_2164057) BOUND_VARIABLE_2164058))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 k_15378 BOUND_VARIABLE_2205543) BOUND_VARIABLE_2205542) BOUND_VARIABLE_2164057) BOUND_VARIABLE_2164058) BOUND_VARIABLE_2164059) BOUND_VARIABLE_2164060))))) (let ((_let_2122 (forall ((BOUND_VARIABLE_2164027 tptp.int) (BOUND_VARIABLE_2164028 tptp.int) (BOUND_VARIABLE_2164029 tptp.int) (BOUND_VARIABLE_2164030 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2164027) BOUND_VARIABLE_2164029))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2164028) BOUND_VARIABLE_2164030))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15380 BOUND_VARIABLE_2164027) BOUND_VARIABLE_2164028) BOUND_VARIABLE_2164029) BOUND_VARIABLE_2164030))))))) (let ((_let_2123 (forall ((BOUND_VARIABLE_2163930 tptp.nat) (BOUND_VARIABLE_2205648 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2163932 tptp.nat) (BOUND_VARIABLE_2163933 tptp.nat) (BOUND_VARIABLE_2163934 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2163934))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2163934))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2163932)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15381 BOUND_VARIABLE_2163930) BOUND_VARIABLE_2205648) BOUND_VARIABLE_2163932) BOUND_VARIABLE_2163933) BOUND_VARIABLE_2163934) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2205648 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2163930))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2205648 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2163933))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2124 (forall ((BOUND_VARIABLE_2163902 tptp.int) (BOUND_VARIABLE_2163903 tptp.int) (BOUND_VARIABLE_2163904 tptp.int) (BOUND_VARIABLE_2163905 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163902) BOUND_VARIABLE_2163904))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163903) BOUND_VARIABLE_2163905))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15382 BOUND_VARIABLE_2163902) BOUND_VARIABLE_2163903) BOUND_VARIABLE_2163904) BOUND_VARIABLE_2163905))))))) (let ((_let_2125 (forall ((BOUND_VARIABLE_2205748 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2163811 tptp.nat) (BOUND_VARIABLE_2163812 tptp.nat) (BOUND_VARIABLE_2163813 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2163813))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2163813))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2205748 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2163811)) (ho_15161 k_15160 BOUND_VARIABLE_2163812)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15383 BOUND_VARIABLE_2205748) BOUND_VARIABLE_2163811) BOUND_VARIABLE_2163812) BOUND_VARIABLE_2163813) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2126 (forall ((BOUND_VARIABLE_2163782 tptp.int) (BOUND_VARIABLE_2163783 tptp.int) (BOUND_VARIABLE_2163784 tptp.int) (BOUND_VARIABLE_2163785 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163782) BOUND_VARIABLE_2163784))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163783) BOUND_VARIABLE_2163785))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15384 BOUND_VARIABLE_2163782) BOUND_VARIABLE_2163783) BOUND_VARIABLE_2163784) BOUND_VARIABLE_2163785))))))) (let ((_let_2127 (forall ((BOUND_VARIABLE_2163685 tptp.nat) (BOUND_VARIABLE_2205842 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2163687 tptp.nat) (BOUND_VARIABLE_2163688 tptp.nat) (BOUND_VARIABLE_2163689 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2163689))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2163689))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2163687)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15385 BOUND_VARIABLE_2163685) BOUND_VARIABLE_2205842) BOUND_VARIABLE_2163687) BOUND_VARIABLE_2163688) BOUND_VARIABLE_2163689) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2205842 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2163685))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2205842 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2163688))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2128 (forall ((BOUND_VARIABLE_2163657 tptp.int) (BOUND_VARIABLE_2163658 tptp.int) (BOUND_VARIABLE_2163659 tptp.int) (BOUND_VARIABLE_2163660 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163657) BOUND_VARIABLE_2163659))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163658) BOUND_VARIABLE_2163660))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15386 BOUND_VARIABLE_2163657) BOUND_VARIABLE_2163658) BOUND_VARIABLE_2163659) BOUND_VARIABLE_2163660))))))) (let ((_let_2129 (forall ((BOUND_VARIABLE_2163560 tptp.nat) (BOUND_VARIABLE_2205942 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2163562 tptp.nat) (BOUND_VARIABLE_2163563 tptp.nat) (BOUND_VARIABLE_2163564 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2163564))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2163564))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2163562)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15387 BOUND_VARIABLE_2163560) BOUND_VARIABLE_2205942) BOUND_VARIABLE_2163562) BOUND_VARIABLE_2163563) BOUND_VARIABLE_2163564) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2205942 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2163560))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2205942 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2163563))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2130 (forall ((BOUND_VARIABLE_2163532 tptp.int) (BOUND_VARIABLE_2163533 tptp.int) (BOUND_VARIABLE_2163534 tptp.int) (BOUND_VARIABLE_2163535 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163532) BOUND_VARIABLE_2163534))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163533) BOUND_VARIABLE_2163535))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15388 BOUND_VARIABLE_2163532) BOUND_VARIABLE_2163533) BOUND_VARIABLE_2163534) BOUND_VARIABLE_2163535))))))) (let ((_let_2131 (forall ((BOUND_VARIABLE_2206045 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2206042 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2163440 tptp.nat) (BOUND_VARIABLE_2163441 tptp.nat) (BOUND_VARIABLE_2163442 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2163442))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2163442))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2163440)) (ho_15161 k_15160 BOUND_VARIABLE_2163441))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15389 BOUND_VARIABLE_2206045) BOUND_VARIABLE_2206042) BOUND_VARIABLE_2163440) BOUND_VARIABLE_2163441) BOUND_VARIABLE_2163442) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2206045 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2206042 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2132 (forall ((BOUND_VARIABLE_2163410 tptp.int) (BOUND_VARIABLE_2163411 tptp.int) (BOUND_VARIABLE_2163412 tptp.int) (BOUND_VARIABLE_2163413 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163410) BOUND_VARIABLE_2163412))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163411) BOUND_VARIABLE_2163413))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15390 BOUND_VARIABLE_2163410) BOUND_VARIABLE_2163411) BOUND_VARIABLE_2163412) BOUND_VARIABLE_2163413))))))) (let ((_let_2133 (forall ((BOUND_VARIABLE_2163313 tptp.nat) (BOUND_VARIABLE_2206140 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2163315 tptp.nat) (BOUND_VARIABLE_2163316 tptp.nat) (BOUND_VARIABLE_2163317 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2163317))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2163317))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2163315)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15391 BOUND_VARIABLE_2163313) BOUND_VARIABLE_2206140) BOUND_VARIABLE_2163315) BOUND_VARIABLE_2163316) BOUND_VARIABLE_2163317) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2206140 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2163313))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2206140 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2163316))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2134 (forall ((BOUND_VARIABLE_2163285 tptp.int) (BOUND_VARIABLE_2163286 tptp.int) (BOUND_VARIABLE_2163287 tptp.int) (BOUND_VARIABLE_2163288 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163285) BOUND_VARIABLE_2163287))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163286) BOUND_VARIABLE_2163288))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15392 BOUND_VARIABLE_2163285) BOUND_VARIABLE_2163286) BOUND_VARIABLE_2163287) BOUND_VARIABLE_2163288))))))) (let ((_let_2135 (forall ((BOUND_VARIABLE_2206240 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2163194 tptp.nat) (BOUND_VARIABLE_2163195 tptp.nat) (BOUND_VARIABLE_2163196 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2163196))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2163196))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2206240 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2163194)) (ho_15161 k_15160 BOUND_VARIABLE_2163195)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15393 BOUND_VARIABLE_2206240) BOUND_VARIABLE_2163194) BOUND_VARIABLE_2163195) BOUND_VARIABLE_2163196) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2136 (forall ((BOUND_VARIABLE_2163165 tptp.int) (BOUND_VARIABLE_2163166 tptp.int) (BOUND_VARIABLE_2163167 tptp.int) (BOUND_VARIABLE_2163168 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163165) BOUND_VARIABLE_2163167))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163166) BOUND_VARIABLE_2163168))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15394 BOUND_VARIABLE_2163165) BOUND_VARIABLE_2163166) BOUND_VARIABLE_2163167) BOUND_VARIABLE_2163168))))))) (let ((_let_2137 (forall ((BOUND_VARIABLE_2163068 tptp.nat) (BOUND_VARIABLE_2206334 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2163070 tptp.nat) (BOUND_VARIABLE_2163071 tptp.nat) (BOUND_VARIABLE_2163072 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2163072))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2163072))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2163070)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15395 BOUND_VARIABLE_2163068) BOUND_VARIABLE_2206334) BOUND_VARIABLE_2163070) BOUND_VARIABLE_2163071) BOUND_VARIABLE_2163072) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2206334 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2163068))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2206334 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2163071))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2138 (forall ((BOUND_VARIABLE_2163040 tptp.int) (BOUND_VARIABLE_2163041 tptp.int) (BOUND_VARIABLE_2163042 tptp.int) (BOUND_VARIABLE_2163043 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163040) BOUND_VARIABLE_2163042))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2163041) BOUND_VARIABLE_2163043))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15396 BOUND_VARIABLE_2163040) BOUND_VARIABLE_2163041) BOUND_VARIABLE_2163042) BOUND_VARIABLE_2163043))))))) (let ((_let_2139 (forall ((BOUND_VARIABLE_2206434 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2162949 tptp.nat) (BOUND_VARIABLE_2162950 tptp.nat) (BOUND_VARIABLE_2162951 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2162951))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2162951))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2206434 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2162949)) (ho_15161 k_15160 BOUND_VARIABLE_2162950)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15397 BOUND_VARIABLE_2206434) BOUND_VARIABLE_2162949) BOUND_VARIABLE_2162950) BOUND_VARIABLE_2162951) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2140 (forall ((BOUND_VARIABLE_2162920 tptp.int) (BOUND_VARIABLE_2162921 tptp.int) (BOUND_VARIABLE_2162922 tptp.int) (BOUND_VARIABLE_2162923 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162920) BOUND_VARIABLE_2162922))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162921) BOUND_VARIABLE_2162923))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15398 BOUND_VARIABLE_2162920) BOUND_VARIABLE_2162921) BOUND_VARIABLE_2162922) BOUND_VARIABLE_2162923))))))) (let ((_let_2141 (forall ((BOUND_VARIABLE_2162823 tptp.nat) (BOUND_VARIABLE_2206528 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2162825 tptp.nat) (BOUND_VARIABLE_2162826 tptp.nat) (BOUND_VARIABLE_2162827 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2162827))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2162827))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2162825)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15399 BOUND_VARIABLE_2162823) BOUND_VARIABLE_2206528) BOUND_VARIABLE_2162825) BOUND_VARIABLE_2162826) BOUND_VARIABLE_2162827) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2206528 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2162823))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2206528 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2162826))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2142 (forall ((BOUND_VARIABLE_2162795 tptp.int) (BOUND_VARIABLE_2162796 tptp.int) (BOUND_VARIABLE_2162797 tptp.int) (BOUND_VARIABLE_2162798 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162795) BOUND_VARIABLE_2162797))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162796) BOUND_VARIABLE_2162798))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15400 BOUND_VARIABLE_2162795) BOUND_VARIABLE_2162796) BOUND_VARIABLE_2162797) BOUND_VARIABLE_2162798))))))) (let ((_let_2143 (forall ((BOUND_VARIABLE_2206628 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2162704 tptp.nat) (BOUND_VARIABLE_2162705 tptp.nat) (BOUND_VARIABLE_2162706 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2162706))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2162706))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2206628 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2162704)) (ho_15161 k_15160 BOUND_VARIABLE_2162705)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15401 BOUND_VARIABLE_2206628) BOUND_VARIABLE_2162704) BOUND_VARIABLE_2162705) BOUND_VARIABLE_2162706) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2144 (forall ((BOUND_VARIABLE_2162675 tptp.int) (BOUND_VARIABLE_2162676 tptp.int) (BOUND_VARIABLE_2162677 tptp.int) (BOUND_VARIABLE_2162678 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162675) BOUND_VARIABLE_2162677))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162676) BOUND_VARIABLE_2162678))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15402 BOUND_VARIABLE_2162675) BOUND_VARIABLE_2162676) BOUND_VARIABLE_2162677) BOUND_VARIABLE_2162678))))))) (let ((_let_2145 (forall ((BOUND_VARIABLE_2162578 tptp.nat) (BOUND_VARIABLE_2206722 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2162580 tptp.nat) (BOUND_VARIABLE_2162581 tptp.nat) (BOUND_VARIABLE_2162582 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2162582))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2162582))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2162580)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15403 BOUND_VARIABLE_2162578) BOUND_VARIABLE_2206722) BOUND_VARIABLE_2162580) BOUND_VARIABLE_2162581) BOUND_VARIABLE_2162582) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2206722 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2162578))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2206722 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2162581))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2146 (forall ((BOUND_VARIABLE_2162550 tptp.int) (BOUND_VARIABLE_2162551 tptp.int) (BOUND_VARIABLE_2162552 tptp.int) (BOUND_VARIABLE_2162553 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162550) BOUND_VARIABLE_2162552))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162551) BOUND_VARIABLE_2162553))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15404 BOUND_VARIABLE_2162550) BOUND_VARIABLE_2162551) BOUND_VARIABLE_2162552) BOUND_VARIABLE_2162553))))))) (let ((_let_2147 (forall ((BOUND_VARIABLE_2206822 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2162459 tptp.nat) (BOUND_VARIABLE_2162460 tptp.nat) (BOUND_VARIABLE_2162461 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2162461))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2162461))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2206822 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2162459)) (ho_15161 k_15160 BOUND_VARIABLE_2162460)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15405 BOUND_VARIABLE_2206822) BOUND_VARIABLE_2162459) BOUND_VARIABLE_2162460) BOUND_VARIABLE_2162461) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2148 (forall ((BOUND_VARIABLE_2162430 tptp.int) (BOUND_VARIABLE_2162431 tptp.int) (BOUND_VARIABLE_2162432 tptp.int) (BOUND_VARIABLE_2162433 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162430) BOUND_VARIABLE_2162432))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162431) BOUND_VARIABLE_2162433))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15406 BOUND_VARIABLE_2162430) BOUND_VARIABLE_2162431) BOUND_VARIABLE_2162432) BOUND_VARIABLE_2162433))))))) (let ((_let_2149 (forall ((BOUND_VARIABLE_2162333 tptp.nat) (BOUND_VARIABLE_2206916 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2162335 tptp.nat) (BOUND_VARIABLE_2162336 tptp.nat) (BOUND_VARIABLE_2162337 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2162337))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2162337))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2162335)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15407 BOUND_VARIABLE_2162333) BOUND_VARIABLE_2206916) BOUND_VARIABLE_2162335) BOUND_VARIABLE_2162336) BOUND_VARIABLE_2162337) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2206916 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2162333))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2206916 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2162336))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2150 (forall ((BOUND_VARIABLE_2162305 tptp.int) (BOUND_VARIABLE_2162306 tptp.int) (BOUND_VARIABLE_2162307 tptp.int) (BOUND_VARIABLE_2162308 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162305) BOUND_VARIABLE_2162307))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162306) BOUND_VARIABLE_2162308))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15408 BOUND_VARIABLE_2162305) BOUND_VARIABLE_2162306) BOUND_VARIABLE_2162307) BOUND_VARIABLE_2162308))))))) (let ((_let_2151 (forall ((BOUND_VARIABLE_2207016 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2162214 tptp.nat) (BOUND_VARIABLE_2162215 tptp.nat) (BOUND_VARIABLE_2162216 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2162216))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2162216))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2207016 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2162214)) (ho_15161 k_15160 BOUND_VARIABLE_2162215)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15409 BOUND_VARIABLE_2207016) BOUND_VARIABLE_2162214) BOUND_VARIABLE_2162215) BOUND_VARIABLE_2162216) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2152 (forall ((BOUND_VARIABLE_2162185 tptp.int) (BOUND_VARIABLE_2162186 tptp.int) (BOUND_VARIABLE_2162187 tptp.int) (BOUND_VARIABLE_2162188 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162185) BOUND_VARIABLE_2162187))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162186) BOUND_VARIABLE_2162188))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15410 BOUND_VARIABLE_2162185) BOUND_VARIABLE_2162186) BOUND_VARIABLE_2162187) BOUND_VARIABLE_2162188))))))) (let ((_let_2153 (forall ((BOUND_VARIABLE_2162088 tptp.nat) (BOUND_VARIABLE_2207110 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2162090 tptp.nat) (BOUND_VARIABLE_2162091 tptp.nat) (BOUND_VARIABLE_2162092 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2162092))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2162092))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2162090)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15411 BOUND_VARIABLE_2162088) BOUND_VARIABLE_2207110) BOUND_VARIABLE_2162090) BOUND_VARIABLE_2162091) BOUND_VARIABLE_2162092) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2207110 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2162088))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2207110 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2162091))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2154 (forall ((BOUND_VARIABLE_2162060 tptp.int) (BOUND_VARIABLE_2162061 tptp.int) (BOUND_VARIABLE_2162062 tptp.int) (BOUND_VARIABLE_2162063 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162060) BOUND_VARIABLE_2162062))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2162061) BOUND_VARIABLE_2162063))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15412 BOUND_VARIABLE_2162060) BOUND_VARIABLE_2162061) BOUND_VARIABLE_2162062) BOUND_VARIABLE_2162063))))))) (let ((_let_2155 (forall ((BOUND_VARIABLE_2207210 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2161969 tptp.nat) (BOUND_VARIABLE_2161970 tptp.nat) (BOUND_VARIABLE_2161971 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2161971))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2161971))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2207210 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2161969)) (ho_15161 k_15160 BOUND_VARIABLE_2161970)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15413 BOUND_VARIABLE_2207210) BOUND_VARIABLE_2161969) BOUND_VARIABLE_2161970) BOUND_VARIABLE_2161971) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2156 (forall ((BOUND_VARIABLE_2161940 tptp.int) (BOUND_VARIABLE_2161941 tptp.int) (BOUND_VARIABLE_2161942 tptp.int) (BOUND_VARIABLE_2161943 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161940) BOUND_VARIABLE_2161942))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161941) BOUND_VARIABLE_2161943))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15414 BOUND_VARIABLE_2161940) BOUND_VARIABLE_2161941) BOUND_VARIABLE_2161942) BOUND_VARIABLE_2161943))))))) (let ((_let_2157 (forall ((BOUND_VARIABLE_2161912 tptp.int) (BOUND_VARIABLE_2161913 tptp.int) (BOUND_VARIABLE_2161914 tptp.int) (BOUND_VARIABLE_2161915 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161912) BOUND_VARIABLE_2161914))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161913) BOUND_VARIABLE_2161915))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15415 BOUND_VARIABLE_2161912) BOUND_VARIABLE_2161913) BOUND_VARIABLE_2161914) BOUND_VARIABLE_2161915))))))) (let ((_let_2158 (forall ((BOUND_VARIABLE_2161884 tptp.int) (BOUND_VARIABLE_2161885 tptp.int) (BOUND_VARIABLE_2161886 tptp.int) (BOUND_VARIABLE_2161887 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161884) BOUND_VARIABLE_2161886))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161885) BOUND_VARIABLE_2161887))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15416 BOUND_VARIABLE_2161884) BOUND_VARIABLE_2161885) BOUND_VARIABLE_2161886) BOUND_VARIABLE_2161887))))))) (let ((_let_2159 (forall ((BOUND_VARIABLE_2161856 tptp.int) (BOUND_VARIABLE_2161857 tptp.int) (BOUND_VARIABLE_2161858 tptp.int) (BOUND_VARIABLE_2161859 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161856) BOUND_VARIABLE_2161858))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161857) BOUND_VARIABLE_2161859))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15417 BOUND_VARIABLE_2161856) BOUND_VARIABLE_2161857) BOUND_VARIABLE_2161858) BOUND_VARIABLE_2161859))))))) (let ((_let_2160 (forall ((BOUND_VARIABLE_2161828 tptp.int) (BOUND_VARIABLE_2161829 tptp.int) (BOUND_VARIABLE_2161830 tptp.int) (BOUND_VARIABLE_2161831 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161828) BOUND_VARIABLE_2161830))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161829) BOUND_VARIABLE_2161831))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15418 BOUND_VARIABLE_2161828) BOUND_VARIABLE_2161829) BOUND_VARIABLE_2161830) BOUND_VARIABLE_2161831))))))) (let ((_let_2161 (forall ((BOUND_VARIABLE_2161731 tptp.nat) (BOUND_VARIABLE_2207396 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2161733 tptp.nat) (BOUND_VARIABLE_2161734 tptp.nat) (BOUND_VARIABLE_2161735 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2161735))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2161735))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2161733)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15419 BOUND_VARIABLE_2161731) BOUND_VARIABLE_2207396) BOUND_VARIABLE_2161733) BOUND_VARIABLE_2161734) BOUND_VARIABLE_2161735) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2207396 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2161731))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2207396 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2161734))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2162 (forall ((BOUND_VARIABLE_2161703 tptp.int) (BOUND_VARIABLE_2161704 tptp.int) (BOUND_VARIABLE_2161705 tptp.int) (BOUND_VARIABLE_2161706 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161703) BOUND_VARIABLE_2161705))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161704) BOUND_VARIABLE_2161706))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15420 BOUND_VARIABLE_2161703) BOUND_VARIABLE_2161704) BOUND_VARIABLE_2161705) BOUND_VARIABLE_2161706))))))) (let ((_let_2163 (forall ((BOUND_VARIABLE_2207496 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2161612 tptp.nat) (BOUND_VARIABLE_2161613 tptp.nat) (BOUND_VARIABLE_2161614 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2161614))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2161614))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2207496 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2161612)) (ho_15161 k_15160 BOUND_VARIABLE_2161613)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15421 BOUND_VARIABLE_2207496) BOUND_VARIABLE_2161612) BOUND_VARIABLE_2161613) BOUND_VARIABLE_2161614) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2164 (forall ((BOUND_VARIABLE_2161583 tptp.int) (BOUND_VARIABLE_2161584 tptp.int) (BOUND_VARIABLE_2161585 tptp.int) (BOUND_VARIABLE_2161586 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161583) BOUND_VARIABLE_2161585))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161584) BOUND_VARIABLE_2161586))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15422 BOUND_VARIABLE_2161583) BOUND_VARIABLE_2161584) BOUND_VARIABLE_2161585) BOUND_VARIABLE_2161586))))))) (let ((_let_2165 (forall ((BOUND_VARIABLE_2161486 tptp.nat) (BOUND_VARIABLE_2207590 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2161488 tptp.nat) (BOUND_VARIABLE_2161489 tptp.nat) (BOUND_VARIABLE_2161490 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2161490))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2161490))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2161488)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15423 BOUND_VARIABLE_2161486) BOUND_VARIABLE_2207590) BOUND_VARIABLE_2161488) BOUND_VARIABLE_2161489) BOUND_VARIABLE_2161490) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2207590 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2161486))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2207590 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2161489))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2166 (forall ((BOUND_VARIABLE_2161458 tptp.int) (BOUND_VARIABLE_2161459 tptp.int) (BOUND_VARIABLE_2161460 tptp.int) (BOUND_VARIABLE_2161461 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161458) BOUND_VARIABLE_2161460))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161459) BOUND_VARIABLE_2161461))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15424 BOUND_VARIABLE_2161458) BOUND_VARIABLE_2161459) BOUND_VARIABLE_2161460) BOUND_VARIABLE_2161461))))))) (let ((_let_2167 (forall ((BOUND_VARIABLE_2207690 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2161367 tptp.nat) (BOUND_VARIABLE_2161368 tptp.nat) (BOUND_VARIABLE_2161369 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2161369))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2161369))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2207690 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2161367)) (ho_15161 k_15160 BOUND_VARIABLE_2161368)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15425 BOUND_VARIABLE_2207690) BOUND_VARIABLE_2161367) BOUND_VARIABLE_2161368) BOUND_VARIABLE_2161369) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2168 (forall ((BOUND_VARIABLE_2161338 tptp.int) (BOUND_VARIABLE_2161339 tptp.int) (BOUND_VARIABLE_2161340 tptp.int) (BOUND_VARIABLE_2161341 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161338) BOUND_VARIABLE_2161340))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161339) BOUND_VARIABLE_2161341))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15426 BOUND_VARIABLE_2161338) BOUND_VARIABLE_2161339) BOUND_VARIABLE_2161340) BOUND_VARIABLE_2161341))))))) (let ((_let_2169 (forall ((BOUND_VARIABLE_2207784 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2161252 tptp.nat) (BOUND_VARIABLE_2161253 tptp.nat) (BOUND_VARIABLE_2161254 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2161254))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2161254))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15427 BOUND_VARIABLE_2207784) BOUND_VARIABLE_2161252) BOUND_VARIABLE_2161253) BOUND_VARIABLE_2161254) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2207784 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2161252)) (ho_15161 k_15160 BOUND_VARIABLE_2161253))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2170 (forall ((BOUND_VARIABLE_2161223 tptp.int) (BOUND_VARIABLE_2161224 tptp.int) (BOUND_VARIABLE_2161225 tptp.int) (BOUND_VARIABLE_2161226 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161223) BOUND_VARIABLE_2161225))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161224) BOUND_VARIABLE_2161226))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15428 BOUND_VARIABLE_2161223) BOUND_VARIABLE_2161224) BOUND_VARIABLE_2161225) BOUND_VARIABLE_2161226))))))) (let ((_let_2171 (forall ((BOUND_VARIABLE_2161126 tptp.nat) (BOUND_VARIABLE_2207875 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2161128 tptp.nat) (BOUND_VARIABLE_2161129 tptp.nat) (BOUND_VARIABLE_2161130 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2161130))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2161130))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2161128)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15429 BOUND_VARIABLE_2161126) BOUND_VARIABLE_2207875) BOUND_VARIABLE_2161128) BOUND_VARIABLE_2161129) BOUND_VARIABLE_2161130) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2207875 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2161126))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2207875 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2161129))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2172 (forall ((BOUND_VARIABLE_2161098 tptp.int) (BOUND_VARIABLE_2161099 tptp.int) (BOUND_VARIABLE_2161100 tptp.int) (BOUND_VARIABLE_2161101 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161098) BOUND_VARIABLE_2161100))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2161099) BOUND_VARIABLE_2161101))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15430 BOUND_VARIABLE_2161098) BOUND_VARIABLE_2161099) BOUND_VARIABLE_2161100) BOUND_VARIABLE_2161101))))))) (let ((_let_2173 (forall ((BOUND_VARIABLE_2161001 tptp.nat) (BOUND_VARIABLE_2207975 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2161003 tptp.nat) (BOUND_VARIABLE_2161004 tptp.nat) (BOUND_VARIABLE_2161005 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2161005))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2161005))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2161003)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15431 BOUND_VARIABLE_2161001) BOUND_VARIABLE_2207975) BOUND_VARIABLE_2161003) BOUND_VARIABLE_2161004) BOUND_VARIABLE_2161005) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2207975 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2161001))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2207975 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2161004))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2174 (forall ((BOUND_VARIABLE_2160973 tptp.int) (BOUND_VARIABLE_2160974 tptp.int) (BOUND_VARIABLE_2160975 tptp.int) (BOUND_VARIABLE_2160976 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160973) BOUND_VARIABLE_2160975))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160974) BOUND_VARIABLE_2160976))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15432 BOUND_VARIABLE_2160973) BOUND_VARIABLE_2160974) BOUND_VARIABLE_2160975) BOUND_VARIABLE_2160976))))))) (let ((_let_2175 (forall ((BOUND_VARIABLE_2160876 tptp.nat) (BOUND_VARIABLE_2208075 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2160878 tptp.nat) (BOUND_VARIABLE_2160879 tptp.nat) (BOUND_VARIABLE_2160880 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2160880))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2160880))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2160878)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15433 BOUND_VARIABLE_2160876) BOUND_VARIABLE_2208075) BOUND_VARIABLE_2160878) BOUND_VARIABLE_2160879) BOUND_VARIABLE_2160880) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2208075 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160876))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2208075 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160879))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2176 (forall ((BOUND_VARIABLE_2160848 tptp.int) (BOUND_VARIABLE_2160849 tptp.int) (BOUND_VARIABLE_2160850 tptp.int) (BOUND_VARIABLE_2160851 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160848) BOUND_VARIABLE_2160850))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160849) BOUND_VARIABLE_2160851))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15434 BOUND_VARIABLE_2160848) BOUND_VARIABLE_2160849) BOUND_VARIABLE_2160850) BOUND_VARIABLE_2160851))))))) (let ((_let_2177 (forall ((BOUND_VARIABLE_2160751 tptp.nat) (BOUND_VARIABLE_2208175 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2160753 tptp.nat) (BOUND_VARIABLE_2160754 tptp.nat) (BOUND_VARIABLE_2160755 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2160755))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2160755))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2160753)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15435 BOUND_VARIABLE_2160751) BOUND_VARIABLE_2208175) BOUND_VARIABLE_2160753) BOUND_VARIABLE_2160754) BOUND_VARIABLE_2160755) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2208175 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160751))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2208175 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160754))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2178 (forall ((BOUND_VARIABLE_2160723 tptp.int) (BOUND_VARIABLE_2160724 tptp.int) (BOUND_VARIABLE_2160725 tptp.int) (BOUND_VARIABLE_2160726 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160723) BOUND_VARIABLE_2160725))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160724) BOUND_VARIABLE_2160726))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15436 BOUND_VARIABLE_2160723) BOUND_VARIABLE_2160724) BOUND_VARIABLE_2160725) BOUND_VARIABLE_2160726))))))) (let ((_let_2179 (forall ((BOUND_VARIABLE_2208278 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2208275 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2160631 tptp.nat) (BOUND_VARIABLE_2160632 tptp.nat) (BOUND_VARIABLE_2160633 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2160633))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2160633))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2160631)) (ho_15161 k_15160 BOUND_VARIABLE_2160632))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15437 BOUND_VARIABLE_2208278) BOUND_VARIABLE_2208275) BOUND_VARIABLE_2160631) BOUND_VARIABLE_2160632) BOUND_VARIABLE_2160633) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2208278 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2208275 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2180 (forall ((BOUND_VARIABLE_2160601 tptp.int) (BOUND_VARIABLE_2160602 tptp.int) (BOUND_VARIABLE_2160603 tptp.int) (BOUND_VARIABLE_2160604 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160601) BOUND_VARIABLE_2160603))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160602) BOUND_VARIABLE_2160604))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15438 BOUND_VARIABLE_2160601) BOUND_VARIABLE_2160602) BOUND_VARIABLE_2160603) BOUND_VARIABLE_2160604))))))) (let ((_let_2181 (forall ((BOUND_VARIABLE_2160504 tptp.nat) (BOUND_VARIABLE_2208373 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2160506 tptp.nat) (BOUND_VARIABLE_2160507 tptp.nat) (BOUND_VARIABLE_2160508 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2160508))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2160508))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2160506)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15439 BOUND_VARIABLE_2160504) BOUND_VARIABLE_2208373) BOUND_VARIABLE_2160506) BOUND_VARIABLE_2160507) BOUND_VARIABLE_2160508) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2208373 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160504))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2208373 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160507))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2182 (forall ((BOUND_VARIABLE_2160476 tptp.int) (BOUND_VARIABLE_2160477 tptp.int) (BOUND_VARIABLE_2160478 tptp.int) (BOUND_VARIABLE_2160479 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160476) BOUND_VARIABLE_2160478))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160477) BOUND_VARIABLE_2160479))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15440 BOUND_VARIABLE_2160476) BOUND_VARIABLE_2160477) BOUND_VARIABLE_2160478) BOUND_VARIABLE_2160479))))))) (let ((_let_2183 (forall ((BOUND_VARIABLE_2160379 tptp.nat) (BOUND_VARIABLE_2208473 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2160381 tptp.nat) (BOUND_VARIABLE_2160382 tptp.nat) (BOUND_VARIABLE_2160383 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2160383))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2160383))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2160381)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15441 BOUND_VARIABLE_2160379) BOUND_VARIABLE_2208473) BOUND_VARIABLE_2160381) BOUND_VARIABLE_2160382) BOUND_VARIABLE_2160383) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2208473 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160379))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2208473 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160382))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2184 (forall ((BOUND_VARIABLE_2160351 tptp.int) (BOUND_VARIABLE_2160352 tptp.int) (BOUND_VARIABLE_2160353 tptp.int) (BOUND_VARIABLE_2160354 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160351) BOUND_VARIABLE_2160353))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160352) BOUND_VARIABLE_2160354))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15442 BOUND_VARIABLE_2160351) BOUND_VARIABLE_2160352) BOUND_VARIABLE_2160353) BOUND_VARIABLE_2160354))))))) (let ((_let_2185 (forall ((BOUND_VARIABLE_2160254 tptp.nat) (BOUND_VARIABLE_2208573 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2160256 tptp.nat) (BOUND_VARIABLE_2160257 tptp.nat) (BOUND_VARIABLE_2160258 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2160258))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2160258))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2160256)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15443 BOUND_VARIABLE_2160254) BOUND_VARIABLE_2208573) BOUND_VARIABLE_2160256) BOUND_VARIABLE_2160257) BOUND_VARIABLE_2160258) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2208573 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160254))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2208573 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160257))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2186 (forall ((BOUND_VARIABLE_2160226 tptp.int) (BOUND_VARIABLE_2160227 tptp.int) (BOUND_VARIABLE_2160228 tptp.int) (BOUND_VARIABLE_2160229 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160226) BOUND_VARIABLE_2160228))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160227) BOUND_VARIABLE_2160229))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15444 BOUND_VARIABLE_2160226) BOUND_VARIABLE_2160227) BOUND_VARIABLE_2160228) BOUND_VARIABLE_2160229))))))) (let ((_let_2187 (forall ((BOUND_VARIABLE_2160129 tptp.nat) (BOUND_VARIABLE_2208673 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2160131 tptp.nat) (BOUND_VARIABLE_2160132 tptp.nat) (BOUND_VARIABLE_2160133 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2160133))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2160133))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2160131)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15445 BOUND_VARIABLE_2160129) BOUND_VARIABLE_2208673) BOUND_VARIABLE_2160131) BOUND_VARIABLE_2160132) BOUND_VARIABLE_2160133) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2208673 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160129))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2208673 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160132))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2188 (forall ((BOUND_VARIABLE_2160101 tptp.int) (BOUND_VARIABLE_2160102 tptp.int) (BOUND_VARIABLE_2160103 tptp.int) (BOUND_VARIABLE_2160104 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160101) BOUND_VARIABLE_2160103))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2160102) BOUND_VARIABLE_2160104))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15446 BOUND_VARIABLE_2160101) BOUND_VARIABLE_2160102) BOUND_VARIABLE_2160103) BOUND_VARIABLE_2160104))))))) (let ((_let_2189 (forall ((BOUND_VARIABLE_2160004 tptp.nat) (BOUND_VARIABLE_2208773 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2160006 tptp.nat) (BOUND_VARIABLE_2160007 tptp.nat) (BOUND_VARIABLE_2160008 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2160008))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2160008))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2160006)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15447 BOUND_VARIABLE_2160004) BOUND_VARIABLE_2208773) BOUND_VARIABLE_2160006) BOUND_VARIABLE_2160007) BOUND_VARIABLE_2160008) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2208773 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160004))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2208773 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2160007))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2190 (forall ((BOUND_VARIABLE_2159976 tptp.int) (BOUND_VARIABLE_2159977 tptp.int) (BOUND_VARIABLE_2159978 tptp.int) (BOUND_VARIABLE_2159979 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159976) BOUND_VARIABLE_2159978))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159977) BOUND_VARIABLE_2159979))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15448 BOUND_VARIABLE_2159976) BOUND_VARIABLE_2159977) BOUND_VARIABLE_2159978) BOUND_VARIABLE_2159979))))))) (let ((_let_2191 (forall ((BOUND_VARIABLE_2159879 tptp.nat) (BOUND_VARIABLE_2208873 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2159881 tptp.nat) (BOUND_VARIABLE_2159882 tptp.nat) (BOUND_VARIABLE_2159883 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2159883))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2159883))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2159881)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15449 BOUND_VARIABLE_2159879) BOUND_VARIABLE_2208873) BOUND_VARIABLE_2159881) BOUND_VARIABLE_2159882) BOUND_VARIABLE_2159883) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2208873 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159879))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2208873 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159882))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2192 (forall ((BOUND_VARIABLE_2159851 tptp.int) (BOUND_VARIABLE_2159852 tptp.int) (BOUND_VARIABLE_2159853 tptp.int) (BOUND_VARIABLE_2159854 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159851) BOUND_VARIABLE_2159853))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159852) BOUND_VARIABLE_2159854))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15450 BOUND_VARIABLE_2159851) BOUND_VARIABLE_2159852) BOUND_VARIABLE_2159853) BOUND_VARIABLE_2159854))))))) (let ((_let_2193 (forall ((BOUND_VARIABLE_2159754 tptp.nat) (BOUND_VARIABLE_2208973 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2159756 tptp.nat) (BOUND_VARIABLE_2159757 tptp.nat) (BOUND_VARIABLE_2159758 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2159758))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2159758))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2159756)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15451 BOUND_VARIABLE_2159754) BOUND_VARIABLE_2208973) BOUND_VARIABLE_2159756) BOUND_VARIABLE_2159757) BOUND_VARIABLE_2159758) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2208973 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159754))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2208973 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159757))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2194 (forall ((BOUND_VARIABLE_2159726 tptp.int) (BOUND_VARIABLE_2159727 tptp.int) (BOUND_VARIABLE_2159728 tptp.int) (BOUND_VARIABLE_2159729 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159726) BOUND_VARIABLE_2159728))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159727) BOUND_VARIABLE_2159729))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15452 BOUND_VARIABLE_2159726) BOUND_VARIABLE_2159727) BOUND_VARIABLE_2159728) BOUND_VARIABLE_2159729))))))) (let ((_let_2195 (forall ((BOUND_VARIABLE_2159629 tptp.nat) (BOUND_VARIABLE_2209073 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2159631 tptp.nat) (BOUND_VARIABLE_2159632 tptp.nat) (BOUND_VARIABLE_2159633 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2159633))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2159633))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2159631)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15453 BOUND_VARIABLE_2159629) BOUND_VARIABLE_2209073) BOUND_VARIABLE_2159631) BOUND_VARIABLE_2159632) BOUND_VARIABLE_2159633) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2209073 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159629))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2209073 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159632))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2196 (forall ((BOUND_VARIABLE_2159601 tptp.int) (BOUND_VARIABLE_2159602 tptp.int) (BOUND_VARIABLE_2159603 tptp.int) (BOUND_VARIABLE_2159604 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159601) BOUND_VARIABLE_2159603))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159602) BOUND_VARIABLE_2159604))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15454 BOUND_VARIABLE_2159601) BOUND_VARIABLE_2159602) BOUND_VARIABLE_2159603) BOUND_VARIABLE_2159604))))))) (let ((_let_2197 (forall ((BOUND_VARIABLE_2159504 tptp.nat) (BOUND_VARIABLE_2209173 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2159506 tptp.nat) (BOUND_VARIABLE_2159507 tptp.nat) (BOUND_VARIABLE_2159508 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2159508))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2159508))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2159506)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15455 BOUND_VARIABLE_2159504) BOUND_VARIABLE_2209173) BOUND_VARIABLE_2159506) BOUND_VARIABLE_2159507) BOUND_VARIABLE_2159508) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2209173 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159504))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2209173 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159507))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2198 (forall ((BOUND_VARIABLE_2159476 tptp.int) (BOUND_VARIABLE_2159477 tptp.int) (BOUND_VARIABLE_2159478 tptp.int) (BOUND_VARIABLE_2159479 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159476) BOUND_VARIABLE_2159478))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159477) BOUND_VARIABLE_2159479))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15456 BOUND_VARIABLE_2159476) BOUND_VARIABLE_2159477) BOUND_VARIABLE_2159478) BOUND_VARIABLE_2159479))))))) (let ((_let_2199 (forall ((BOUND_VARIABLE_2209273 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2159390 tptp.nat) (BOUND_VARIABLE_2159391 tptp.nat) (BOUND_VARIABLE_2159392 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2159392))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2159392))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15457 BOUND_VARIABLE_2209273) BOUND_VARIABLE_2159390) BOUND_VARIABLE_2159391) BOUND_VARIABLE_2159392) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2209273 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2159390)) (ho_15161 k_15160 BOUND_VARIABLE_2159391))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2200 (forall ((BOUND_VARIABLE_2159361 tptp.int) (BOUND_VARIABLE_2159362 tptp.int) (BOUND_VARIABLE_2159363 tptp.int) (BOUND_VARIABLE_2159364 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159361) BOUND_VARIABLE_2159363))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159362) BOUND_VARIABLE_2159364))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15458 BOUND_VARIABLE_2159361) BOUND_VARIABLE_2159362) BOUND_VARIABLE_2159363) BOUND_VARIABLE_2159364))))))) (let ((_let_2201 (forall ((BOUND_VARIABLE_2159264 tptp.nat) (BOUND_VARIABLE_2209364 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2159266 tptp.nat) (BOUND_VARIABLE_2159267 tptp.nat) (BOUND_VARIABLE_2159268 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2159268))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2159268))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2159266)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15459 BOUND_VARIABLE_2159264) BOUND_VARIABLE_2209364) BOUND_VARIABLE_2159266) BOUND_VARIABLE_2159267) BOUND_VARIABLE_2159268) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2209364 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159264))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2209364 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159267))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2202 (forall ((BOUND_VARIABLE_2159236 tptp.int) (BOUND_VARIABLE_2159237 tptp.int) (BOUND_VARIABLE_2159238 tptp.int) (BOUND_VARIABLE_2159239 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159236) BOUND_VARIABLE_2159238))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159237) BOUND_VARIABLE_2159239))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15460 BOUND_VARIABLE_2159236) BOUND_VARIABLE_2159237) BOUND_VARIABLE_2159238) BOUND_VARIABLE_2159239))))))) (let ((_let_2203 (forall ((BOUND_VARIABLE_2159139 tptp.nat) (BOUND_VARIABLE_2209464 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2159141 tptp.nat) (BOUND_VARIABLE_2159142 tptp.nat) (BOUND_VARIABLE_2159143 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2159143))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2159143))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2159141)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15461 BOUND_VARIABLE_2159139) BOUND_VARIABLE_2209464) BOUND_VARIABLE_2159141) BOUND_VARIABLE_2159142) BOUND_VARIABLE_2159143) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2209464 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159139))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2209464 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159142))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2204 (forall ((BOUND_VARIABLE_2159111 tptp.int) (BOUND_VARIABLE_2159112 tptp.int) (BOUND_VARIABLE_2159113 tptp.int) (BOUND_VARIABLE_2159114 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159111) BOUND_VARIABLE_2159113))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2159112) BOUND_VARIABLE_2159114))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15462 BOUND_VARIABLE_2159111) BOUND_VARIABLE_2159112) BOUND_VARIABLE_2159113) BOUND_VARIABLE_2159114))))))) (let ((_let_2205 (forall ((BOUND_VARIABLE_2159014 tptp.nat) (BOUND_VARIABLE_2209564 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2159016 tptp.nat) (BOUND_VARIABLE_2159017 tptp.nat) (BOUND_VARIABLE_2159018 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2159018))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2159018))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2159016)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15463 BOUND_VARIABLE_2159014) BOUND_VARIABLE_2209564) BOUND_VARIABLE_2159016) BOUND_VARIABLE_2159017) BOUND_VARIABLE_2159018) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2209564 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159014))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2209564 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2159017))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2206 (forall ((BOUND_VARIABLE_2158986 tptp.int) (BOUND_VARIABLE_2158987 tptp.int) (BOUND_VARIABLE_2158988 tptp.int) (BOUND_VARIABLE_2158989 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158986) BOUND_VARIABLE_2158988))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158987) BOUND_VARIABLE_2158989))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15464 BOUND_VARIABLE_2158986) BOUND_VARIABLE_2158987) BOUND_VARIABLE_2158988) BOUND_VARIABLE_2158989))))))) (let ((_let_2207 (forall ((BOUND_VARIABLE_2158958 tptp.int) (BOUND_VARIABLE_2158959 tptp.int) (BOUND_VARIABLE_2158960 tptp.int) (BOUND_VARIABLE_2158961 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158958) BOUND_VARIABLE_2158960))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158959) BOUND_VARIABLE_2158961))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15465 BOUND_VARIABLE_2158958) BOUND_VARIABLE_2158959) BOUND_VARIABLE_2158960) BOUND_VARIABLE_2158961))))))) (let ((_let_2208 (forall ((BOUND_VARIABLE_2158861 tptp.nat) (BOUND_VARIABLE_2209687 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2158863 tptp.nat) (BOUND_VARIABLE_2158864 tptp.nat) (BOUND_VARIABLE_2158865 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2158865))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2158865))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2158863)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15466 BOUND_VARIABLE_2158861) BOUND_VARIABLE_2209687) BOUND_VARIABLE_2158863) BOUND_VARIABLE_2158864) BOUND_VARIABLE_2158865) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2209687 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2158861))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2209687 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2158864))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2209 (forall ((BOUND_VARIABLE_2158833 tptp.int) (BOUND_VARIABLE_2158834 tptp.int) (BOUND_VARIABLE_2158835 tptp.int) (BOUND_VARIABLE_2158836 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158833) BOUND_VARIABLE_2158835))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158834) BOUND_VARIABLE_2158836))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15467 BOUND_VARIABLE_2158833) BOUND_VARIABLE_2158834) BOUND_VARIABLE_2158835) BOUND_VARIABLE_2158836))))))) (let ((_let_2210 (forall ((BOUND_VARIABLE_2158736 tptp.nat) (BOUND_VARIABLE_2209787 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2158738 tptp.nat) (BOUND_VARIABLE_2158739 tptp.nat) (BOUND_VARIABLE_2158740 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2158740))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2158740))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2158738)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15468 BOUND_VARIABLE_2158736) BOUND_VARIABLE_2209787) BOUND_VARIABLE_2158738) BOUND_VARIABLE_2158739) BOUND_VARIABLE_2158740) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2209787 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2158736))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2209787 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2158739))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2211 (forall ((BOUND_VARIABLE_2158708 tptp.int) (BOUND_VARIABLE_2158709 tptp.int) (BOUND_VARIABLE_2158710 tptp.int) (BOUND_VARIABLE_2158711 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158708) BOUND_VARIABLE_2158710))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158709) BOUND_VARIABLE_2158711))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15469 BOUND_VARIABLE_2158708) BOUND_VARIABLE_2158709) BOUND_VARIABLE_2158710) BOUND_VARIABLE_2158711))))))) (let ((_let_2212 (forall ((BOUND_VARIABLE_2158680 tptp.int) (BOUND_VARIABLE_2158681 tptp.int) (BOUND_VARIABLE_2158682 tptp.int) (BOUND_VARIABLE_2158683 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158680) BOUND_VARIABLE_2158682))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158681) BOUND_VARIABLE_2158683))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15470 BOUND_VARIABLE_2158680) BOUND_VARIABLE_2158681) BOUND_VARIABLE_2158682) BOUND_VARIABLE_2158683))))))) (let ((_let_2213 (forall ((BOUND_VARIABLE_2209910 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2158594 tptp.nat) (BOUND_VARIABLE_2158595 tptp.nat) (BOUND_VARIABLE_2158596 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2158596))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2158596))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15471 BOUND_VARIABLE_2209910) BOUND_VARIABLE_2158594) BOUND_VARIABLE_2158595) BOUND_VARIABLE_2158596) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2209910 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2158594)) (ho_15161 k_15160 BOUND_VARIABLE_2158595))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2214 (forall ((BOUND_VARIABLE_2158565 tptp.int) (BOUND_VARIABLE_2158566 tptp.int) (BOUND_VARIABLE_2158567 tptp.int) (BOUND_VARIABLE_2158568 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158565) BOUND_VARIABLE_2158567))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158566) BOUND_VARIABLE_2158568))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15472 BOUND_VARIABLE_2158565) BOUND_VARIABLE_2158566) BOUND_VARIABLE_2158567) BOUND_VARIABLE_2158568))))))) (let ((_let_2215 (forall ((BOUND_VARIABLE_2210001 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2158479 tptp.nat) (BOUND_VARIABLE_2158480 tptp.nat) (BOUND_VARIABLE_2158481 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2158481))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2158481))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15473 BOUND_VARIABLE_2210001) BOUND_VARIABLE_2158479) BOUND_VARIABLE_2158480) BOUND_VARIABLE_2158481) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2210001 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2158479)) (ho_15161 k_15160 BOUND_VARIABLE_2158480))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2216 (forall ((BOUND_VARIABLE_2158450 tptp.int) (BOUND_VARIABLE_2158451 tptp.int) (BOUND_VARIABLE_2158452 tptp.int) (BOUND_VARIABLE_2158453 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158450) BOUND_VARIABLE_2158452))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158451) BOUND_VARIABLE_2158453))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15474 BOUND_VARIABLE_2158450) BOUND_VARIABLE_2158451) BOUND_VARIABLE_2158452) BOUND_VARIABLE_2158453))))))) (let ((_let_2217 (forall ((BOUND_VARIABLE_2158353 tptp.nat) (BOUND_VARIABLE_2210092 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2158355 tptp.nat) (BOUND_VARIABLE_2158356 tptp.nat) (BOUND_VARIABLE_2158357 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2158357))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2158357))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2158355)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15475 BOUND_VARIABLE_2158353) BOUND_VARIABLE_2210092) BOUND_VARIABLE_2158355) BOUND_VARIABLE_2158356) BOUND_VARIABLE_2158357) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2210092 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2158353))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2210092 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2158356))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2218 (forall ((BOUND_VARIABLE_2158325 tptp.int) (BOUND_VARIABLE_2158326 tptp.int) (BOUND_VARIABLE_2158327 tptp.int) (BOUND_VARIABLE_2158328 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158325) BOUND_VARIABLE_2158327))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158326) BOUND_VARIABLE_2158328))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15476 BOUND_VARIABLE_2158325) BOUND_VARIABLE_2158326) BOUND_VARIABLE_2158327) BOUND_VARIABLE_2158328))))))) (let ((_let_2219 (forall ((BOUND_VARIABLE_2210192 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2158239 tptp.nat) (BOUND_VARIABLE_2158240 tptp.nat) (BOUND_VARIABLE_2158241 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2158241))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2158241))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15477 BOUND_VARIABLE_2210192) BOUND_VARIABLE_2158239) BOUND_VARIABLE_2158240) BOUND_VARIABLE_2158241) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2210192 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2158239)) (ho_15161 k_15160 BOUND_VARIABLE_2158240))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2220 (forall ((BOUND_VARIABLE_2158210 tptp.int) (BOUND_VARIABLE_2158211 tptp.int) (BOUND_VARIABLE_2158212 tptp.int) (BOUND_VARIABLE_2158213 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158210) BOUND_VARIABLE_2158212))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158211) BOUND_VARIABLE_2158213))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15478 BOUND_VARIABLE_2158210) BOUND_VARIABLE_2158211) BOUND_VARIABLE_2158212) BOUND_VARIABLE_2158213))))))) (let ((_let_2221 (forall ((BOUND_VARIABLE_2158113 tptp.nat) (BOUND_VARIABLE_2210283 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2158115 tptp.nat) (BOUND_VARIABLE_2158116 tptp.nat) (BOUND_VARIABLE_2158117 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2158117))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2158117))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2158115)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15479 BOUND_VARIABLE_2158113) BOUND_VARIABLE_2210283) BOUND_VARIABLE_2158115) BOUND_VARIABLE_2158116) BOUND_VARIABLE_2158117) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2210283 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2158113))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2210283 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2158116))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2222 (forall ((BOUND_VARIABLE_2158085 tptp.int) (BOUND_VARIABLE_2158086 tptp.int) (BOUND_VARIABLE_2158087 tptp.int) (BOUND_VARIABLE_2158088 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158085) BOUND_VARIABLE_2158087))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2158086) BOUND_VARIABLE_2158088))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15480 BOUND_VARIABLE_2158085) BOUND_VARIABLE_2158086) BOUND_VARIABLE_2158087) BOUND_VARIABLE_2158088))))))) (let ((_let_2223 (forall ((BOUND_VARIABLE_2157988 tptp.nat) (BOUND_VARIABLE_2210383 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2157990 tptp.nat) (BOUND_VARIABLE_2157991 tptp.nat) (BOUND_VARIABLE_2157992 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2157992))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2157992))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2157990)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15481 BOUND_VARIABLE_2157988) BOUND_VARIABLE_2210383) BOUND_VARIABLE_2157990) BOUND_VARIABLE_2157991) BOUND_VARIABLE_2157992) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2210383 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2157988))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2210383 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2157991))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2224 (forall ((BOUND_VARIABLE_2157960 tptp.int) (BOUND_VARIABLE_2157961 tptp.int) (BOUND_VARIABLE_2157962 tptp.int) (BOUND_VARIABLE_2157963 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157960) BOUND_VARIABLE_2157962))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157961) BOUND_VARIABLE_2157963))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15482 BOUND_VARIABLE_2157960) BOUND_VARIABLE_2157961) BOUND_VARIABLE_2157962) BOUND_VARIABLE_2157963))))))) (let ((_let_2225 (forall ((BOUND_VARIABLE_2210486 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2210483 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2157868 tptp.nat) (BOUND_VARIABLE_2157869 tptp.nat) (BOUND_VARIABLE_2157870 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2157870))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2157870))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2157868)) (ho_15161 k_15160 BOUND_VARIABLE_2157869))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15483 BOUND_VARIABLE_2210486) BOUND_VARIABLE_2210483) BOUND_VARIABLE_2157868) BOUND_VARIABLE_2157869) BOUND_VARIABLE_2157870) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2210486 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2210483 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2226 (forall ((BOUND_VARIABLE_2157838 tptp.int) (BOUND_VARIABLE_2157839 tptp.int) (BOUND_VARIABLE_2157840 tptp.int) (BOUND_VARIABLE_2157841 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157838) BOUND_VARIABLE_2157840))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157839) BOUND_VARIABLE_2157841))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15484 BOUND_VARIABLE_2157838) BOUND_VARIABLE_2157839) BOUND_VARIABLE_2157840) BOUND_VARIABLE_2157841))))))) (let ((_let_2227 (forall ((BOUND_VARIABLE_2210581 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2157752 tptp.nat) (BOUND_VARIABLE_2157753 tptp.nat) (BOUND_VARIABLE_2157754 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2157754))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2157754))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15485 BOUND_VARIABLE_2210581) BOUND_VARIABLE_2157752) BOUND_VARIABLE_2157753) BOUND_VARIABLE_2157754) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2210581 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2157752)) (ho_15161 k_15160 BOUND_VARIABLE_2157753))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2228 (forall ((BOUND_VARIABLE_2157723 tptp.int) (BOUND_VARIABLE_2157724 tptp.int) (BOUND_VARIABLE_2157725 tptp.int) (BOUND_VARIABLE_2157726 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157723) BOUND_VARIABLE_2157725))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157724) BOUND_VARIABLE_2157726))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15486 BOUND_VARIABLE_2157723) BOUND_VARIABLE_2157724) BOUND_VARIABLE_2157725) BOUND_VARIABLE_2157726))))))) (let ((_let_2229 (forall ((BOUND_VARIABLE_2210672 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2157637 tptp.nat) (BOUND_VARIABLE_2157638 tptp.nat) (BOUND_VARIABLE_2157639 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2157639))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2157639))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15487 BOUND_VARIABLE_2210672) BOUND_VARIABLE_2157637) BOUND_VARIABLE_2157638) BOUND_VARIABLE_2157639) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2210672 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2157637)) (ho_15161 k_15160 BOUND_VARIABLE_2157638))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2230 (forall ((BOUND_VARIABLE_2157608 tptp.int) (BOUND_VARIABLE_2157609 tptp.int) (BOUND_VARIABLE_2157610 tptp.int) (BOUND_VARIABLE_2157611 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157608) BOUND_VARIABLE_2157610))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157609) BOUND_VARIABLE_2157611))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15488 BOUND_VARIABLE_2157608) BOUND_VARIABLE_2157609) BOUND_VARIABLE_2157610) BOUND_VARIABLE_2157611))))))) (let ((_let_2231 (forall ((BOUND_VARIABLE_2210767 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2210763 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2157514 tptp.nat) (BOUND_VARIABLE_2157515 tptp.nat) (BOUND_VARIABLE_2157516 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2157516))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2157516))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2157514)) (ho_15161 k_15160 BOUND_VARIABLE_2157515))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15489 BOUND_VARIABLE_2210767) BOUND_VARIABLE_2210763) BOUND_VARIABLE_2157514) BOUND_VARIABLE_2157515) BOUND_VARIABLE_2157516) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2210767 _let_9))) (ho_15122 k_15121 (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2210763 _let_9))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2232 (forall ((BOUND_VARIABLE_2157484 tptp.int) (BOUND_VARIABLE_2157485 tptp.int) (BOUND_VARIABLE_2157486 tptp.int) (BOUND_VARIABLE_2157487 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157484) BOUND_VARIABLE_2157486))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157485) BOUND_VARIABLE_2157487))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15490 BOUND_VARIABLE_2157484) BOUND_VARIABLE_2157485) BOUND_VARIABLE_2157486) BOUND_VARIABLE_2157487))))))) (let ((_let_2233 (forall ((BOUND_VARIABLE_2157387 tptp.nat) (BOUND_VARIABLE_2210863 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2157389 tptp.nat) (BOUND_VARIABLE_2157390 tptp.nat) (BOUND_VARIABLE_2157391 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2157391))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2157391))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2157389)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15491 BOUND_VARIABLE_2157387) BOUND_VARIABLE_2210863) BOUND_VARIABLE_2157389) BOUND_VARIABLE_2157390) BOUND_VARIABLE_2157391) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2210863 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2157387))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2210863 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2157390))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2234 (forall ((BOUND_VARIABLE_2157359 tptp.int) (BOUND_VARIABLE_2157360 tptp.int) (BOUND_VARIABLE_2157361 tptp.int) (BOUND_VARIABLE_2157362 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157359) BOUND_VARIABLE_2157361))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157360) BOUND_VARIABLE_2157362))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15492 BOUND_VARIABLE_2157359) BOUND_VARIABLE_2157360) BOUND_VARIABLE_2157361) BOUND_VARIABLE_2157362))))))) (let ((_let_2235 (forall ((BOUND_VARIABLE_2157331 tptp.int) (BOUND_VARIABLE_2157332 tptp.int) (BOUND_VARIABLE_2157333 tptp.int) (BOUND_VARIABLE_2157334 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157331) BOUND_VARIABLE_2157333))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157332) BOUND_VARIABLE_2157334))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15493 BOUND_VARIABLE_2157331) BOUND_VARIABLE_2157332) BOUND_VARIABLE_2157333) BOUND_VARIABLE_2157334))))))) (let ((_let_2236 (forall ((BOUND_VARIABLE_2210981 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2157251 tptp.nat) (BOUND_VARIABLE_2157252 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2157252))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2157252))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15495 k_15494 BOUND_VARIABLE_2210981) BOUND_VARIABLE_2157251) BOUND_VARIABLE_2157252) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2210981 BOUND_VARIABLE_2157251)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2237 (forall ((BOUND_VARIABLE_2157222 tptp.int) (BOUND_VARIABLE_2157223 tptp.int) (BOUND_VARIABLE_2157224 tptp.int) (BOUND_VARIABLE_2157225 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157222) BOUND_VARIABLE_2157224))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157223) BOUND_VARIABLE_2157225))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15496 BOUND_VARIABLE_2157222) BOUND_VARIABLE_2157223) BOUND_VARIABLE_2157224) BOUND_VARIABLE_2157225))))))) (let ((_let_2238 (forall ((BOUND_VARIABLE_2157125 tptp.nat) (BOUND_VARIABLE_2211074 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2157127 tptp.nat) (BOUND_VARIABLE_2157128 tptp.nat) (BOUND_VARIABLE_2157129 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2157129))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2157129))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2157127)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15497 BOUND_VARIABLE_2157125) BOUND_VARIABLE_2211074) BOUND_VARIABLE_2157127) BOUND_VARIABLE_2157128) BOUND_VARIABLE_2157129) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2211074 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2157125))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2211074 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2157128))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2239 (forall ((BOUND_VARIABLE_2157097 tptp.int) (BOUND_VARIABLE_2157098 tptp.int) (BOUND_VARIABLE_2157099 tptp.int) (BOUND_VARIABLE_2157100 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157097) BOUND_VARIABLE_2157099))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2157098) BOUND_VARIABLE_2157100))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15498 BOUND_VARIABLE_2157097) BOUND_VARIABLE_2157098) BOUND_VARIABLE_2157099) BOUND_VARIABLE_2157100))))))) (let ((_let_2240 (forall ((BOUND_VARIABLE_2157000 tptp.nat) (BOUND_VARIABLE_2211174 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2157002 tptp.nat) (BOUND_VARIABLE_2157003 tptp.nat) (BOUND_VARIABLE_2157004 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2157004))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2157004))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2157002)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15499 BOUND_VARIABLE_2157000) BOUND_VARIABLE_2211174) BOUND_VARIABLE_2157002) BOUND_VARIABLE_2157003) BOUND_VARIABLE_2157004) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2211174 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2157000))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2211174 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2157003))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2241 (forall ((BOUND_VARIABLE_2156972 tptp.int) (BOUND_VARIABLE_2156973 tptp.int) (BOUND_VARIABLE_2156974 tptp.int) (BOUND_VARIABLE_2156975 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156972) BOUND_VARIABLE_2156974))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156973) BOUND_VARIABLE_2156975))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15500 BOUND_VARIABLE_2156972) BOUND_VARIABLE_2156973) BOUND_VARIABLE_2156974) BOUND_VARIABLE_2156975))))))) (let ((_let_2242 (forall ((BOUND_VARIABLE_2156863 tptp.nat) (BOUND_VARIABLE_2211276 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2211274 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2156866 tptp.nat) (BOUND_VARIABLE_2156867 tptp.nat) (BOUND_VARIABLE_2156868 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2156868))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2156868))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2156866)))) (let ((_let_10 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156867))))) (let ((_let_11 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_12 (ho_15139 _let_11 k_15153))) (let ((_let_13 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156863))))) (let ((_let_14 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_15501 BOUND_VARIABLE_2156863) BOUND_VARIABLE_2211276) BOUND_VARIABLE_2211274) BOUND_VARIABLE_2156866) BOUND_VARIABLE_2156867) BOUND_VARIABLE_2156868) (and (= (ho_15122 (ho_15125 (ho_15139 _let_11 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_12 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2211276 _let_13)) (ho_15120 BOUND_VARIABLE_2211274 _let_13))) (ho_15122 k_15121 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2211276 _let_10)) (ho_15120 BOUND_VARIABLE_2211274 _let_10))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))))) (let ((_let_2243 (forall ((BOUND_VARIABLE_2156835 tptp.int) (BOUND_VARIABLE_2156836 tptp.int) (BOUND_VARIABLE_2156837 tptp.int) (BOUND_VARIABLE_2156838 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156835) BOUND_VARIABLE_2156837))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156836) BOUND_VARIABLE_2156838))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15503 BOUND_VARIABLE_2156835) BOUND_VARIABLE_2156836) BOUND_VARIABLE_2156837) BOUND_VARIABLE_2156838))))))) (let ((_let_2244 (forall ((BOUND_VARIABLE_2156738 tptp.nat) (BOUND_VARIABLE_2211387 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2156740 tptp.nat) (BOUND_VARIABLE_2156741 tptp.nat) (BOUND_VARIABLE_2156742 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2156742))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2156742))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2156740)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15504 BOUND_VARIABLE_2156738) BOUND_VARIABLE_2211387) BOUND_VARIABLE_2156740) BOUND_VARIABLE_2156741) BOUND_VARIABLE_2156742) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2211387 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156738))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2211387 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156741))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2245 (forall ((BOUND_VARIABLE_2156710 tptp.int) (BOUND_VARIABLE_2156711 tptp.int) (BOUND_VARIABLE_2156712 tptp.int) (BOUND_VARIABLE_2156713 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156710) BOUND_VARIABLE_2156712))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156711) BOUND_VARIABLE_2156713))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15505 BOUND_VARIABLE_2156710) BOUND_VARIABLE_2156711) BOUND_VARIABLE_2156712) BOUND_VARIABLE_2156713))))))) (let ((_let_2246 (forall ((BOUND_VARIABLE_2156611 tptp.nat) (BOUND_VARIABLE_2211487 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2156613 tptp.nat) (BOUND_VARIABLE_2156614 tptp.nat) (BOUND_VARIABLE_2156615 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2156615))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2156615))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2156613)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15506 BOUND_VARIABLE_2156611) BOUND_VARIABLE_2211487) BOUND_VARIABLE_2156613) BOUND_VARIABLE_2156614) BOUND_VARIABLE_2156615) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2211487 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156611)))))) (ho_15122 k_15121 (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2211487 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156614)))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2247 (forall ((BOUND_VARIABLE_2156583 tptp.int) (BOUND_VARIABLE_2156584 tptp.int) (BOUND_VARIABLE_2156585 tptp.int) (BOUND_VARIABLE_2156586 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156583) BOUND_VARIABLE_2156585))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156584) BOUND_VARIABLE_2156586))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15507 BOUND_VARIABLE_2156583) BOUND_VARIABLE_2156584) BOUND_VARIABLE_2156585) BOUND_VARIABLE_2156586))))))) (let ((_let_2248 (forall ((BOUND_VARIABLE_2156499 tptp.rat) (BOUND_VARIABLE_2156500 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2156500))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2156500))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 k_15508 BOUND_VARIABLE_2156499) BOUND_VARIABLE_2156500) (and (= (ho_15122 (ho_15125 (ho_15139 _let_9 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2156499) (ho_15122 k_15121 BOUND_VARIABLE_2156499))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2249 (forall ((BOUND_VARIABLE_2156471 tptp.int) (BOUND_VARIABLE_2156472 tptp.int) (BOUND_VARIABLE_2156473 tptp.int) (BOUND_VARIABLE_2156474 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156471) BOUND_VARIABLE_2156473))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156472) BOUND_VARIABLE_2156474))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15509 BOUND_VARIABLE_2156471) BOUND_VARIABLE_2156472) BOUND_VARIABLE_2156473) BOUND_VARIABLE_2156474))))))) (let ((_let_2250 (forall ((BOUND_VARIABLE_2156374 tptp.nat) (BOUND_VARIABLE_2211671 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2156376 tptp.nat) (BOUND_VARIABLE_2156377 tptp.nat) (BOUND_VARIABLE_2156378 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2156378))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2156378))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2156376)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15510 BOUND_VARIABLE_2156374) BOUND_VARIABLE_2211671) BOUND_VARIABLE_2156376) BOUND_VARIABLE_2156377) BOUND_VARIABLE_2156378) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2211671 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156374))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2211671 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156377))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2251 (forall ((BOUND_VARIABLE_2156346 tptp.int) (BOUND_VARIABLE_2156347 tptp.int) (BOUND_VARIABLE_2156348 tptp.int) (BOUND_VARIABLE_2156349 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156346) BOUND_VARIABLE_2156348))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156347) BOUND_VARIABLE_2156349))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15511 BOUND_VARIABLE_2156346) BOUND_VARIABLE_2156347) BOUND_VARIABLE_2156348) BOUND_VARIABLE_2156349))))))) (let ((_let_2252 (forall ((BOUND_VARIABLE_2156249 tptp.nat) (BOUND_VARIABLE_2211771 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2156251 tptp.nat) (BOUND_VARIABLE_2156252 tptp.nat) (BOUND_VARIABLE_2156253 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2156253))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2156253))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2156251)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15512 BOUND_VARIABLE_2156249) BOUND_VARIABLE_2211771) BOUND_VARIABLE_2156251) BOUND_VARIABLE_2156252) BOUND_VARIABLE_2156253) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2211771 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156249))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2211771 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156252))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2253 (forall ((BOUND_VARIABLE_2156221 tptp.int) (BOUND_VARIABLE_2156222 tptp.int) (BOUND_VARIABLE_2156223 tptp.int) (BOUND_VARIABLE_2156224 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156221) BOUND_VARIABLE_2156223))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156222) BOUND_VARIABLE_2156224))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15513 BOUND_VARIABLE_2156221) BOUND_VARIABLE_2156222) BOUND_VARIABLE_2156223) BOUND_VARIABLE_2156224))))))) (let ((_let_2254 (forall ((BOUND_VARIABLE_2156112 tptp.nat) (BOUND_VARIABLE_2211873 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2211871 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2156115 tptp.nat) (BOUND_VARIABLE_2156116 tptp.nat) (BOUND_VARIABLE_2156117 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2156117))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2156117))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2156115)))) (let ((_let_10 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156116))))) (let ((_let_11 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_12 (ho_15139 _let_11 k_15127))) (let ((_let_13 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2156112))))) (let ((_let_14 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_15514 BOUND_VARIABLE_2156112) BOUND_VARIABLE_2211873) BOUND_VARIABLE_2211871) BOUND_VARIABLE_2156115) BOUND_VARIABLE_2156116) BOUND_VARIABLE_2156117) (and (= (ho_15122 (ho_15125 _let_12 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_11 k_15153) (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2211873 _let_13)) (ho_15120 BOUND_VARIABLE_2211871 _let_13))) (ho_15122 k_15121 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2211873 _let_10)) (ho_15120 BOUND_VARIABLE_2211871 _let_10))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))))) (let ((_let_2255 (forall ((BOUND_VARIABLE_2156084 tptp.int) (BOUND_VARIABLE_2156085 tptp.int) (BOUND_VARIABLE_2156086 tptp.int) (BOUND_VARIABLE_2156087 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156084) BOUND_VARIABLE_2156086))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2156085) BOUND_VARIABLE_2156087))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15515 BOUND_VARIABLE_2156084) BOUND_VARIABLE_2156085) BOUND_VARIABLE_2156086) BOUND_VARIABLE_2156087))))))) (let ((_let_2256 (forall ((BOUND_VARIABLE_2155987 tptp.nat) (BOUND_VARIABLE_2211980 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2155989 tptp.nat) (BOUND_VARIABLE_2155990 tptp.nat) (BOUND_VARIABLE_2155991 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2155991))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2155991))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2155989)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15516 BOUND_VARIABLE_2155987) BOUND_VARIABLE_2211980) BOUND_VARIABLE_2155989) BOUND_VARIABLE_2155990) BOUND_VARIABLE_2155991) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2211980 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155987))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2211980 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155990))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2257 (forall ((BOUND_VARIABLE_2155959 tptp.int) (BOUND_VARIABLE_2155960 tptp.int) (BOUND_VARIABLE_2155961 tptp.int) (BOUND_VARIABLE_2155962 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155959) BOUND_VARIABLE_2155961))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155960) BOUND_VARIABLE_2155962))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15517 BOUND_VARIABLE_2155959) BOUND_VARIABLE_2155960) BOUND_VARIABLE_2155961) BOUND_VARIABLE_2155962))))))) (let ((_let_2258 (forall ((BOUND_VARIABLE_2155862 tptp.nat) (BOUND_VARIABLE_2212080 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2155864 tptp.nat) (BOUND_VARIABLE_2155865 tptp.nat) (BOUND_VARIABLE_2155866 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2155866))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2155866))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2155864)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15518 BOUND_VARIABLE_2155862) BOUND_VARIABLE_2212080) BOUND_VARIABLE_2155864) BOUND_VARIABLE_2155865) BOUND_VARIABLE_2155866) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2212080 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155862))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2212080 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155865))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2259 (forall ((BOUND_VARIABLE_2155834 tptp.int) (BOUND_VARIABLE_2155835 tptp.int) (BOUND_VARIABLE_2155836 tptp.int) (BOUND_VARIABLE_2155837 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155834) BOUND_VARIABLE_2155836))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155835) BOUND_VARIABLE_2155837))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15519 BOUND_VARIABLE_2155834) BOUND_VARIABLE_2155835) BOUND_VARIABLE_2155836) BOUND_VARIABLE_2155837))))))) (let ((_let_2260 (forall ((BOUND_VARIABLE_2155723 tptp.nat) (BOUND_VARIABLE_2212183 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2212180 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2155726 tptp.nat) (BOUND_VARIABLE_2155727 tptp.nat) (BOUND_VARIABLE_2155728 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2155728))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2155728))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2155726)))) (let ((_let_10 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155727))))) (let ((_let_11 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_12 (ho_15139 _let_11 k_15153))) (let ((_let_13 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155723))))) (let ((_let_14 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_15520 BOUND_VARIABLE_2155723) BOUND_VARIABLE_2212183) BOUND_VARIABLE_2212180) BOUND_VARIABLE_2155726) BOUND_VARIABLE_2155727) BOUND_VARIABLE_2155728) (and (= (ho_15122 (ho_15125 (ho_15139 _let_11 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_12 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2212183 _let_13)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2212180 _let_13)))) (ho_15122 k_15121 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2212183 _let_10)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2212180 _let_10)))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))))) (let ((_let_2261 (forall ((BOUND_VARIABLE_2155695 tptp.int) (BOUND_VARIABLE_2155696 tptp.int) (BOUND_VARIABLE_2155697 tptp.int) (BOUND_VARIABLE_2155698 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155695) BOUND_VARIABLE_2155697))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155696) BOUND_VARIABLE_2155698))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15521 BOUND_VARIABLE_2155695) BOUND_VARIABLE_2155696) BOUND_VARIABLE_2155697) BOUND_VARIABLE_2155698))))))) (let ((_let_2262 (forall ((BOUND_VARIABLE_2155598 tptp.nat) (BOUND_VARIABLE_2212291 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2155600 tptp.nat) (BOUND_VARIABLE_2155601 tptp.nat) (BOUND_VARIABLE_2155602 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2155602))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2155602))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2155600)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15522 BOUND_VARIABLE_2155598) BOUND_VARIABLE_2212291) BOUND_VARIABLE_2155600) BOUND_VARIABLE_2155601) BOUND_VARIABLE_2155602) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2212291 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155598))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2212291 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155601))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2263 (forall ((BOUND_VARIABLE_2155570 tptp.int) (BOUND_VARIABLE_2155571 tptp.int) (BOUND_VARIABLE_2155572 tptp.int) (BOUND_VARIABLE_2155573 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155570) BOUND_VARIABLE_2155572))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155571) BOUND_VARIABLE_2155573))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15523 BOUND_VARIABLE_2155570) BOUND_VARIABLE_2155571) BOUND_VARIABLE_2155572) BOUND_VARIABLE_2155573))))))) (let ((_let_2264 (forall ((BOUND_VARIABLE_2212391 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2155484 tptp.nat) (BOUND_VARIABLE_2155485 tptp.nat) (BOUND_VARIABLE_2155486 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2155486))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2155486))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15524 BOUND_VARIABLE_2212391) BOUND_VARIABLE_2155484) BOUND_VARIABLE_2155485) BOUND_VARIABLE_2155486) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2212391 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2155484)) (ho_15161 k_15160 BOUND_VARIABLE_2155485))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2265 (forall ((BOUND_VARIABLE_2155455 tptp.int) (BOUND_VARIABLE_2155456 tptp.int) (BOUND_VARIABLE_2155457 tptp.int) (BOUND_VARIABLE_2155458 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155455) BOUND_VARIABLE_2155457))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155456) BOUND_VARIABLE_2155458))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15525 BOUND_VARIABLE_2155455) BOUND_VARIABLE_2155456) BOUND_VARIABLE_2155457) BOUND_VARIABLE_2155458))))))) (let ((_let_2266 (forall ((BOUND_VARIABLE_2155356 tptp.nat) (BOUND_VARIABLE_2212482 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2155358 tptp.nat) (BOUND_VARIABLE_2155359 tptp.nat) (BOUND_VARIABLE_2155360 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2155360))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2155360))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2155358)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15526 BOUND_VARIABLE_2155356) BOUND_VARIABLE_2212482) BOUND_VARIABLE_2155358) BOUND_VARIABLE_2155359) BOUND_VARIABLE_2155360) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2212482 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155356)))))) (ho_15122 k_15121 (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2212482 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155359)))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2267 (forall ((BOUND_VARIABLE_2155328 tptp.int) (BOUND_VARIABLE_2155329 tptp.int) (BOUND_VARIABLE_2155330 tptp.int) (BOUND_VARIABLE_2155331 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155328) BOUND_VARIABLE_2155330))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155329) BOUND_VARIABLE_2155331))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15527 BOUND_VARIABLE_2155328) BOUND_VARIABLE_2155329) BOUND_VARIABLE_2155330) BOUND_VARIABLE_2155331))))))) (let ((_let_2268 (forall ((BOUND_VARIABLE_2155300 tptp.int) (BOUND_VARIABLE_2155301 tptp.int) (BOUND_VARIABLE_2155302 tptp.int) (BOUND_VARIABLE_2155303 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155300) BOUND_VARIABLE_2155302))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155301) BOUND_VARIABLE_2155303))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15528 BOUND_VARIABLE_2155300) BOUND_VARIABLE_2155301) BOUND_VARIABLE_2155302) BOUND_VARIABLE_2155303))))))) (let ((_let_2269 (forall ((BOUND_VARIABLE_2155203 tptp.nat) (BOUND_VARIABLE_2212607 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2155205 tptp.nat) (BOUND_VARIABLE_2155206 tptp.nat) (BOUND_VARIABLE_2155207 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2155207))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2155207))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2155205)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15529 BOUND_VARIABLE_2155203) BOUND_VARIABLE_2212607) BOUND_VARIABLE_2155205) BOUND_VARIABLE_2155206) BOUND_VARIABLE_2155207) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2212607 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155203))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2212607 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155206))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2270 (forall ((BOUND_VARIABLE_2155175 tptp.int) (BOUND_VARIABLE_2155176 tptp.int) (BOUND_VARIABLE_2155177 tptp.int) (BOUND_VARIABLE_2155178 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155175) BOUND_VARIABLE_2155177))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155176) BOUND_VARIABLE_2155178))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15530 BOUND_VARIABLE_2155175) BOUND_VARIABLE_2155176) BOUND_VARIABLE_2155177) BOUND_VARIABLE_2155178))))))) (let ((_let_2271 (forall ((BOUND_VARIABLE_2155147 tptp.int) (BOUND_VARIABLE_2155148 tptp.int) (BOUND_VARIABLE_2155149 tptp.int) (BOUND_VARIABLE_2155150 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155147) BOUND_VARIABLE_2155149))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155148) BOUND_VARIABLE_2155150))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15531 BOUND_VARIABLE_2155147) BOUND_VARIABLE_2155148) BOUND_VARIABLE_2155149) BOUND_VARIABLE_2155150))))))) (let ((_let_2272 (forall ((BOUND_VARIABLE_2155050 tptp.nat) (BOUND_VARIABLE_2212730 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2155052 tptp.nat) (BOUND_VARIABLE_2155053 tptp.nat) (BOUND_VARIABLE_2155054 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2155054))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2155054))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2155052)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15532 BOUND_VARIABLE_2155050) BOUND_VARIABLE_2212730) BOUND_VARIABLE_2155052) BOUND_VARIABLE_2155053) BOUND_VARIABLE_2155054) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2212730 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155050))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2212730 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2155053))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2273 (forall ((BOUND_VARIABLE_2155022 tptp.int) (BOUND_VARIABLE_2155023 tptp.int) (BOUND_VARIABLE_2155024 tptp.int) (BOUND_VARIABLE_2155025 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155022) BOUND_VARIABLE_2155024))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2155023) BOUND_VARIABLE_2155025))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15533 BOUND_VARIABLE_2155022) BOUND_VARIABLE_2155023) BOUND_VARIABLE_2155024) BOUND_VARIABLE_2155025))))))) (let ((_let_2274 (forall ((BOUND_VARIABLE_2154925 tptp.nat) (BOUND_VARIABLE_2212830 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2154927 tptp.nat) (BOUND_VARIABLE_2154928 tptp.nat) (BOUND_VARIABLE_2154929 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2154929))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2154929))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2154927)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15534 BOUND_VARIABLE_2154925) BOUND_VARIABLE_2212830) BOUND_VARIABLE_2154927) BOUND_VARIABLE_2154928) BOUND_VARIABLE_2154929) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2212830 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2154925))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2212830 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2154928))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2275 (forall ((BOUND_VARIABLE_2154828 tptp.nat) (BOUND_VARIABLE_2212907 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2154830 tptp.nat) (BOUND_VARIABLE_2154831 tptp.nat) (BOUND_VARIABLE_2154832 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2154832))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2154832))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2154830)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15535 BOUND_VARIABLE_2154828) BOUND_VARIABLE_2212907) BOUND_VARIABLE_2154830) BOUND_VARIABLE_2154831) BOUND_VARIABLE_2154832) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2212907 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2154828))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2212907 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2154831))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2276 (forall ((BOUND_VARIABLE_2154736 tptp.nat) (BOUND_VARIABLE_2212932 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2154738 tptp.nat) (BOUND_VARIABLE_2154739 tptp.nat) (BOUND_VARIABLE_2154740 tptp.int) (BOUND_VARIABLE_2154741 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15184 BOUND_VARIABLE_2154741) BOUND_VARIABLE_2154740)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15185 BOUND_VARIABLE_2154736) BOUND_VARIABLE_2212932) BOUND_VARIABLE_2154738) BOUND_VARIABLE_2154739))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15536 BOUND_VARIABLE_2154736) BOUND_VARIABLE_2212932) BOUND_VARIABLE_2154738) BOUND_VARIABLE_2154739) BOUND_VARIABLE_2154740) BOUND_VARIABLE_2154741))))) (let ((_let_2277 (forall ((BOUND_VARIABLE_2154708 tptp.int) (BOUND_VARIABLE_2154709 tptp.int) (BOUND_VARIABLE_2154710 tptp.int) (BOUND_VARIABLE_2154711 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2154708) BOUND_VARIABLE_2154710))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2154709) BOUND_VARIABLE_2154711))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15537 BOUND_VARIABLE_2154708) BOUND_VARIABLE_2154709) BOUND_VARIABLE_2154710) BOUND_VARIABLE_2154711))))))) (let ((_let_2278 (forall ((BOUND_VARIABLE_2154680 tptp.int) (BOUND_VARIABLE_2154681 tptp.int) (BOUND_VARIABLE_2154682 tptp.int) (BOUND_VARIABLE_2154683 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2154680) BOUND_VARIABLE_2154682))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2154681) BOUND_VARIABLE_2154683))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15538 BOUND_VARIABLE_2154680) BOUND_VARIABLE_2154681) BOUND_VARIABLE_2154682) BOUND_VARIABLE_2154683))))))) (let ((_let_2279 (forall ((BOUND_VARIABLE_2154583 tptp.nat) (BOUND_VARIABLE_2213056 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2154585 tptp.nat) (BOUND_VARIABLE_2154586 tptp.nat) (BOUND_VARIABLE_2154587 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2154587))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2154587))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2154585)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15539 BOUND_VARIABLE_2154583) BOUND_VARIABLE_2213056) BOUND_VARIABLE_2154585) BOUND_VARIABLE_2154586) BOUND_VARIABLE_2154587) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2213056 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2154583))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2213056 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2154586))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2280 (forall ((BOUND_VARIABLE_2154539 tptp.int) (BOUND_VARIABLE_2154540 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15186 BOUND_VARIABLE_2154540) BOUND_VARIABLE_2154539)) (ho_15260 k_15259 k_15540)) (ho_15108 (ho_15107 k_15541 BOUND_VARIABLE_2154539) BOUND_VARIABLE_2154540))))) (let ((_let_2281 (forall ((BOUND_VARIABLE_2154442 tptp.nat) (BOUND_VARIABLE_2213146 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2154444 tptp.nat) (BOUND_VARIABLE_2154445 tptp.nat) (BOUND_VARIABLE_2154446 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2154446))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2154446))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2154444)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15542 BOUND_VARIABLE_2154442) BOUND_VARIABLE_2213146) BOUND_VARIABLE_2154444) BOUND_VARIABLE_2154445) BOUND_VARIABLE_2154446) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2213146 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2154442))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2213146 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2154445))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2282 (forall ((BOUND_VARIABLE_2154350 tptp.nat) (BOUND_VARIABLE_2213171 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2154352 tptp.nat) (BOUND_VARIABLE_2154353 tptp.nat) (BOUND_VARIABLE_2154354 tptp.int) (BOUND_VARIABLE_2154355 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15187 BOUND_VARIABLE_2154355) BOUND_VARIABLE_2154354)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15188 BOUND_VARIABLE_2154350) BOUND_VARIABLE_2213171) BOUND_VARIABLE_2154352) BOUND_VARIABLE_2154353))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15543 BOUND_VARIABLE_2154350) BOUND_VARIABLE_2213171) BOUND_VARIABLE_2154352) BOUND_VARIABLE_2154353) BOUND_VARIABLE_2154354) BOUND_VARIABLE_2154355))))) (let ((_let_2283 (forall ((BOUND_VARIABLE_2154322 tptp.int) (BOUND_VARIABLE_2154323 tptp.int) (BOUND_VARIABLE_2154324 tptp.int) (BOUND_VARIABLE_2154325 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2154322) BOUND_VARIABLE_2154324))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2154323) BOUND_VARIABLE_2154325))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15544 BOUND_VARIABLE_2154322) BOUND_VARIABLE_2154323) BOUND_VARIABLE_2154324) BOUND_VARIABLE_2154325))))))) (let ((_let_2284 (forall ((BOUND_VARIABLE_2213272 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2154236 tptp.nat) (BOUND_VARIABLE_2154237 tptp.nat) (BOUND_VARIABLE_2154238 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2154238))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2154238))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15545 BOUND_VARIABLE_2213272) BOUND_VARIABLE_2154236) BOUND_VARIABLE_2154237) BOUND_VARIABLE_2154238) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2213272 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2154236)) (ho_15161 k_15160 BOUND_VARIABLE_2154237))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2285 (forall ((BOUND_VARIABLE_2213340 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2154149 tptp.nat) (BOUND_VARIABLE_2154150 tptp.nat) (BOUND_VARIABLE_2154151 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2154151))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2154151))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15546 BOUND_VARIABLE_2213340) BOUND_VARIABLE_2154149) BOUND_VARIABLE_2154150) BOUND_VARIABLE_2154151) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2213340 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2154149)) (ho_15161 k_15160 BOUND_VARIABLE_2154150))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2286 (forall ((BOUND_VARIABLE_2213356 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2154074 tptp.nat) (BOUND_VARIABLE_2154075 tptp.nat) (BOUND_VARIABLE_2154076 tptp.int) (BOUND_VARIABLE_2154077 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15189 BOUND_VARIABLE_2154077) BOUND_VARIABLE_2154076)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15190 BOUND_VARIABLE_2213356) BOUND_VARIABLE_2154074) BOUND_VARIABLE_2154075))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_15547 BOUND_VARIABLE_2213356) BOUND_VARIABLE_2154074) BOUND_VARIABLE_2154075) BOUND_VARIABLE_2154076) BOUND_VARIABLE_2154077))))) (let ((_let_2287 (forall ((BOUND_VARIABLE_2154045 tptp.int) (BOUND_VARIABLE_2154046 tptp.int) (BOUND_VARIABLE_2154047 tptp.int) (BOUND_VARIABLE_2154048 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2154045) BOUND_VARIABLE_2154047))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2154046) BOUND_VARIABLE_2154048))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15548 BOUND_VARIABLE_2154045) BOUND_VARIABLE_2154046) BOUND_VARIABLE_2154047) BOUND_VARIABLE_2154048))))))) (let ((_let_2288 (forall ((BOUND_VARIABLE_2154017 tptp.int) (BOUND_VARIABLE_2154018 tptp.int) (BOUND_VARIABLE_2154019 tptp.int) (BOUND_VARIABLE_2154020 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2154017) BOUND_VARIABLE_2154019))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2154018) BOUND_VARIABLE_2154020))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15549 BOUND_VARIABLE_2154017) BOUND_VARIABLE_2154018) BOUND_VARIABLE_2154019) BOUND_VARIABLE_2154020))))))) (let ((_let_2289 (forall ((BOUND_VARIABLE_2213477 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2153931 tptp.nat) (BOUND_VARIABLE_2153932 tptp.nat) (BOUND_VARIABLE_2153933 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2153933))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2153933))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15550 BOUND_VARIABLE_2213477) BOUND_VARIABLE_2153931) BOUND_VARIABLE_2153932) BOUND_VARIABLE_2153933) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2213477 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2153931)) (ho_15161 k_15160 BOUND_VARIABLE_2153932))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2290 (forall ((BOUND_VARIABLE_2153886 tptp.int) (BOUND_VARIABLE_2153887 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15191 BOUND_VARIABLE_2153887) BOUND_VARIABLE_2153886)) (ho_15260 k_15259 k_15551)) (ho_15108 (ho_15107 k_15552 BOUND_VARIABLE_2153886) BOUND_VARIABLE_2153887))))) (let ((_let_2291 (forall ((BOUND_VARIABLE_2213558 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2153800 tptp.nat) (BOUND_VARIABLE_2153801 tptp.nat) (BOUND_VARIABLE_2153802 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2153802))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2153802))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15553 BOUND_VARIABLE_2213558) BOUND_VARIABLE_2153800) BOUND_VARIABLE_2153801) BOUND_VARIABLE_2153802) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2213558 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2153800)) (ho_15161 k_15160 BOUND_VARIABLE_2153801))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2292 (forall ((BOUND_VARIABLE_2213574 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2153725 tptp.nat) (BOUND_VARIABLE_2153726 tptp.nat) (BOUND_VARIABLE_2153727 tptp.int) (BOUND_VARIABLE_2153728 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15192 BOUND_VARIABLE_2153728) BOUND_VARIABLE_2153727)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15193 BOUND_VARIABLE_2213574) BOUND_VARIABLE_2153725) BOUND_VARIABLE_2153726))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_15554 BOUND_VARIABLE_2213574) BOUND_VARIABLE_2153725) BOUND_VARIABLE_2153726) BOUND_VARIABLE_2153727) BOUND_VARIABLE_2153728))))) (let ((_let_2293 (forall ((BOUND_VARIABLE_2153696 tptp.int) (BOUND_VARIABLE_2153697 tptp.int) (BOUND_VARIABLE_2153698 tptp.int) (BOUND_VARIABLE_2153699 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153696) BOUND_VARIABLE_2153698))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153697) BOUND_VARIABLE_2153699))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15555 BOUND_VARIABLE_2153696) BOUND_VARIABLE_2153697) BOUND_VARIABLE_2153698) BOUND_VARIABLE_2153699))))))) (let ((_let_2294 (forall ((BOUND_VARIABLE_2153668 tptp.int) (BOUND_VARIABLE_2153669 tptp.int) (BOUND_VARIABLE_2153670 tptp.int) (BOUND_VARIABLE_2153671 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153668) BOUND_VARIABLE_2153670))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153669) BOUND_VARIABLE_2153671))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15556 BOUND_VARIABLE_2153668) BOUND_VARIABLE_2153669) BOUND_VARIABLE_2153670) BOUND_VARIABLE_2153671))))))) (let ((_let_2295 (forall ((BOUND_VARIABLE_2213695 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2153582 tptp.nat) (BOUND_VARIABLE_2153583 tptp.nat) (BOUND_VARIABLE_2153584 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2153584))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2153584))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15557 BOUND_VARIABLE_2213695) BOUND_VARIABLE_2153582) BOUND_VARIABLE_2153583) BOUND_VARIABLE_2153584) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2213695 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2153582)) (ho_15161 k_15160 BOUND_VARIABLE_2153583))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2296 (forall ((BOUND_VARIABLE_2153553 tptp.int) (BOUND_VARIABLE_2153554 tptp.int) (BOUND_VARIABLE_2153555 tptp.int) (BOUND_VARIABLE_2153556 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153553) BOUND_VARIABLE_2153555))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153554) BOUND_VARIABLE_2153556))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15558 BOUND_VARIABLE_2153553) BOUND_VARIABLE_2153554) BOUND_VARIABLE_2153555) BOUND_VARIABLE_2153556))))))) (let ((_let_2297 (forall ((BOUND_VARIABLE_2213786 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2153467 tptp.nat) (BOUND_VARIABLE_2153468 tptp.nat) (BOUND_VARIABLE_2153469 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2153469))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2153469))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15559 BOUND_VARIABLE_2213786) BOUND_VARIABLE_2153467) BOUND_VARIABLE_2153468) BOUND_VARIABLE_2153469) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2213786 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2153467)) (ho_15161 k_15160 BOUND_VARIABLE_2153468))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2298 (forall ((BOUND_VARIABLE_2153438 tptp.int) (BOUND_VARIABLE_2153439 tptp.int) (BOUND_VARIABLE_2153440 tptp.int) (BOUND_VARIABLE_2153441 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153438) BOUND_VARIABLE_2153440))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153439) BOUND_VARIABLE_2153441))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15560 BOUND_VARIABLE_2153438) BOUND_VARIABLE_2153439) BOUND_VARIABLE_2153440) BOUND_VARIABLE_2153441))))))) (let ((_let_2299 (forall ((BOUND_VARIABLE_2213877 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2153352 tptp.nat) (BOUND_VARIABLE_2153353 tptp.nat) (BOUND_VARIABLE_2153354 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2153354))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2153354))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15561 BOUND_VARIABLE_2213877) BOUND_VARIABLE_2153352) BOUND_VARIABLE_2153353) BOUND_VARIABLE_2153354) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2213877 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2153352)) (ho_15161 k_15160 BOUND_VARIABLE_2153353))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2300 (forall ((BOUND_VARIABLE_2153323 tptp.int) (BOUND_VARIABLE_2153324 tptp.int) (BOUND_VARIABLE_2153325 tptp.int) (BOUND_VARIABLE_2153326 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153323) BOUND_VARIABLE_2153325))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153324) BOUND_VARIABLE_2153326))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15562 BOUND_VARIABLE_2153323) BOUND_VARIABLE_2153324) BOUND_VARIABLE_2153325) BOUND_VARIABLE_2153326))))))) (let ((_let_2301 (forall ((BOUND_VARIABLE_2153295 tptp.int) (BOUND_VARIABLE_2153296 tptp.int) (BOUND_VARIABLE_2153297 tptp.int) (BOUND_VARIABLE_2153298 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153295) BOUND_VARIABLE_2153297))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153296) BOUND_VARIABLE_2153298))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15563 BOUND_VARIABLE_2153295) BOUND_VARIABLE_2153296) BOUND_VARIABLE_2153297) BOUND_VARIABLE_2153298))))))) (let ((_let_2302 (forall ((BOUND_VARIABLE_2213991 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2153209 tptp.nat) (BOUND_VARIABLE_2153210 tptp.nat) (BOUND_VARIABLE_2153211 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2153211))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2153211))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15564 BOUND_VARIABLE_2213991) BOUND_VARIABLE_2153209) BOUND_VARIABLE_2153210) BOUND_VARIABLE_2153211) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2213991 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2153209)) (ho_15161 k_15160 BOUND_VARIABLE_2153210))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2303 (forall ((BOUND_VARIABLE_2153180 tptp.int) (BOUND_VARIABLE_2153181 tptp.int) (BOUND_VARIABLE_2153182 tptp.int) (BOUND_VARIABLE_2153183 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153180) BOUND_VARIABLE_2153182))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153181) BOUND_VARIABLE_2153183))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15565 BOUND_VARIABLE_2153180) BOUND_VARIABLE_2153181) BOUND_VARIABLE_2153182) BOUND_VARIABLE_2153183))))))) (let ((_let_2304 (forall ((BOUND_VARIABLE_2214082 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2153094 tptp.nat) (BOUND_VARIABLE_2153095 tptp.nat) (BOUND_VARIABLE_2153096 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2153096))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2153096))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15566 BOUND_VARIABLE_2214082) BOUND_VARIABLE_2153094) BOUND_VARIABLE_2153095) BOUND_VARIABLE_2153096) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2214082 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2153094)) (ho_15161 k_15160 BOUND_VARIABLE_2153095))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2305 (forall ((BOUND_VARIABLE_2153065 tptp.int) (BOUND_VARIABLE_2153066 tptp.int) (BOUND_VARIABLE_2153067 tptp.int) (BOUND_VARIABLE_2153068 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153065) BOUND_VARIABLE_2153067))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2153066) BOUND_VARIABLE_2153068))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15567 BOUND_VARIABLE_2153065) BOUND_VARIABLE_2153066) BOUND_VARIABLE_2153067) BOUND_VARIABLE_2153068))))))) (let ((_let_2306 (forall ((BOUND_VARIABLE_2214173 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2152979 tptp.nat) (BOUND_VARIABLE_2152980 tptp.nat) (BOUND_VARIABLE_2152981 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2152981))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2152981))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15568 BOUND_VARIABLE_2214173) BOUND_VARIABLE_2152979) BOUND_VARIABLE_2152980) BOUND_VARIABLE_2152981) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2214173 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2152979)) (ho_15161 k_15160 BOUND_VARIABLE_2152980))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2307 (forall ((BOUND_VARIABLE_2152950 tptp.int) (BOUND_VARIABLE_2152951 tptp.int) (BOUND_VARIABLE_2152952 tptp.int) (BOUND_VARIABLE_2152953 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152950) BOUND_VARIABLE_2152952))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152951) BOUND_VARIABLE_2152953))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15569 BOUND_VARIABLE_2152950) BOUND_VARIABLE_2152951) BOUND_VARIABLE_2152952) BOUND_VARIABLE_2152953))))))) (let ((_let_2308 (forall ((BOUND_VARIABLE_2214267 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2214264 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2152858 tptp.nat) (BOUND_VARIABLE_2152859 tptp.nat) (BOUND_VARIABLE_2152860 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2152860))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2152860))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2152858)) (ho_15161 k_15160 BOUND_VARIABLE_2152859))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15570 BOUND_VARIABLE_2214267) BOUND_VARIABLE_2214264) BOUND_VARIABLE_2152858) BOUND_VARIABLE_2152859) BOUND_VARIABLE_2152860) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2214267 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2214264 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2309 (forall ((BOUND_VARIABLE_2152828 tptp.int) (BOUND_VARIABLE_2152829 tptp.int) (BOUND_VARIABLE_2152830 tptp.int) (BOUND_VARIABLE_2152831 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152828) BOUND_VARIABLE_2152830))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152829) BOUND_VARIABLE_2152831))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15571 BOUND_VARIABLE_2152828) BOUND_VARIABLE_2152829) BOUND_VARIABLE_2152830) BOUND_VARIABLE_2152831))))))) (let ((_let_2310 (forall ((BOUND_VARIABLE_2214362 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2152742 tptp.nat) (BOUND_VARIABLE_2152743 tptp.nat) (BOUND_VARIABLE_2152744 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2152744))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2152744))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15572 BOUND_VARIABLE_2214362) BOUND_VARIABLE_2152742) BOUND_VARIABLE_2152743) BOUND_VARIABLE_2152744) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2214362 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2152742)) (ho_15161 k_15160 BOUND_VARIABLE_2152743))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2311 (forall ((BOUND_VARIABLE_2152713 tptp.int) (BOUND_VARIABLE_2152714 tptp.int) (BOUND_VARIABLE_2152715 tptp.int) (BOUND_VARIABLE_2152716 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152713) BOUND_VARIABLE_2152715))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152714) BOUND_VARIABLE_2152716))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15573 BOUND_VARIABLE_2152713) BOUND_VARIABLE_2152714) BOUND_VARIABLE_2152715) BOUND_VARIABLE_2152716))))))) (let ((_let_2312 (forall ((BOUND_VARIABLE_2214453 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2152627 tptp.nat) (BOUND_VARIABLE_2152628 tptp.nat) (BOUND_VARIABLE_2152629 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2152629))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2152629))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15574 BOUND_VARIABLE_2214453) BOUND_VARIABLE_2152627) BOUND_VARIABLE_2152628) BOUND_VARIABLE_2152629) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2214453 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2152627)) (ho_15161 k_15160 BOUND_VARIABLE_2152628))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2313 (forall ((BOUND_VARIABLE_2152598 tptp.int) (BOUND_VARIABLE_2152599 tptp.int) (BOUND_VARIABLE_2152600 tptp.int) (BOUND_VARIABLE_2152601 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152598) BOUND_VARIABLE_2152600))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152599) BOUND_VARIABLE_2152601))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15575 BOUND_VARIABLE_2152598) BOUND_VARIABLE_2152599) BOUND_VARIABLE_2152600) BOUND_VARIABLE_2152601))))))) (let ((_let_2314 (forall ((BOUND_VARIABLE_2214546 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2214544 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2152507 tptp.nat) (BOUND_VARIABLE_2152508 tptp.nat) (BOUND_VARIABLE_2152509 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2152509))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2152509))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2152507)) (ho_15161 k_15160 BOUND_VARIABLE_2152508))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15576 BOUND_VARIABLE_2214546) BOUND_VARIABLE_2214544) BOUND_VARIABLE_2152507) BOUND_VARIABLE_2152508) BOUND_VARIABLE_2152509) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2214546 _let_9)) (ho_15120 BOUND_VARIABLE_2214544 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2315 (forall ((BOUND_VARIABLE_2152477 tptp.int) (BOUND_VARIABLE_2152478 tptp.int) (BOUND_VARIABLE_2152479 tptp.int) (BOUND_VARIABLE_2152480 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152477) BOUND_VARIABLE_2152479))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152478) BOUND_VARIABLE_2152480))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15577 BOUND_VARIABLE_2152477) BOUND_VARIABLE_2152478) BOUND_VARIABLE_2152479) BOUND_VARIABLE_2152480))))))) (let ((_let_2316 (forall ((BOUND_VARIABLE_2214641 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2152391 tptp.nat) (BOUND_VARIABLE_2152392 tptp.nat) (BOUND_VARIABLE_2152393 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2152393))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2152393))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15578 BOUND_VARIABLE_2214641) BOUND_VARIABLE_2152391) BOUND_VARIABLE_2152392) BOUND_VARIABLE_2152393) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2214641 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2152391)) (ho_15161 k_15160 BOUND_VARIABLE_2152392))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2317 (forall ((BOUND_VARIABLE_2152362 tptp.int) (BOUND_VARIABLE_2152363 tptp.int) (BOUND_VARIABLE_2152364 tptp.int) (BOUND_VARIABLE_2152365 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152362) BOUND_VARIABLE_2152364))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152363) BOUND_VARIABLE_2152365))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15579 BOUND_VARIABLE_2152362) BOUND_VARIABLE_2152363) BOUND_VARIABLE_2152364) BOUND_VARIABLE_2152365))))))) (let ((_let_2318 (forall ((BOUND_VARIABLE_2214732 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2152275 tptp.nat) (BOUND_VARIABLE_2152276 tptp.nat) (BOUND_VARIABLE_2152277 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2152277))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2152277))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15580 BOUND_VARIABLE_2214732) BOUND_VARIABLE_2152275) BOUND_VARIABLE_2152276) BOUND_VARIABLE_2152277) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2214732 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2152275)) (ho_15161 k_15160 BOUND_VARIABLE_2152276)))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2319 (forall ((BOUND_VARIABLE_2152246 tptp.int) (BOUND_VARIABLE_2152247 tptp.int) (BOUND_VARIABLE_2152248 tptp.int) (BOUND_VARIABLE_2152249 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152246) BOUND_VARIABLE_2152248))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152247) BOUND_VARIABLE_2152249))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15581 BOUND_VARIABLE_2152246) BOUND_VARIABLE_2152247) BOUND_VARIABLE_2152248) BOUND_VARIABLE_2152249))))))) (let ((_let_2320 (forall ((BOUND_VARIABLE_2152167 tptp.rat) (BOUND_VARIABLE_2152168 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2152168))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2152168))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2152167 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15582 BOUND_VARIABLE_2152167) BOUND_VARIABLE_2152168)))))))))))))) (let ((_let_2321 (forall ((BOUND_VARIABLE_2152139 tptp.int) (BOUND_VARIABLE_2152140 tptp.int) (BOUND_VARIABLE_2152141 tptp.int) (BOUND_VARIABLE_2152142 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152139) BOUND_VARIABLE_2152141))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152140) BOUND_VARIABLE_2152142))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15583 BOUND_VARIABLE_2152139) BOUND_VARIABLE_2152140) BOUND_VARIABLE_2152141) BOUND_VARIABLE_2152142))))))) (let ((_let_2322 (forall ((BOUND_VARIABLE_2214903 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2152053 tptp.nat) (BOUND_VARIABLE_2152054 tptp.nat) (BOUND_VARIABLE_2152055 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2152055))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2152055))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_15584 BOUND_VARIABLE_2214903) BOUND_VARIABLE_2152053) BOUND_VARIABLE_2152054) BOUND_VARIABLE_2152055) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2214903 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2152053)) (ho_15161 k_15160 BOUND_VARIABLE_2152054))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2323 (forall ((BOUND_VARIABLE_2152024 tptp.int) (BOUND_VARIABLE_2152025 tptp.int) (BOUND_VARIABLE_2152026 tptp.int) (BOUND_VARIABLE_2152027 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152024) BOUND_VARIABLE_2152026))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2152025) BOUND_VARIABLE_2152027))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15585 BOUND_VARIABLE_2152024) BOUND_VARIABLE_2152025) BOUND_VARIABLE_2152026) BOUND_VARIABLE_2152027))))))) (let ((_let_2324 (forall ((BOUND_VARIABLE_2151996 tptp.int) (BOUND_VARIABLE_2151997 tptp.int) (BOUND_VARIABLE_2151998 tptp.int) (BOUND_VARIABLE_2151999 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2151996) BOUND_VARIABLE_2151998))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2151997) BOUND_VARIABLE_2151999))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15586 BOUND_VARIABLE_2151996) BOUND_VARIABLE_2151997) BOUND_VARIABLE_2151998) BOUND_VARIABLE_2151999))))))) (let ((_let_2325 (forall ((BOUND_VARIABLE_2215012 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2151916 tptp.nat) (BOUND_VARIABLE_2151917 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2151917))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2151917))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15495 k_15587 BOUND_VARIABLE_2215012) BOUND_VARIABLE_2151916) BOUND_VARIABLE_2151917) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2215012 BOUND_VARIABLE_2151916)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2326 (forall ((BOUND_VARIABLE_2151887 tptp.int) (BOUND_VARIABLE_2151888 tptp.int) (BOUND_VARIABLE_2151889 tptp.int) (BOUND_VARIABLE_2151890 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2151887) BOUND_VARIABLE_2151889))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2151888) BOUND_VARIABLE_2151890))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15588 BOUND_VARIABLE_2151887) BOUND_VARIABLE_2151888) BOUND_VARIABLE_2151889) BOUND_VARIABLE_2151890))))))) (let ((_let_2327 (forall ((BOUND_VARIABLE_2151859 tptp.int) (BOUND_VARIABLE_2151860 tptp.int) (BOUND_VARIABLE_2151861 tptp.int) (BOUND_VARIABLE_2151862 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2151859) BOUND_VARIABLE_2151861))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2151860) BOUND_VARIABLE_2151862))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15589 BOUND_VARIABLE_2151859) BOUND_VARIABLE_2151860) BOUND_VARIABLE_2151861) BOUND_VARIABLE_2151862))))))) (let ((_let_2328 (forall ((BOUND_VARIABLE_2215126 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2215124 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2151768 tptp.nat) (BOUND_VARIABLE_2151769 tptp.nat) (BOUND_VARIABLE_2151770 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2151770))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2151770))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2151768)) (ho_15161 k_15160 BOUND_VARIABLE_2151769))))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15590 BOUND_VARIABLE_2215126) BOUND_VARIABLE_2215124) BOUND_VARIABLE_2151768) BOUND_VARIABLE_2151769) BOUND_VARIABLE_2151770) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_10 (ho_15120 BOUND_VARIABLE_2215126 _let_9)) (ho_15120 BOUND_VARIABLE_2215124 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2329 (forall ((BOUND_VARIABLE_2151736 tptp.nat) (BOUND_VARIABLE_2151737 tptp.num)) (let ((_let_1 (ho_15114 k_15113 tptp.one))) (let ((_let_2 (ho_15118 k_15117 _let_1))) (let ((_let_3 (ho_15118 k_15117 (ho_15114 k_15113 (ho_15152 k_15151 tptp.one))))) (let ((_let_4 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15594 (ho_15161 k_15160 (ho_15118 k_15117 (ho_15114 k_15113 BOUND_VARIABLE_2151737)))) (ho_15161 k_15160 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 (ho_15593 (ho_15592 k_15591 _let_3) BOUND_VARIABLE_2151736))) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 (ho_15161 k_15160 _let_2))) _let_1)))))))) (let ((_let_5 (ho_15195 (ho_15598 k_15597 tptp.one) tptp.one))) (= (ho_15195 (ho_15608 k_15607 BOUND_VARIABLE_2151736) BOUND_VARIABLE_2151737) (ho_15603 (ho_15606 (ho_15605 k_15604 _let_5) k_15194) (ho_15603 (ho_15602 (ho_15601 k_15600 (= _let_4 (ho_15593 (ho_15592 k_15599 _let_2) _let_3))) _let_5) (ho_15195 k_15196 (ho_15596 k_15595 _let_4))))))))))))) (let ((_let_2330 (forall ((BOUND_VARIABLE_2151710 tptp.nat) (BOUND_VARIABLE_2151711 tptp.num)) (let ((_let_1 (ho_15114 k_15113 tptp.one))) (let ((_let_2 (ho_15118 k_15117 _let_1))) (let ((_let_3 (ho_15118 k_15117 (ho_15114 k_15113 (ho_15152 k_15151 tptp.one))))) (let ((_let_4 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15594 (ho_15161 k_15160 (ho_15118 k_15117 (ho_15114 k_15113 BOUND_VARIABLE_2151711)))) (ho_15161 k_15160 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 (ho_15593 (ho_15592 k_15591 _let_3) BOUND_VARIABLE_2151710))) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 (ho_15161 k_15160 _let_2))) _let_1)))))))) (= (ho_15195 (ho_15608 k_15609 BOUND_VARIABLE_2151710) BOUND_VARIABLE_2151711) (ho_15195 k_15196 (ho_15614 (ho_15613 (ho_15612 k_15611 tptp.one) k_15610) (ho_15603 (ho_15602 (ho_15601 k_15600 (= (ho_15593 (ho_15592 k_15599 _let_2) _let_3) _let_4)) (ho_15195 (ho_15598 k_15597 tptp.one) tptp.one)) (ho_15195 k_15196 (ho_15596 k_15595 _let_4))))))))))))) (let ((_let_2331 (forall ((BOUND_VARIABLE_2151608 tptp.int) (BOUND_VARIABLE_2151609 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2151609))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2151609))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15615 BOUND_VARIABLE_2151608) BOUND_VARIABLE_2151609) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2151608) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2151608)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2151608))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2332 (forall ((BOUND_VARIABLE_2151513 tptp.int) (BOUND_VARIABLE_2151514 tptp.int) (BOUND_VARIABLE_2151515 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15197 BOUND_VARIABLE_2151515) BOUND_VARIABLE_2151514)) (ho_15260 k_15259 (ho_15141 k_15198 BOUND_VARIABLE_2151513))) (ho_15108 (ho_15107 (ho_15106 k_15616 BOUND_VARIABLE_2151513) BOUND_VARIABLE_2151514) BOUND_VARIABLE_2151515))))) (let ((_let_2333 (forall ((BOUND_VARIABLE_2151434 tptp.rat) (BOUND_VARIABLE_2151435 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2151435))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2151435))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2151434 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15617 BOUND_VARIABLE_2151434) BOUND_VARIABLE_2151435)))))))))))))) (let ((_let_2334 (forall ((BOUND_VARIABLE_2151377 tptp.rat) (BOUND_VARIABLE_2151378 tptp.int) (BOUND_VARIABLE_2151379 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15199 BOUND_VARIABLE_2151379) BOUND_VARIABLE_2151378)) (ho_15260 k_15259 (ho_15145 k_15200 BOUND_VARIABLE_2151377))) (ho_15108 (ho_15107 (ho_15266 k_15618 BOUND_VARIABLE_2151377) BOUND_VARIABLE_2151378) BOUND_VARIABLE_2151379))))) (let ((_let_2335 (forall ((BOUND_VARIABLE_2151273 tptp.int) (BOUND_VARIABLE_2151274 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2151274))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2151274))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2151273) _let_3))) (= (ho_15142 (ho_15141 k_15619 BOUND_VARIABLE_2151273) BOUND_VARIABLE_2151274) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2336 (forall ((BOUND_VARIABLE_2151171 tptp.int) (BOUND_VARIABLE_2151172 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2151172))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2151172))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15620 BOUND_VARIABLE_2151171) BOUND_VARIABLE_2151172) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2151171) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2151171)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2151171))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2337 (forall ((BOUND_VARIABLE_2151076 tptp.int) (BOUND_VARIABLE_2151077 tptp.int) (BOUND_VARIABLE_2151078 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15201 BOUND_VARIABLE_2151078) BOUND_VARIABLE_2151077)) (ho_15260 k_15259 (ho_15141 k_15202 BOUND_VARIABLE_2151076))) (ho_15108 (ho_15107 (ho_15106 k_15621 BOUND_VARIABLE_2151076) BOUND_VARIABLE_2151077) BOUND_VARIABLE_2151078))))) (let ((_let_2338 (forall ((BOUND_VARIABLE_2150997 tptp.rat) (BOUND_VARIABLE_2150998 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2150998))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2150998))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2150997 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15622 BOUND_VARIABLE_2150997) BOUND_VARIABLE_2150998)))))))))))))) (let ((_let_2339 (forall ((BOUND_VARIABLE_2150940 tptp.rat) (BOUND_VARIABLE_2150941 tptp.int) (BOUND_VARIABLE_2150942 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15203 BOUND_VARIABLE_2150942) BOUND_VARIABLE_2150941)) (ho_15260 k_15259 (ho_15145 k_15204 BOUND_VARIABLE_2150940))) (ho_15108 (ho_15107 (ho_15266 k_15623 BOUND_VARIABLE_2150940) BOUND_VARIABLE_2150941) BOUND_VARIABLE_2150942))))) (let ((_let_2340 (forall ((BOUND_VARIABLE_2150836 tptp.int) (BOUND_VARIABLE_2150837 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2150837))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2150837))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2150836) _let_3))) (= (ho_15142 (ho_15141 k_15624 BOUND_VARIABLE_2150836) BOUND_VARIABLE_2150837) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2341 (forall ((BOUND_VARIABLE_2150808 tptp.int) (BOUND_VARIABLE_2150809 tptp.int) (BOUND_VARIABLE_2150810 tptp.int) (BOUND_VARIABLE_2150811 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2150808) BOUND_VARIABLE_2150810))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2150809) BOUND_VARIABLE_2150811))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15625 BOUND_VARIABLE_2150808) BOUND_VARIABLE_2150809) BOUND_VARIABLE_2150810) BOUND_VARIABLE_2150811))))))) (let ((_let_2342 (forall ((BOUND_VARIABLE_2150704 tptp.int) (BOUND_VARIABLE_2150705 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2150705))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2150705))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2150704) _let_3))) (= (ho_15142 (ho_15141 k_15626 BOUND_VARIABLE_2150704) BOUND_VARIABLE_2150705) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2343 (forall ((BOUND_VARIABLE_2150676 tptp.int) (BOUND_VARIABLE_2150677 tptp.int) (BOUND_VARIABLE_2150678 tptp.int) (BOUND_VARIABLE_2150679 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2150676) BOUND_VARIABLE_2150678))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2150677) BOUND_VARIABLE_2150679))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15627 BOUND_VARIABLE_2150676) BOUND_VARIABLE_2150677) BOUND_VARIABLE_2150678) BOUND_VARIABLE_2150679))))))) (let ((_let_2344 (forall ((BOUND_VARIABLE_2150592 tptp.rat) (BOUND_VARIABLE_2150593 tptp.rat) (BOUND_VARIABLE_2150594 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2150594))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2150594))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15628 BOUND_VARIABLE_2150592) BOUND_VARIABLE_2150593) BOUND_VARIABLE_2150594) (and (= (ho_15122 (ho_15125 _let_10 BOUND_VARIABLE_2150592) BOUND_VARIABLE_2150593) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2345 (forall ((BOUND_VARIABLE_2150490 tptp.int) (BOUND_VARIABLE_2150491 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2150491))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2150491))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15629 BOUND_VARIABLE_2150490) BOUND_VARIABLE_2150491) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2150490) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2150490)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2150490))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2346 (forall ((BOUND_VARIABLE_2150395 tptp.int) (BOUND_VARIABLE_2150396 tptp.int) (BOUND_VARIABLE_2150397 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15205 BOUND_VARIABLE_2150397) BOUND_VARIABLE_2150396)) (ho_15260 k_15259 (ho_15141 k_15206 BOUND_VARIABLE_2150395))) (ho_15108 (ho_15107 (ho_15106 k_15630 BOUND_VARIABLE_2150395) BOUND_VARIABLE_2150396) BOUND_VARIABLE_2150397))))) (let ((_let_2347 (forall ((BOUND_VARIABLE_2150311 tptp.rat) (BOUND_VARIABLE_2150312 tptp.rat) (BOUND_VARIABLE_2150313 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2150313))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2150313))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15631 BOUND_VARIABLE_2150311) BOUND_VARIABLE_2150312) BOUND_VARIABLE_2150313) (and (= (ho_15122 (ho_15125 _let_10 BOUND_VARIABLE_2150311) BOUND_VARIABLE_2150312) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2348 (forall ((BOUND_VARIABLE_2150247 tptp.rat) (BOUND_VARIABLE_2150248 tptp.rat) (BOUND_VARIABLE_2150249 tptp.int) (BOUND_VARIABLE_2150250 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15207 BOUND_VARIABLE_2150250) BOUND_VARIABLE_2150249)) (ho_15260 k_15259 (ho_15145 (ho_15209 k_15208 BOUND_VARIABLE_2150247) BOUND_VARIABLE_2150248))) (ho_15108 (ho_15107 (ho_15266 (ho_15633 k_15632 BOUND_VARIABLE_2150247) BOUND_VARIABLE_2150248) BOUND_VARIABLE_2150249) BOUND_VARIABLE_2150250))))) (let ((_let_2349 (forall ((BOUND_VARIABLE_2150143 tptp.int) (BOUND_VARIABLE_2150144 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2150144))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2150144))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2150143) _let_3))) (= (ho_15142 (ho_15141 k_15634 BOUND_VARIABLE_2150143) BOUND_VARIABLE_2150144) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2350 (forall ((BOUND_VARIABLE_2150115 tptp.int) (BOUND_VARIABLE_2150116 tptp.int) (BOUND_VARIABLE_2150117 tptp.int) (BOUND_VARIABLE_2150118 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2150115) BOUND_VARIABLE_2150117))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2150116) BOUND_VARIABLE_2150118))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15635 BOUND_VARIABLE_2150115) BOUND_VARIABLE_2150116) BOUND_VARIABLE_2150117) BOUND_VARIABLE_2150118))))))) (let ((_let_2351 (forall ((BOUND_VARIABLE_2150011 tptp.int) (BOUND_VARIABLE_2150012 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2150012))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2150012))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2150011) _let_3))) (= (ho_15142 (ho_15141 k_15636 BOUND_VARIABLE_2150011) BOUND_VARIABLE_2150012) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2352 (forall ((BOUND_VARIABLE_2149983 tptp.int) (BOUND_VARIABLE_2149984 tptp.int) (BOUND_VARIABLE_2149985 tptp.int) (BOUND_VARIABLE_2149986 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149983) BOUND_VARIABLE_2149985))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149984) BOUND_VARIABLE_2149986))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15637 BOUND_VARIABLE_2149983) BOUND_VARIABLE_2149984) BOUND_VARIABLE_2149985) BOUND_VARIABLE_2149986))))))) (let ((_let_2353 (forall ((BOUND_VARIABLE_2149904 tptp.rat) (BOUND_VARIABLE_2149905 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2149905))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2149905))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2149904 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15638 BOUND_VARIABLE_2149904) BOUND_VARIABLE_2149905)))))))))))))) (let ((_let_2354 (forall ((BOUND_VARIABLE_2149876 tptp.int) (BOUND_VARIABLE_2149877 tptp.int) (BOUND_VARIABLE_2149878 tptp.int) (BOUND_VARIABLE_2149879 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149876) BOUND_VARIABLE_2149878))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149877) BOUND_VARIABLE_2149879))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15639 BOUND_VARIABLE_2149876) BOUND_VARIABLE_2149877) BOUND_VARIABLE_2149878) BOUND_VARIABLE_2149879))))))) (let ((_let_2355 (forall ((BOUND_VARIABLE_2149772 tptp.int) (BOUND_VARIABLE_2149773 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2149773))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2149773))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2149772) _let_3))) (= (ho_15142 (ho_15141 k_15640 BOUND_VARIABLE_2149772) BOUND_VARIABLE_2149773) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2356 (forall ((BOUND_VARIABLE_2149744 tptp.int) (BOUND_VARIABLE_2149745 tptp.int) (BOUND_VARIABLE_2149746 tptp.int) (BOUND_VARIABLE_2149747 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149744) BOUND_VARIABLE_2149746))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149745) BOUND_VARIABLE_2149747))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15641 BOUND_VARIABLE_2149744) BOUND_VARIABLE_2149745) BOUND_VARIABLE_2149746) BOUND_VARIABLE_2149747))))))) (let ((_let_2357 (forall ((BOUND_VARIABLE_2149665 tptp.rat) (BOUND_VARIABLE_2149666 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2149666))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2149666))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2149665 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15642 BOUND_VARIABLE_2149665) BOUND_VARIABLE_2149666)))))))))))))) (let ((_let_2358 (forall ((BOUND_VARIABLE_2149637 tptp.int) (BOUND_VARIABLE_2149638 tptp.int) (BOUND_VARIABLE_2149639 tptp.int) (BOUND_VARIABLE_2149640 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149637) BOUND_VARIABLE_2149639))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149638) BOUND_VARIABLE_2149640))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15643 BOUND_VARIABLE_2149637) BOUND_VARIABLE_2149638) BOUND_VARIABLE_2149639) BOUND_VARIABLE_2149640))))))) (let ((_let_2359 (forall ((BOUND_VARIABLE_2149609 tptp.int) (BOUND_VARIABLE_2149610 tptp.int) (BOUND_VARIABLE_2149611 tptp.int) (BOUND_VARIABLE_2149612 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149609) BOUND_VARIABLE_2149611))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149610) BOUND_VARIABLE_2149612))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15644 BOUND_VARIABLE_2149609) BOUND_VARIABLE_2149610) BOUND_VARIABLE_2149611) BOUND_VARIABLE_2149612))))))) (let ((_let_2360 (forall ((BOUND_VARIABLE_2149524 tptp.rat) (BOUND_VARIABLE_2149525 tptp.rat) (BOUND_VARIABLE_2149526 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2149526))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2149526))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15145 (ho_15209 k_15645 BOUND_VARIABLE_2149524) BOUND_VARIABLE_2149525) BOUND_VARIABLE_2149526) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2149524) (ho_15122 k_15121 BOUND_VARIABLE_2149525)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2361 (forall ((BOUND_VARIABLE_2149496 tptp.int) (BOUND_VARIABLE_2149497 tptp.int) (BOUND_VARIABLE_2149498 tptp.int) (BOUND_VARIABLE_2149499 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149496) BOUND_VARIABLE_2149498))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149497) BOUND_VARIABLE_2149499))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15646 BOUND_VARIABLE_2149496) BOUND_VARIABLE_2149497) BOUND_VARIABLE_2149498) BOUND_VARIABLE_2149499))))))) (let ((_let_2362 (forall ((BOUND_VARIABLE_2149468 tptp.int) (BOUND_VARIABLE_2149469 tptp.int) (BOUND_VARIABLE_2149470 tptp.int) (BOUND_VARIABLE_2149471 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149468) BOUND_VARIABLE_2149470))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149469) BOUND_VARIABLE_2149471))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15647 BOUND_VARIABLE_2149468) BOUND_VARIABLE_2149469) BOUND_VARIABLE_2149470) BOUND_VARIABLE_2149471))))))) (let ((_let_2363 (forall ((BOUND_VARIABLE_2149389 tptp.rat) (BOUND_VARIABLE_2149390 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2149390))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2149390))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2149389 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15648 BOUND_VARIABLE_2149389) BOUND_VARIABLE_2149390)))))))))))))) (let ((_let_2364 (forall ((BOUND_VARIABLE_2149361 tptp.int) (BOUND_VARIABLE_2149362 tptp.int) (BOUND_VARIABLE_2149363 tptp.int) (BOUND_VARIABLE_2149364 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149361) BOUND_VARIABLE_2149363))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149362) BOUND_VARIABLE_2149364))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15649 BOUND_VARIABLE_2149361) BOUND_VARIABLE_2149362) BOUND_VARIABLE_2149363) BOUND_VARIABLE_2149364))))))) (let ((_let_2365 (forall ((BOUND_VARIABLE_2149333 tptp.int) (BOUND_VARIABLE_2149334 tptp.int) (BOUND_VARIABLE_2149335 tptp.int) (BOUND_VARIABLE_2149336 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149333) BOUND_VARIABLE_2149335))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2149334) BOUND_VARIABLE_2149336))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15650 BOUND_VARIABLE_2149333) BOUND_VARIABLE_2149334) BOUND_VARIABLE_2149335) BOUND_VARIABLE_2149336))))))) (let ((_let_2366 (forall ((BOUND_VARIABLE_2149254 tptp.rat) (BOUND_VARIABLE_2149255 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2149255))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2149255))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2149254 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15651 BOUND_VARIABLE_2149254) BOUND_VARIABLE_2149255)))))))))))))) (let ((_let_2367 (forall ((BOUND_VARIABLE_2149152 tptp.int) (BOUND_VARIABLE_2149153 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2149153))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2149153))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15652 BOUND_VARIABLE_2149152) BOUND_VARIABLE_2149153) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2149152) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2149152)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2149152))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2368 (forall ((BOUND_VARIABLE_2149057 tptp.int) (BOUND_VARIABLE_2149058 tptp.int) (BOUND_VARIABLE_2149059 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15210 BOUND_VARIABLE_2149059) BOUND_VARIABLE_2149058)) (ho_15260 k_15259 (ho_15141 k_15211 BOUND_VARIABLE_2149057))) (ho_15108 (ho_15107 (ho_15106 k_15653 BOUND_VARIABLE_2149057) BOUND_VARIABLE_2149058) BOUND_VARIABLE_2149059))))) (let ((_let_2369 (forall ((BOUND_VARIABLE_2148978 tptp.rat) (BOUND_VARIABLE_2148979 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2148979))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2148979))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2148978 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15654 BOUND_VARIABLE_2148978) BOUND_VARIABLE_2148979)))))))))))))) (let ((_let_2370 (forall ((BOUND_VARIABLE_2148921 tptp.rat) (BOUND_VARIABLE_2148922 tptp.int) (BOUND_VARIABLE_2148923 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15212 BOUND_VARIABLE_2148923) BOUND_VARIABLE_2148922)) (ho_15260 k_15259 (ho_15145 k_15213 BOUND_VARIABLE_2148921))) (ho_15108 (ho_15107 (ho_15266 k_15655 BOUND_VARIABLE_2148921) BOUND_VARIABLE_2148922) BOUND_VARIABLE_2148923))))) (let ((_let_2371 (forall ((BOUND_VARIABLE_2148817 tptp.int) (BOUND_VARIABLE_2148818 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2148818))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2148818))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2148817) _let_3))) (= (ho_15142 (ho_15141 k_15656 BOUND_VARIABLE_2148817) BOUND_VARIABLE_2148818) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2372 (forall ((BOUND_VARIABLE_2148789 tptp.int) (BOUND_VARIABLE_2148790 tptp.int) (BOUND_VARIABLE_2148791 tptp.int) (BOUND_VARIABLE_2148792 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2148789) BOUND_VARIABLE_2148791))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2148790) BOUND_VARIABLE_2148792))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15657 BOUND_VARIABLE_2148789) BOUND_VARIABLE_2148790) BOUND_VARIABLE_2148791) BOUND_VARIABLE_2148792))))))) (let ((_let_2373 (forall ((BOUND_VARIABLE_2148685 tptp.int) (BOUND_VARIABLE_2148686 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2148686))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2148686))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2148685) _let_3))) (= (ho_15142 (ho_15141 k_15658 BOUND_VARIABLE_2148685) BOUND_VARIABLE_2148686) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2374 (forall ((BOUND_VARIABLE_2148657 tptp.int) (BOUND_VARIABLE_2148658 tptp.int) (BOUND_VARIABLE_2148659 tptp.int) (BOUND_VARIABLE_2148660 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2148657) BOUND_VARIABLE_2148659))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2148658) BOUND_VARIABLE_2148660))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15659 BOUND_VARIABLE_2148657) BOUND_VARIABLE_2148658) BOUND_VARIABLE_2148659) BOUND_VARIABLE_2148660))))))) (let ((_let_2375 (forall ((BOUND_VARIABLE_2148578 tptp.rat) (BOUND_VARIABLE_2148579 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2148579))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2148579))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2148578 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15660 BOUND_VARIABLE_2148578) BOUND_VARIABLE_2148579)))))))))))))) (let ((_let_2376 (forall ((BOUND_VARIABLE_2148550 tptp.int) (BOUND_VARIABLE_2148551 tptp.int) (BOUND_VARIABLE_2148552 tptp.int) (BOUND_VARIABLE_2148553 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2148550) BOUND_VARIABLE_2148552))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2148551) BOUND_VARIABLE_2148553))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15661 BOUND_VARIABLE_2148550) BOUND_VARIABLE_2148551) BOUND_VARIABLE_2148552) BOUND_VARIABLE_2148553))))))) (let ((_let_2377 (forall ((BOUND_VARIABLE_2148446 tptp.int) (BOUND_VARIABLE_2148447 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2148447))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2148447))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2148446) _let_3))) (= (ho_15142 (ho_15141 k_15662 BOUND_VARIABLE_2148446) BOUND_VARIABLE_2148447) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2378 (forall ((BOUND_VARIABLE_2148418 tptp.int) (BOUND_VARIABLE_2148419 tptp.int) (BOUND_VARIABLE_2148420 tptp.int) (BOUND_VARIABLE_2148421 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2148418) BOUND_VARIABLE_2148420))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2148419) BOUND_VARIABLE_2148421))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15663 BOUND_VARIABLE_2148418) BOUND_VARIABLE_2148419) BOUND_VARIABLE_2148420) BOUND_VARIABLE_2148421))))))) (let ((_let_2379 (forall ((BOUND_VARIABLE_2148339 tptp.rat) (BOUND_VARIABLE_2148340 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2148340))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2148340))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2148339 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15664 BOUND_VARIABLE_2148339) BOUND_VARIABLE_2148340)))))))))))))) (let ((_let_2380 (forall ((BOUND_VARIABLE_2148237 tptp.int) (BOUND_VARIABLE_2148238 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2148238))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2148238))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15665 BOUND_VARIABLE_2148237) BOUND_VARIABLE_2148238) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2148237) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2148237)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2148237))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2381 (forall ((BOUND_VARIABLE_2148142 tptp.int) (BOUND_VARIABLE_2148143 tptp.int) (BOUND_VARIABLE_2148144 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15214 BOUND_VARIABLE_2148144) BOUND_VARIABLE_2148143)) (ho_15260 k_15259 (ho_15141 k_15215 BOUND_VARIABLE_2148142))) (ho_15108 (ho_15107 (ho_15106 k_15666 BOUND_VARIABLE_2148142) BOUND_VARIABLE_2148143) BOUND_VARIABLE_2148144))))) (let ((_let_2382 (forall ((BOUND_VARIABLE_2148063 tptp.rat) (BOUND_VARIABLE_2148064 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2148064))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2148064))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2148063 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15667 BOUND_VARIABLE_2148063) BOUND_VARIABLE_2148064)))))))))))))) (let ((_let_2383 (forall ((BOUND_VARIABLE_2148006 tptp.rat) (BOUND_VARIABLE_2148007 tptp.int) (BOUND_VARIABLE_2148008 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15216 BOUND_VARIABLE_2148008) BOUND_VARIABLE_2148007)) (ho_15260 k_15259 (ho_15145 k_15217 BOUND_VARIABLE_2148006))) (ho_15108 (ho_15107 (ho_15266 k_15668 BOUND_VARIABLE_2148006) BOUND_VARIABLE_2148007) BOUND_VARIABLE_2148008))))) (let ((_let_2384 (forall ((BOUND_VARIABLE_2147902 tptp.int) (BOUND_VARIABLE_2147903 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2147903))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2147903))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2147902) _let_3))) (= (ho_15142 (ho_15141 k_15669 BOUND_VARIABLE_2147902) BOUND_VARIABLE_2147903) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2385 (forall ((BOUND_VARIABLE_2147874 tptp.int) (BOUND_VARIABLE_2147875 tptp.int) (BOUND_VARIABLE_2147876 tptp.int) (BOUND_VARIABLE_2147877 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147874) BOUND_VARIABLE_2147876))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147875) BOUND_VARIABLE_2147877))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15670 BOUND_VARIABLE_2147874) BOUND_VARIABLE_2147875) BOUND_VARIABLE_2147876) BOUND_VARIABLE_2147877))))))) (let ((_let_2386 (forall ((BOUND_VARIABLE_2147846 tptp.int) (BOUND_VARIABLE_2147847 tptp.int) (BOUND_VARIABLE_2147848 tptp.int) (BOUND_VARIABLE_2147849 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147846) BOUND_VARIABLE_2147848))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147847) BOUND_VARIABLE_2147849))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15671 BOUND_VARIABLE_2147846) BOUND_VARIABLE_2147847) BOUND_VARIABLE_2147848) BOUND_VARIABLE_2147849))))))) (let ((_let_2387 (forall ((BOUND_VARIABLE_2147767 tptp.rat) (BOUND_VARIABLE_2147768 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2147768))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2147768))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2147767 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15672 BOUND_VARIABLE_2147767) BOUND_VARIABLE_2147768)))))))))))))) (let ((_let_2388 (forall ((BOUND_VARIABLE_2147739 tptp.int) (BOUND_VARIABLE_2147740 tptp.int) (BOUND_VARIABLE_2147741 tptp.int) (BOUND_VARIABLE_2147742 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147739) BOUND_VARIABLE_2147741))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147740) BOUND_VARIABLE_2147742))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15673 BOUND_VARIABLE_2147739) BOUND_VARIABLE_2147740) BOUND_VARIABLE_2147741) BOUND_VARIABLE_2147742))))))) (let ((_let_2389 (forall ((BOUND_VARIABLE_2147711 tptp.int) (BOUND_VARIABLE_2147712 tptp.int) (BOUND_VARIABLE_2147713 tptp.int) (BOUND_VARIABLE_2147714 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147711) BOUND_VARIABLE_2147713))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147712) BOUND_VARIABLE_2147714))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15674 BOUND_VARIABLE_2147711) BOUND_VARIABLE_2147712) BOUND_VARIABLE_2147713) BOUND_VARIABLE_2147714))))))) (let ((_let_2390 (forall ((BOUND_VARIABLE_2147632 tptp.rat) (BOUND_VARIABLE_2147633 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2147633))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2147633))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2147632 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15675 BOUND_VARIABLE_2147632) BOUND_VARIABLE_2147633)))))))))))))) (let ((_let_2391 (forall ((BOUND_VARIABLE_2147604 tptp.int) (BOUND_VARIABLE_2147605 tptp.int) (BOUND_VARIABLE_2147606 tptp.int) (BOUND_VARIABLE_2147607 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147604) BOUND_VARIABLE_2147606))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147605) BOUND_VARIABLE_2147607))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15676 BOUND_VARIABLE_2147604) BOUND_VARIABLE_2147605) BOUND_VARIABLE_2147606) BOUND_VARIABLE_2147607))))))) (let ((_let_2392 (forall ((BOUND_VARIABLE_2147576 tptp.int) (BOUND_VARIABLE_2147577 tptp.int) (BOUND_VARIABLE_2147578 tptp.int) (BOUND_VARIABLE_2147579 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147576) BOUND_VARIABLE_2147578))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147577) BOUND_VARIABLE_2147579))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15677 BOUND_VARIABLE_2147576) BOUND_VARIABLE_2147577) BOUND_VARIABLE_2147578) BOUND_VARIABLE_2147579))))))) (let ((_let_2393 (forall ((BOUND_VARIABLE_2147548 tptp.int) (BOUND_VARIABLE_2147549 tptp.int) (BOUND_VARIABLE_2147550 tptp.int) (BOUND_VARIABLE_2147551 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147548) BOUND_VARIABLE_2147550))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147549) BOUND_VARIABLE_2147551))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15678 BOUND_VARIABLE_2147548) BOUND_VARIABLE_2147549) BOUND_VARIABLE_2147550) BOUND_VARIABLE_2147551))))))) (let ((_let_2394 (forall ((BOUND_VARIABLE_2147469 tptp.rat) (BOUND_VARIABLE_2147470 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2147470))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2147470))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2147469 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15679 BOUND_VARIABLE_2147469) BOUND_VARIABLE_2147470)))))))))))))) (let ((_let_2395 (forall ((BOUND_VARIABLE_2147441 tptp.int) (BOUND_VARIABLE_2147442 tptp.int) (BOUND_VARIABLE_2147443 tptp.int) (BOUND_VARIABLE_2147444 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147441) BOUND_VARIABLE_2147443))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147442) BOUND_VARIABLE_2147444))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15680 BOUND_VARIABLE_2147441) BOUND_VARIABLE_2147442) BOUND_VARIABLE_2147443) BOUND_VARIABLE_2147444))))))) (let ((_let_2396 (forall ((BOUND_VARIABLE_2147362 tptp.rat) (BOUND_VARIABLE_2147363 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2147363))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2147363))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2147362 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15681 BOUND_VARIABLE_2147362) BOUND_VARIABLE_2147363)))))))))))))) (let ((_let_2397 (forall ((BOUND_VARIABLE_2147334 tptp.int) (BOUND_VARIABLE_2147335 tptp.int) (BOUND_VARIABLE_2147336 tptp.int) (BOUND_VARIABLE_2147337 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147334) BOUND_VARIABLE_2147336))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147335) BOUND_VARIABLE_2147337))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15682 BOUND_VARIABLE_2147334) BOUND_VARIABLE_2147335) BOUND_VARIABLE_2147336) BOUND_VARIABLE_2147337))))))) (let ((_let_2398 (forall ((BOUND_VARIABLE_2147306 tptp.int) (BOUND_VARIABLE_2147307 tptp.int) (BOUND_VARIABLE_2147308 tptp.int) (BOUND_VARIABLE_2147309 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147306) BOUND_VARIABLE_2147308))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147307) BOUND_VARIABLE_2147309))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15683 BOUND_VARIABLE_2147306) BOUND_VARIABLE_2147307) BOUND_VARIABLE_2147308) BOUND_VARIABLE_2147309))))))) (let ((_let_2399 (forall ((BOUND_VARIABLE_2147227 tptp.rat) (BOUND_VARIABLE_2147228 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2147228))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2147228))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2147227 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15684 BOUND_VARIABLE_2147227) BOUND_VARIABLE_2147228)))))))))))))) (let ((_let_2400 (forall ((BOUND_VARIABLE_2147199 tptp.int) (BOUND_VARIABLE_2147200 tptp.int) (BOUND_VARIABLE_2147201 tptp.int) (BOUND_VARIABLE_2147202 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147199) BOUND_VARIABLE_2147201))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147200) BOUND_VARIABLE_2147202))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15685 BOUND_VARIABLE_2147199) BOUND_VARIABLE_2147200) BOUND_VARIABLE_2147201) BOUND_VARIABLE_2147202))))))) (let ((_let_2401 (forall ((BOUND_VARIABLE_2147171 tptp.int) (BOUND_VARIABLE_2147172 tptp.int) (BOUND_VARIABLE_2147173 tptp.int) (BOUND_VARIABLE_2147174 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147171) BOUND_VARIABLE_2147173))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147172) BOUND_VARIABLE_2147174))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15686 BOUND_VARIABLE_2147171) BOUND_VARIABLE_2147172) BOUND_VARIABLE_2147173) BOUND_VARIABLE_2147174))))))) (let ((_let_2402 (forall ((BOUND_VARIABLE_2147092 tptp.rat) (BOUND_VARIABLE_2147093 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2147093))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2147093))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2147092 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15687 BOUND_VARIABLE_2147092) BOUND_VARIABLE_2147093)))))))))))))) (let ((_let_2403 (forall ((BOUND_VARIABLE_2147064 tptp.int) (BOUND_VARIABLE_2147065 tptp.int) (BOUND_VARIABLE_2147066 tptp.int) (BOUND_VARIABLE_2147067 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147064) BOUND_VARIABLE_2147066))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147065) BOUND_VARIABLE_2147067))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15688 BOUND_VARIABLE_2147064) BOUND_VARIABLE_2147065) BOUND_VARIABLE_2147066) BOUND_VARIABLE_2147067))))))) (let ((_let_2404 (forall ((BOUND_VARIABLE_2147036 tptp.int) (BOUND_VARIABLE_2147037 tptp.int) (BOUND_VARIABLE_2147038 tptp.int) (BOUND_VARIABLE_2147039 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147036) BOUND_VARIABLE_2147038))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2147037) BOUND_VARIABLE_2147039))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15689 BOUND_VARIABLE_2147036) BOUND_VARIABLE_2147037) BOUND_VARIABLE_2147038) BOUND_VARIABLE_2147039))))))) (let ((_let_2405 (forall ((BOUND_VARIABLE_2146957 tptp.rat) (BOUND_VARIABLE_2146958 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2146958))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2146958))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2146957 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15690 BOUND_VARIABLE_2146957) BOUND_VARIABLE_2146958)))))))))))))) (let ((_let_2406 (forall ((BOUND_VARIABLE_2146929 tptp.int) (BOUND_VARIABLE_2146930 tptp.int) (BOUND_VARIABLE_2146931 tptp.int) (BOUND_VARIABLE_2146932 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2146929) BOUND_VARIABLE_2146931))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2146930) BOUND_VARIABLE_2146932))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15691 BOUND_VARIABLE_2146929) BOUND_VARIABLE_2146930) BOUND_VARIABLE_2146931) BOUND_VARIABLE_2146932))))))) (let ((_let_2407 (forall ((BOUND_VARIABLE_2146901 tptp.int) (BOUND_VARIABLE_2146902 tptp.int) (BOUND_VARIABLE_2146903 tptp.int) (BOUND_VARIABLE_2146904 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2146901) BOUND_VARIABLE_2146903))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2146902) BOUND_VARIABLE_2146904))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15692 BOUND_VARIABLE_2146901) BOUND_VARIABLE_2146902) BOUND_VARIABLE_2146903) BOUND_VARIABLE_2146904))))))) (let ((_let_2408 (forall ((BOUND_VARIABLE_2146797 tptp.int) (BOUND_VARIABLE_2146798 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2146798))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2146798))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2146797) _let_3))) (= (ho_15142 (ho_15141 k_15693 BOUND_VARIABLE_2146797) BOUND_VARIABLE_2146798) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2409 (forall ((BOUND_VARIABLE_2146769 tptp.int) (BOUND_VARIABLE_2146770 tptp.int) (BOUND_VARIABLE_2146771 tptp.int) (BOUND_VARIABLE_2146772 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2146769) BOUND_VARIABLE_2146771))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2146770) BOUND_VARIABLE_2146772))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15694 BOUND_VARIABLE_2146769) BOUND_VARIABLE_2146770) BOUND_VARIABLE_2146771) BOUND_VARIABLE_2146772))))))) (let ((_let_2410 (forall ((BOUND_VARIABLE_2146690 tptp.rat) (BOUND_VARIABLE_2146691 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2146691))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2146691))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2146690 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15695 BOUND_VARIABLE_2146690) BOUND_VARIABLE_2146691)))))))))))))) (let ((_let_2411 (forall ((BOUND_VARIABLE_2146662 tptp.int) (BOUND_VARIABLE_2146663 tptp.int) (BOUND_VARIABLE_2146664 tptp.int) (BOUND_VARIABLE_2146665 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2146662) BOUND_VARIABLE_2146664))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2146663) BOUND_VARIABLE_2146665))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15696 BOUND_VARIABLE_2146662) BOUND_VARIABLE_2146663) BOUND_VARIABLE_2146664) BOUND_VARIABLE_2146665))))))) (let ((_let_2412 (forall ((BOUND_VARIABLE_2146558 tptp.int) (BOUND_VARIABLE_2146559 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2146559))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2146559))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2146558) _let_3))) (= (ho_15142 (ho_15141 k_15697 BOUND_VARIABLE_2146558) BOUND_VARIABLE_2146559) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2413 (forall ((BOUND_VARIABLE_2146530 tptp.int) (BOUND_VARIABLE_2146531 tptp.int) (BOUND_VARIABLE_2146532 tptp.int) (BOUND_VARIABLE_2146533 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2146530) BOUND_VARIABLE_2146532))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2146531) BOUND_VARIABLE_2146533))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15698 BOUND_VARIABLE_2146530) BOUND_VARIABLE_2146531) BOUND_VARIABLE_2146532) BOUND_VARIABLE_2146533))))))) (let ((_let_2414 (forall ((BOUND_VARIABLE_2146451 tptp.rat) (BOUND_VARIABLE_2146452 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2146452))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2146452))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2146451 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15699 BOUND_VARIABLE_2146451) BOUND_VARIABLE_2146452)))))))))))))) (let ((_let_2415 (forall ((BOUND_VARIABLE_2146349 tptp.int) (BOUND_VARIABLE_2146350 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2146350))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2146350))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15700 BOUND_VARIABLE_2146349) BOUND_VARIABLE_2146350) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2146349) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2146349)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2146349))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2416 (forall ((BOUND_VARIABLE_2146254 tptp.int) (BOUND_VARIABLE_2146255 tptp.int) (BOUND_VARIABLE_2146256 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15218 BOUND_VARIABLE_2146256) BOUND_VARIABLE_2146255)) (ho_15260 k_15259 (ho_15141 k_15219 BOUND_VARIABLE_2146254))) (ho_15108 (ho_15107 (ho_15106 k_15701 BOUND_VARIABLE_2146254) BOUND_VARIABLE_2146255) BOUND_VARIABLE_2146256))))) (let ((_let_2417 (forall ((BOUND_VARIABLE_2146175 tptp.rat) (BOUND_VARIABLE_2146176 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2146176))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2146176))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2146175 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15702 BOUND_VARIABLE_2146175) BOUND_VARIABLE_2146176)))))))))))))) (let ((_let_2418 (forall ((BOUND_VARIABLE_2146118 tptp.rat) (BOUND_VARIABLE_2146119 tptp.int) (BOUND_VARIABLE_2146120 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15220 BOUND_VARIABLE_2146120) BOUND_VARIABLE_2146119)) (ho_15260 k_15259 (ho_15145 k_15221 BOUND_VARIABLE_2146118))) (ho_15108 (ho_15107 (ho_15266 k_15703 BOUND_VARIABLE_2146118) BOUND_VARIABLE_2146119) BOUND_VARIABLE_2146120))))) (let ((_let_2419 (forall ((BOUND_VARIABLE_2146014 tptp.int) (BOUND_VARIABLE_2146015 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2146015))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2146015))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2146014) _let_3))) (= (ho_15142 (ho_15141 k_15704 BOUND_VARIABLE_2146014) BOUND_VARIABLE_2146015) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2420 (forall ((BOUND_VARIABLE_2145912 tptp.int) (BOUND_VARIABLE_2145913 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2145913))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2145913))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15705 BOUND_VARIABLE_2145912) BOUND_VARIABLE_2145913) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2145912) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2145912)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2145912))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2421 (forall ((BOUND_VARIABLE_2145817 tptp.int) (BOUND_VARIABLE_2145818 tptp.int) (BOUND_VARIABLE_2145819 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15222 BOUND_VARIABLE_2145819) BOUND_VARIABLE_2145818)) (ho_15260 k_15259 (ho_15141 k_15223 BOUND_VARIABLE_2145817))) (ho_15108 (ho_15107 (ho_15106 k_15706 BOUND_VARIABLE_2145817) BOUND_VARIABLE_2145818) BOUND_VARIABLE_2145819))))) (let ((_let_2422 (forall ((BOUND_VARIABLE_2145738 tptp.rat) (BOUND_VARIABLE_2145739 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2145739))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2145739))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2145738 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15707 BOUND_VARIABLE_2145738) BOUND_VARIABLE_2145739)))))))))))))) (let ((_let_2423 (forall ((BOUND_VARIABLE_2145681 tptp.rat) (BOUND_VARIABLE_2145682 tptp.int) (BOUND_VARIABLE_2145683 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15224 BOUND_VARIABLE_2145683) BOUND_VARIABLE_2145682)) (ho_15260 k_15259 (ho_15145 k_15225 BOUND_VARIABLE_2145681))) (ho_15108 (ho_15107 (ho_15266 k_15708 BOUND_VARIABLE_2145681) BOUND_VARIABLE_2145682) BOUND_VARIABLE_2145683))))) (let ((_let_2424 (forall ((BOUND_VARIABLE_2145577 tptp.int) (BOUND_VARIABLE_2145578 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2145578))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2145578))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2145577) _let_3))) (= (ho_15142 (ho_15141 k_15709 BOUND_VARIABLE_2145577) BOUND_VARIABLE_2145578) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2425 (forall ((BOUND_VARIABLE_2145549 tptp.int) (BOUND_VARIABLE_2145550 tptp.int) (BOUND_VARIABLE_2145551 tptp.int) (BOUND_VARIABLE_2145552 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2145549) BOUND_VARIABLE_2145551))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2145550) BOUND_VARIABLE_2145552))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15710 BOUND_VARIABLE_2145549) BOUND_VARIABLE_2145550) BOUND_VARIABLE_2145551) BOUND_VARIABLE_2145552))))))) (let ((_let_2426 (forall ((BOUND_VARIABLE_2145445 tptp.int) (BOUND_VARIABLE_2145446 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2145446))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2145446))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2145445) _let_3))) (= (ho_15142 (ho_15141 k_15711 BOUND_VARIABLE_2145445) BOUND_VARIABLE_2145446) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2427 (forall ((BOUND_VARIABLE_2145417 tptp.int) (BOUND_VARIABLE_2145418 tptp.int) (BOUND_VARIABLE_2145419 tptp.int) (BOUND_VARIABLE_2145420 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2145417) BOUND_VARIABLE_2145419))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2145418) BOUND_VARIABLE_2145420))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15712 BOUND_VARIABLE_2145417) BOUND_VARIABLE_2145418) BOUND_VARIABLE_2145419) BOUND_VARIABLE_2145420))))))) (let ((_let_2428 (forall ((BOUND_VARIABLE_2145338 tptp.rat) (BOUND_VARIABLE_2145339 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2145339))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2145339))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2145338 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15713 BOUND_VARIABLE_2145338) BOUND_VARIABLE_2145339)))))))))))))) (let ((_let_2429 (forall ((BOUND_VARIABLE_2145310 tptp.int) (BOUND_VARIABLE_2145311 tptp.int) (BOUND_VARIABLE_2145312 tptp.int) (BOUND_VARIABLE_2145313 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2145310) BOUND_VARIABLE_2145312))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2145311) BOUND_VARIABLE_2145313))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15714 BOUND_VARIABLE_2145310) BOUND_VARIABLE_2145311) BOUND_VARIABLE_2145312) BOUND_VARIABLE_2145313))))))) (let ((_let_2430 (forall ((BOUND_VARIABLE_2145206 tptp.int) (BOUND_VARIABLE_2145207 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2145207))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2145207))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2145206) _let_3))) (= (ho_15142 (ho_15141 k_15715 BOUND_VARIABLE_2145206) BOUND_VARIABLE_2145207) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2431 (forall ((BOUND_VARIABLE_2145178 tptp.int) (BOUND_VARIABLE_2145179 tptp.int) (BOUND_VARIABLE_2145180 tptp.int) (BOUND_VARIABLE_2145181 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2145178) BOUND_VARIABLE_2145180))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2145179) BOUND_VARIABLE_2145181))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15716 BOUND_VARIABLE_2145178) BOUND_VARIABLE_2145179) BOUND_VARIABLE_2145180) BOUND_VARIABLE_2145181))))))) (let ((_let_2432 (forall ((BOUND_VARIABLE_2145099 tptp.rat) (BOUND_VARIABLE_2145100 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2145100))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2145100))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2145099 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15717 BOUND_VARIABLE_2145099) BOUND_VARIABLE_2145100)))))))))))))) (let ((_let_2433 (forall ((BOUND_VARIABLE_2144997 tptp.int) (BOUND_VARIABLE_2144998 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2144998))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2144998))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15718 BOUND_VARIABLE_2144997) BOUND_VARIABLE_2144998) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2144997) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2144997)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2144997))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2434 (forall ((BOUND_VARIABLE_2144902 tptp.int) (BOUND_VARIABLE_2144903 tptp.int) (BOUND_VARIABLE_2144904 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15226 BOUND_VARIABLE_2144904) BOUND_VARIABLE_2144903)) (ho_15260 k_15259 (ho_15141 k_15227 BOUND_VARIABLE_2144902))) (ho_15108 (ho_15107 (ho_15106 k_15719 BOUND_VARIABLE_2144902) BOUND_VARIABLE_2144903) BOUND_VARIABLE_2144904))))) (let ((_let_2435 (forall ((BOUND_VARIABLE_2144823 tptp.rat) (BOUND_VARIABLE_2144824 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2144824))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2144824))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2144823 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15720 BOUND_VARIABLE_2144823) BOUND_VARIABLE_2144824)))))))))))))) (let ((_let_2436 (forall ((BOUND_VARIABLE_2144766 tptp.rat) (BOUND_VARIABLE_2144767 tptp.int) (BOUND_VARIABLE_2144768 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15228 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BOUND_VARIABLE_2144662) _let_3))) (= (ho_15142 (ho_15141 k_15722 BOUND_VARIABLE_2144662) BOUND_VARIABLE_2144663) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2438 (forall ((BOUND_VARIABLE_2144560 tptp.int) (BOUND_VARIABLE_2144561 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2144561))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2144561))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15723 BOUND_VARIABLE_2144560) BOUND_VARIABLE_2144561) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2144560) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2144560)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2144560))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2439 (forall ((BOUND_VARIABLE_2144465 tptp.int) (BOUND_VARIABLE_2144466 tptp.int) (BOUND_VARIABLE_2144467 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15230 BOUND_VARIABLE_2144467) BOUND_VARIABLE_2144466)) (ho_15260 k_15259 (ho_15141 k_15231 BOUND_VARIABLE_2144465))) (ho_15108 (ho_15107 (ho_15106 k_15724 BOUND_VARIABLE_2144465) BOUND_VARIABLE_2144466) BOUND_VARIABLE_2144467))))) (let ((_let_2440 (forall ((BOUND_VARIABLE_2144386 tptp.rat) (BOUND_VARIABLE_2144387 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2144387))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2144387))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2144386 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15725 BOUND_VARIABLE_2144386) BOUND_VARIABLE_2144387)))))))))))))) (let ((_let_2441 (forall ((BOUND_VARIABLE_2144329 tptp.rat) (BOUND_VARIABLE_2144330 tptp.int) (BOUND_VARIABLE_2144331 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15232 BOUND_VARIABLE_2144331) BOUND_VARIABLE_2144330)) (ho_15260 k_15259 (ho_15145 k_15233 BOUND_VARIABLE_2144329))) (ho_15108 (ho_15107 (ho_15266 k_15726 BOUND_VARIABLE_2144329) BOUND_VARIABLE_2144330) BOUND_VARIABLE_2144331))))) (let ((_let_2442 (forall ((BOUND_VARIABLE_2144225 tptp.int) (BOUND_VARIABLE_2144226 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2144226))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2144226))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2144225) _let_3))) (= (ho_15142 (ho_15141 k_15727 BOUND_VARIABLE_2144225) BOUND_VARIABLE_2144226) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2443 (forall ((BOUND_VARIABLE_2144197 tptp.int) (BOUND_VARIABLE_2144198 tptp.int) (BOUND_VARIABLE_2144199 tptp.int) (BOUND_VARIABLE_2144200 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2144197) BOUND_VARIABLE_2144199))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2144198) BOUND_VARIABLE_2144200))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15728 BOUND_VARIABLE_2144197) BOUND_VARIABLE_2144198) BOUND_VARIABLE_2144199) BOUND_VARIABLE_2144200))))))) (let ((_let_2444 (forall ((BOUND_VARIABLE_2144093 tptp.int) (BOUND_VARIABLE_2144094 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2144094))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2144094))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2144093) _let_3))) (= (ho_15142 (ho_15141 k_15729 BOUND_VARIABLE_2144093) BOUND_VARIABLE_2144094) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2445 (forall ((BOUND_VARIABLE_2144065 tptp.int) (BOUND_VARIABLE_2144066 tptp.int) (BOUND_VARIABLE_2144067 tptp.int) (BOUND_VARIABLE_2144068 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2144065) BOUND_VARIABLE_2144067))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2144066) BOUND_VARIABLE_2144068))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15730 BOUND_VARIABLE_2144065) BOUND_VARIABLE_2144066) BOUND_VARIABLE_2144067) BOUND_VARIABLE_2144068))))))) (let ((_let_2446 (forall ((BOUND_VARIABLE_2143986 tptp.rat) (BOUND_VARIABLE_2143987 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2143987))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2143987))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2143986 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15731 BOUND_VARIABLE_2143986) BOUND_VARIABLE_2143987)))))))))))))) (let ((_let_2447 (forall ((BOUND_VARIABLE_2143958 tptp.int) (BOUND_VARIABLE_2143959 tptp.int) (BOUND_VARIABLE_2143960 tptp.int) (BOUND_VARIABLE_2143961 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2143958) BOUND_VARIABLE_2143960))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2143959) BOUND_VARIABLE_2143961))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15732 BOUND_VARIABLE_2143958) BOUND_VARIABLE_2143959) BOUND_VARIABLE_2143960) BOUND_VARIABLE_2143961))))))) (let ((_let_2448 (forall ((BOUND_VARIABLE_2143854 tptp.int) (BOUND_VARIABLE_2143855 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2143855))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2143855))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2143854) _let_3))) (= (ho_15142 (ho_15141 k_15733 BOUND_VARIABLE_2143854) BOUND_VARIABLE_2143855) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2449 (forall ((BOUND_VARIABLE_2143826 tptp.int) (BOUND_VARIABLE_2143827 tptp.int) (BOUND_VARIABLE_2143828 tptp.int) (BOUND_VARIABLE_2143829 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2143826) BOUND_VARIABLE_2143828))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2143827) BOUND_VARIABLE_2143829))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15734 BOUND_VARIABLE_2143826) BOUND_VARIABLE_2143827) BOUND_VARIABLE_2143828) BOUND_VARIABLE_2143829))))))) (let ((_let_2450 (forall ((BOUND_VARIABLE_2143747 tptp.rat) (BOUND_VARIABLE_2143748 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2143748))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2143748))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2143747 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15735 BOUND_VARIABLE_2143747) BOUND_VARIABLE_2143748)))))))))))))) (let ((_let_2451 (forall ((BOUND_VARIABLE_2143645 tptp.int) (BOUND_VARIABLE_2143646 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2143646))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2143646))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15736 BOUND_VARIABLE_2143645) BOUND_VARIABLE_2143646) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2143645) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2143645)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2143645))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2452 (forall ((BOUND_VARIABLE_2143550 tptp.int) (BOUND_VARIABLE_2143551 tptp.int) (BOUND_VARIABLE_2143552 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15234 BOUND_VARIABLE_2143552) BOUND_VARIABLE_2143551)) (ho_15260 k_15259 (ho_15141 k_15235 BOUND_VARIABLE_2143550))) (ho_15108 (ho_15107 (ho_15106 k_15737 BOUND_VARIABLE_2143550) BOUND_VARIABLE_2143551) BOUND_VARIABLE_2143552))))) (let ((_let_2453 (forall ((BOUND_VARIABLE_2143471 tptp.rat) (BOUND_VARIABLE_2143472 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2143472))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2143472))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2143471 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15738 BOUND_VARIABLE_2143471) BOUND_VARIABLE_2143472)))))))))))))) (let ((_let_2454 (forall ((BOUND_VARIABLE_2143414 tptp.rat) (BOUND_VARIABLE_2143415 tptp.int) (BOUND_VARIABLE_2143416 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15236 BOUND_VARIABLE_2143416) BOUND_VARIABLE_2143415)) (ho_15260 k_15259 (ho_15145 k_15237 BOUND_VARIABLE_2143414))) (ho_15108 (ho_15107 (ho_15266 k_15739 BOUND_VARIABLE_2143414) BOUND_VARIABLE_2143415) BOUND_VARIABLE_2143416))))) (let ((_let_2455 (forall ((BOUND_VARIABLE_2143310 tptp.int) (BOUND_VARIABLE_2143311 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2143311))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2143311))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2143310) _let_3))) (= (ho_15142 (ho_15141 k_15740 BOUND_VARIABLE_2143310) BOUND_VARIABLE_2143311) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2456 (forall ((BOUND_VARIABLE_2143208 tptp.int) (BOUND_VARIABLE_2143209 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2143209))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2143209))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15741 BOUND_VARIABLE_2143208) BOUND_VARIABLE_2143209) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2143208) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2143208)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2143208))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2457 (forall ((BOUND_VARIABLE_2143113 tptp.int) (BOUND_VARIABLE_2143114 tptp.int) (BOUND_VARIABLE_2143115 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15238 BOUND_VARIABLE_2143115) BOUND_VARIABLE_2143114)) (ho_15260 k_15259 (ho_15141 k_15239 BOUND_VARIABLE_2143113))) (ho_15108 (ho_15107 (ho_15106 k_15742 BOUND_VARIABLE_2143113) BOUND_VARIABLE_2143114) BOUND_VARIABLE_2143115))))) (let ((_let_2458 (forall ((BOUND_VARIABLE_2143034 tptp.rat) (BOUND_VARIABLE_2143035 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2143035))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2143035))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2143034 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15743 BOUND_VARIABLE_2143034) BOUND_VARIABLE_2143035)))))))))))))) (let ((_let_2459 (forall ((BOUND_VARIABLE_2142977 tptp.rat) (BOUND_VARIABLE_2142978 tptp.int) (BOUND_VARIABLE_2142979 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15240 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BOUND_VARIABLE_2142873) _let_3))) (= (ho_15142 (ho_15141 k_15745 BOUND_VARIABLE_2142873) BOUND_VARIABLE_2142874) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2461 (forall ((BOUND_VARIABLE_2142845 tptp.int) (BOUND_VARIABLE_2142846 tptp.int) (BOUND_VARIABLE_2142847 tptp.int) (BOUND_VARIABLE_2142848 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2142845) BOUND_VARIABLE_2142847))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2142846) BOUND_VARIABLE_2142848))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15746 BOUND_VARIABLE_2142845) BOUND_VARIABLE_2142846) BOUND_VARIABLE_2142847) BOUND_VARIABLE_2142848))))))) (let ((_let_2462 (forall ((BOUND_VARIABLE_2142741 tptp.int) (BOUND_VARIABLE_2142742 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2142742))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2142742))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2142741) _let_3))) (= (ho_15142 (ho_15141 k_15747 BOUND_VARIABLE_2142741) BOUND_VARIABLE_2142742) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2463 (forall ((BOUND_VARIABLE_2142713 tptp.int) (BOUND_VARIABLE_2142714 tptp.int) (BOUND_VARIABLE_2142715 tptp.int) (BOUND_VARIABLE_2142716 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2142713) BOUND_VARIABLE_2142715))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2142714) BOUND_VARIABLE_2142716))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15748 BOUND_VARIABLE_2142713) BOUND_VARIABLE_2142714) BOUND_VARIABLE_2142715) BOUND_VARIABLE_2142716))))))) (let ((_let_2464 (forall ((BOUND_VARIABLE_2142634 tptp.rat) (BOUND_VARIABLE_2142635 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2142635))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2142635))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2142634 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15749 BOUND_VARIABLE_2142634) BOUND_VARIABLE_2142635)))))))))))))) (let ((_let_2465 (forall ((BOUND_VARIABLE_2142606 tptp.int) (BOUND_VARIABLE_2142607 tptp.int) (BOUND_VARIABLE_2142608 tptp.int) (BOUND_VARIABLE_2142609 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2142606) BOUND_VARIABLE_2142608))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2142607) BOUND_VARIABLE_2142609))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15750 BOUND_VARIABLE_2142606) BOUND_VARIABLE_2142607) BOUND_VARIABLE_2142608) BOUND_VARIABLE_2142609))))))) (let ((_let_2466 (forall ((BOUND_VARIABLE_2142502 tptp.int) (BOUND_VARIABLE_2142503 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2142503))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2142503))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2142502) _let_3))) (= (ho_15142 (ho_15141 k_15751 BOUND_VARIABLE_2142502) BOUND_VARIABLE_2142503) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2467 (forall ((BOUND_VARIABLE_2142474 tptp.int) (BOUND_VARIABLE_2142475 tptp.int) (BOUND_VARIABLE_2142476 tptp.int) (BOUND_VARIABLE_2142477 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2142474) BOUND_VARIABLE_2142476))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2142475) BOUND_VARIABLE_2142477))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15752 BOUND_VARIABLE_2142474) BOUND_VARIABLE_2142475) BOUND_VARIABLE_2142476) BOUND_VARIABLE_2142477))))))) (let ((_let_2468 (forall ((BOUND_VARIABLE_2142395 tptp.rat) (BOUND_VARIABLE_2142396 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2142396))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2142396))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2142395 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15753 BOUND_VARIABLE_2142395) BOUND_VARIABLE_2142396)))))))))))))) (let ((_let_2469 (forall ((BOUND_VARIABLE_2142293 tptp.int) (BOUND_VARIABLE_2142294 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2142294))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2142294))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15754 BOUND_VARIABLE_2142293) BOUND_VARIABLE_2142294) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2142293) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2142293)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2142293))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2470 (forall ((BOUND_VARIABLE_2142198 tptp.int) (BOUND_VARIABLE_2142199 tptp.int) (BOUND_VARIABLE_2142200 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15242 BOUND_VARIABLE_2142200) BOUND_VARIABLE_2142199)) (ho_15260 k_15259 (ho_15141 k_15243 BOUND_VARIABLE_2142198))) (ho_15108 (ho_15107 (ho_15106 k_15755 BOUND_VARIABLE_2142198) BOUND_VARIABLE_2142199) BOUND_VARIABLE_2142200))))) (let ((_let_2471 (forall ((BOUND_VARIABLE_2142119 tptp.rat) (BOUND_VARIABLE_2142120 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2142120))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2142120))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2142119 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15756 BOUND_VARIABLE_2142119) BOUND_VARIABLE_2142120)))))))))))))) (let ((_let_2472 (forall ((BOUND_VARIABLE_2142062 tptp.rat) (BOUND_VARIABLE_2142063 tptp.int) (BOUND_VARIABLE_2142064 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15244 BOUND_VARIABLE_2142064) BOUND_VARIABLE_2142063)) (ho_15260 k_15259 (ho_15145 k_15245 BOUND_VARIABLE_2142062))) (ho_15108 (ho_15107 (ho_15266 k_15757 BOUND_VARIABLE_2142062) BOUND_VARIABLE_2142063) BOUND_VARIABLE_2142064))))) (let ((_let_2473 (forall ((BOUND_VARIABLE_2141958 tptp.int) (BOUND_VARIABLE_2141959 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2141959))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2141959))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2141958) _let_3))) (= (ho_15142 (ho_15141 k_15758 BOUND_VARIABLE_2141958) BOUND_VARIABLE_2141959) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2474 (forall ((BOUND_VARIABLE_2141856 tptp.int) (BOUND_VARIABLE_2141857 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2141857))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2141857))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15759 BOUND_VARIABLE_2141856) BOUND_VARIABLE_2141857) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 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k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2141682 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15761 BOUND_VARIABLE_2141682) BOUND_VARIABLE_2141683)))))))))))))) (let ((_let_2477 (forall ((BOUND_VARIABLE_2141625 tptp.rat) (BOUND_VARIABLE_2141626 tptp.int) (BOUND_VARIABLE_2141627 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15248 BOUND_VARIABLE_2141627) BOUND_VARIABLE_2141626)) (ho_15260 k_15259 (ho_15145 k_15249 BOUND_VARIABLE_2141625))) (ho_15108 (ho_15107 (ho_15266 k_15762 BOUND_VARIABLE_2141625) BOUND_VARIABLE_2141626) BOUND_VARIABLE_2141627))))) (let ((_let_2478 (forall ((BOUND_VARIABLE_2141521 tptp.int) (BOUND_VARIABLE_2141522 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2141522))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2141522))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2141521) _let_3))) (= (ho_15142 (ho_15141 k_15763 BOUND_VARIABLE_2141521) BOUND_VARIABLE_2141522) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2479 (forall ((BOUND_VARIABLE_2141493 tptp.int) (BOUND_VARIABLE_2141494 tptp.int) (BOUND_VARIABLE_2141495 tptp.int) (BOUND_VARIABLE_2141496 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2141493) BOUND_VARIABLE_2141495))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2141494) BOUND_VARIABLE_2141496))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15764 BOUND_VARIABLE_2141493) BOUND_VARIABLE_2141494) BOUND_VARIABLE_2141495) BOUND_VARIABLE_2141496))))))) (let ((_let_2480 (forall ((BOUND_VARIABLE_2141389 tptp.int) (BOUND_VARIABLE_2141390 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2141390))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2141390))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2141389) _let_3))) (= (ho_15142 (ho_15141 k_15765 BOUND_VARIABLE_2141389) BOUND_VARIABLE_2141390) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2481 (forall ((BOUND_VARIABLE_2141361 tptp.int) (BOUND_VARIABLE_2141362 tptp.int) (BOUND_VARIABLE_2141363 tptp.int) (BOUND_VARIABLE_2141364 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2141361) BOUND_VARIABLE_2141363))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2141362) BOUND_VARIABLE_2141364))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15766 BOUND_VARIABLE_2141361) BOUND_VARIABLE_2141362) BOUND_VARIABLE_2141363) BOUND_VARIABLE_2141364))))))) (let ((_let_2482 (forall ((BOUND_VARIABLE_2141282 tptp.rat) (BOUND_VARIABLE_2141283 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2141283))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2141283))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2141282 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15767 BOUND_VARIABLE_2141282) BOUND_VARIABLE_2141283)))))))))))))) (let ((_let_2483 (forall ((BOUND_VARIABLE_2141180 tptp.int) (BOUND_VARIABLE_2141181 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2141181))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2141181))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15768 BOUND_VARIABLE_2141180) BOUND_VARIABLE_2141181) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2141180) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2141180)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2141180))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2484 (forall ((BOUND_VARIABLE_2141085 tptp.int) (BOUND_VARIABLE_2141086 tptp.int) (BOUND_VARIABLE_2141087 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15250 BOUND_VARIABLE_2141087) BOUND_VARIABLE_2141086)) (ho_15260 k_15259 (ho_15141 k_15251 BOUND_VARIABLE_2141085))) (ho_15108 (ho_15107 (ho_15106 k_15769 BOUND_VARIABLE_2141085) BOUND_VARIABLE_2141086) BOUND_VARIABLE_2141087))))) (let ((_let_2485 (forall ((BOUND_VARIABLE_2141006 tptp.rat) (BOUND_VARIABLE_2141007 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2141007))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2141007))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2141006 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15770 BOUND_VARIABLE_2141006) BOUND_VARIABLE_2141007)))))))))))))) (let ((_let_2486 (forall ((BOUND_VARIABLE_2140949 tptp.rat) (BOUND_VARIABLE_2140950 tptp.int) (BOUND_VARIABLE_2140951 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15252 BOUND_VARIABLE_2140951) BOUND_VARIABLE_2140950)) (ho_15260 k_15259 (ho_15145 k_15253 BOUND_VARIABLE_2140949))) (ho_15108 (ho_15107 (ho_15266 k_15771 BOUND_VARIABLE_2140949) BOUND_VARIABLE_2140950) BOUND_VARIABLE_2140951))))) (let ((_let_2487 (forall ((BOUND_VARIABLE_2140845 tptp.int) (BOUND_VARIABLE_2140846 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2140846))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2140846))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2140845) _let_3))) (= (ho_15142 (ho_15141 k_15772 BOUND_VARIABLE_2140845) BOUND_VARIABLE_2140846) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2488 (forall ((BOUND_VARIABLE_2140743 tptp.int) (BOUND_VARIABLE_2140744 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2140744))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2140744))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15773 BOUND_VARIABLE_2140743) BOUND_VARIABLE_2140744) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2140743) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2140743)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2140743))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2489 (forall ((BOUND_VARIABLE_2140648 tptp.int) (BOUND_VARIABLE_2140649 tptp.int) (BOUND_VARIABLE_2140650 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15254 BOUND_VARIABLE_2140650) BOUND_VARIABLE_2140649)) (ho_15260 k_15259 (ho_15141 k_15255 BOUND_VARIABLE_2140648))) (ho_15108 (ho_15107 (ho_15106 k_15774 BOUND_VARIABLE_2140648) BOUND_VARIABLE_2140649) BOUND_VARIABLE_2140650))))) (let ((_let_2490 (forall ((BOUND_VARIABLE_2140569 tptp.rat) (BOUND_VARIABLE_2140570 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2140570))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2140570))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2140569 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15775 BOUND_VARIABLE_2140569) BOUND_VARIABLE_2140570)))))))))))))) (let ((_let_2491 (forall ((BOUND_VARIABLE_2140512 tptp.rat) (BOUND_VARIABLE_2140513 tptp.int) (BOUND_VARIABLE_2140514 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15256 BOUND_VARIABLE_2140514) BOUND_VARIABLE_2140513)) (ho_15260 k_15259 (ho_15145 k_15257 BOUND_VARIABLE_2140512))) (ho_15108 (ho_15107 (ho_15266 k_15776 BOUND_VARIABLE_2140512) BOUND_VARIABLE_2140513) BOUND_VARIABLE_2140514))))) (let ((_let_2492 (forall ((BOUND_VARIABLE_2140408 tptp.int) (BOUND_VARIABLE_2140409 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2140409))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2140409))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2140408) _let_3))) (= (ho_15142 (ho_15141 k_15777 BOUND_VARIABLE_2140408) BOUND_VARIABLE_2140409) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2493 (forall ((BOUND_VARIABLE_2140380 tptp.int) (BOUND_VARIABLE_2140381 tptp.int) (BOUND_VARIABLE_2140382 tptp.int) (BOUND_VARIABLE_2140383 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2140380) BOUND_VARIABLE_2140382))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2140381) BOUND_VARIABLE_2140383))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15778 BOUND_VARIABLE_2140380) BOUND_VARIABLE_2140381) BOUND_VARIABLE_2140382) BOUND_VARIABLE_2140383))))))) (let ((_let_2494 (forall ((BOUND_VARIABLE_2140276 tptp.int) (BOUND_VARIABLE_2140277 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2140277))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2140277))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2140276) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15779 BOUND_VARIABLE_2140276) BOUND_VARIABLE_2140277) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2495 (forall ((BOUND_VARIABLE_2140248 tptp.int) (BOUND_VARIABLE_2140249 tptp.int) (BOUND_VARIABLE_2140250 tptp.int) (BOUND_VARIABLE_2140251 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2140248) BOUND_VARIABLE_2140250))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2140249) BOUND_VARIABLE_2140251))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15780 BOUND_VARIABLE_2140248) BOUND_VARIABLE_2140249) BOUND_VARIABLE_2140250) BOUND_VARIABLE_2140251))))))) (let ((_let_2496 (forall ((BOUND_VARIABLE_2140165 tptp.rat) (BOUND_VARIABLE_2140166 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2140166))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2140166))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15139 _let_9 k_15127))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 k_15781 BOUND_VARIABLE_2140165) BOUND_VARIABLE_2140166) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2140165) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2497 (forall ((BOUND_VARIABLE_2139994 tptp.rat) (BOUND_VARIABLE_2139995 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15265 BOUND_VARIABLE_2139994)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15258 BOUND_VARIABLE_2139995))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15263 BOUND_VARIABLE_2139995)) (ho_15260 k_15259 (ho_15145 k_15264 BOUND_VARIABLE_2139994))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15267 BOUND_VARIABLE_2139995))))) (ho_15108 (ho_15783 k_15782 BOUND_VARIABLE_2139994) BOUND_VARIABLE_2139995)))))) (let ((_let_2498 (forall ((BOUND_VARIABLE_2139966 tptp.int) (BOUND_VARIABLE_2139967 tptp.int) (BOUND_VARIABLE_2139968 tptp.int) (BOUND_VARIABLE_2139969 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2139966) BOUND_VARIABLE_2139968))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2139967) BOUND_VARIABLE_2139969))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15784 BOUND_VARIABLE_2139966) BOUND_VARIABLE_2139967) BOUND_VARIABLE_2139968) BOUND_VARIABLE_2139969))))))) (let ((_let_2499 (forall ((BOUND_VARIABLE_2139862 tptp.int) (BOUND_VARIABLE_2139863 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2139863))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2139863))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2139862) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15785 BOUND_VARIABLE_2139862) BOUND_VARIABLE_2139863) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2500 (forall ((BOUND_VARIABLE_2139834 tptp.int) (BOUND_VARIABLE_2139835 tptp.int) (BOUND_VARIABLE_2139836 tptp.int) (BOUND_VARIABLE_2139837 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2139834) BOUND_VARIABLE_2139836))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2139835) BOUND_VARIABLE_2139837))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15786 BOUND_VARIABLE_2139834) BOUND_VARIABLE_2139835) BOUND_VARIABLE_2139836) BOUND_VARIABLE_2139837))))))) (let ((_let_2501 (forall ((BOUND_VARIABLE_2139755 tptp.rat) (BOUND_VARIABLE_2139756 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2139756))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2139756))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2139755 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15787 BOUND_VARIABLE_2139755) BOUND_VARIABLE_2139756)))))))))))))) (let ((_let_2502 (forall ((BOUND_VARIABLE_2139727 tptp.int) (BOUND_VARIABLE_2139728 tptp.int) (BOUND_VARIABLE_2139729 tptp.int) (BOUND_VARIABLE_2139730 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2139727) BOUND_VARIABLE_2139729))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2139728) BOUND_VARIABLE_2139730))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15788 BOUND_VARIABLE_2139727) BOUND_VARIABLE_2139728) BOUND_VARIABLE_2139729) BOUND_VARIABLE_2139730))))))) (let ((_let_2503 (forall ((BOUND_VARIABLE_2139623 tptp.int) (BOUND_VARIABLE_2139624 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2139624))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2139624))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2139623) _let_3))) (= (ho_15142 (ho_15141 k_15789 BOUND_VARIABLE_2139623) BOUND_VARIABLE_2139624) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2504 (forall ((BOUND_VARIABLE_2139595 tptp.int) (BOUND_VARIABLE_2139596 tptp.int) (BOUND_VARIABLE_2139597 tptp.int) (BOUND_VARIABLE_2139598 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2139595) BOUND_VARIABLE_2139597))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2139596) BOUND_VARIABLE_2139598))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15790 BOUND_VARIABLE_2139595) BOUND_VARIABLE_2139596) BOUND_VARIABLE_2139597) BOUND_VARIABLE_2139598))))))) (let ((_let_2505 (forall ((BOUND_VARIABLE_2139510 tptp.rat) (BOUND_VARIABLE_2139511 tptp.rat) (BOUND_VARIABLE_2139512 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2139512))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2139512))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15791 BOUND_VARIABLE_2139510) BOUND_VARIABLE_2139511) BOUND_VARIABLE_2139512) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 BOUND_VARIABLE_2139510)) BOUND_VARIABLE_2139511) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2506 (forall ((BOUND_VARIABLE_2139408 tptp.int) (BOUND_VARIABLE_2139409 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2139409))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2139409))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15792 BOUND_VARIABLE_2139408) BOUND_VARIABLE_2139409) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2139408) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2139408)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2139408))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2507 (forall ((BOUND_VARIABLE_2139313 tptp.int) (BOUND_VARIABLE_2139314 tptp.int) (BOUND_VARIABLE_2139315 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15268 BOUND_VARIABLE_2139315) BOUND_VARIABLE_2139314)) (ho_15260 k_15259 (ho_15141 k_15269 BOUND_VARIABLE_2139313))) (ho_15108 (ho_15107 (ho_15106 k_15793 BOUND_VARIABLE_2139313) BOUND_VARIABLE_2139314) BOUND_VARIABLE_2139315))))) (let ((_let_2508 (forall ((BOUND_VARIABLE_2139228 tptp.rat) (BOUND_VARIABLE_2139229 tptp.rat) (BOUND_VARIABLE_2139230 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2139230))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2139230))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15794 BOUND_VARIABLE_2139228) BOUND_VARIABLE_2139229) BOUND_VARIABLE_2139230) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 BOUND_VARIABLE_2139228)) BOUND_VARIABLE_2139229) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2509 (forall ((BOUND_VARIABLE_2139162 tptp.rat) (BOUND_VARIABLE_2139163 tptp.rat) (BOUND_VARIABLE_2139164 tptp.int) (BOUND_VARIABLE_2139165 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15270 BOUND_VARIABLE_2139165) BOUND_VARIABLE_2139164)) (ho_15260 k_15259 (ho_15145 (ho_15209 k_15271 BOUND_VARIABLE_2139162) BOUND_VARIABLE_2139163))) (ho_15108 (ho_15107 (ho_15266 (ho_15633 k_15795 BOUND_VARIABLE_2139162) BOUND_VARIABLE_2139163) BOUND_VARIABLE_2139164) BOUND_VARIABLE_2139165))))) (let ((_let_2510 (forall ((BOUND_VARIABLE_2139058 tptp.int) (BOUND_VARIABLE_2139059 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2139059))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2139059))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2139058) _let_3))) (= (ho_15142 (ho_15141 k_15796 BOUND_VARIABLE_2139058) BOUND_VARIABLE_2139059) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2511 (forall ((BOUND_VARIABLE_2138956 tptp.int) (BOUND_VARIABLE_2138957 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2138957))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2138957))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15797 BOUND_VARIABLE_2138956) BOUND_VARIABLE_2138957) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2138956) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2138956)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2138956))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2512 (forall ((BOUND_VARIABLE_2138861 tptp.int) (BOUND_VARIABLE_2138862 tptp.int) (BOUND_VARIABLE_2138863 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15272 BOUND_VARIABLE_2138863) BOUND_VARIABLE_2138862)) (ho_15260 k_15259 (ho_15141 k_15273 BOUND_VARIABLE_2138861))) (ho_15108 (ho_15107 (ho_15106 k_15798 BOUND_VARIABLE_2138861) BOUND_VARIABLE_2138862) BOUND_VARIABLE_2138863))))) (let ((_let_2513 (forall ((BOUND_VARIABLE_2138776 tptp.rat) (BOUND_VARIABLE_2138777 tptp.rat) (BOUND_VARIABLE_2138778 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2138778))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2138778))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15799 BOUND_VARIABLE_2138776) BOUND_VARIABLE_2138777) BOUND_VARIABLE_2138778) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 BOUND_VARIABLE_2138776)) BOUND_VARIABLE_2138777) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2514 (forall ((BOUND_VARIABLE_2138710 tptp.rat) (BOUND_VARIABLE_2138711 tptp.rat) (BOUND_VARIABLE_2138712 tptp.int) (BOUND_VARIABLE_2138713 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15274 BOUND_VARIABLE_2138713) BOUND_VARIABLE_2138712)) (ho_15260 k_15259 (ho_15145 (ho_15209 k_15275 BOUND_VARIABLE_2138710) BOUND_VARIABLE_2138711))) (ho_15108 (ho_15107 (ho_15266 (ho_15633 k_15800 BOUND_VARIABLE_2138710) BOUND_VARIABLE_2138711) BOUND_VARIABLE_2138712) BOUND_VARIABLE_2138713))))) (let ((_let_2515 (forall ((BOUND_VARIABLE_2138606 tptp.int) (BOUND_VARIABLE_2138607 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2138607))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2138607))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2138606) _let_3))) (= (ho_15142 (ho_15141 k_15801 BOUND_VARIABLE_2138606) BOUND_VARIABLE_2138607) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2516 (forall ((BOUND_VARIABLE_2138578 tptp.int) (BOUND_VARIABLE_2138579 tptp.int) (BOUND_VARIABLE_2138580 tptp.int) (BOUND_VARIABLE_2138581 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2138578) BOUND_VARIABLE_2138580))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2138579) BOUND_VARIABLE_2138581))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15802 BOUND_VARIABLE_2138578) BOUND_VARIABLE_2138579) BOUND_VARIABLE_2138580) BOUND_VARIABLE_2138581))))))) (let ((_let_2517 (forall ((BOUND_VARIABLE_2138474 tptp.int) (BOUND_VARIABLE_2138475 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2138475))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2138475))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2138474) _let_3))) (= (ho_15142 (ho_15141 k_15803 BOUND_VARIABLE_2138474) BOUND_VARIABLE_2138475) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2518 (forall ((BOUND_VARIABLE_2138446 tptp.int) (BOUND_VARIABLE_2138447 tptp.int) (BOUND_VARIABLE_2138448 tptp.int) (BOUND_VARIABLE_2138449 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2138446) BOUND_VARIABLE_2138448))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2138447) BOUND_VARIABLE_2138449))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15804 BOUND_VARIABLE_2138446) BOUND_VARIABLE_2138447) BOUND_VARIABLE_2138448) BOUND_VARIABLE_2138449))))))) (let ((_let_2519 (forall ((BOUND_VARIABLE_2138361 tptp.rat) (BOUND_VARIABLE_2138362 tptp.rat) (BOUND_VARIABLE_2138363 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2138363))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2138363))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15805 BOUND_VARIABLE_2138361) BOUND_VARIABLE_2138362) BOUND_VARIABLE_2138363) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 BOUND_VARIABLE_2138361)) BOUND_VARIABLE_2138362) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2520 (forall ((BOUND_VARIABLE_2138259 tptp.int) (BOUND_VARIABLE_2138260 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2138260))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2138260))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15806 BOUND_VARIABLE_2138259) BOUND_VARIABLE_2138260) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2138259) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2138259)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2138259))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2521 (forall ((BOUND_VARIABLE_2138164 tptp.int) (BOUND_VARIABLE_2138165 tptp.int) (BOUND_VARIABLE_2138166 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15276 BOUND_VARIABLE_2138166) BOUND_VARIABLE_2138165)) (ho_15260 k_15259 (ho_15141 k_15277 BOUND_VARIABLE_2138164))) (ho_15108 (ho_15107 (ho_15106 k_15807 BOUND_VARIABLE_2138164) BOUND_VARIABLE_2138165) BOUND_VARIABLE_2138166))))) (let ((_let_2522 (forall ((BOUND_VARIABLE_2138079 tptp.rat) (BOUND_VARIABLE_2138080 tptp.rat) (BOUND_VARIABLE_2138081 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2138081))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2138081))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15808 BOUND_VARIABLE_2138079) BOUND_VARIABLE_2138080) BOUND_VARIABLE_2138081) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 BOUND_VARIABLE_2138079)) BOUND_VARIABLE_2138080) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2523 (forall ((BOUND_VARIABLE_2138013 tptp.rat) (BOUND_VARIABLE_2138014 tptp.rat) (BOUND_VARIABLE_2138015 tptp.int) (BOUND_VARIABLE_2138016 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15278 BOUND_VARIABLE_2138016) BOUND_VARIABLE_2138015)) (ho_15260 k_15259 (ho_15145 (ho_15209 k_15279 BOUND_VARIABLE_2138013) BOUND_VARIABLE_2138014))) (ho_15108 (ho_15107 (ho_15266 (ho_15633 k_15809 BOUND_VARIABLE_2138013) BOUND_VARIABLE_2138014) BOUND_VARIABLE_2138015) BOUND_VARIABLE_2138016))))) (let ((_let_2524 (forall ((BOUND_VARIABLE_2137909 tptp.int) (BOUND_VARIABLE_2137910 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2137910))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2137910))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2137909) _let_3))) (= (ho_15142 (ho_15141 k_15810 BOUND_VARIABLE_2137909) BOUND_VARIABLE_2137910) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2525 (forall ((BOUND_VARIABLE_2137881 tptp.int) (BOUND_VARIABLE_2137882 tptp.int) (BOUND_VARIABLE_2137883 tptp.int) (BOUND_VARIABLE_2137884 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2137881) BOUND_VARIABLE_2137883))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2137882) BOUND_VARIABLE_2137884))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15811 BOUND_VARIABLE_2137881) BOUND_VARIABLE_2137882) BOUND_VARIABLE_2137883) BOUND_VARIABLE_2137884))))))) (let ((_let_2526 (forall ((BOUND_VARIABLE_2137777 tptp.int) (BOUND_VARIABLE_2137778 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2137778))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2137778))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2137777) _let_3))) (= (ho_15142 (ho_15141 k_15812 BOUND_VARIABLE_2137777) BOUND_VARIABLE_2137778) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2527 (forall ((BOUND_VARIABLE_2137749 tptp.int) (BOUND_VARIABLE_2137750 tptp.int) (BOUND_VARIABLE_2137751 tptp.int) (BOUND_VARIABLE_2137752 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2137749) BOUND_VARIABLE_2137751))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2137750) BOUND_VARIABLE_2137752))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15813 BOUND_VARIABLE_2137749) BOUND_VARIABLE_2137750) BOUND_VARIABLE_2137751) BOUND_VARIABLE_2137752))))))) (let ((_let_2528 (forall ((BOUND_VARIABLE_2137664 tptp.rat) (BOUND_VARIABLE_2137665 tptp.rat) (BOUND_VARIABLE_2137666 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2137666))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2137666))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_15814 BOUND_VARIABLE_2137664) BOUND_VARIABLE_2137665) BOUND_VARIABLE_2137666) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 BOUND_VARIABLE_2137664)) BOUND_VARIABLE_2137665) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2529 (forall ((BOUND_VARIABLE_2137562 tptp.int) (BOUND_VARIABLE_2137563 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2137563))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2137563))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15815 BOUND_VARIABLE_2137562) BOUND_VARIABLE_2137563) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2137562) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2137562)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2137562))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2530 (forall ((BOUND_VARIABLE_2137467 tptp.int) (BOUND_VARIABLE_2137468 tptp.int) (BOUND_VARIABLE_2137469 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15280 BOUND_VARIABLE_2137469) BOUND_VARIABLE_2137468)) (ho_15260 k_15259 (ho_15141 k_15281 BOUND_VARIABLE_2137467))) (ho_15108 (ho_15107 (ho_15106 k_15816 BOUND_VARIABLE_2137467) BOUND_VARIABLE_2137468) BOUND_VARIABLE_2137469))))) (let ((_let_2531 (forall ((BOUND_VARIABLE_2137388 tptp.rat) (BOUND_VARIABLE_2137389 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2137389))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2137389))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2137388 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15817 BOUND_VARIABLE_2137388) BOUND_VARIABLE_2137389)))))))))))))) (let ((_let_2532 (forall ((BOUND_VARIABLE_2137331 tptp.rat) (BOUND_VARIABLE_2137332 tptp.int) (BOUND_VARIABLE_2137333 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15282 BOUND_VARIABLE_2137333) BOUND_VARIABLE_2137332)) (ho_15260 k_15259 (ho_15145 k_15283 BOUND_VARIABLE_2137331))) (ho_15108 (ho_15107 (ho_15266 k_15818 BOUND_VARIABLE_2137331) BOUND_VARIABLE_2137332) BOUND_VARIABLE_2137333))))) (let ((_let_2533 (forall ((BOUND_VARIABLE_2137227 tptp.int) (BOUND_VARIABLE_2137228 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2137228))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2137228))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2137227) _let_3))) (= (ho_15142 (ho_15141 k_15819 BOUND_VARIABLE_2137227) BOUND_VARIABLE_2137228) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2534 (forall ((BOUND_VARIABLE_2137199 tptp.int) (BOUND_VARIABLE_2137200 tptp.int) (BOUND_VARIABLE_2137201 tptp.int) (BOUND_VARIABLE_2137202 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2137199) BOUND_VARIABLE_2137201))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2137200) BOUND_VARIABLE_2137202))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15820 BOUND_VARIABLE_2137199) BOUND_VARIABLE_2137200) BOUND_VARIABLE_2137201) BOUND_VARIABLE_2137202))))))) (let ((_let_2535 (forall ((BOUND_VARIABLE_2137095 tptp.int) (BOUND_VARIABLE_2137096 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2137096))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2137096))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2137095) _let_3))) (= (ho_15142 (ho_15141 k_15821 BOUND_VARIABLE_2137095) BOUND_VARIABLE_2137096) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2536 (forall ((BOUND_VARIABLE_2137067 tptp.int) (BOUND_VARIABLE_2137068 tptp.int) (BOUND_VARIABLE_2137069 tptp.int) (BOUND_VARIABLE_2137070 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2137067) BOUND_VARIABLE_2137069))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2137068) BOUND_VARIABLE_2137070))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15822 BOUND_VARIABLE_2137067) BOUND_VARIABLE_2137068) BOUND_VARIABLE_2137069) BOUND_VARIABLE_2137070))))))) (let ((_let_2537 (forall ((BOUND_VARIABLE_2136988 tptp.rat) (BOUND_VARIABLE_2136989 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2136989))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2136989))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2136988 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15823 BOUND_VARIABLE_2136988) BOUND_VARIABLE_2136989)))))))))))))) (let ((_let_2538 (forall ((BOUND_VARIABLE_2136886 tptp.int) (BOUND_VARIABLE_2136887 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2136887))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2136887))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15824 BOUND_VARIABLE_2136886) BOUND_VARIABLE_2136887) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2136886) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2136886)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2136886))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2539 (forall ((BOUND_VARIABLE_2136791 tptp.int) (BOUND_VARIABLE_2136792 tptp.int) (BOUND_VARIABLE_2136793 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15284 BOUND_VARIABLE_2136793) BOUND_VARIABLE_2136792)) (ho_15260 k_15259 (ho_15141 k_15285 BOUND_VARIABLE_2136791))) (ho_15108 (ho_15107 (ho_15106 k_15825 BOUND_VARIABLE_2136791) BOUND_VARIABLE_2136792) BOUND_VARIABLE_2136793))))) (let ((_let_2540 (forall ((BOUND_VARIABLE_2136712 tptp.rat) (BOUND_VARIABLE_2136713 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2136713))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2136713))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2136712 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15826 BOUND_VARIABLE_2136712) BOUND_VARIABLE_2136713)))))))))))))) (let ((_let_2541 (forall ((BOUND_VARIABLE_2136655 tptp.rat) (BOUND_VARIABLE_2136656 tptp.int) (BOUND_VARIABLE_2136657 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15286 BOUND_VARIABLE_2136657) BOUND_VARIABLE_2136656)) (ho_15260 k_15259 (ho_15145 k_15287 BOUND_VARIABLE_2136655))) (ho_15108 (ho_15107 (ho_15266 k_15827 BOUND_VARIABLE_2136655) BOUND_VARIABLE_2136656) BOUND_VARIABLE_2136657))))) (let ((_let_2542 (forall ((BOUND_VARIABLE_2136551 tptp.int) (BOUND_VARIABLE_2136552 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2136552))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2136552))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2136551) _let_3))) (= (ho_15142 (ho_15141 k_15828 BOUND_VARIABLE_2136551) BOUND_VARIABLE_2136552) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2543 (forall ((BOUND_VARIABLE_2136523 tptp.int) (BOUND_VARIABLE_2136524 tptp.int) (BOUND_VARIABLE_2136525 tptp.int) (BOUND_VARIABLE_2136526 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2136523) BOUND_VARIABLE_2136525))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2136524) BOUND_VARIABLE_2136526))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15829 BOUND_VARIABLE_2136523) BOUND_VARIABLE_2136524) BOUND_VARIABLE_2136525) BOUND_VARIABLE_2136526))))))) (let ((_let_2544 (forall ((BOUND_VARIABLE_2136419 tptp.int) (BOUND_VARIABLE_2136420 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2136420))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2136420))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2136419) _let_3))) (= (ho_15142 (ho_15141 k_15830 BOUND_VARIABLE_2136419) BOUND_VARIABLE_2136420) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2545 (forall ((BOUND_VARIABLE_2136391 tptp.int) (BOUND_VARIABLE_2136392 tptp.int) (BOUND_VARIABLE_2136393 tptp.int) (BOUND_VARIABLE_2136394 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2136391) BOUND_VARIABLE_2136393))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2136392) BOUND_VARIABLE_2136394))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15831 BOUND_VARIABLE_2136391) BOUND_VARIABLE_2136392) BOUND_VARIABLE_2136393) BOUND_VARIABLE_2136394))))))) (let ((_let_2546 (forall ((BOUND_VARIABLE_2136312 tptp.rat) (BOUND_VARIABLE_2136313 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2136313))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2136313))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2136312 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15832 BOUND_VARIABLE_2136312) BOUND_VARIABLE_2136313)))))))))))))) (let ((_let_2547 (forall ((BOUND_VARIABLE_2136210 tptp.int) (BOUND_VARIABLE_2136211 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2136211))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2136211))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15833 BOUND_VARIABLE_2136210) BOUND_VARIABLE_2136211) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2136210) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2136210)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2136210))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2548 (forall ((BOUND_VARIABLE_2136115 tptp.int) (BOUND_VARIABLE_2136116 tptp.int) (BOUND_VARIABLE_2136117 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15288 BOUND_VARIABLE_2136117) BOUND_VARIABLE_2136116)) (ho_15260 k_15259 (ho_15141 k_15289 BOUND_VARIABLE_2136115))) (ho_15108 (ho_15107 (ho_15106 k_15834 BOUND_VARIABLE_2136115) BOUND_VARIABLE_2136116) BOUND_VARIABLE_2136117))))) (let ((_let_2549 (forall ((BOUND_VARIABLE_2136036 tptp.rat) (BOUND_VARIABLE_2136037 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2136037))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2136037))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2136036 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15835 BOUND_VARIABLE_2136036) BOUND_VARIABLE_2136037)))))))))))))) (let ((_let_2550 (forall ((BOUND_VARIABLE_2135979 tptp.rat) (BOUND_VARIABLE_2135980 tptp.int) (BOUND_VARIABLE_2135981 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15290 BOUND_VARIABLE_2135981) BOUND_VARIABLE_2135980)) (ho_15260 k_15259 (ho_15145 k_15291 BOUND_VARIABLE_2135979))) (ho_15108 (ho_15107 (ho_15266 k_15836 BOUND_VARIABLE_2135979) BOUND_VARIABLE_2135980) BOUND_VARIABLE_2135981))))) (let ((_let_2551 (forall ((BOUND_VARIABLE_2135875 tptp.int) (BOUND_VARIABLE_2135876 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2135876))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2135876))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2135875) _let_3))) (= (ho_15142 (ho_15141 k_15837 BOUND_VARIABLE_2135875) BOUND_VARIABLE_2135876) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2552 (forall ((BOUND_VARIABLE_2135847 tptp.int) (BOUND_VARIABLE_2135848 tptp.int) (BOUND_VARIABLE_2135849 tptp.int) (BOUND_VARIABLE_2135850 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135847) BOUND_VARIABLE_2135849))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135848) BOUND_VARIABLE_2135850))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15838 BOUND_VARIABLE_2135847) BOUND_VARIABLE_2135848) BOUND_VARIABLE_2135849) BOUND_VARIABLE_2135850))))))) (let ((_let_2553 (forall ((BOUND_VARIABLE_2135743 tptp.int) (BOUND_VARIABLE_2135744 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2135744))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2135744))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2135743) _let_3))) (= (ho_15142 (ho_15141 k_15839 BOUND_VARIABLE_2135743) BOUND_VARIABLE_2135744) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2554 (forall ((BOUND_VARIABLE_2135715 tptp.int) (BOUND_VARIABLE_2135716 tptp.int) (BOUND_VARIABLE_2135717 tptp.int) (BOUND_VARIABLE_2135718 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135715) BOUND_VARIABLE_2135717))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135716) BOUND_VARIABLE_2135718))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15840 BOUND_VARIABLE_2135715) BOUND_VARIABLE_2135716) BOUND_VARIABLE_2135717) BOUND_VARIABLE_2135718))))))) (let ((_let_2555 (forall ((BOUND_VARIABLE_2135636 tptp.rat) (BOUND_VARIABLE_2135637 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2135637))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2135637))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2135636 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15841 BOUND_VARIABLE_2135636) BOUND_VARIABLE_2135637)))))))))))))) (let ((_let_2556 (forall ((BOUND_VARIABLE_2135608 tptp.int) (BOUND_VARIABLE_2135609 tptp.int) (BOUND_VARIABLE_2135610 tptp.int) (BOUND_VARIABLE_2135611 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135608) BOUND_VARIABLE_2135610))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135609) BOUND_VARIABLE_2135611))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15842 BOUND_VARIABLE_2135608) BOUND_VARIABLE_2135609) BOUND_VARIABLE_2135610) BOUND_VARIABLE_2135611))))))) (let ((_let_2557 (forall ((BOUND_VARIABLE_2135504 tptp.int) (BOUND_VARIABLE_2135505 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2135505))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2135505))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2135504) _let_3))) (= (ho_15142 (ho_15141 k_15843 BOUND_VARIABLE_2135504) BOUND_VARIABLE_2135505) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2558 (forall ((BOUND_VARIABLE_2135476 tptp.int) (BOUND_VARIABLE_2135477 tptp.int) (BOUND_VARIABLE_2135478 tptp.int) (BOUND_VARIABLE_2135479 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135476) BOUND_VARIABLE_2135478))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135477) BOUND_VARIABLE_2135479))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15844 BOUND_VARIABLE_2135476) BOUND_VARIABLE_2135477) BOUND_VARIABLE_2135478) BOUND_VARIABLE_2135479))))))) (let ((_let_2559 (forall ((BOUND_VARIABLE_2135397 tptp.rat) (BOUND_VARIABLE_2135398 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2135398))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2135398))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2135397 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15845 BOUND_VARIABLE_2135397) BOUND_VARIABLE_2135398)))))))))))))) (let ((_let_2560 (forall ((BOUND_VARIABLE_2135369 tptp.int) (BOUND_VARIABLE_2135370 tptp.int) (BOUND_VARIABLE_2135371 tptp.int) (BOUND_VARIABLE_2135372 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135369) BOUND_VARIABLE_2135371))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135370) BOUND_VARIABLE_2135372))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15846 BOUND_VARIABLE_2135369) BOUND_VARIABLE_2135370) BOUND_VARIABLE_2135371) BOUND_VARIABLE_2135372))))))) (let ((_let_2561 (forall ((BOUND_VARIABLE_2135265 tptp.int) (BOUND_VARIABLE_2135266 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2135266))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2135266))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2135265) _let_3))) (= (ho_15142 (ho_15141 k_15847 BOUND_VARIABLE_2135265) BOUND_VARIABLE_2135266) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2562 (forall ((BOUND_VARIABLE_2135237 tptp.int) (BOUND_VARIABLE_2135238 tptp.int) (BOUND_VARIABLE_2135239 tptp.int) (BOUND_VARIABLE_2135240 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135237) BOUND_VARIABLE_2135239))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2135238) BOUND_VARIABLE_2135240))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15848 BOUND_VARIABLE_2135237) BOUND_VARIABLE_2135238) BOUND_VARIABLE_2135239) BOUND_VARIABLE_2135240))))))) (let ((_let_2563 (forall ((BOUND_VARIABLE_2135158 tptp.rat) (BOUND_VARIABLE_2135159 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2135159))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2135159))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2135158 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15849 BOUND_VARIABLE_2135158) BOUND_VARIABLE_2135159)))))))))))))) (let ((_let_2564 (forall ((BOUND_VARIABLE_2135056 tptp.int) (BOUND_VARIABLE_2135057 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2135057))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2135057))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15850 BOUND_VARIABLE_2135056) BOUND_VARIABLE_2135057) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2135056) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2135056)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2135056))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2565 (forall ((BOUND_VARIABLE_2134961 tptp.int) (BOUND_VARIABLE_2134962 tptp.int) (BOUND_VARIABLE_2134963 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15292 BOUND_VARIABLE_2134963) BOUND_VARIABLE_2134962)) (ho_15260 k_15259 (ho_15141 k_15293 BOUND_VARIABLE_2134961))) (ho_15108 (ho_15107 (ho_15106 k_15851 BOUND_VARIABLE_2134961) BOUND_VARIABLE_2134962) BOUND_VARIABLE_2134963))))) (let ((_let_2566 (forall ((BOUND_VARIABLE_2134882 tptp.rat) (BOUND_VARIABLE_2134883 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2134883))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2134883))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2134882 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15852 BOUND_VARIABLE_2134882) BOUND_VARIABLE_2134883)))))))))))))) (let ((_let_2567 (forall ((BOUND_VARIABLE_2134825 tptp.rat) (BOUND_VARIABLE_2134826 tptp.int) (BOUND_VARIABLE_2134827 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15294 BOUND_VARIABLE_2134827) BOUND_VARIABLE_2134826)) (ho_15260 k_15259 (ho_15145 k_15295 BOUND_VARIABLE_2134825))) (ho_15108 (ho_15107 (ho_15266 k_15853 BOUND_VARIABLE_2134825) BOUND_VARIABLE_2134826) BOUND_VARIABLE_2134827))))) (let ((_let_2568 (forall ((BOUND_VARIABLE_2134721 tptp.int) (BOUND_VARIABLE_2134722 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2134722))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2134722))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2134721) _let_3))) (= (ho_15142 (ho_15141 k_15854 BOUND_VARIABLE_2134721) BOUND_VARIABLE_2134722) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2569 (forall ((BOUND_VARIABLE_2134693 tptp.int) (BOUND_VARIABLE_2134694 tptp.int) (BOUND_VARIABLE_2134695 tptp.int) (BOUND_VARIABLE_2134696 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134693) BOUND_VARIABLE_2134695))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134694) BOUND_VARIABLE_2134696))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15855 BOUND_VARIABLE_2134693) BOUND_VARIABLE_2134694) BOUND_VARIABLE_2134695) BOUND_VARIABLE_2134696))))))) (let ((_let_2570 (forall ((BOUND_VARIABLE_2134589 tptp.int) (BOUND_VARIABLE_2134590 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2134590))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2134590))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2134589) _let_3))) (= (ho_15142 (ho_15141 k_15856 BOUND_VARIABLE_2134589) BOUND_VARIABLE_2134590) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2571 (forall ((BOUND_VARIABLE_2134561 tptp.int) (BOUND_VARIABLE_2134562 tptp.int) (BOUND_VARIABLE_2134563 tptp.int) (BOUND_VARIABLE_2134564 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134561) BOUND_VARIABLE_2134563))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134562) BOUND_VARIABLE_2134564))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15857 BOUND_VARIABLE_2134561) BOUND_VARIABLE_2134562) BOUND_VARIABLE_2134563) BOUND_VARIABLE_2134564))))))) (let ((_let_2572 (forall ((BOUND_VARIABLE_2134482 tptp.rat) (BOUND_VARIABLE_2134483 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2134483))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2134483))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 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_let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2575 (forall ((BOUND_VARIABLE_2134322 tptp.int) (BOUND_VARIABLE_2134323 tptp.int) (BOUND_VARIABLE_2134324 tptp.int) (BOUND_VARIABLE_2134325 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134322) BOUND_VARIABLE_2134324))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134323) BOUND_VARIABLE_2134325))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15861 BOUND_VARIABLE_2134322) BOUND_VARIABLE_2134323) BOUND_VARIABLE_2134324) BOUND_VARIABLE_2134325))))))) (let ((_let_2576 (forall ((BOUND_VARIABLE_2134239 tptp.rat) (BOUND_VARIABLE_2134240 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2134240))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2134240))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15862 BOUND_VARIABLE_2134239) BOUND_VARIABLE_2134240) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2134239) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2577 (forall ((BOUND_VARIABLE_2134211 tptp.int) (BOUND_VARIABLE_2134212 tptp.int) (BOUND_VARIABLE_2134213 tptp.int) (BOUND_VARIABLE_2134214 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134211) BOUND_VARIABLE_2134213))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134212) BOUND_VARIABLE_2134214))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15863 BOUND_VARIABLE_2134211) BOUND_VARIABLE_2134212) BOUND_VARIABLE_2134213) BOUND_VARIABLE_2134214))))))) (let ((_let_2578 (forall ((BOUND_VARIABLE_2134183 tptp.int) (BOUND_VARIABLE_2134184 tptp.int) (BOUND_VARIABLE_2134185 tptp.int) (BOUND_VARIABLE_2134186 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134183) BOUND_VARIABLE_2134185))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134184) BOUND_VARIABLE_2134186))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15864 BOUND_VARIABLE_2134183) BOUND_VARIABLE_2134184) BOUND_VARIABLE_2134185) BOUND_VARIABLE_2134186))))))) (let ((_let_2579 (forall ((BOUND_VARIABLE_2134104 tptp.rat) (BOUND_VARIABLE_2134105 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2134105))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2134105))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2134104 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15865 BOUND_VARIABLE_2134104) BOUND_VARIABLE_2134105)))))))))))))) (let ((_let_2580 (forall ((BOUND_VARIABLE_2134076 tptp.int) (BOUND_VARIABLE_2134077 tptp.int) (BOUND_VARIABLE_2134078 tptp.int) (BOUND_VARIABLE_2134079 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134076) BOUND_VARIABLE_2134078))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134077) BOUND_VARIABLE_2134079))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15866 BOUND_VARIABLE_2134076) BOUND_VARIABLE_2134077) BOUND_VARIABLE_2134078) BOUND_VARIABLE_2134079))))))) (let ((_let_2581 (forall ((BOUND_VARIABLE_2134048 tptp.int) (BOUND_VARIABLE_2134049 tptp.int) (BOUND_VARIABLE_2134050 tptp.int) (BOUND_VARIABLE_2134051 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134048) BOUND_VARIABLE_2134050))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2134049) BOUND_VARIABLE_2134051))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15867 BOUND_VARIABLE_2134048) BOUND_VARIABLE_2134049) BOUND_VARIABLE_2134050) BOUND_VARIABLE_2134051))))))) (let ((_let_2582 (forall ((BOUND_VARIABLE_2133969 tptp.rat) (BOUND_VARIABLE_2133970 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2133970))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2133970))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2133969 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15868 BOUND_VARIABLE_2133969) BOUND_VARIABLE_2133970)))))))))))))) (let ((_let_2583 (forall ((BOUND_VARIABLE_2133941 tptp.int) (BOUND_VARIABLE_2133942 tptp.int) (BOUND_VARIABLE_2133943 tptp.int) (BOUND_VARIABLE_2133944 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2133941) BOUND_VARIABLE_2133943))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2133942) BOUND_VARIABLE_2133944))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15869 BOUND_VARIABLE_2133941) BOUND_VARIABLE_2133942) BOUND_VARIABLE_2133943) BOUND_VARIABLE_2133944))))))) (let ((_let_2584 (forall ((BOUND_VARIABLE_2133913 tptp.int) (BOUND_VARIABLE_2133914 tptp.int) (BOUND_VARIABLE_2133915 tptp.int) (BOUND_VARIABLE_2133916 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2133913) BOUND_VARIABLE_2133915))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2133914) BOUND_VARIABLE_2133916))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15870 BOUND_VARIABLE_2133913) BOUND_VARIABLE_2133914) BOUND_VARIABLE_2133915) BOUND_VARIABLE_2133916))))))) (let ((_let_2585 (forall ((BOUND_VARIABLE_2133834 tptp.rat) (BOUND_VARIABLE_2133835 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2133835))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2133835))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2133834 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15871 BOUND_VARIABLE_2133834) BOUND_VARIABLE_2133835)))))))))))))) (let ((_let_2586 (forall ((BOUND_VARIABLE_2133806 tptp.int) (BOUND_VARIABLE_2133807 tptp.int) (BOUND_VARIABLE_2133808 tptp.int) (BOUND_VARIABLE_2133809 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2133806) BOUND_VARIABLE_2133808))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2133807) BOUND_VARIABLE_2133809))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15872 BOUND_VARIABLE_2133806) BOUND_VARIABLE_2133807) BOUND_VARIABLE_2133808) BOUND_VARIABLE_2133809))))))) (let ((_let_2587 (forall ((BOUND_VARIABLE_2133778 tptp.int) (BOUND_VARIABLE_2133779 tptp.int) (BOUND_VARIABLE_2133780 tptp.int) (BOUND_VARIABLE_2133781 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2133778) BOUND_VARIABLE_2133780))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2133779) BOUND_VARIABLE_2133781))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15873 BOUND_VARIABLE_2133778) BOUND_VARIABLE_2133779) BOUND_VARIABLE_2133780) BOUND_VARIABLE_2133781))))))) (let ((_let_2588 (forall ((BOUND_VARIABLE_2133669 tptp.rat) (BOUND_VARIABLE_2133670 tptp.int) (BOUND_VARIABLE_2133671 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2133671))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2133671))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15141 (ho_15875 k_15874 BOUND_VARIABLE_2133669) BOUND_VARIABLE_2133670) BOUND_VARIABLE_2133671) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2133669) (ho_15122 k_15121 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2133670) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2133670)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2133670))))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2589 (forall ((BOUND_VARIABLE_2133567 tptp.int) (BOUND_VARIABLE_2133568 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2133568))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2133568))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15876 BOUND_VARIABLE_2133567) BOUND_VARIABLE_2133568) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2133567) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2133567)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2133567))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2590 (forall ((BOUND_VARIABLE_2133472 tptp.int) (BOUND_VARIABLE_2133473 tptp.int) (BOUND_VARIABLE_2133474 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15296 BOUND_VARIABLE_2133474) BOUND_VARIABLE_2133473)) (ho_15260 k_15259 (ho_15141 k_15297 BOUND_VARIABLE_2133472))) (ho_15108 (ho_15107 (ho_15106 k_15877 BOUND_VARIABLE_2133472) BOUND_VARIABLE_2133473) BOUND_VARIABLE_2133474))))) (let ((_let_2591 (forall ((BOUND_VARIABLE_2133389 tptp.rat) (BOUND_VARIABLE_2133390 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2133390))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2133390))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15878 BOUND_VARIABLE_2133389) BOUND_VARIABLE_2133390) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2133389) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2592 (forall ((BOUND_VARIABLE_2133328 tptp.rat) (BOUND_VARIABLE_2133329 tptp.int) (BOUND_VARIABLE_2133330 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15298 BOUND_VARIABLE_2133330) BOUND_VARIABLE_2133329)) (ho_15260 k_15259 (ho_15145 k_15299 BOUND_VARIABLE_2133328))) (ho_15108 (ho_15107 (ho_15266 k_15879 BOUND_VARIABLE_2133328) BOUND_VARIABLE_2133329) BOUND_VARIABLE_2133330))))) (let ((_let_2593 (forall ((BOUND_VARIABLE_2133224 tptp.int) (BOUND_VARIABLE_2133225 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2133225))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2133225))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2133224) _let_3))) (= (ho_15142 (ho_15141 k_15880 BOUND_VARIABLE_2133224) BOUND_VARIABLE_2133225) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 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(ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2594 (forall ((BOUND_VARIABLE_2133047 tptp.rat) (BOUND_VARIABLE_2133048 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15303 BOUND_VARIABLE_2133047)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15300 BOUND_VARIABLE_2133048))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15301 BOUND_VARIABLE_2133048)) (ho_15260 k_15259 (ho_15145 k_15302 BOUND_VARIABLE_2133047))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15304 BOUND_VARIABLE_2133048))))) (ho_15108 (ho_15783 k_15881 BOUND_VARIABLE_2133047) BOUND_VARIABLE_2133048)))))) (let ((_let_2595 (forall ((BOUND_VARIABLE_2133019 tptp.int) (BOUND_VARIABLE_2133020 tptp.int) (BOUND_VARIABLE_2133021 tptp.int) (BOUND_VARIABLE_2133022 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k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2132915) _let_3))) (= (ho_15142 (ho_15141 k_15883 BOUND_VARIABLE_2132915) BOUND_VARIABLE_2132916) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2597 (forall ((BOUND_VARIABLE_2132887 tptp.int) (BOUND_VARIABLE_2132888 tptp.int) (BOUND_VARIABLE_2132889 tptp.int) (BOUND_VARIABLE_2132890 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132887) BOUND_VARIABLE_2132889))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132888) BOUND_VARIABLE_2132890))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15884 BOUND_VARIABLE_2132887) BOUND_VARIABLE_2132888) BOUND_VARIABLE_2132889) BOUND_VARIABLE_2132890))))))) (let ((_let_2598 (forall ((BOUND_VARIABLE_2132804 tptp.rat) (BOUND_VARIABLE_2132805 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2132805))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2132805))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15885 BOUND_VARIABLE_2132804) BOUND_VARIABLE_2132805) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2132804) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2599 (forall ((BOUND_VARIABLE_2132776 tptp.int) (BOUND_VARIABLE_2132777 tptp.int) (BOUND_VARIABLE_2132778 tptp.int) (BOUND_VARIABLE_2132779 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132776) BOUND_VARIABLE_2132778))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132777) BOUND_VARIABLE_2132779))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15886 BOUND_VARIABLE_2132776) BOUND_VARIABLE_2132777) BOUND_VARIABLE_2132778) BOUND_VARIABLE_2132779))))))) (let ((_let_2600 (forall ((BOUND_VARIABLE_2132748 tptp.int) (BOUND_VARIABLE_2132749 tptp.int) (BOUND_VARIABLE_2132750 tptp.int) (BOUND_VARIABLE_2132751 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132748) BOUND_VARIABLE_2132750))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132749) BOUND_VARIABLE_2132751))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15887 BOUND_VARIABLE_2132748) BOUND_VARIABLE_2132749) BOUND_VARIABLE_2132750) BOUND_VARIABLE_2132751))))))) (let ((_let_2601 (forall ((BOUND_VARIABLE_2132646 tptp.int) (BOUND_VARIABLE_2132647 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2132647))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2132647))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15888 BOUND_VARIABLE_2132646) BOUND_VARIABLE_2132647) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2132646) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2132646)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2132646))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2602 (forall ((BOUND_VARIABLE_2132618 tptp.int) (BOUND_VARIABLE_2132619 tptp.int) (BOUND_VARIABLE_2132620 tptp.int) (BOUND_VARIABLE_2132621 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132618) BOUND_VARIABLE_2132620))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132619) BOUND_VARIABLE_2132621))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15889 BOUND_VARIABLE_2132618) BOUND_VARIABLE_2132619) BOUND_VARIABLE_2132620) BOUND_VARIABLE_2132621))))))) (let ((_let_2603 (forall ((BOUND_VARIABLE_2132590 tptp.int) (BOUND_VARIABLE_2132591 tptp.int) (BOUND_VARIABLE_2132592 tptp.int) (BOUND_VARIABLE_2132593 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132590) BOUND_VARIABLE_2132592))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132591) BOUND_VARIABLE_2132593))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15890 BOUND_VARIABLE_2132590) BOUND_VARIABLE_2132591) BOUND_VARIABLE_2132592) BOUND_VARIABLE_2132593))))))) (let ((_let_2604 (forall ((BOUND_VARIABLE_2132511 tptp.rat) (BOUND_VARIABLE_2132512 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2132512))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2132512))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2132511 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15891 BOUND_VARIABLE_2132511) BOUND_VARIABLE_2132512)))))))))))))) (let ((_let_2605 (forall ((BOUND_VARIABLE_2132483 tptp.int) (BOUND_VARIABLE_2132484 tptp.int) (BOUND_VARIABLE_2132485 tptp.int) (BOUND_VARIABLE_2132486 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132483) BOUND_VARIABLE_2132485))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132484) BOUND_VARIABLE_2132486))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15892 BOUND_VARIABLE_2132483) BOUND_VARIABLE_2132484) BOUND_VARIABLE_2132485) BOUND_VARIABLE_2132486))))))) (let ((_let_2606 (forall ((BOUND_VARIABLE_2132455 tptp.int) (BOUND_VARIABLE_2132456 tptp.int) (BOUND_VARIABLE_2132457 tptp.int) (BOUND_VARIABLE_2132458 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132455) BOUND_VARIABLE_2132457))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132456) BOUND_VARIABLE_2132458))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15893 BOUND_VARIABLE_2132455) BOUND_VARIABLE_2132456) BOUND_VARIABLE_2132457) BOUND_VARIABLE_2132458))))))) (let ((_let_2607 (forall ((BOUND_VARIABLE_2132370 tptp.rat) (BOUND_VARIABLE_2132371 tptp.rat) (BOUND_VARIABLE_2132372 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2132372))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2132372))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15145 (ho_15209 k_15894 BOUND_VARIABLE_2132370) BOUND_VARIABLE_2132371) BOUND_VARIABLE_2132372) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2132370) (ho_15122 k_15121 BOUND_VARIABLE_2132371)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2608 (forall ((BOUND_VARIABLE_2132342 tptp.int) (BOUND_VARIABLE_2132343 tptp.int) (BOUND_VARIABLE_2132344 tptp.int) (BOUND_VARIABLE_2132345 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132342) BOUND_VARIABLE_2132344))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132343) BOUND_VARIABLE_2132345))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15895 BOUND_VARIABLE_2132342) BOUND_VARIABLE_2132343) BOUND_VARIABLE_2132344) BOUND_VARIABLE_2132345))))))) (let ((_let_2609 (forall ((BOUND_VARIABLE_2132257 tptp.rat) (BOUND_VARIABLE_2132258 tptp.rat) (BOUND_VARIABLE_2132259 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2132259))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2132259))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15145 (ho_15209 k_15896 BOUND_VARIABLE_2132257) BOUND_VARIABLE_2132258) BOUND_VARIABLE_2132259) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2132257) (ho_15122 k_15121 BOUND_VARIABLE_2132258)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2610 (forall ((BOUND_VARIABLE_2132229 tptp.int) (BOUND_VARIABLE_2132230 tptp.int) (BOUND_VARIABLE_2132231 tptp.int) (BOUND_VARIABLE_2132232 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132229) BOUND_VARIABLE_2132231))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132230) BOUND_VARIABLE_2132232))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15897 BOUND_VARIABLE_2132229) BOUND_VARIABLE_2132230) BOUND_VARIABLE_2132231) BOUND_VARIABLE_2132232))))))) (let ((_let_2611 (forall ((BOUND_VARIABLE_2132201 tptp.int) (BOUND_VARIABLE_2132202 tptp.int) (BOUND_VARIABLE_2132203 tptp.int) (BOUND_VARIABLE_2132204 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132201) BOUND_VARIABLE_2132203))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132202) BOUND_VARIABLE_2132204))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15898 BOUND_VARIABLE_2132201) BOUND_VARIABLE_2132202) BOUND_VARIABLE_2132203) BOUND_VARIABLE_2132204))))))) (let ((_let_2612 (forall ((BOUND_VARIABLE_2132116 tptp.rat) (BOUND_VARIABLE_2132117 tptp.rat) (BOUND_VARIABLE_2132118 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2132118))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2132118))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15145 (ho_15209 k_15899 BOUND_VARIABLE_2132116) BOUND_VARIABLE_2132117) BOUND_VARIABLE_2132118) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2132116) (ho_15122 k_15121 BOUND_VARIABLE_2132117)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2613 (forall ((BOUND_VARIABLE_2132088 tptp.int) (BOUND_VARIABLE_2132089 tptp.int) (BOUND_VARIABLE_2132090 tptp.int) (BOUND_VARIABLE_2132091 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132088) BOUND_VARIABLE_2132090))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2132089) BOUND_VARIABLE_2132091))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15900 BOUND_VARIABLE_2132088) BOUND_VARIABLE_2132089) BOUND_VARIABLE_2132090) BOUND_VARIABLE_2132091))))))) (let ((_let_2614 (forall ((BOUND_VARIABLE_2132009 tptp.rat) (BOUND_VARIABLE_2132010 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2132010))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2132010))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2132009 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15901 BOUND_VARIABLE_2132009) BOUND_VARIABLE_2132010)))))))))))))) (let ((_let_2615 (forall ((BOUND_VARIABLE_2131981 tptp.int) (BOUND_VARIABLE_2131982 tptp.int) (BOUND_VARIABLE_2131983 tptp.int) (BOUND_VARIABLE_2131984 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131981) BOUND_VARIABLE_2131983))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131982) BOUND_VARIABLE_2131984))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15902 BOUND_VARIABLE_2131981) BOUND_VARIABLE_2131982) BOUND_VARIABLE_2131983) BOUND_VARIABLE_2131984))))))) (let ((_let_2616 (forall ((BOUND_VARIABLE_2131953 tptp.int) (BOUND_VARIABLE_2131954 tptp.int) (BOUND_VARIABLE_2131955 tptp.int) (BOUND_VARIABLE_2131956 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131953) BOUND_VARIABLE_2131955))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131954) BOUND_VARIABLE_2131956))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15903 BOUND_VARIABLE_2131953) BOUND_VARIABLE_2131954) BOUND_VARIABLE_2131955) BOUND_VARIABLE_2131956))))))) (let ((_let_2617 (forall ((BOUND_VARIABLE_2131874 tptp.rat) (BOUND_VARIABLE_2131875 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2131875))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2131875))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2131874 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15904 BOUND_VARIABLE_2131874) BOUND_VARIABLE_2131875)))))))))))))) (let ((_let_2618 (forall ((BOUND_VARIABLE_2131846 tptp.int) (BOUND_VARIABLE_2131847 tptp.int) (BOUND_VARIABLE_2131848 tptp.int) (BOUND_VARIABLE_2131849 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131846) BOUND_VARIABLE_2131848))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131847) BOUND_VARIABLE_2131849))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15905 BOUND_VARIABLE_2131846) BOUND_VARIABLE_2131847) BOUND_VARIABLE_2131848) BOUND_VARIABLE_2131849))))))) (let ((_let_2619 (forall ((BOUND_VARIABLE_2131818 tptp.int) (BOUND_VARIABLE_2131819 tptp.int) (BOUND_VARIABLE_2131820 tptp.int) (BOUND_VARIABLE_2131821 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131818) BOUND_VARIABLE_2131820))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131819) BOUND_VARIABLE_2131821))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15906 BOUND_VARIABLE_2131818) BOUND_VARIABLE_2131819) BOUND_VARIABLE_2131820) BOUND_VARIABLE_2131821))))))) (let ((_let_2620 (forall ((BOUND_VARIABLE_2131739 tptp.rat) (BOUND_VARIABLE_2131740 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2131740))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2131740))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2131739 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15907 BOUND_VARIABLE_2131739) BOUND_VARIABLE_2131740)))))))))))))) (let ((_let_2621 (forall ((BOUND_VARIABLE_2131711 tptp.int) (BOUND_VARIABLE_2131712 tptp.int) (BOUND_VARIABLE_2131713 tptp.int) (BOUND_VARIABLE_2131714 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131711) BOUND_VARIABLE_2131713))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131712) BOUND_VARIABLE_2131714))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15908 BOUND_VARIABLE_2131711) BOUND_VARIABLE_2131712) BOUND_VARIABLE_2131713) BOUND_VARIABLE_2131714))))))) (let ((_let_2622 (forall ((BOUND_VARIABLE_2131683 tptp.int) (BOUND_VARIABLE_2131684 tptp.int) (BOUND_VARIABLE_2131685 tptp.int) (BOUND_VARIABLE_2131686 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131683) BOUND_VARIABLE_2131685))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131684) BOUND_VARIABLE_2131686))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15909 BOUND_VARIABLE_2131683) BOUND_VARIABLE_2131684) BOUND_VARIABLE_2131685) BOUND_VARIABLE_2131686))))))) (let ((_let_2623 (forall ((BOUND_VARIABLE_2131604 tptp.rat) (BOUND_VARIABLE_2131605 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2131605))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2131605))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2131604 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15910 BOUND_VARIABLE_2131604) BOUND_VARIABLE_2131605)))))))))))))) (let ((_let_2624 (forall ((BOUND_VARIABLE_2131576 tptp.int) (BOUND_VARIABLE_2131577 tptp.int) (BOUND_VARIABLE_2131578 tptp.int) (BOUND_VARIABLE_2131579 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131576) BOUND_VARIABLE_2131578))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131577) BOUND_VARIABLE_2131579))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15911 BOUND_VARIABLE_2131576) BOUND_VARIABLE_2131577) BOUND_VARIABLE_2131578) BOUND_VARIABLE_2131579))))))) (let ((_let_2625 (forall ((BOUND_VARIABLE_2131548 tptp.int) (BOUND_VARIABLE_2131549 tptp.int) (BOUND_VARIABLE_2131550 tptp.int) (BOUND_VARIABLE_2131551 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131548) BOUND_VARIABLE_2131550))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131549) BOUND_VARIABLE_2131551))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15912 BOUND_VARIABLE_2131548) BOUND_VARIABLE_2131549) BOUND_VARIABLE_2131550) BOUND_VARIABLE_2131551))))))) (let ((_let_2626 (forall ((BOUND_VARIABLE_2131469 tptp.rat) (BOUND_VARIABLE_2131470 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2131470))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2131470))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2131469 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15913 BOUND_VARIABLE_2131469) BOUND_VARIABLE_2131470)))))))))))))) (let ((_let_2627 (forall ((BOUND_VARIABLE_2131441 tptp.int) (BOUND_VARIABLE_2131442 tptp.int) (BOUND_VARIABLE_2131443 tptp.int) (BOUND_VARIABLE_2131444 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131441) BOUND_VARIABLE_2131443))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131442) BOUND_VARIABLE_2131444))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15914 BOUND_VARIABLE_2131441) BOUND_VARIABLE_2131442) BOUND_VARIABLE_2131443) BOUND_VARIABLE_2131444))))))) (let ((_let_2628 (forall ((BOUND_VARIABLE_2131413 tptp.int) (BOUND_VARIABLE_2131414 tptp.int) (BOUND_VARIABLE_2131415 tptp.int) (BOUND_VARIABLE_2131416 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131413) BOUND_VARIABLE_2131415))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131414) BOUND_VARIABLE_2131416))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15915 BOUND_VARIABLE_2131413) BOUND_VARIABLE_2131414) BOUND_VARIABLE_2131415) BOUND_VARIABLE_2131416))))))) (let ((_let_2629 (forall ((BOUND_VARIABLE_2131328 tptp.rat) (BOUND_VARIABLE_2131329 tptp.rat) (BOUND_VARIABLE_2131330 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2131330))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2131330))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15145 (ho_15209 k_15916 BOUND_VARIABLE_2131328) BOUND_VARIABLE_2131329) BOUND_VARIABLE_2131330) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2131328) (ho_15122 k_15121 BOUND_VARIABLE_2131329)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2630 (forall ((BOUND_VARIABLE_2131300 tptp.int) (BOUND_VARIABLE_2131301 tptp.int) (BOUND_VARIABLE_2131302 tptp.int) (BOUND_VARIABLE_2131303 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131300) BOUND_VARIABLE_2131302))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131301) BOUND_VARIABLE_2131303))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15917 BOUND_VARIABLE_2131300) BOUND_VARIABLE_2131301) BOUND_VARIABLE_2131302) BOUND_VARIABLE_2131303))))))) (let ((_let_2631 (forall ((BOUND_VARIABLE_2131272 tptp.int) (BOUND_VARIABLE_2131273 tptp.int) (BOUND_VARIABLE_2131274 tptp.int) (BOUND_VARIABLE_2131275 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131272) BOUND_VARIABLE_2131274))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131273) BOUND_VARIABLE_2131275))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15918 BOUND_VARIABLE_2131272) BOUND_VARIABLE_2131273) BOUND_VARIABLE_2131274) BOUND_VARIABLE_2131275))))))) (let ((_let_2632 (forall ((BOUND_VARIABLE_2131187 tptp.rat) (BOUND_VARIABLE_2131188 tptp.rat) (BOUND_VARIABLE_2131189 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2131189))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2131189))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15145 (ho_15209 k_15919 BOUND_VARIABLE_2131187) BOUND_VARIABLE_2131188) BOUND_VARIABLE_2131189) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2131187) (ho_15122 k_15121 BOUND_VARIABLE_2131188)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2633 (forall ((BOUND_VARIABLE_2131159 tptp.int) (BOUND_VARIABLE_2131160 tptp.int) (BOUND_VARIABLE_2131161 tptp.int) (BOUND_VARIABLE_2131162 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131159) BOUND_VARIABLE_2131161))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131160) BOUND_VARIABLE_2131162))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15920 BOUND_VARIABLE_2131159) BOUND_VARIABLE_2131160) BOUND_VARIABLE_2131161) BOUND_VARIABLE_2131162))))))) (let ((_let_2634 (forall ((BOUND_VARIABLE_2131080 tptp.rat) (BOUND_VARIABLE_2131081 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2131081))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2131081))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2131080 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15921 BOUND_VARIABLE_2131080) BOUND_VARIABLE_2131081)))))))))))))) (let ((_let_2635 (forall ((BOUND_VARIABLE_2131052 tptp.int) (BOUND_VARIABLE_2131053 tptp.int) (BOUND_VARIABLE_2131054 tptp.int) (BOUND_VARIABLE_2131055 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131052) BOUND_VARIABLE_2131054))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131053) BOUND_VARIABLE_2131055))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15922 BOUND_VARIABLE_2131052) BOUND_VARIABLE_2131053) BOUND_VARIABLE_2131054) BOUND_VARIABLE_2131055))))))) (let ((_let_2636 (forall ((BOUND_VARIABLE_2131024 tptp.int) (BOUND_VARIABLE_2131025 tptp.int) (BOUND_VARIABLE_2131026 tptp.int) (BOUND_VARIABLE_2131027 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131024) BOUND_VARIABLE_2131026))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2131025) BOUND_VARIABLE_2131027))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15923 BOUND_VARIABLE_2131024) BOUND_VARIABLE_2131025) BOUND_VARIABLE_2131026) BOUND_VARIABLE_2131027))))))) (let ((_let_2637 (forall ((BOUND_VARIABLE_2130945 tptp.rat) (BOUND_VARIABLE_2130946 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2130946))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2130946))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2130945 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15924 BOUND_VARIABLE_2130945) BOUND_VARIABLE_2130946)))))))))))))) (let ((_let_2638 (forall ((BOUND_VARIABLE_2130866 tptp.rat) (BOUND_VARIABLE_2130867 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2130867))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2130867))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2130866 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15925 BOUND_VARIABLE_2130866) BOUND_VARIABLE_2130867)))))))))))))) (let ((_let_2639 (forall ((BOUND_VARIABLE_2130809 tptp.rat) (BOUND_VARIABLE_2130810 tptp.int) (BOUND_VARIABLE_2130811 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15305 BOUND_VARIABLE_2130811) BOUND_VARIABLE_2130810)) (ho_15260 k_15259 (ho_15145 k_15306 BOUND_VARIABLE_2130809))) (ho_15108 (ho_15107 (ho_15266 k_15926 BOUND_VARIABLE_2130809) BOUND_VARIABLE_2130810) BOUND_VARIABLE_2130811))))) (let ((_let_2640 (forall ((BOUND_VARIABLE_2130765 tptp.int) (BOUND_VARIABLE_2130766 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15307 BOUND_VARIABLE_2130766) BOUND_VARIABLE_2130765)) (ho_15260 k_15259 k_15927)) (ho_15108 (ho_15107 k_15928 BOUND_VARIABLE_2130765) BOUND_VARIABLE_2130766))))) (let ((_let_2641 (forall ((BOUND_VARIABLE_2130686 tptp.rat) (BOUND_VARIABLE_2130687 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2130687))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2130687))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2130686 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15929 BOUND_VARIABLE_2130686) BOUND_VARIABLE_2130687)))))))))))))) (let ((_let_2642 (forall ((BOUND_VARIABLE_2130629 tptp.rat) (BOUND_VARIABLE_2130630 tptp.int) (BOUND_VARIABLE_2130631 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15308 BOUND_VARIABLE_2130631) BOUND_VARIABLE_2130630)) (ho_15260 k_15259 (ho_15145 k_15309 BOUND_VARIABLE_2130629))) (ho_15108 (ho_15107 (ho_15266 k_15930 BOUND_VARIABLE_2130629) BOUND_VARIABLE_2130630) BOUND_VARIABLE_2130631))))) (let ((_let_2643 (forall ((BOUND_VARIABLE_2130601 tptp.int) (BOUND_VARIABLE_2130602 tptp.int) (BOUND_VARIABLE_2130603 tptp.int) (BOUND_VARIABLE_2130604 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130601) BOUND_VARIABLE_2130603))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130602) BOUND_VARIABLE_2130604))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15931 BOUND_VARIABLE_2130601) BOUND_VARIABLE_2130602) BOUND_VARIABLE_2130603) BOUND_VARIABLE_2130604))))))) (let ((_let_2644 (forall ((BOUND_VARIABLE_2130573 tptp.int) (BOUND_VARIABLE_2130574 tptp.int) (BOUND_VARIABLE_2130575 tptp.int) (BOUND_VARIABLE_2130576 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130573) BOUND_VARIABLE_2130575))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130574) BOUND_VARIABLE_2130576))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15932 BOUND_VARIABLE_2130573) BOUND_VARIABLE_2130574) BOUND_VARIABLE_2130575) BOUND_VARIABLE_2130576))))))) (let ((_let_2645 (forall ((BOUND_VARIABLE_2130488 tptp.rat) (BOUND_VARIABLE_2130489 tptp.rat) (BOUND_VARIABLE_2130490 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2130490))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2130490))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15145 (ho_15209 k_15933 BOUND_VARIABLE_2130488) BOUND_VARIABLE_2130489) BOUND_VARIABLE_2130490) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2130488) (ho_15122 k_15121 BOUND_VARIABLE_2130489)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2646 (forall ((BOUND_VARIABLE_2130460 tptp.int) (BOUND_VARIABLE_2130461 tptp.int) (BOUND_VARIABLE_2130462 tptp.int) (BOUND_VARIABLE_2130463 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130460) BOUND_VARIABLE_2130462))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130461) BOUND_VARIABLE_2130463))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15934 BOUND_VARIABLE_2130460) BOUND_VARIABLE_2130461) BOUND_VARIABLE_2130462) BOUND_VARIABLE_2130463))))))) (let ((_let_2647 (forall ((BOUND_VARIABLE_2130432 tptp.int) (BOUND_VARIABLE_2130433 tptp.int) (BOUND_VARIABLE_2130434 tptp.int) (BOUND_VARIABLE_2130435 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130432) BOUND_VARIABLE_2130434))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130433) BOUND_VARIABLE_2130435))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15935 BOUND_VARIABLE_2130432) BOUND_VARIABLE_2130433) BOUND_VARIABLE_2130434) BOUND_VARIABLE_2130435))))))) (let ((_let_2648 (forall ((BOUND_VARIABLE_2130353 tptp.rat) (BOUND_VARIABLE_2130354 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2130354))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2130354))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2130353 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15936 BOUND_VARIABLE_2130353) BOUND_VARIABLE_2130354)))))))))))))) (let ((_let_2649 (forall ((BOUND_VARIABLE_2130325 tptp.int) (BOUND_VARIABLE_2130326 tptp.int) (BOUND_VARIABLE_2130327 tptp.int) (BOUND_VARIABLE_2130328 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130325) BOUND_VARIABLE_2130327))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130326) BOUND_VARIABLE_2130328))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15937 BOUND_VARIABLE_2130325) BOUND_VARIABLE_2130326) BOUND_VARIABLE_2130327) BOUND_VARIABLE_2130328))))))) (let ((_let_2650 (forall ((BOUND_VARIABLE_2130297 tptp.int) (BOUND_VARIABLE_2130298 tptp.int) (BOUND_VARIABLE_2130299 tptp.int) (BOUND_VARIABLE_2130300 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130297) BOUND_VARIABLE_2130299))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130298) BOUND_VARIABLE_2130300))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15938 BOUND_VARIABLE_2130297) BOUND_VARIABLE_2130298) BOUND_VARIABLE_2130299) BOUND_VARIABLE_2130300))))))) (let ((_let_2651 (forall ((BOUND_VARIABLE_2130218 tptp.rat) (BOUND_VARIABLE_2130219 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2130219))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2130219))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2130218 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15939 BOUND_VARIABLE_2130218) BOUND_VARIABLE_2130219)))))))))))))) (let ((_let_2652 (forall ((BOUND_VARIABLE_2130190 tptp.int) (BOUND_VARIABLE_2130191 tptp.int) (BOUND_VARIABLE_2130192 tptp.int) (BOUND_VARIABLE_2130193 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130190) BOUND_VARIABLE_2130192))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130191) BOUND_VARIABLE_2130193))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15940 BOUND_VARIABLE_2130190) BOUND_VARIABLE_2130191) BOUND_VARIABLE_2130192) BOUND_VARIABLE_2130193))))))) (let ((_let_2653 (forall ((BOUND_VARIABLE_2130111 tptp.rat) (BOUND_VARIABLE_2130112 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2130112))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2130112))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2130111 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15941 BOUND_VARIABLE_2130111) BOUND_VARIABLE_2130112)))))))))))))) (let ((_let_2654 (forall ((BOUND_VARIABLE_2130083 tptp.int) (BOUND_VARIABLE_2130084 tptp.int) (BOUND_VARIABLE_2130085 tptp.int) (BOUND_VARIABLE_2130086 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130083) BOUND_VARIABLE_2130085))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130084) BOUND_VARIABLE_2130086))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15942 BOUND_VARIABLE_2130083) BOUND_VARIABLE_2130084) BOUND_VARIABLE_2130085) BOUND_VARIABLE_2130086))))))) (let ((_let_2655 (forall ((BOUND_VARIABLE_2130055 tptp.int) (BOUND_VARIABLE_2130056 tptp.int) (BOUND_VARIABLE_2130057 tptp.int) (BOUND_VARIABLE_2130058 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130055) BOUND_VARIABLE_2130057))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2130056) BOUND_VARIABLE_2130058))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15943 BOUND_VARIABLE_2130055) BOUND_VARIABLE_2130056) BOUND_VARIABLE_2130057) BOUND_VARIABLE_2130058))))))) (let ((_let_2656 (forall ((BOUND_VARIABLE_2129976 tptp.rat) (BOUND_VARIABLE_2129977 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2129977))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2129977))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2129976 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15944 BOUND_VARIABLE_2129976) BOUND_VARIABLE_2129977)))))))))))))) (let ((_let_2657 (forall ((BOUND_VARIABLE_2129948 tptp.int) (BOUND_VARIABLE_2129949 tptp.int) (BOUND_VARIABLE_2129950 tptp.int) (BOUND_VARIABLE_2129951 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129948) BOUND_VARIABLE_2129950))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129949) BOUND_VARIABLE_2129951))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15945 BOUND_VARIABLE_2129948) BOUND_VARIABLE_2129949) BOUND_VARIABLE_2129950) BOUND_VARIABLE_2129951))))))) (let ((_let_2658 (forall ((BOUND_VARIABLE_2129869 tptp.rat) (BOUND_VARIABLE_2129870 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2129870))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2129870))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2129869 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15946 BOUND_VARIABLE_2129869) BOUND_VARIABLE_2129870)))))))))))))) (let ((_let_2659 (forall ((BOUND_VARIABLE_2129841 tptp.int) (BOUND_VARIABLE_2129842 tptp.int) (BOUND_VARIABLE_2129843 tptp.int) (BOUND_VARIABLE_2129844 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129841) BOUND_VARIABLE_2129843))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129842) BOUND_VARIABLE_2129844))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15947 BOUND_VARIABLE_2129841) BOUND_VARIABLE_2129842) BOUND_VARIABLE_2129843) BOUND_VARIABLE_2129844))))))) (let ((_let_2660 (forall ((BOUND_VARIABLE_2129813 tptp.int) (BOUND_VARIABLE_2129814 tptp.int) (BOUND_VARIABLE_2129815 tptp.int) (BOUND_VARIABLE_2129816 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129813) BOUND_VARIABLE_2129815))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129814) BOUND_VARIABLE_2129816))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15948 BOUND_VARIABLE_2129813) BOUND_VARIABLE_2129814) BOUND_VARIABLE_2129815) BOUND_VARIABLE_2129816))))))) (let ((_let_2661 (forall ((BOUND_VARIABLE_2129734 tptp.rat) (BOUND_VARIABLE_2129735 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2129735))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2129735))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2129734 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15949 BOUND_VARIABLE_2129734) BOUND_VARIABLE_2129735)))))))))))))) (let ((_let_2662 (forall ((BOUND_VARIABLE_2129706 tptp.int) (BOUND_VARIABLE_2129707 tptp.int) (BOUND_VARIABLE_2129708 tptp.int) (BOUND_VARIABLE_2129709 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129706) BOUND_VARIABLE_2129708))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129707) BOUND_VARIABLE_2129709))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15950 BOUND_VARIABLE_2129706) BOUND_VARIABLE_2129707) BOUND_VARIABLE_2129708) BOUND_VARIABLE_2129709))))))) (let ((_let_2663 (forall ((BOUND_VARIABLE_2129678 tptp.int) (BOUND_VARIABLE_2129679 tptp.int) (BOUND_VARIABLE_2129680 tptp.int) (BOUND_VARIABLE_2129681 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129678) BOUND_VARIABLE_2129680))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129679) BOUND_VARIABLE_2129681))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15951 BOUND_VARIABLE_2129678) BOUND_VARIABLE_2129679) BOUND_VARIABLE_2129680) BOUND_VARIABLE_2129681))))))) (let ((_let_2664 (forall ((BOUND_VARIABLE_2129599 tptp.rat) (BOUND_VARIABLE_2129600 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2129600))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2129600))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2129599 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15952 BOUND_VARIABLE_2129599) BOUND_VARIABLE_2129600)))))))))))))) (let ((_let_2665 (forall ((BOUND_VARIABLE_2129571 tptp.int) (BOUND_VARIABLE_2129572 tptp.int) (BOUND_VARIABLE_2129573 tptp.int) (BOUND_VARIABLE_2129574 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129571) BOUND_VARIABLE_2129573))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129572) BOUND_VARIABLE_2129574))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15953 BOUND_VARIABLE_2129571) BOUND_VARIABLE_2129572) BOUND_VARIABLE_2129573) BOUND_VARIABLE_2129574))))))) (let ((_let_2666 (forall ((BOUND_VARIABLE_2129543 tptp.int) (BOUND_VARIABLE_2129544 tptp.int) (BOUND_VARIABLE_2129545 tptp.int) (BOUND_VARIABLE_2129546 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129543) BOUND_VARIABLE_2129545))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129544) BOUND_VARIABLE_2129546))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15954 BOUND_VARIABLE_2129543) BOUND_VARIABLE_2129544) BOUND_VARIABLE_2129545) BOUND_VARIABLE_2129546))))))) (let ((_let_2667 (forall ((BOUND_VARIABLE_2129464 tptp.rat) (BOUND_VARIABLE_2129465 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2129465))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2129465))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2129464 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15955 BOUND_VARIABLE_2129464) BOUND_VARIABLE_2129465)))))))))))))) (let ((_let_2668 (forall ((BOUND_VARIABLE_2129436 tptp.int) (BOUND_VARIABLE_2129437 tptp.int) (BOUND_VARIABLE_2129438 tptp.int) (BOUND_VARIABLE_2129439 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129436) BOUND_VARIABLE_2129438))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129437) BOUND_VARIABLE_2129439))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15956 BOUND_VARIABLE_2129436) BOUND_VARIABLE_2129437) BOUND_VARIABLE_2129438) BOUND_VARIABLE_2129439))))))) (let ((_let_2669 (forall ((BOUND_VARIABLE_2129408 tptp.int) (BOUND_VARIABLE_2129409 tptp.int) (BOUND_VARIABLE_2129410 tptp.int) (BOUND_VARIABLE_2129411 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129408) BOUND_VARIABLE_2129410))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2129409) BOUND_VARIABLE_2129411))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15957 BOUND_VARIABLE_2129408) BOUND_VARIABLE_2129409) BOUND_VARIABLE_2129410) BOUND_VARIABLE_2129411))))))) (let ((_let_2670 (forall ((BOUND_VARIABLE_2129299 tptp.rat) (BOUND_VARIABLE_2129300 tptp.int) (BOUND_VARIABLE_2129301 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2129301))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2129301))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15141 (ho_15875 k_15958 BOUND_VARIABLE_2129299) BOUND_VARIABLE_2129300) BOUND_VARIABLE_2129301) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2129299) (ho_15122 k_15121 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2129300) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2129300)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2129300))))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2671 (forall ((BOUND_VARIABLE_2129197 tptp.int) (BOUND_VARIABLE_2129198 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2129198))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2129198))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15959 BOUND_VARIABLE_2129197) BOUND_VARIABLE_2129198) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2129197) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2129197)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2129197))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2672 (forall ((BOUND_VARIABLE_2129102 tptp.int) (BOUND_VARIABLE_2129103 tptp.int) (BOUND_VARIABLE_2129104 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15310 BOUND_VARIABLE_2129104) BOUND_VARIABLE_2129103)) (ho_15260 k_15259 (ho_15141 k_15311 BOUND_VARIABLE_2129102))) (ho_15108 (ho_15107 (ho_15106 k_15960 BOUND_VARIABLE_2129102) BOUND_VARIABLE_2129103) BOUND_VARIABLE_2129104))))) (let ((_let_2673 (forall ((BOUND_VARIABLE_2129019 tptp.rat) (BOUND_VARIABLE_2129020 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2129020))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2129020))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15961 BOUND_VARIABLE_2129019) BOUND_VARIABLE_2129020) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2129019) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2674 (forall ((BOUND_VARIABLE_2128958 tptp.rat) (BOUND_VARIABLE_2128959 tptp.int) (BOUND_VARIABLE_2128960 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15312 BOUND_VARIABLE_2128960) BOUND_VARIABLE_2128959)) (ho_15260 k_15259 (ho_15145 k_15313 BOUND_VARIABLE_2128958))) (ho_15108 (ho_15107 (ho_15266 k_15962 BOUND_VARIABLE_2128958) BOUND_VARIABLE_2128959) BOUND_VARIABLE_2128960))))) (let ((_let_2675 (forall ((BOUND_VARIABLE_2128854 tptp.int) (BOUND_VARIABLE_2128855 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2128855))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2128855))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2128854) _let_3))) (= (ho_15142 (ho_15141 k_15963 BOUND_VARIABLE_2128854) BOUND_VARIABLE_2128855) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2676 (forall ((BOUND_VARIABLE_2128677 tptp.rat) (BOUND_VARIABLE_2128678 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15317 BOUND_VARIABLE_2128677)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15314 BOUND_VARIABLE_2128678))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15315 BOUND_VARIABLE_2128678)) (ho_15260 k_15259 (ho_15145 k_15316 BOUND_VARIABLE_2128677))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15318 BOUND_VARIABLE_2128678))))) (ho_15108 (ho_15783 k_15964 BOUND_VARIABLE_2128677) BOUND_VARIABLE_2128678)))))) (let ((_let_2677 (forall ((BOUND_VARIABLE_2128649 tptp.int) (BOUND_VARIABLE_2128650 tptp.int) (BOUND_VARIABLE_2128651 tptp.int) (BOUND_VARIABLE_2128652 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128649) BOUND_VARIABLE_2128651))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128650) BOUND_VARIABLE_2128652))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15965 BOUND_VARIABLE_2128649) BOUND_VARIABLE_2128650) BOUND_VARIABLE_2128651) BOUND_VARIABLE_2128652))))))) (let ((_let_2678 (forall ((BOUND_VARIABLE_2128545 tptp.int) (BOUND_VARIABLE_2128546 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2128546))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2128546))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2128545) _let_3))) (= (ho_15142 (ho_15141 k_15966 BOUND_VARIABLE_2128545) BOUND_VARIABLE_2128546) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2679 (forall ((BOUND_VARIABLE_2128517 tptp.int) (BOUND_VARIABLE_2128518 tptp.int) (BOUND_VARIABLE_2128519 tptp.int) (BOUND_VARIABLE_2128520 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128517) BOUND_VARIABLE_2128519))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128518) BOUND_VARIABLE_2128520))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15967 BOUND_VARIABLE_2128517) BOUND_VARIABLE_2128518) BOUND_VARIABLE_2128519) BOUND_VARIABLE_2128520))))))) (let ((_let_2680 (forall ((BOUND_VARIABLE_2128434 tptp.rat) (BOUND_VARIABLE_2128435 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2128435))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2128435))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15968 BOUND_VARIABLE_2128434) BOUND_VARIABLE_2128435) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2128434) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2681 (forall ((BOUND_VARIABLE_2128406 tptp.int) (BOUND_VARIABLE_2128407 tptp.int) (BOUND_VARIABLE_2128408 tptp.int) (BOUND_VARIABLE_2128409 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128406) BOUND_VARIABLE_2128408))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128407) BOUND_VARIABLE_2128409))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15969 BOUND_VARIABLE_2128406) BOUND_VARIABLE_2128407) BOUND_VARIABLE_2128408) BOUND_VARIABLE_2128409))))))) (let ((_let_2682 (forall ((BOUND_VARIABLE_2128378 tptp.int) (BOUND_VARIABLE_2128379 tptp.int) (BOUND_VARIABLE_2128380 tptp.int) (BOUND_VARIABLE_2128381 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128378) BOUND_VARIABLE_2128380))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128379) BOUND_VARIABLE_2128381))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15970 BOUND_VARIABLE_2128378) BOUND_VARIABLE_2128379) BOUND_VARIABLE_2128380) BOUND_VARIABLE_2128381))))))) (let ((_let_2683 (forall ((BOUND_VARIABLE_2128299 tptp.rat) (BOUND_VARIABLE_2128300 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2128300))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2128300))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2128299 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15971 BOUND_VARIABLE_2128299) BOUND_VARIABLE_2128300)))))))))))))) (let ((_let_2684 (forall ((BOUND_VARIABLE_2128271 tptp.int) (BOUND_VARIABLE_2128272 tptp.int) (BOUND_VARIABLE_2128273 tptp.int) (BOUND_VARIABLE_2128274 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128271) BOUND_VARIABLE_2128273))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128272) BOUND_VARIABLE_2128274))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15972 BOUND_VARIABLE_2128271) BOUND_VARIABLE_2128272) BOUND_VARIABLE_2128273) BOUND_VARIABLE_2128274))))))) (let ((_let_2685 (forall ((BOUND_VARIABLE_2128243 tptp.int) (BOUND_VARIABLE_2128244 tptp.int) (BOUND_VARIABLE_2128245 tptp.int) (BOUND_VARIABLE_2128246 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128243) BOUND_VARIABLE_2128245))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128244) BOUND_VARIABLE_2128246))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15973 BOUND_VARIABLE_2128243) BOUND_VARIABLE_2128244) BOUND_VARIABLE_2128245) BOUND_VARIABLE_2128246))))))) (let ((_let_2686 (forall ((BOUND_VARIABLE_2128164 tptp.rat) (BOUND_VARIABLE_2128165 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2128165))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2128165))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2128164 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15974 BOUND_VARIABLE_2128164) BOUND_VARIABLE_2128165)))))))))))))) (let ((_let_2687 (forall ((BOUND_VARIABLE_2128136 tptp.int) (BOUND_VARIABLE_2128137 tptp.int) (BOUND_VARIABLE_2128138 tptp.int) (BOUND_VARIABLE_2128139 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128136) BOUND_VARIABLE_2128138))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128137) BOUND_VARIABLE_2128139))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15975 BOUND_VARIABLE_2128136) BOUND_VARIABLE_2128137) BOUND_VARIABLE_2128138) BOUND_VARIABLE_2128139))))))) (let ((_let_2688 (forall ((BOUND_VARIABLE_2128108 tptp.int) (BOUND_VARIABLE_2128109 tptp.int) (BOUND_VARIABLE_2128110 tptp.int) (BOUND_VARIABLE_2128111 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128108) BOUND_VARIABLE_2128110))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128109) BOUND_VARIABLE_2128111))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15976 BOUND_VARIABLE_2128108) BOUND_VARIABLE_2128109) BOUND_VARIABLE_2128110) BOUND_VARIABLE_2128111))))))) (let ((_let_2689 (forall ((BOUND_VARIABLE_2128029 tptp.rat) (BOUND_VARIABLE_2128030 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2128030))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2128030))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2128029 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15977 BOUND_VARIABLE_2128029) BOUND_VARIABLE_2128030)))))))))))))) (let ((_let_2690 (forall ((BOUND_VARIABLE_2128001 tptp.int) (BOUND_VARIABLE_2128002 tptp.int) (BOUND_VARIABLE_2128003 tptp.int) (BOUND_VARIABLE_2128004 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128001) BOUND_VARIABLE_2128003))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2128002) BOUND_VARIABLE_2128004))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15978 BOUND_VARIABLE_2128001) BOUND_VARIABLE_2128002) BOUND_VARIABLE_2128003) BOUND_VARIABLE_2128004))))))) (let ((_let_2691 (forall ((BOUND_VARIABLE_2127973 tptp.int) (BOUND_VARIABLE_2127974 tptp.int) (BOUND_VARIABLE_2127975 tptp.int) (BOUND_VARIABLE_2127976 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127973) BOUND_VARIABLE_2127975))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127974) BOUND_VARIABLE_2127976))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15979 BOUND_VARIABLE_2127973) BOUND_VARIABLE_2127974) BOUND_VARIABLE_2127975) BOUND_VARIABLE_2127976))))))) (let ((_let_2692 (forall ((BOUND_VARIABLE_2127894 tptp.rat) (BOUND_VARIABLE_2127895 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2127895))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2127895))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2127894 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15980 BOUND_VARIABLE_2127894) BOUND_VARIABLE_2127895)))))))))))))) (let ((_let_2693 (forall ((BOUND_VARIABLE_2127866 tptp.int) (BOUND_VARIABLE_2127867 tptp.int) (BOUND_VARIABLE_2127868 tptp.int) (BOUND_VARIABLE_2127869 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127866) BOUND_VARIABLE_2127868))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127867) BOUND_VARIABLE_2127869))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15981 BOUND_VARIABLE_2127866) BOUND_VARIABLE_2127867) BOUND_VARIABLE_2127868) BOUND_VARIABLE_2127869))))))) (let ((_let_2694 (forall ((BOUND_VARIABLE_2127787 tptp.rat) (BOUND_VARIABLE_2127788 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2127788))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2127788))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2127787 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15982 BOUND_VARIABLE_2127787) BOUND_VARIABLE_2127788)))))))))))))) (let ((_let_2695 (forall ((BOUND_VARIABLE_2127759 tptp.int) (BOUND_VARIABLE_2127760 tptp.int) (BOUND_VARIABLE_2127761 tptp.int) (BOUND_VARIABLE_2127762 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127759) BOUND_VARIABLE_2127761))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127760) BOUND_VARIABLE_2127762))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15983 BOUND_VARIABLE_2127759) BOUND_VARIABLE_2127760) BOUND_VARIABLE_2127761) BOUND_VARIABLE_2127762))))))) (let ((_let_2696 (forall ((BOUND_VARIABLE_2127731 tptp.int) (BOUND_VARIABLE_2127732 tptp.int) (BOUND_VARIABLE_2127733 tptp.int) (BOUND_VARIABLE_2127734 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127731) BOUND_VARIABLE_2127733))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127732) BOUND_VARIABLE_2127734))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15984 BOUND_VARIABLE_2127731) BOUND_VARIABLE_2127732) BOUND_VARIABLE_2127733) BOUND_VARIABLE_2127734))))))) (let ((_let_2697 (forall ((BOUND_VARIABLE_2127652 tptp.rat) (BOUND_VARIABLE_2127653 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2127653))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2127653))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2127652 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15985 BOUND_VARIABLE_2127652) BOUND_VARIABLE_2127653)))))))))))))) (let ((_let_2698 (forall ((BOUND_VARIABLE_2127624 tptp.int) (BOUND_VARIABLE_2127625 tptp.int) (BOUND_VARIABLE_2127626 tptp.int) (BOUND_VARIABLE_2127627 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127624) BOUND_VARIABLE_2127626))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127625) BOUND_VARIABLE_2127627))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15986 BOUND_VARIABLE_2127624) BOUND_VARIABLE_2127625) BOUND_VARIABLE_2127626) BOUND_VARIABLE_2127627))))))) (let ((_let_2699 (forall ((BOUND_VARIABLE_2127596 tptp.int) (BOUND_VARIABLE_2127597 tptp.int) (BOUND_VARIABLE_2127598 tptp.int) (BOUND_VARIABLE_2127599 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127596) BOUND_VARIABLE_2127598))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127597) BOUND_VARIABLE_2127599))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15987 BOUND_VARIABLE_2127596) BOUND_VARIABLE_2127597) BOUND_VARIABLE_2127598) BOUND_VARIABLE_2127599))))))) (let ((_let_2700 (forall ((BOUND_VARIABLE_2127517 tptp.rat) (BOUND_VARIABLE_2127518 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2127518))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2127518))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2127517 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15988 BOUND_VARIABLE_2127517) BOUND_VARIABLE_2127518)))))))))))))) (let ((_let_2701 (forall ((BOUND_VARIABLE_2127489 tptp.int) (BOUND_VARIABLE_2127490 tptp.int) (BOUND_VARIABLE_2127491 tptp.int) (BOUND_VARIABLE_2127492 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127489) BOUND_VARIABLE_2127491))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127490) BOUND_VARIABLE_2127492))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15989 BOUND_VARIABLE_2127489) BOUND_VARIABLE_2127490) BOUND_VARIABLE_2127491) BOUND_VARIABLE_2127492))))))) (let ((_let_2702 (forall ((BOUND_VARIABLE_2127461 tptp.int) (BOUND_VARIABLE_2127462 tptp.int) (BOUND_VARIABLE_2127463 tptp.int) (BOUND_VARIABLE_2127464 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127461) BOUND_VARIABLE_2127463))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2127462) BOUND_VARIABLE_2127464))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_15990 BOUND_VARIABLE_2127461) BOUND_VARIABLE_2127462) BOUND_VARIABLE_2127463) BOUND_VARIABLE_2127464))))))) (let ((_let_2703 (forall ((BOUND_VARIABLE_2127382 tptp.rat) (BOUND_VARIABLE_2127383 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2127383))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2127383))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2127382 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_15991 BOUND_VARIABLE_2127382) BOUND_VARIABLE_2127383)))))))))))))) (let ((_let_2704 (forall ((BOUND_VARIABLE_2127280 tptp.int) (BOUND_VARIABLE_2127281 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2127281))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2127281))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15992 BOUND_VARIABLE_2127280) BOUND_VARIABLE_2127281) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2127280) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2127280)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2127280))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2705 (forall ((BOUND_VARIABLE_2127185 tptp.int) (BOUND_VARIABLE_2127186 tptp.int) (BOUND_VARIABLE_2127187 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15319 BOUND_VARIABLE_2127187) BOUND_VARIABLE_2127186)) (ho_15260 k_15259 (ho_15141 k_15320 BOUND_VARIABLE_2127185))) (ho_15108 (ho_15107 (ho_15106 k_15993 BOUND_VARIABLE_2127185) BOUND_VARIABLE_2127186) BOUND_VARIABLE_2127187))))) (let ((_let_2706 (forall ((BOUND_VARIABLE_2127102 tptp.rat) (BOUND_VARIABLE_2127103 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2127103))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2127103))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15139 _let_10 k_15127))) (= (ho_15142 (ho_15145 k_15994 BOUND_VARIABLE_2127102) BOUND_VARIABLE_2127103) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2127102) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one))) (ho_15122 (ho_15125 _let_11 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2707 (forall ((BOUND_VARIABLE_2127041 tptp.rat) (BOUND_VARIABLE_2127042 tptp.int) (BOUND_VARIABLE_2127043 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15321 BOUND_VARIABLE_2127043) BOUND_VARIABLE_2127042)) (ho_15260 k_15259 (ho_15145 k_15322 BOUND_VARIABLE_2127041))) (ho_15108 (ho_15107 (ho_15266 k_15995 BOUND_VARIABLE_2127041) BOUND_VARIABLE_2127042) BOUND_VARIABLE_2127043))))) (let ((_let_2708 (forall ((BOUND_VARIABLE_2126937 tptp.int) (BOUND_VARIABLE_2126938 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2126938))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2126938))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2126937) _let_3))) (= (ho_15142 (ho_15141 k_15996 BOUND_VARIABLE_2126937) BOUND_VARIABLE_2126938) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2709 (forall ((BOUND_VARIABLE_2126835 tptp.int) (BOUND_VARIABLE_2126836 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2126836))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2126836))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_15997 BOUND_VARIABLE_2126835) BOUND_VARIABLE_2126836) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2126835) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2126835)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2126835))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2710 (forall ((BOUND_VARIABLE_2126740 tptp.int) (BOUND_VARIABLE_2126741 tptp.int) (BOUND_VARIABLE_2126742 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15323 BOUND_VARIABLE_2126742) BOUND_VARIABLE_2126741)) (ho_15260 k_15259 (ho_15141 k_15324 BOUND_VARIABLE_2126740))) (ho_15108 (ho_15107 (ho_15106 k_15998 BOUND_VARIABLE_2126740) BOUND_VARIABLE_2126741) BOUND_VARIABLE_2126742))))) (let ((_let_2711 (forall ((BOUND_VARIABLE_2126657 tptp.rat) (BOUND_VARIABLE_2126658 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2126658))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2126658))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15139 _let_9 k_15127))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 k_15999 BOUND_VARIABLE_2126657) BOUND_VARIABLE_2126658) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2126657) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2712 (forall ((BOUND_VARIABLE_2126596 tptp.rat) (BOUND_VARIABLE_2126597 tptp.int) (BOUND_VARIABLE_2126598 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15325 BOUND_VARIABLE_2126598) BOUND_VARIABLE_2126597)) (ho_15260 k_15259 (ho_15145 k_15326 BOUND_VARIABLE_2126596))) (ho_15108 (ho_15107 (ho_15266 k_16000 BOUND_VARIABLE_2126596) BOUND_VARIABLE_2126597) BOUND_VARIABLE_2126598))))) (let ((_let_2713 (forall ((BOUND_VARIABLE_2126492 tptp.int) (BOUND_VARIABLE_2126493 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2126493))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2126493))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2126492) _let_3))) (= (ho_15142 (ho_15141 k_16001 BOUND_VARIABLE_2126492) BOUND_VARIABLE_2126493) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2714 (forall ((BOUND_VARIABLE_2126464 tptp.int) (BOUND_VARIABLE_2126465 tptp.int) (BOUND_VARIABLE_2126466 tptp.int) (BOUND_VARIABLE_2126467 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2126464) BOUND_VARIABLE_2126466))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2126465) BOUND_VARIABLE_2126467))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16002 BOUND_VARIABLE_2126464) BOUND_VARIABLE_2126465) BOUND_VARIABLE_2126466) BOUND_VARIABLE_2126467))))))) (let ((_let_2715 (forall ((BOUND_VARIABLE_2126360 tptp.int) (BOUND_VARIABLE_2126361 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2126361))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2126361))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2126360) _let_3))) (= (ho_15142 (ho_15141 k_16003 BOUND_VARIABLE_2126360) BOUND_VARIABLE_2126361) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2716 (forall ((BOUND_VARIABLE_2126332 tptp.int) (BOUND_VARIABLE_2126333 tptp.int) (BOUND_VARIABLE_2126334 tptp.int) (BOUND_VARIABLE_2126335 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2126332) BOUND_VARIABLE_2126334))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2126333) BOUND_VARIABLE_2126335))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16004 BOUND_VARIABLE_2126332) BOUND_VARIABLE_2126333) BOUND_VARIABLE_2126334) BOUND_VARIABLE_2126335))))))) (let ((_let_2717 (forall ((BOUND_VARIABLE_2126249 tptp.rat) (BOUND_VARIABLE_2126250 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2126250))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2126250))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15139 _let_9 k_15127))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 k_16005 BOUND_VARIABLE_2126249) BOUND_VARIABLE_2126250) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2126249) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15150 k_15149 (ho_15152 k_15151 tptp.one)))) (ho_15150 k_15149 tptp.one)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2718 (forall ((BOUND_VARIABLE_2126221 tptp.int) (BOUND_VARIABLE_2126222 tptp.int) (BOUND_VARIABLE_2126223 tptp.int) (BOUND_VARIABLE_2126224 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2126221) BOUND_VARIABLE_2126223))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2126222) BOUND_VARIABLE_2126224))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16006 BOUND_VARIABLE_2126221) BOUND_VARIABLE_2126222) BOUND_VARIABLE_2126223) BOUND_VARIABLE_2126224))))))) (let ((_let_2719 (forall ((BOUND_VARIABLE_2231530 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2126135 tptp.nat) (BOUND_VARIABLE_2126136 tptp.nat) (BOUND_VARIABLE_2126137 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2126137))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2126137))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16007 BOUND_VARIABLE_2231530) BOUND_VARIABLE_2126135) BOUND_VARIABLE_2126136) BOUND_VARIABLE_2126137) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2231530 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2126135)) (ho_15161 k_15160 BOUND_VARIABLE_2126136))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2720 (forall ((BOUND_VARIABLE_2231598 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2126048 tptp.nat) (BOUND_VARIABLE_2126049 tptp.nat) (BOUND_VARIABLE_2126050 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2126050))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2126050))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16008 BOUND_VARIABLE_2231598) BOUND_VARIABLE_2126048) BOUND_VARIABLE_2126049) BOUND_VARIABLE_2126050) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2231598 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2126048)) (ho_15161 k_15160 BOUND_VARIABLE_2126049))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2721 (forall ((BOUND_VARIABLE_2231614 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2125973 tptp.nat) (BOUND_VARIABLE_2125974 tptp.nat) (BOUND_VARIABLE_2125975 tptp.int) (BOUND_VARIABLE_2125976 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15327 BOUND_VARIABLE_2125976) BOUND_VARIABLE_2125975)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15328 BOUND_VARIABLE_2231614) BOUND_VARIABLE_2125973) BOUND_VARIABLE_2125974))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16009 BOUND_VARIABLE_2231614) BOUND_VARIABLE_2125973) BOUND_VARIABLE_2125974) BOUND_VARIABLE_2125975) BOUND_VARIABLE_2125976))))) (let ((_let_2722 (forall ((BOUND_VARIABLE_2125960 tptp.nat) (BOUND_VARIABLE_2125961 tptp.nat)) (= (ho_16012 (ho_16011 k_16010 BOUND_VARIABLE_2125960) BOUND_VARIABLE_2125961) (ho_16012 k_16013 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15077 (ho_15161 k_15160 BOUND_VARIABLE_2125960)) (ho_15161 k_15160 BOUND_VARIABLE_2125961)))))))) (let ((_let_2723 (forall ((BOUND_VARIABLE_2125948 tptp.nat) (BOUND_VARIABLE_2125949 tptp.nat)) (= (ho_16012 (ho_16011 k_16014 BOUND_VARIABLE_2125948) BOUND_VARIABLE_2125949) (ho_16012 k_16013 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15077 (ho_15161 k_15160 BOUND_VARIABLE_2125948)) (ho_15161 k_15160 BOUND_VARIABLE_2125949)))))))) (let ((_let_2724 (forall ((BOUND_VARIABLE_2125936 tptp.nat) (BOUND_VARIABLE_2125937 tptp.nat)) (= (ho_16012 (ho_16011 k_16015 BOUND_VARIABLE_2125936) BOUND_VARIABLE_2125937) (ho_16012 k_16013 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2125936)) (ho_15161 k_15160 BOUND_VARIABLE_2125937)))))))) (let ((_let_2725 (forall ((BOUND_VARIABLE_2125924 tptp.nat) (BOUND_VARIABLE_2125925 tptp.nat)) (= (ho_16012 (ho_16011 k_16016 BOUND_VARIABLE_2125924) BOUND_VARIABLE_2125925) (ho_16012 k_16013 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2125924)) (ho_15161 k_15160 BOUND_VARIABLE_2125925)))))))) (let ((_let_2726 (forall ((BOUND_VARIABLE_2125912 tptp.nat) (BOUND_VARIABLE_2125913 tptp.nat)) (= (ho_16012 (ho_16011 k_16017 BOUND_VARIABLE_2125912) BOUND_VARIABLE_2125913) (ho_16012 k_16013 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2125912)) (ho_15161 k_15160 BOUND_VARIABLE_2125913)))))))) (let ((_let_2727 (forall ((BOUND_VARIABLE_2125900 tptp.nat) (BOUND_VARIABLE_2125901 tptp.nat)) (= (ho_16012 (ho_16011 k_16018 BOUND_VARIABLE_2125900) BOUND_VARIABLE_2125901) (ho_16012 k_16013 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2125900)) (ho_15161 k_15160 BOUND_VARIABLE_2125901)))))))) (let ((_let_2728 (forall ((BOUND_VARIABLE_2125872 tptp.int) (BOUND_VARIABLE_2125873 tptp.int) (BOUND_VARIABLE_2125874 tptp.int) (BOUND_VARIABLE_2125875 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2125872) BOUND_VARIABLE_2125874))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2125873) BOUND_VARIABLE_2125875))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16019 BOUND_VARIABLE_2125872) BOUND_VARIABLE_2125873) BOUND_VARIABLE_2125874) BOUND_VARIABLE_2125875))))))) (let ((_let_2729 (forall ((BOUND_VARIABLE_2231797 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2125786 tptp.nat) (BOUND_VARIABLE_2125787 tptp.nat) (BOUND_VARIABLE_2125788 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2125788))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2125788))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16020 BOUND_VARIABLE_2231797) BOUND_VARIABLE_2125786) BOUND_VARIABLE_2125787) BOUND_VARIABLE_2125788) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2231797 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2125786)) (ho_15161 k_15160 BOUND_VARIABLE_2125787))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2730 (forall ((BOUND_VARIABLE_2125757 tptp.int) (BOUND_VARIABLE_2125758 tptp.int) (BOUND_VARIABLE_2125759 tptp.int) (BOUND_VARIABLE_2125760 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2125757) BOUND_VARIABLE_2125759))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2125758) BOUND_VARIABLE_2125760))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16021 BOUND_VARIABLE_2125757) BOUND_VARIABLE_2125758) BOUND_VARIABLE_2125759) BOUND_VARIABLE_2125760))))))) (let ((_let_2731 (forall ((BOUND_VARIABLE_2125678 tptp.rat) (BOUND_VARIABLE_2125679 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2125679))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2125679))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2125678 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16022 BOUND_VARIABLE_2125678) BOUND_VARIABLE_2125679)))))))))))))) (let ((_let_2732 (forall ((BOUND_VARIABLE_2125576 tptp.int) (BOUND_VARIABLE_2125577 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2125577))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2125577))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16023 BOUND_VARIABLE_2125576) BOUND_VARIABLE_2125577) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2125576) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2125576)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2125576)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2733 (forall ((BOUND_VARIABLE_2125481 tptp.int) (BOUND_VARIABLE_2125482 tptp.int) (BOUND_VARIABLE_2125483 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15329 BOUND_VARIABLE_2125483) BOUND_VARIABLE_2125482)) (ho_15260 k_15259 (ho_15141 k_15330 BOUND_VARIABLE_2125481))) (ho_15108 (ho_15107 (ho_15106 k_16024 BOUND_VARIABLE_2125481) BOUND_VARIABLE_2125482) BOUND_VARIABLE_2125483))))) (let ((_let_2734 (forall ((BOUND_VARIABLE_2125402 tptp.rat) (BOUND_VARIABLE_2125403 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2125403))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2125403))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2125402 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16025 BOUND_VARIABLE_2125402) BOUND_VARIABLE_2125403)))))))))))))) (let ((_let_2735 (forall ((BOUND_VARIABLE_2125345 tptp.rat) (BOUND_VARIABLE_2125346 tptp.int) (BOUND_VARIABLE_2125347 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15331 BOUND_VARIABLE_2125347) BOUND_VARIABLE_2125346)) (ho_15260 k_15259 (ho_15145 k_15332 BOUND_VARIABLE_2125345))) (ho_15108 (ho_15107 (ho_15266 k_16026 BOUND_VARIABLE_2125345) BOUND_VARIABLE_2125346) BOUND_VARIABLE_2125347))))) (let ((_let_2736 (forall ((BOUND_VARIABLE_2125241 tptp.int) (BOUND_VARIABLE_2125242 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2125242))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2125242))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2125241) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16027 BOUND_VARIABLE_2125241) BOUND_VARIABLE_2125242) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2737 (forall ((BOUND_VARIABLE_2125213 tptp.int) (BOUND_VARIABLE_2125214 tptp.int) (BOUND_VARIABLE_2125215 tptp.int) (BOUND_VARIABLE_2125216 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2125213) BOUND_VARIABLE_2125215))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2125214) BOUND_VARIABLE_2125216))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16028 BOUND_VARIABLE_2125213) BOUND_VARIABLE_2125214) BOUND_VARIABLE_2125215) BOUND_VARIABLE_2125216))))))) (let ((_let_2738 (forall ((BOUND_VARIABLE_2125116 tptp.nat) (BOUND_VARIABLE_2232201 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2125118 tptp.nat) (BOUND_VARIABLE_2125119 tptp.nat) (BOUND_VARIABLE_2125120 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2125120))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2125120))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2125118)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16029 BOUND_VARIABLE_2125116) BOUND_VARIABLE_2232201) BOUND_VARIABLE_2125118) BOUND_VARIABLE_2125119) BOUND_VARIABLE_2125120) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2232201 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2125116))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2232201 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2125119))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2739 (forall ((BOUND_VARIABLE_2125019 tptp.nat) (BOUND_VARIABLE_2232278 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2125021 tptp.nat) (BOUND_VARIABLE_2125022 tptp.nat) (BOUND_VARIABLE_2125023 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2125023))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2125023))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2125021)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16030 BOUND_VARIABLE_2125019) BOUND_VARIABLE_2232278) BOUND_VARIABLE_2125021) BOUND_VARIABLE_2125022) BOUND_VARIABLE_2125023) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2232278 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2125019))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2232278 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2125022))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2740 (forall ((BOUND_VARIABLE_2124927 tptp.nat) (BOUND_VARIABLE_2232303 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2124929 tptp.nat) (BOUND_VARIABLE_2124930 tptp.nat) (BOUND_VARIABLE_2124931 tptp.int) (BOUND_VARIABLE_2124932 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15333 BOUND_VARIABLE_2124932) BOUND_VARIABLE_2124931)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15334 BOUND_VARIABLE_2124927) BOUND_VARIABLE_2232303) BOUND_VARIABLE_2124929) BOUND_VARIABLE_2124930))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16031 BOUND_VARIABLE_2124927) BOUND_VARIABLE_2232303) BOUND_VARIABLE_2124929) BOUND_VARIABLE_2124930) BOUND_VARIABLE_2124931) BOUND_VARIABLE_2124932))))) (let ((_let_2741 (forall ((BOUND_VARIABLE_2124899 tptp.int) (BOUND_VARIABLE_2124900 tptp.int) (BOUND_VARIABLE_2124901 tptp.int) (BOUND_VARIABLE_2124902 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2124899) BOUND_VARIABLE_2124901))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2124900) BOUND_VARIABLE_2124902))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16032 BOUND_VARIABLE_2124899) BOUND_VARIABLE_2124900) BOUND_VARIABLE_2124901) BOUND_VARIABLE_2124902))))))) (let ((_let_2742 (forall ((BOUND_VARIABLE_2124802 tptp.nat) (BOUND_VARIABLE_2232404 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2124804 tptp.nat) (BOUND_VARIABLE_2124805 tptp.nat) (BOUND_VARIABLE_2124806 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2124806))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2124806))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2124804)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16033 BOUND_VARIABLE_2124802) BOUND_VARIABLE_2232404) BOUND_VARIABLE_2124804) BOUND_VARIABLE_2124805) BOUND_VARIABLE_2124806) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2232404 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2124802))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2232404 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2124805))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2743 (forall ((BOUND_VARIABLE_2124705 tptp.nat) (BOUND_VARIABLE_2232481 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2124707 tptp.nat) (BOUND_VARIABLE_2124708 tptp.nat) (BOUND_VARIABLE_2124709 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2124709))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2124709))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2124707)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16034 BOUND_VARIABLE_2124705) BOUND_VARIABLE_2232481) BOUND_VARIABLE_2124707) BOUND_VARIABLE_2124708) BOUND_VARIABLE_2124709) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2232481 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2124705))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2232481 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2124708))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2744 (forall ((BOUND_VARIABLE_2124613 tptp.nat) (BOUND_VARIABLE_2232506 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2124615 tptp.nat) (BOUND_VARIABLE_2124616 tptp.nat) (BOUND_VARIABLE_2124617 tptp.int) (BOUND_VARIABLE_2124618 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15335 BOUND_VARIABLE_2124618) BOUND_VARIABLE_2124617)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15336 BOUND_VARIABLE_2124613) BOUND_VARIABLE_2232506) BOUND_VARIABLE_2124615) BOUND_VARIABLE_2124616))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16035 BOUND_VARIABLE_2124613) BOUND_VARIABLE_2232506) BOUND_VARIABLE_2124615) BOUND_VARIABLE_2124616) BOUND_VARIABLE_2124617) BOUND_VARIABLE_2124618))))) (let ((_let_2745 (forall ((BOUND_VARIABLE_2124585 tptp.int) (BOUND_VARIABLE_2124586 tptp.int) (BOUND_VARIABLE_2124587 tptp.int) (BOUND_VARIABLE_2124588 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2124585) BOUND_VARIABLE_2124587))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2124586) BOUND_VARIABLE_2124588))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16036 BOUND_VARIABLE_2124585) BOUND_VARIABLE_2124586) BOUND_VARIABLE_2124587) BOUND_VARIABLE_2124588))))))) (let ((_let_2746 (forall ((BOUND_VARIABLE_2124488 tptp.nat) (BOUND_VARIABLE_2232607 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2124490 tptp.nat) (BOUND_VARIABLE_2124491 tptp.nat) (BOUND_VARIABLE_2124492 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2124492))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2124492))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2124490)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16037 BOUND_VARIABLE_2124488) BOUND_VARIABLE_2232607) BOUND_VARIABLE_2124490) BOUND_VARIABLE_2124491) BOUND_VARIABLE_2124492) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2232607 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2124488))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2232607 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2124491))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2747 (forall ((BOUND_VARIABLE_2124391 tptp.nat) (BOUND_VARIABLE_2232684 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2124393 tptp.nat) (BOUND_VARIABLE_2124394 tptp.nat) (BOUND_VARIABLE_2124395 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2124395))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2124395))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2124393)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16038 BOUND_VARIABLE_2124391) BOUND_VARIABLE_2232684) BOUND_VARIABLE_2124393) BOUND_VARIABLE_2124394) BOUND_VARIABLE_2124395) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2232684 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2124391))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2232684 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2124394))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2748 (forall ((BOUND_VARIABLE_2124299 tptp.nat) (BOUND_VARIABLE_2232709 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2124301 tptp.nat) (BOUND_VARIABLE_2124302 tptp.nat) (BOUND_VARIABLE_2124303 tptp.int) (BOUND_VARIABLE_2124304 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15337 BOUND_VARIABLE_2124304) BOUND_VARIABLE_2124303)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15338 BOUND_VARIABLE_2124299) BOUND_VARIABLE_2232709) BOUND_VARIABLE_2124301) BOUND_VARIABLE_2124302))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16039 BOUND_VARIABLE_2124299) BOUND_VARIABLE_2232709) BOUND_VARIABLE_2124301) BOUND_VARIABLE_2124302) BOUND_VARIABLE_2124303) BOUND_VARIABLE_2124304))))) (let ((_let_2749 (forall ((BOUND_VARIABLE_2232787 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2124213 tptp.nat) (BOUND_VARIABLE_2124214 tptp.nat) (BOUND_VARIABLE_2124215 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2124215))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2124215))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16040 BOUND_VARIABLE_2232787) BOUND_VARIABLE_2124213) BOUND_VARIABLE_2124214) BOUND_VARIABLE_2124215) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2232787 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2124213)) (ho_15161 k_15160 BOUND_VARIABLE_2124214))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2750 (forall ((BOUND_VARIABLE_2232803 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2124138 tptp.nat) (BOUND_VARIABLE_2124139 tptp.nat) (BOUND_VARIABLE_2124140 tptp.int) (BOUND_VARIABLE_2124141 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15339 BOUND_VARIABLE_2124141) BOUND_VARIABLE_2124140)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15340 BOUND_VARIABLE_2232803) BOUND_VARIABLE_2124138) BOUND_VARIABLE_2124139))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16041 BOUND_VARIABLE_2232803) BOUND_VARIABLE_2124138) BOUND_VARIABLE_2124139) BOUND_VARIABLE_2124140) BOUND_VARIABLE_2124141))))) (let ((_let_2751 (forall ((BOUND_VARIABLE_2124109 tptp.int) (BOUND_VARIABLE_2124110 tptp.int) (BOUND_VARIABLE_2124111 tptp.int) (BOUND_VARIABLE_2124112 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2124109) BOUND_VARIABLE_2124111))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2124110) BOUND_VARIABLE_2124112))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16042 BOUND_VARIABLE_2124109) BOUND_VARIABLE_2124110) BOUND_VARIABLE_2124111) BOUND_VARIABLE_2124112))))))) (let ((_let_2752 (forall ((BOUND_VARIABLE_2232901 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2123962 tptp.nat) (BOUND_VARIABLE_2123963 tptp.nat) (BOUND_VARIABLE_2123964 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2123964))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2123964))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2232901 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2123962)) (ho_15161 k_15160 BOUND_VARIABLE_2123963)))))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16045 BOUND_VARIABLE_2232901) BOUND_VARIABLE_2123962) BOUND_VARIABLE_2123963) BOUND_VARIABLE_2123964) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16044) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15341 BOUND_VARIABLE_2232901) BOUND_VARIABLE_2123962) BOUND_VARIABLE_2123963))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 k_15342 BOUND_VARIABLE_2232901) BOUND_VARIABLE_2123962) BOUND_VARIABLE_2123963)) (ho_15260 k_15259 k_16043))))) (ho_15122 k_15121 _let_9)) _let_9)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2753 (forall ((BOUND_VARIABLE_2123864 tptp.nat) (BOUND_VARIABLE_2232989 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2123866 tptp.nat) (BOUND_VARIABLE_2123867 tptp.nat) (BOUND_VARIABLE_2123868 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2123868))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2123868))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2123866)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16046 BOUND_VARIABLE_2123864) BOUND_VARIABLE_2232989) BOUND_VARIABLE_2123866) BOUND_VARIABLE_2123867) BOUND_VARIABLE_2123868) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2232989 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2123864))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2232989 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2123867))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2754 (forall ((BOUND_VARIABLE_2123772 tptp.nat) (BOUND_VARIABLE_2233014 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2123774 tptp.nat) (BOUND_VARIABLE_2123775 tptp.nat) (BOUND_VARIABLE_2123776 tptp.int) (BOUND_VARIABLE_2123777 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15346 BOUND_VARIABLE_2123777) BOUND_VARIABLE_2123776)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15347 BOUND_VARIABLE_2123772) BOUND_VARIABLE_2233014) BOUND_VARIABLE_2123774) BOUND_VARIABLE_2123775))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16047 BOUND_VARIABLE_2123772) BOUND_VARIABLE_2233014) BOUND_VARIABLE_2123774) BOUND_VARIABLE_2123775) BOUND_VARIABLE_2123776) BOUND_VARIABLE_2123777))))) (let ((_let_2755 (forall ((BOUND_VARIABLE_2123744 tptp.int) (BOUND_VARIABLE_2123745 tptp.int) (BOUND_VARIABLE_2123746 tptp.int) (BOUND_VARIABLE_2123747 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2123744) BOUND_VARIABLE_2123746))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2123745) BOUND_VARIABLE_2123747))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16048 BOUND_VARIABLE_2123744) BOUND_VARIABLE_2123745) BOUND_VARIABLE_2123746) BOUND_VARIABLE_2123747))))))) (let ((_let_2756 (forall ((BOUND_VARIABLE_2123567 tptp.nat) (BOUND_VARIABLE_2233115 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2123569 tptp.nat) (BOUND_VARIABLE_2123570 tptp.nat) (BOUND_VARIABLE_2123571 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2123571))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2123571))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2123569)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2233115 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2123567))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2233115 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2123570)))))))) (let ((_let_12 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16051 BOUND_VARIABLE_2123567) BOUND_VARIABLE_2233115) BOUND_VARIABLE_2123569) BOUND_VARIABLE_2123570) BOUND_VARIABLE_2123571) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16050) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15348 BOUND_VARIABLE_2123567) BOUND_VARIABLE_2233115) BOUND_VARIABLE_2123569) BOUND_VARIABLE_2123570))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15349 BOUND_VARIABLE_2123567) BOUND_VARIABLE_2233115) BOUND_VARIABLE_2123569) BOUND_VARIABLE_2123570)) (ho_15260 k_15259 k_16049))))) (ho_15122 k_15121 _let_11)) _let_11)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))) (let ((_let_2757 (forall ((BOUND_VARIABLE_2123470 tptp.nat) (BOUND_VARIABLE_2233214 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2123472 tptp.nat) (BOUND_VARIABLE_2123473 tptp.nat) (BOUND_VARIABLE_2123474 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2123474))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2123474))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2123472)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16052 BOUND_VARIABLE_2123470) BOUND_VARIABLE_2233214) BOUND_VARIABLE_2123472) BOUND_VARIABLE_2123473) BOUND_VARIABLE_2123474) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2233214 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2123470))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2233214 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2123473))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2758 (forall ((BOUND_VARIABLE_2123378 tptp.nat) (BOUND_VARIABLE_2233239 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2123380 tptp.nat) (BOUND_VARIABLE_2123381 tptp.nat) (BOUND_VARIABLE_2123382 tptp.int) (BOUND_VARIABLE_2123383 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15351 BOUND_VARIABLE_2123383) BOUND_VARIABLE_2123382)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15352 BOUND_VARIABLE_2123378) BOUND_VARIABLE_2233239) BOUND_VARIABLE_2123380) BOUND_VARIABLE_2123381))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16053 BOUND_VARIABLE_2123378) BOUND_VARIABLE_2233239) BOUND_VARIABLE_2123380) BOUND_VARIABLE_2123381) BOUND_VARIABLE_2123382) BOUND_VARIABLE_2123383))))) (let ((_let_2759 (forall ((BOUND_VARIABLE_2123350 tptp.int) (BOUND_VARIABLE_2123351 tptp.int) (BOUND_VARIABLE_2123352 tptp.int) (BOUND_VARIABLE_2123353 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2123350) BOUND_VARIABLE_2123352))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2123351) BOUND_VARIABLE_2123353))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16054 BOUND_VARIABLE_2123350) BOUND_VARIABLE_2123351) BOUND_VARIABLE_2123352) BOUND_VARIABLE_2123353))))))) (let ((_let_2760 (forall ((BOUND_VARIABLE_2123173 tptp.nat) (BOUND_VARIABLE_2233340 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2123175 tptp.nat) (BOUND_VARIABLE_2123176 tptp.nat) (BOUND_VARIABLE_2123177 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2123177))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2123177))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2123175)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2233340 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2123173))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2233340 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2123176)))))))) (let ((_let_12 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16055 BOUND_VARIABLE_2123173) BOUND_VARIABLE_2233340) BOUND_VARIABLE_2123175) BOUND_VARIABLE_2123176) BOUND_VARIABLE_2123177) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16050) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15353 BOUND_VARIABLE_2123173) BOUND_VARIABLE_2233340) BOUND_VARIABLE_2123175) BOUND_VARIABLE_2123176))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15354 BOUND_VARIABLE_2123173) BOUND_VARIABLE_2233340) BOUND_VARIABLE_2123175) BOUND_VARIABLE_2123176)) (ho_15260 k_15259 k_16049))))) (ho_15122 k_15121 _let_11)) _let_11)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))) (let ((_let_2761 (forall ((BOUND_VARIABLE_2233435 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2123082 tptp.nat) (BOUND_VARIABLE_2123083 tptp.nat) (BOUND_VARIABLE_2123084 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2123084))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2123084))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2233435 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2123082)) (ho_15161 k_15160 BOUND_VARIABLE_2123083)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16056 BOUND_VARIABLE_2233435) BOUND_VARIABLE_2123082) BOUND_VARIABLE_2123083) BOUND_VARIABLE_2123084) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2762 (forall ((BOUND_VARIABLE_2233454 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2123001 tptp.nat) (BOUND_VARIABLE_2123002 tptp.nat) (BOUND_VARIABLE_2123003 tptp.int) (BOUND_VARIABLE_2123004 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15355 BOUND_VARIABLE_2123004) BOUND_VARIABLE_2123003)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15356 BOUND_VARIABLE_2233454) BOUND_VARIABLE_2123001) BOUND_VARIABLE_2123002))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16057 BOUND_VARIABLE_2233454) BOUND_VARIABLE_2123001) BOUND_VARIABLE_2123002) BOUND_VARIABLE_2123003) BOUND_VARIABLE_2123004))))) (let ((_let_2763 (forall ((BOUND_VARIABLE_2122972 tptp.int) (BOUND_VARIABLE_2122973 tptp.int) (BOUND_VARIABLE_2122974 tptp.int) (BOUND_VARIABLE_2122975 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2122972) BOUND_VARIABLE_2122974))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2122973) BOUND_VARIABLE_2122975))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16058 BOUND_VARIABLE_2122972) BOUND_VARIABLE_2122973) BOUND_VARIABLE_2122974) BOUND_VARIABLE_2122975))))))) (let ((_let_2764 (forall ((BOUND_VARIABLE_2233552 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2122813 tptp.nat) (BOUND_VARIABLE_2122814 tptp.nat) (BOUND_VARIABLE_2122815 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2122815))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2122815))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2233552 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2122813)) (ho_15161 k_15160 BOUND_VARIABLE_2122814)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9)))) (let ((_let_12 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16059 BOUND_VARIABLE_2233552) BOUND_VARIABLE_2122813) BOUND_VARIABLE_2122814) BOUND_VARIABLE_2122815) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16044) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15357 BOUND_VARIABLE_2233552) BOUND_VARIABLE_2122813) BOUND_VARIABLE_2122814))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 k_15358 BOUND_VARIABLE_2233552) BOUND_VARIABLE_2122813) BOUND_VARIABLE_2122814)) (ho_15260 k_15259 k_16043))))) (ho_15122 k_15121 _let_11)) _let_11)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))) (let ((_let_2765 (forall ((BOUND_VARIABLE_2122784 tptp.int) (BOUND_VARIABLE_2122785 tptp.int) (BOUND_VARIABLE_2122786 tptp.int) (BOUND_VARIABLE_2122787 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2122784) BOUND_VARIABLE_2122786))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2122785) BOUND_VARIABLE_2122787))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16060 BOUND_VARIABLE_2122784) BOUND_VARIABLE_2122785) BOUND_VARIABLE_2122786) BOUND_VARIABLE_2122787))))))) (let ((_let_2766 (forall ((BOUND_VARIABLE_2233662 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2122698 tptp.nat) (BOUND_VARIABLE_2122699 tptp.nat) (BOUND_VARIABLE_2122700 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2122700))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2122700))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16061 BOUND_VARIABLE_2233662) BOUND_VARIABLE_2122698) BOUND_VARIABLE_2122699) BOUND_VARIABLE_2122700) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2233662 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2122698)) (ho_15161 k_15160 BOUND_VARIABLE_2122699))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2767 (forall ((BOUND_VARIABLE_2122669 tptp.int) (BOUND_VARIABLE_2122670 tptp.int) (BOUND_VARIABLE_2122671 tptp.int) (BOUND_VARIABLE_2122672 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2122669) BOUND_VARIABLE_2122671))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2122670) BOUND_VARIABLE_2122672))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16062 BOUND_VARIABLE_2122669) BOUND_VARIABLE_2122670) BOUND_VARIABLE_2122671) BOUND_VARIABLE_2122672))))))) (let ((_let_2768 (forall ((BOUND_VARIABLE_2122590 tptp.rat) (BOUND_VARIABLE_2122591 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2122591))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2122591))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2122590 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16063 BOUND_VARIABLE_2122590) BOUND_VARIABLE_2122591)))))))))))))) (let ((_let_2769 (forall ((BOUND_VARIABLE_2233809 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2122504 tptp.nat) (BOUND_VARIABLE_2122505 tptp.nat) (BOUND_VARIABLE_2122506 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2122506))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2122506))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16064 BOUND_VARIABLE_2233809) BOUND_VARIABLE_2122504) BOUND_VARIABLE_2122505) BOUND_VARIABLE_2122506) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2233809 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2122504)) (ho_15161 k_15160 BOUND_VARIABLE_2122505))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2770 (forall ((BOUND_VARIABLE_2233825 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2122429 tptp.nat) (BOUND_VARIABLE_2122430 tptp.nat) (BOUND_VARIABLE_2122431 tptp.int) (BOUND_VARIABLE_2122432 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15359 BOUND_VARIABLE_2122432) BOUND_VARIABLE_2122431)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15360 BOUND_VARIABLE_2233825) BOUND_VARIABLE_2122429) BOUND_VARIABLE_2122430))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16065 BOUND_VARIABLE_2233825) BOUND_VARIABLE_2122429) BOUND_VARIABLE_2122430) BOUND_VARIABLE_2122431) BOUND_VARIABLE_2122432))))) (let ((_let_2771 (forall ((BOUND_VARIABLE_2122400 tptp.int) (BOUND_VARIABLE_2122401 tptp.int) (BOUND_VARIABLE_2122402 tptp.int) (BOUND_VARIABLE_2122403 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2122400) BOUND_VARIABLE_2122402))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2122401) BOUND_VARIABLE_2122403))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16066 BOUND_VARIABLE_2122400) BOUND_VARIABLE_2122401) BOUND_VARIABLE_2122402) BOUND_VARIABLE_2122403))))))) (let ((_let_2772 (forall ((BOUND_VARIABLE_2233923 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2122253 tptp.nat) (BOUND_VARIABLE_2122254 tptp.nat) (BOUND_VARIABLE_2122255 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2122255))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2122255))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2233923 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2122253)) (ho_15161 k_15160 BOUND_VARIABLE_2122254)))))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16067 BOUND_VARIABLE_2233923) BOUND_VARIABLE_2122253) BOUND_VARIABLE_2122254) BOUND_VARIABLE_2122255) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16044) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15361 BOUND_VARIABLE_2233923) BOUND_VARIABLE_2122253) BOUND_VARIABLE_2122254))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 k_15362 BOUND_VARIABLE_2233923) BOUND_VARIABLE_2122253) BOUND_VARIABLE_2122254)) (ho_15260 k_15259 k_16043))))) (ho_15122 k_15121 _let_9)) _let_9)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2773 (forall ((BOUND_VARIABLE_2234007 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2122166 tptp.nat) (BOUND_VARIABLE_2122167 tptp.nat) (BOUND_VARIABLE_2122168 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2122168))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2122168))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16068 BOUND_VARIABLE_2234007) BOUND_VARIABLE_2122166) BOUND_VARIABLE_2122167) BOUND_VARIABLE_2122168) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2234007 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2122166)) (ho_15161 k_15160 BOUND_VARIABLE_2122167))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2774 (forall ((BOUND_VARIABLE_2234023 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2122091 tptp.nat) (BOUND_VARIABLE_2122092 tptp.nat) (BOUND_VARIABLE_2122093 tptp.int) (BOUND_VARIABLE_2122094 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15363 BOUND_VARIABLE_2122094) BOUND_VARIABLE_2122093)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15364 BOUND_VARIABLE_2234023) BOUND_VARIABLE_2122091) BOUND_VARIABLE_2122092))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16069 BOUND_VARIABLE_2234023) BOUND_VARIABLE_2122091) BOUND_VARIABLE_2122092) BOUND_VARIABLE_2122093) BOUND_VARIABLE_2122094))))) (let ((_let_2775 (forall ((BOUND_VARIABLE_2122062 tptp.int) (BOUND_VARIABLE_2122063 tptp.int) (BOUND_VARIABLE_2122064 tptp.int) (BOUND_VARIABLE_2122065 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2122062) BOUND_VARIABLE_2122064))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2122063) BOUND_VARIABLE_2122065))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16070 BOUND_VARIABLE_2122062) BOUND_VARIABLE_2122063) BOUND_VARIABLE_2122064) BOUND_VARIABLE_2122065))))))) (let ((_let_2776 (forall ((BOUND_VARIABLE_2234121 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2121915 tptp.nat) (BOUND_VARIABLE_2121916 tptp.nat) (BOUND_VARIABLE_2121917 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2121917))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2121917))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2234121 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2121915)) (ho_15161 k_15160 BOUND_VARIABLE_2121916)))))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16071 BOUND_VARIABLE_2234121) BOUND_VARIABLE_2121915) BOUND_VARIABLE_2121916) BOUND_VARIABLE_2121917) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16044) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15365 BOUND_VARIABLE_2234121) BOUND_VARIABLE_2121915) BOUND_VARIABLE_2121916))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 k_15366 BOUND_VARIABLE_2234121) BOUND_VARIABLE_2121915) BOUND_VARIABLE_2121916)) (ho_15260 k_15259 k_16043))))) (ho_15122 k_15121 _let_9)) _let_9)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_2777 (forall ((BOUND_VARIABLE_2121817 tptp.nat) (BOUND_VARIABLE_2234205 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2121819 tptp.nat) (BOUND_VARIABLE_2121820 tptp.nat) (BOUND_VARIABLE_2121821 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2121821))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2121821))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2121819)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16072 BOUND_VARIABLE_2121817) BOUND_VARIABLE_2234205) BOUND_VARIABLE_2121819) BOUND_VARIABLE_2121820) BOUND_VARIABLE_2121821) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2234205 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2121817))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2234205 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2121820))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2778 (forall ((BOUND_VARIABLE_2121725 tptp.nat) (BOUND_VARIABLE_2234230 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2121727 tptp.nat) (BOUND_VARIABLE_2121728 tptp.nat) (BOUND_VARIABLE_2121729 tptp.int) (BOUND_VARIABLE_2121730 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15367 BOUND_VARIABLE_2121730) BOUND_VARIABLE_2121729)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15368 BOUND_VARIABLE_2121725) BOUND_VARIABLE_2234230) BOUND_VARIABLE_2121727) BOUND_VARIABLE_2121728))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16073 BOUND_VARIABLE_2121725) BOUND_VARIABLE_2234230) BOUND_VARIABLE_2121727) BOUND_VARIABLE_2121728) BOUND_VARIABLE_2121729) BOUND_VARIABLE_2121730))))) (let ((_let_2779 (forall ((BOUND_VARIABLE_2121697 tptp.int) (BOUND_VARIABLE_2121698 tptp.int) (BOUND_VARIABLE_2121699 tptp.int) (BOUND_VARIABLE_2121700 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2121697) BOUND_VARIABLE_2121699))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2121698) BOUND_VARIABLE_2121700))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16074 BOUND_VARIABLE_2121697) BOUND_VARIABLE_2121698) BOUND_VARIABLE_2121699) BOUND_VARIABLE_2121700))))))) (let ((_let_2780 (forall ((BOUND_VARIABLE_2121520 tptp.nat) (BOUND_VARIABLE_2234331 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2121522 tptp.nat) (BOUND_VARIABLE_2121523 tptp.nat) (BOUND_VARIABLE_2121524 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2121524))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2121524))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2121522)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2234331 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2121520))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2234331 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2121523)))))))) (let ((_let_12 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16075 BOUND_VARIABLE_2121520) BOUND_VARIABLE_2234331) BOUND_VARIABLE_2121522) BOUND_VARIABLE_2121523) BOUND_VARIABLE_2121524) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16050) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15369 BOUND_VARIABLE_2121520) BOUND_VARIABLE_2234331) BOUND_VARIABLE_2121522) BOUND_VARIABLE_2121523))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15370 BOUND_VARIABLE_2121520) BOUND_VARIABLE_2234331) BOUND_VARIABLE_2121522) BOUND_VARIABLE_2121523)) (ho_15260 k_15259 k_16049))))) (ho_15122 k_15121 _let_11)) _let_11)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))) (let ((_let_2781 (forall ((BOUND_VARIABLE_2121423 tptp.nat) (BOUND_VARIABLE_2234426 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2121425 tptp.nat) (BOUND_VARIABLE_2121426 tptp.nat) (BOUND_VARIABLE_2121427 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2121427))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2121427))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2121425)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16076 BOUND_VARIABLE_2121423) BOUND_VARIABLE_2234426) BOUND_VARIABLE_2121425) BOUND_VARIABLE_2121426) BOUND_VARIABLE_2121427) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2234426 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2121423))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2234426 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2121426))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2782 (forall ((BOUND_VARIABLE_2121331 tptp.nat) (BOUND_VARIABLE_2234451 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2121333 tptp.nat) (BOUND_VARIABLE_2121334 tptp.nat) (BOUND_VARIABLE_2121335 tptp.int) (BOUND_VARIABLE_2121336 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15371 BOUND_VARIABLE_2121336) BOUND_VARIABLE_2121335)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15372 BOUND_VARIABLE_2121331) BOUND_VARIABLE_2234451) BOUND_VARIABLE_2121333) BOUND_VARIABLE_2121334))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16077 BOUND_VARIABLE_2121331) BOUND_VARIABLE_2234451) BOUND_VARIABLE_2121333) BOUND_VARIABLE_2121334) BOUND_VARIABLE_2121335) BOUND_VARIABLE_2121336))))) (let ((_let_2783 (forall ((BOUND_VARIABLE_2121303 tptp.int) (BOUND_VARIABLE_2121304 tptp.int) (BOUND_VARIABLE_2121305 tptp.int) (BOUND_VARIABLE_2121306 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2121303) BOUND_VARIABLE_2121305))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2121304) BOUND_VARIABLE_2121306))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16078 BOUND_VARIABLE_2121303) BOUND_VARIABLE_2121304) BOUND_VARIABLE_2121305) BOUND_VARIABLE_2121306))))))) (let ((_let_2784 (forall ((BOUND_VARIABLE_2121126 tptp.nat) (BOUND_VARIABLE_2234552 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2121128 tptp.nat) (BOUND_VARIABLE_2121129 tptp.nat) (BOUND_VARIABLE_2121130 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2121130))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2121130))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2121128)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2234552 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2121126))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2234552 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2121129)))))))) (let ((_let_12 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16079 BOUND_VARIABLE_2121126) BOUND_VARIABLE_2234552) BOUND_VARIABLE_2121128) BOUND_VARIABLE_2121129) BOUND_VARIABLE_2121130) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16050) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15373 BOUND_VARIABLE_2121126) BOUND_VARIABLE_2234552) BOUND_VARIABLE_2121128) BOUND_VARIABLE_2121129))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15374 BOUND_VARIABLE_2121126) BOUND_VARIABLE_2234552) BOUND_VARIABLE_2121128) BOUND_VARIABLE_2121129)) (ho_15260 k_15259 k_16049))))) (ho_15122 k_15121 _let_11)) _let_11)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))) (let ((_let_2785 (forall ((BOUND_VARIABLE_2234650 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2234647 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2121034 tptp.nat) (BOUND_VARIABLE_2121035 tptp.nat) (BOUND_VARIABLE_2121036 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2121036))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2121036))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2121034)) (ho_15161 k_15160 BOUND_VARIABLE_2121035))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16080 BOUND_VARIABLE_2234650) BOUND_VARIABLE_2234647) BOUND_VARIABLE_2121034) BOUND_VARIABLE_2121035) BOUND_VARIABLE_2121036) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2234650 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2234647 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2786 (forall ((BOUND_VARIABLE_2234671 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2234670 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2120948 tptp.nat) (BOUND_VARIABLE_2120949 tptp.nat) (BOUND_VARIABLE_2120950 tptp.int) (BOUND_VARIABLE_2120951 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15375 BOUND_VARIABLE_2120951) BOUND_VARIABLE_2120950)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15376 BOUND_VARIABLE_2234671) BOUND_VARIABLE_2234670) BOUND_VARIABLE_2120948) BOUND_VARIABLE_2120949))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 k_16081 BOUND_VARIABLE_2234671) BOUND_VARIABLE_2234670) BOUND_VARIABLE_2120948) BOUND_VARIABLE_2120949) BOUND_VARIABLE_2120950) BOUND_VARIABLE_2120951))))) (let ((_let_2787 (forall ((BOUND_VARIABLE_2120918 tptp.int) (BOUND_VARIABLE_2120919 tptp.int) (BOUND_VARIABLE_2120920 tptp.int) (BOUND_VARIABLE_2120921 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120918) BOUND_VARIABLE_2120920))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120919) BOUND_VARIABLE_2120921))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16082 BOUND_VARIABLE_2120918) BOUND_VARIABLE_2120919) BOUND_VARIABLE_2120920) BOUND_VARIABLE_2120921))))))) (let ((_let_2788 (forall ((BOUND_VARIABLE_2234775 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2234772 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2120752 tptp.nat) (BOUND_VARIABLE_2120753 tptp.nat) (BOUND_VARIABLE_2120754 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2120754))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2120754))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2120752)) (ho_15161 k_15160 BOUND_VARIABLE_2120753))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2234775 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2234772 _let_9))))) (let ((_let_12 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16083 BOUND_VARIABLE_2234775) BOUND_VARIABLE_2234772) BOUND_VARIABLE_2120752) BOUND_VARIABLE_2120753) BOUND_VARIABLE_2120754) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16044) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15377 BOUND_VARIABLE_2234775) BOUND_VARIABLE_2234772) BOUND_VARIABLE_2120752) BOUND_VARIABLE_2120753))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 (ho_15379 k_15378 BOUND_VARIABLE_2234775) BOUND_VARIABLE_2234772) BOUND_VARIABLE_2120752) BOUND_VARIABLE_2120753)) (ho_15260 k_15259 k_16043))))) (ho_15122 k_15121 _let_11)) _let_11)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))) (let ((_let_2789 (forall ((BOUND_VARIABLE_2120722 tptp.int) (BOUND_VARIABLE_2120723 tptp.int) (BOUND_VARIABLE_2120724 tptp.int) (BOUND_VARIABLE_2120725 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120722) BOUND_VARIABLE_2120724))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120723) BOUND_VARIABLE_2120725))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16084 BOUND_VARIABLE_2120722) BOUND_VARIABLE_2120723) BOUND_VARIABLE_2120724) BOUND_VARIABLE_2120725))))))) (let ((_let_2790 (forall ((BOUND_VARIABLE_2234888 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2120636 tptp.nat) (BOUND_VARIABLE_2120637 tptp.nat) (BOUND_VARIABLE_2120638 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2120638))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2120638))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16085 BOUND_VARIABLE_2234888) BOUND_VARIABLE_2120636) BOUND_VARIABLE_2120637) BOUND_VARIABLE_2120638) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2234888 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2120636)) (ho_15161 k_15160 BOUND_VARIABLE_2120637))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2791 (forall ((BOUND_VARIABLE_2120607 tptp.int) (BOUND_VARIABLE_2120608 tptp.int) (BOUND_VARIABLE_2120609 tptp.int) (BOUND_VARIABLE_2120610 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120607) BOUND_VARIABLE_2120609))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120608) BOUND_VARIABLE_2120610))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16086 BOUND_VARIABLE_2120607) BOUND_VARIABLE_2120608) BOUND_VARIABLE_2120609) BOUND_VARIABLE_2120610))))))) (let ((_let_2792 (forall ((BOUND_VARIABLE_2120528 tptp.rat) (BOUND_VARIABLE_2120529 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2120529))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2120529))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2120528 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16087 BOUND_VARIABLE_2120528) BOUND_VARIABLE_2120529)))))))))))))) (let ((_let_2793 (forall ((BOUND_VARIABLE_2120500 tptp.int) (BOUND_VARIABLE_2120501 tptp.int) (BOUND_VARIABLE_2120502 tptp.int) (BOUND_VARIABLE_2120503 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120500) BOUND_VARIABLE_2120502))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120501) BOUND_VARIABLE_2120503))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16088 BOUND_VARIABLE_2120500) BOUND_VARIABLE_2120501) BOUND_VARIABLE_2120502) BOUND_VARIABLE_2120503))))))) (let ((_let_2794 (forall ((BOUND_VARIABLE_2235058 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2120414 tptp.nat) (BOUND_VARIABLE_2120415 tptp.nat) (BOUND_VARIABLE_2120416 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2120416))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2120416))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16089 BOUND_VARIABLE_2235058) BOUND_VARIABLE_2120414) BOUND_VARIABLE_2120415) BOUND_VARIABLE_2120416) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2235058 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2120414)) (ho_15161 k_15160 BOUND_VARIABLE_2120415))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2795 (forall ((BOUND_VARIABLE_2120385 tptp.int) (BOUND_VARIABLE_2120386 tptp.int) (BOUND_VARIABLE_2120387 tptp.int) (BOUND_VARIABLE_2120388 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120385) BOUND_VARIABLE_2120387))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120386) BOUND_VARIABLE_2120388))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16090 BOUND_VARIABLE_2120385) BOUND_VARIABLE_2120386) BOUND_VARIABLE_2120387) BOUND_VARIABLE_2120388))))))) (let ((_let_2796 (forall ((BOUND_VARIABLE_2120306 tptp.rat) (BOUND_VARIABLE_2120307 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2120307))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2120307))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2120306 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16091 BOUND_VARIABLE_2120306) BOUND_VARIABLE_2120307)))))))))))))) (let ((_let_2797 (forall ((BOUND_VARIABLE_2120278 tptp.int) (BOUND_VARIABLE_2120279 tptp.int) (BOUND_VARIABLE_2120280 tptp.int) (BOUND_VARIABLE_2120281 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120278) BOUND_VARIABLE_2120280))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2120279) BOUND_VARIABLE_2120281))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16092 BOUND_VARIABLE_2120278) BOUND_VARIABLE_2120279) BOUND_VARIABLE_2120280) BOUND_VARIABLE_2120281))))))) (let ((_let_2798 (forall ((BOUND_VARIABLE_2120181 tptp.nat) (BOUND_VARIABLE_2235228 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2120183 tptp.nat) (BOUND_VARIABLE_2120184 tptp.nat) (BOUND_VARIABLE_2120185 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2120185))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2120185))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2120183)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16093 BOUND_VARIABLE_2120181) BOUND_VARIABLE_2235228) BOUND_VARIABLE_2120183) BOUND_VARIABLE_2120184) BOUND_VARIABLE_2120185) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2235228 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2120181))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2235228 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2120184))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2799 (forall ((BOUND_VARIABLE_2120084 tptp.nat) (BOUND_VARIABLE_2235305 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2120086 tptp.nat) (BOUND_VARIABLE_2120087 tptp.nat) (BOUND_VARIABLE_2120088 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2120088))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2120088))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2120086)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16094 BOUND_VARIABLE_2120084) BOUND_VARIABLE_2235305) BOUND_VARIABLE_2120086) BOUND_VARIABLE_2120087) BOUND_VARIABLE_2120088) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2235305 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2120084))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2235305 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2120087))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2800 (forall ((BOUND_VARIABLE_2119992 tptp.nat) (BOUND_VARIABLE_2235330 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2119994 tptp.nat) (BOUND_VARIABLE_2119995 tptp.nat) (BOUND_VARIABLE_2119996 tptp.int) (BOUND_VARIABLE_2119997 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15380 BOUND_VARIABLE_2119997) BOUND_VARIABLE_2119996)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15381 BOUND_VARIABLE_2119992) BOUND_VARIABLE_2235330) BOUND_VARIABLE_2119994) BOUND_VARIABLE_2119995))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16095 BOUND_VARIABLE_2119992) BOUND_VARIABLE_2235330) BOUND_VARIABLE_2119994) BOUND_VARIABLE_2119995) BOUND_VARIABLE_2119996) BOUND_VARIABLE_2119997))))) (let ((_let_2801 (forall ((BOUND_VARIABLE_2119964 tptp.int) (BOUND_VARIABLE_2119965 tptp.int) (BOUND_VARIABLE_2119966 tptp.int) (BOUND_VARIABLE_2119967 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2119964) BOUND_VARIABLE_2119966))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2119965) BOUND_VARIABLE_2119967))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16096 BOUND_VARIABLE_2119964) BOUND_VARIABLE_2119965) BOUND_VARIABLE_2119966) BOUND_VARIABLE_2119967))))))) (let ((_let_2802 (forall ((BOUND_VARIABLE_2235431 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2119873 tptp.nat) (BOUND_VARIABLE_2119874 tptp.nat) (BOUND_VARIABLE_2119875 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2119875))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2119875))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2235431 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2119873)) (ho_15161 k_15160 BOUND_VARIABLE_2119874)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16097 BOUND_VARIABLE_2235431) BOUND_VARIABLE_2119873) BOUND_VARIABLE_2119874) BOUND_VARIABLE_2119875) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2803 (forall ((BOUND_VARIABLE_2235502 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2119781 tptp.nat) (BOUND_VARIABLE_2119782 tptp.nat) (BOUND_VARIABLE_2119783 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2119783))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2119783))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2235502 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2119781)) (ho_15161 k_15160 BOUND_VARIABLE_2119782)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16098 BOUND_VARIABLE_2235502) BOUND_VARIABLE_2119781) BOUND_VARIABLE_2119782) BOUND_VARIABLE_2119783) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2804 (forall ((BOUND_VARIABLE_2235521 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2119700 tptp.nat) (BOUND_VARIABLE_2119701 tptp.nat) (BOUND_VARIABLE_2119702 tptp.int) (BOUND_VARIABLE_2119703 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15382 BOUND_VARIABLE_2119703) BOUND_VARIABLE_2119702)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15383 BOUND_VARIABLE_2235521) BOUND_VARIABLE_2119700) BOUND_VARIABLE_2119701))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16099 BOUND_VARIABLE_2235521) BOUND_VARIABLE_2119700) BOUND_VARIABLE_2119701) BOUND_VARIABLE_2119702) BOUND_VARIABLE_2119703))))) (let ((_let_2805 (forall ((BOUND_VARIABLE_2119671 tptp.int) (BOUND_VARIABLE_2119672 tptp.int) (BOUND_VARIABLE_2119673 tptp.int) (BOUND_VARIABLE_2119674 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2119671) BOUND_VARIABLE_2119673))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2119672) BOUND_VARIABLE_2119674))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16100 BOUND_VARIABLE_2119671) BOUND_VARIABLE_2119672) BOUND_VARIABLE_2119673) BOUND_VARIABLE_2119674))))))) (let ((_let_2806 (forall ((BOUND_VARIABLE_2119574 tptp.nat) (BOUND_VARIABLE_2235619 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2119576 tptp.nat) (BOUND_VARIABLE_2119577 tptp.nat) (BOUND_VARIABLE_2119578 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2119578))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2119578))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2119576)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16101 BOUND_VARIABLE_2119574) BOUND_VARIABLE_2235619) BOUND_VARIABLE_2119576) BOUND_VARIABLE_2119577) BOUND_VARIABLE_2119578) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2235619 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2119574))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2235619 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2119577))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2807 (forall ((BOUND_VARIABLE_2119477 tptp.nat) (BOUND_VARIABLE_2235696 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2119479 tptp.nat) (BOUND_VARIABLE_2119480 tptp.nat) (BOUND_VARIABLE_2119481 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2119481))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2119481))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2119479)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16102 BOUND_VARIABLE_2119477) BOUND_VARIABLE_2235696) BOUND_VARIABLE_2119479) BOUND_VARIABLE_2119480) BOUND_VARIABLE_2119481) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2235696 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2119477))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2235696 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2119480))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2808 (forall ((BOUND_VARIABLE_2119385 tptp.nat) (BOUND_VARIABLE_2235721 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2119387 tptp.nat) (BOUND_VARIABLE_2119388 tptp.nat) (BOUND_VARIABLE_2119389 tptp.int) (BOUND_VARIABLE_2119390 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15384 BOUND_VARIABLE_2119390) BOUND_VARIABLE_2119389)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15385 BOUND_VARIABLE_2119385) BOUND_VARIABLE_2235721) BOUND_VARIABLE_2119387) BOUND_VARIABLE_2119388))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16103 BOUND_VARIABLE_2119385) BOUND_VARIABLE_2235721) BOUND_VARIABLE_2119387) BOUND_VARIABLE_2119388) BOUND_VARIABLE_2119389) BOUND_VARIABLE_2119390))))) (let ((_let_2809 (forall ((BOUND_VARIABLE_2119357 tptp.int) (BOUND_VARIABLE_2119358 tptp.int) (BOUND_VARIABLE_2119359 tptp.int) (BOUND_VARIABLE_2119360 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2119357) BOUND_VARIABLE_2119359))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2119358) BOUND_VARIABLE_2119360))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16104 BOUND_VARIABLE_2119357) BOUND_VARIABLE_2119358) BOUND_VARIABLE_2119359) BOUND_VARIABLE_2119360))))))) (let ((_let_2810 (forall ((BOUND_VARIABLE_2119260 tptp.nat) (BOUND_VARIABLE_2235822 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2119262 tptp.nat) (BOUND_VARIABLE_2119263 tptp.nat) (BOUND_VARIABLE_2119264 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2119264))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2119264))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2119262)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16105 BOUND_VARIABLE_2119260) BOUND_VARIABLE_2235822) BOUND_VARIABLE_2119262) BOUND_VARIABLE_2119263) BOUND_VARIABLE_2119264) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2235822 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2119260))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2235822 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2119263))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2811 (forall ((BOUND_VARIABLE_2119163 tptp.nat) (BOUND_VARIABLE_2235899 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2119165 tptp.nat) (BOUND_VARIABLE_2119166 tptp.nat) (BOUND_VARIABLE_2119167 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2119167))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2119167))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2119165)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16106 BOUND_VARIABLE_2119163) BOUND_VARIABLE_2235899) BOUND_VARIABLE_2119165) BOUND_VARIABLE_2119166) BOUND_VARIABLE_2119167) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2235899 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2119163))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2235899 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2119166))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2812 (forall ((BOUND_VARIABLE_2119071 tptp.nat) (BOUND_VARIABLE_2235924 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2119073 tptp.nat) (BOUND_VARIABLE_2119074 tptp.nat) (BOUND_VARIABLE_2119075 tptp.int) (BOUND_VARIABLE_2119076 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15386 BOUND_VARIABLE_2119076) BOUND_VARIABLE_2119075)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15387 BOUND_VARIABLE_2119071) BOUND_VARIABLE_2235924) BOUND_VARIABLE_2119073) BOUND_VARIABLE_2119074))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16107 BOUND_VARIABLE_2119071) BOUND_VARIABLE_2235924) BOUND_VARIABLE_2119073) BOUND_VARIABLE_2119074) BOUND_VARIABLE_2119075) BOUND_VARIABLE_2119076))))) (let ((_let_2813 (forall ((BOUND_VARIABLE_2119043 tptp.int) (BOUND_VARIABLE_2119044 tptp.int) (BOUND_VARIABLE_2119045 tptp.int) (BOUND_VARIABLE_2119046 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2119043) BOUND_VARIABLE_2119045))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2119044) BOUND_VARIABLE_2119046))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16108 BOUND_VARIABLE_2119043) BOUND_VARIABLE_2119044) BOUND_VARIABLE_2119045) BOUND_VARIABLE_2119046))))))) (let ((_let_2814 (forall ((BOUND_VARIABLE_2236028 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2236025 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2118951 tptp.nat) (BOUND_VARIABLE_2118952 tptp.nat) (BOUND_VARIABLE_2118953 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2118953))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2118953))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2118951)) (ho_15161 k_15160 BOUND_VARIABLE_2118952))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16109 BOUND_VARIABLE_2236028) BOUND_VARIABLE_2236025) BOUND_VARIABLE_2118951) BOUND_VARIABLE_2118952) BOUND_VARIABLE_2118953) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2236028 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2236025 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2815 (forall ((BOUND_VARIABLE_2236103 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2236100 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2118857 tptp.nat) (BOUND_VARIABLE_2118858 tptp.nat) (BOUND_VARIABLE_2118859 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2118859))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2118859))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2118857)) (ho_15161 k_15160 BOUND_VARIABLE_2118858))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16110 BOUND_VARIABLE_2236103) BOUND_VARIABLE_2236100) BOUND_VARIABLE_2118857) BOUND_VARIABLE_2118858) BOUND_VARIABLE_2118859) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2236103 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2236100 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2816 (forall ((BOUND_VARIABLE_2236124 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2236123 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2118771 tptp.nat) (BOUND_VARIABLE_2118772 tptp.nat) (BOUND_VARIABLE_2118773 tptp.int) (BOUND_VARIABLE_2118774 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15388 BOUND_VARIABLE_2118774) BOUND_VARIABLE_2118773)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15389 BOUND_VARIABLE_2236124) BOUND_VARIABLE_2236123) BOUND_VARIABLE_2118771) BOUND_VARIABLE_2118772))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 k_16111 BOUND_VARIABLE_2236124) BOUND_VARIABLE_2236123) BOUND_VARIABLE_2118771) BOUND_VARIABLE_2118772) BOUND_VARIABLE_2118773) BOUND_VARIABLE_2118774))))) (let ((_let_2817 (forall ((BOUND_VARIABLE_2118741 tptp.int) (BOUND_VARIABLE_2118742 tptp.int) (BOUND_VARIABLE_2118743 tptp.int) (BOUND_VARIABLE_2118744 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2118741) BOUND_VARIABLE_2118743))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2118742) BOUND_VARIABLE_2118744))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16112 BOUND_VARIABLE_2118741) BOUND_VARIABLE_2118742) BOUND_VARIABLE_2118743) BOUND_VARIABLE_2118744))))))) (let ((_let_2818 (forall ((BOUND_VARIABLE_2118644 tptp.nat) (BOUND_VARIABLE_2236225 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2118646 tptp.nat) (BOUND_VARIABLE_2118647 tptp.nat) (BOUND_VARIABLE_2118648 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2118648))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2118648))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2118646)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16113 BOUND_VARIABLE_2118644) BOUND_VARIABLE_2236225) BOUND_VARIABLE_2118646) BOUND_VARIABLE_2118647) BOUND_VARIABLE_2118648) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2236225 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2118644))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2236225 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2118647))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2819 (forall ((BOUND_VARIABLE_2118547 tptp.nat) (BOUND_VARIABLE_2236302 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2118549 tptp.nat) (BOUND_VARIABLE_2118550 tptp.nat) (BOUND_VARIABLE_2118551 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2118551))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2118551))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2118549)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16114 BOUND_VARIABLE_2118547) BOUND_VARIABLE_2236302) BOUND_VARIABLE_2118549) BOUND_VARIABLE_2118550) BOUND_VARIABLE_2118551) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2236302 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2118547))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2236302 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2118550))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2820 (forall ((BOUND_VARIABLE_2118455 tptp.nat) (BOUND_VARIABLE_2236327 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2118457 tptp.nat) (BOUND_VARIABLE_2118458 tptp.nat) (BOUND_VARIABLE_2118459 tptp.int) (BOUND_VARIABLE_2118460 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15390 BOUND_VARIABLE_2118460) BOUND_VARIABLE_2118459)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15391 BOUND_VARIABLE_2118455) BOUND_VARIABLE_2236327) BOUND_VARIABLE_2118457) BOUND_VARIABLE_2118458))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16115 BOUND_VARIABLE_2118455) BOUND_VARIABLE_2236327) BOUND_VARIABLE_2118457) BOUND_VARIABLE_2118458) BOUND_VARIABLE_2118459) BOUND_VARIABLE_2118460))))) (let ((_let_2821 (forall ((BOUND_VARIABLE_2118427 tptp.int) (BOUND_VARIABLE_2118428 tptp.int) (BOUND_VARIABLE_2118429 tptp.int) (BOUND_VARIABLE_2118430 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2118427) BOUND_VARIABLE_2118429))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2118428) BOUND_VARIABLE_2118430))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16116 BOUND_VARIABLE_2118427) BOUND_VARIABLE_2118428) BOUND_VARIABLE_2118429) BOUND_VARIABLE_2118430))))))) (let ((_let_2822 (forall ((BOUND_VARIABLE_2236428 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2118336 tptp.nat) (BOUND_VARIABLE_2118337 tptp.nat) (BOUND_VARIABLE_2118338 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2118338))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2118338))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2236428 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2118336)) (ho_15161 k_15160 BOUND_VARIABLE_2118337)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16117 BOUND_VARIABLE_2236428) BOUND_VARIABLE_2118336) BOUND_VARIABLE_2118337) BOUND_VARIABLE_2118338) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2823 (forall ((BOUND_VARIABLE_2236499 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2118244 tptp.nat) (BOUND_VARIABLE_2118245 tptp.nat) (BOUND_VARIABLE_2118246 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2118246))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2118246))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2236499 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2118244)) (ho_15161 k_15160 BOUND_VARIABLE_2118245)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16118 BOUND_VARIABLE_2236499) BOUND_VARIABLE_2118244) BOUND_VARIABLE_2118245) BOUND_VARIABLE_2118246) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2824 (forall ((BOUND_VARIABLE_2236518 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2118163 tptp.nat) (BOUND_VARIABLE_2118164 tptp.nat) (BOUND_VARIABLE_2118165 tptp.int) (BOUND_VARIABLE_2118166 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15392 BOUND_VARIABLE_2118166) BOUND_VARIABLE_2118165)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15393 BOUND_VARIABLE_2236518) BOUND_VARIABLE_2118163) BOUND_VARIABLE_2118164))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16119 BOUND_VARIABLE_2236518) BOUND_VARIABLE_2118163) BOUND_VARIABLE_2118164) BOUND_VARIABLE_2118165) BOUND_VARIABLE_2118166))))) (let ((_let_2825 (forall ((BOUND_VARIABLE_2118134 tptp.int) (BOUND_VARIABLE_2118135 tptp.int) (BOUND_VARIABLE_2118136 tptp.int) (BOUND_VARIABLE_2118137 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2118134) BOUND_VARIABLE_2118136))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2118135) BOUND_VARIABLE_2118137))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16120 BOUND_VARIABLE_2118134) BOUND_VARIABLE_2118135) BOUND_VARIABLE_2118136) BOUND_VARIABLE_2118137))))))) (let ((_let_2826 (forall ((BOUND_VARIABLE_2118037 tptp.nat) (BOUND_VARIABLE_2236616 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2118039 tptp.nat) (BOUND_VARIABLE_2118040 tptp.nat) (BOUND_VARIABLE_2118041 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2118041))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2118041))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2118039)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16121 BOUND_VARIABLE_2118037) BOUND_VARIABLE_2236616) BOUND_VARIABLE_2118039) BOUND_VARIABLE_2118040) BOUND_VARIABLE_2118041) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2236616 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2118037))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2236616 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2118040))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2827 (forall ((BOUND_VARIABLE_2117940 tptp.nat) (BOUND_VARIABLE_2236693 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2117942 tptp.nat) (BOUND_VARIABLE_2117943 tptp.nat) (BOUND_VARIABLE_2117944 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2117944))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2117944))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2117942)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16122 BOUND_VARIABLE_2117940) BOUND_VARIABLE_2236693) BOUND_VARIABLE_2117942) BOUND_VARIABLE_2117943) BOUND_VARIABLE_2117944) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2236693 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2117940))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2236693 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2117943))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2828 (forall ((BOUND_VARIABLE_2117848 tptp.nat) (BOUND_VARIABLE_2236718 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2117850 tptp.nat) (BOUND_VARIABLE_2117851 tptp.nat) (BOUND_VARIABLE_2117852 tptp.int) (BOUND_VARIABLE_2117853 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15394 BOUND_VARIABLE_2117853) BOUND_VARIABLE_2117852)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15395 BOUND_VARIABLE_2117848) BOUND_VARIABLE_2236718) BOUND_VARIABLE_2117850) BOUND_VARIABLE_2117851))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16123 BOUND_VARIABLE_2117848) BOUND_VARIABLE_2236718) BOUND_VARIABLE_2117850) BOUND_VARIABLE_2117851) BOUND_VARIABLE_2117852) BOUND_VARIABLE_2117853))))) (let ((_let_2829 (forall ((BOUND_VARIABLE_2117820 tptp.int) (BOUND_VARIABLE_2117821 tptp.int) (BOUND_VARIABLE_2117822 tptp.int) (BOUND_VARIABLE_2117823 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2117820) BOUND_VARIABLE_2117822))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2117821) BOUND_VARIABLE_2117823))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16124 BOUND_VARIABLE_2117820) BOUND_VARIABLE_2117821) BOUND_VARIABLE_2117822) BOUND_VARIABLE_2117823))))))) (let ((_let_2830 (forall ((BOUND_VARIABLE_2236819 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2117729 tptp.nat) (BOUND_VARIABLE_2117730 tptp.nat) (BOUND_VARIABLE_2117731 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2117731))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2117731))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2236819 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2117729)) (ho_15161 k_15160 BOUND_VARIABLE_2117730)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16125 BOUND_VARIABLE_2236819) BOUND_VARIABLE_2117729) BOUND_VARIABLE_2117730) BOUND_VARIABLE_2117731) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2831 (forall ((BOUND_VARIABLE_2236890 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2117637 tptp.nat) (BOUND_VARIABLE_2117638 tptp.nat) (BOUND_VARIABLE_2117639 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2117639))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2117639))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2236890 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2117637)) (ho_15161 k_15160 BOUND_VARIABLE_2117638)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16126 BOUND_VARIABLE_2236890) BOUND_VARIABLE_2117637) BOUND_VARIABLE_2117638) BOUND_VARIABLE_2117639) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2832 (forall ((BOUND_VARIABLE_2236909 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2117556 tptp.nat) (BOUND_VARIABLE_2117557 tptp.nat) (BOUND_VARIABLE_2117558 tptp.int) (BOUND_VARIABLE_2117559 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15396 BOUND_VARIABLE_2117559) BOUND_VARIABLE_2117558)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15397 BOUND_VARIABLE_2236909) BOUND_VARIABLE_2117556) BOUND_VARIABLE_2117557))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16127 BOUND_VARIABLE_2236909) BOUND_VARIABLE_2117556) BOUND_VARIABLE_2117557) BOUND_VARIABLE_2117558) BOUND_VARIABLE_2117559))))) (let ((_let_2833 (forall ((BOUND_VARIABLE_2117527 tptp.int) (BOUND_VARIABLE_2117528 tptp.int) (BOUND_VARIABLE_2117529 tptp.int) (BOUND_VARIABLE_2117530 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2117527) BOUND_VARIABLE_2117529))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2117528) BOUND_VARIABLE_2117530))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16128 BOUND_VARIABLE_2117527) BOUND_VARIABLE_2117528) BOUND_VARIABLE_2117529) BOUND_VARIABLE_2117530))))))) (let ((_let_2834 (forall ((BOUND_VARIABLE_2117430 tptp.nat) (BOUND_VARIABLE_2237007 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2117432 tptp.nat) (BOUND_VARIABLE_2117433 tptp.nat) (BOUND_VARIABLE_2117434 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2117434))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2117434))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2117432)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16129 BOUND_VARIABLE_2117430) BOUND_VARIABLE_2237007) BOUND_VARIABLE_2117432) BOUND_VARIABLE_2117433) BOUND_VARIABLE_2117434) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2237007 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2117430))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2237007 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2117433))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2835 (forall ((BOUND_VARIABLE_2117333 tptp.nat) (BOUND_VARIABLE_2237084 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2117335 tptp.nat) (BOUND_VARIABLE_2117336 tptp.nat) (BOUND_VARIABLE_2117337 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2117337))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2117337))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2117335)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16130 BOUND_VARIABLE_2117333) BOUND_VARIABLE_2237084) BOUND_VARIABLE_2117335) BOUND_VARIABLE_2117336) BOUND_VARIABLE_2117337) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2237084 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2117333))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2237084 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2117336))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2836 (forall ((BOUND_VARIABLE_2117241 tptp.nat) (BOUND_VARIABLE_2237109 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2117243 tptp.nat) (BOUND_VARIABLE_2117244 tptp.nat) (BOUND_VARIABLE_2117245 tptp.int) (BOUND_VARIABLE_2117246 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15398 BOUND_VARIABLE_2117246) BOUND_VARIABLE_2117245)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15399 BOUND_VARIABLE_2117241) BOUND_VARIABLE_2237109) BOUND_VARIABLE_2117243) BOUND_VARIABLE_2117244))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16131 BOUND_VARIABLE_2117241) BOUND_VARIABLE_2237109) BOUND_VARIABLE_2117243) BOUND_VARIABLE_2117244) BOUND_VARIABLE_2117245) BOUND_VARIABLE_2117246))))) (let ((_let_2837 (forall ((BOUND_VARIABLE_2117213 tptp.int) (BOUND_VARIABLE_2117214 tptp.int) (BOUND_VARIABLE_2117215 tptp.int) (BOUND_VARIABLE_2117216 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2117213) BOUND_VARIABLE_2117215))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2117214) BOUND_VARIABLE_2117216))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16132 BOUND_VARIABLE_2117213) BOUND_VARIABLE_2117214) BOUND_VARIABLE_2117215) BOUND_VARIABLE_2117216))))))) (let ((_let_2838 (forall ((BOUND_VARIABLE_2237210 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2117122 tptp.nat) (BOUND_VARIABLE_2117123 tptp.nat) (BOUND_VARIABLE_2117124 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2117124))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2117124))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2237210 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2117122)) (ho_15161 k_15160 BOUND_VARIABLE_2117123)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16133 BOUND_VARIABLE_2237210) BOUND_VARIABLE_2117122) BOUND_VARIABLE_2117123) BOUND_VARIABLE_2117124) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2839 (forall ((BOUND_VARIABLE_2237281 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2117030 tptp.nat) (BOUND_VARIABLE_2117031 tptp.nat) (BOUND_VARIABLE_2117032 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2117032))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2117032))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2237281 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2117030)) (ho_15161 k_15160 BOUND_VARIABLE_2117031)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16134 BOUND_VARIABLE_2237281) BOUND_VARIABLE_2117030) BOUND_VARIABLE_2117031) BOUND_VARIABLE_2117032) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2840 (forall ((BOUND_VARIABLE_2237300 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2116949 tptp.nat) (BOUND_VARIABLE_2116950 tptp.nat) (BOUND_VARIABLE_2116951 tptp.int) (BOUND_VARIABLE_2116952 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15400 BOUND_VARIABLE_2116952) BOUND_VARIABLE_2116951)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15401 BOUND_VARIABLE_2237300) BOUND_VARIABLE_2116949) BOUND_VARIABLE_2116950))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16135 BOUND_VARIABLE_2237300) BOUND_VARIABLE_2116949) BOUND_VARIABLE_2116950) BOUND_VARIABLE_2116951) BOUND_VARIABLE_2116952))))) (let ((_let_2841 (forall ((BOUND_VARIABLE_2116920 tptp.int) (BOUND_VARIABLE_2116921 tptp.int) (BOUND_VARIABLE_2116922 tptp.int) (BOUND_VARIABLE_2116923 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2116920) BOUND_VARIABLE_2116922))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2116921) BOUND_VARIABLE_2116923))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16136 BOUND_VARIABLE_2116920) BOUND_VARIABLE_2116921) BOUND_VARIABLE_2116922) BOUND_VARIABLE_2116923))))))) (let ((_let_2842 (forall ((BOUND_VARIABLE_2116823 tptp.nat) (BOUND_VARIABLE_2237398 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2116825 tptp.nat) (BOUND_VARIABLE_2116826 tptp.nat) (BOUND_VARIABLE_2116827 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2116827))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2116827))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2116825)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16137 BOUND_VARIABLE_2116823) BOUND_VARIABLE_2237398) BOUND_VARIABLE_2116825) BOUND_VARIABLE_2116826) BOUND_VARIABLE_2116827) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2237398 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2116823))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2237398 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2116826))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2843 (forall ((BOUND_VARIABLE_2116726 tptp.nat) (BOUND_VARIABLE_2237475 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2116728 tptp.nat) (BOUND_VARIABLE_2116729 tptp.nat) (BOUND_VARIABLE_2116730 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2116730))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2116730))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2116728)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16138 BOUND_VARIABLE_2116726) BOUND_VARIABLE_2237475) BOUND_VARIABLE_2116728) BOUND_VARIABLE_2116729) BOUND_VARIABLE_2116730) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2237475 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2116726))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2237475 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2116729))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2844 (forall ((BOUND_VARIABLE_2116634 tptp.nat) (BOUND_VARIABLE_2237500 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2116636 tptp.nat) (BOUND_VARIABLE_2116637 tptp.nat) (BOUND_VARIABLE_2116638 tptp.int) (BOUND_VARIABLE_2116639 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15402 BOUND_VARIABLE_2116639) BOUND_VARIABLE_2116638)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15403 BOUND_VARIABLE_2116634) BOUND_VARIABLE_2237500) BOUND_VARIABLE_2116636) BOUND_VARIABLE_2116637))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16139 BOUND_VARIABLE_2116634) BOUND_VARIABLE_2237500) BOUND_VARIABLE_2116636) BOUND_VARIABLE_2116637) BOUND_VARIABLE_2116638) BOUND_VARIABLE_2116639))))) (let ((_let_2845 (forall ((BOUND_VARIABLE_2116606 tptp.int) (BOUND_VARIABLE_2116607 tptp.int) (BOUND_VARIABLE_2116608 tptp.int) (BOUND_VARIABLE_2116609 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2116606) BOUND_VARIABLE_2116608))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2116607) BOUND_VARIABLE_2116609))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16140 BOUND_VARIABLE_2116606) BOUND_VARIABLE_2116607) BOUND_VARIABLE_2116608) BOUND_VARIABLE_2116609))))))) (let ((_let_2846 (forall ((BOUND_VARIABLE_2237601 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2116515 tptp.nat) (BOUND_VARIABLE_2116516 tptp.nat) (BOUND_VARIABLE_2116517 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2116517))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2116517))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2237601 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2116515)) (ho_15161 k_15160 BOUND_VARIABLE_2116516)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16141 BOUND_VARIABLE_2237601) BOUND_VARIABLE_2116515) BOUND_VARIABLE_2116516) BOUND_VARIABLE_2116517) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2847 (forall ((BOUND_VARIABLE_2237672 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2116423 tptp.nat) (BOUND_VARIABLE_2116424 tptp.nat) (BOUND_VARIABLE_2116425 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2116425))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2116425))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2237672 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2116423)) (ho_15161 k_15160 BOUND_VARIABLE_2116424)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16142 BOUND_VARIABLE_2237672) BOUND_VARIABLE_2116423) BOUND_VARIABLE_2116424) BOUND_VARIABLE_2116425) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2848 (forall ((BOUND_VARIABLE_2237691 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2116342 tptp.nat) (BOUND_VARIABLE_2116343 tptp.nat) (BOUND_VARIABLE_2116344 tptp.int) (BOUND_VARIABLE_2116345 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15404 BOUND_VARIABLE_2116345) BOUND_VARIABLE_2116344)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15405 BOUND_VARIABLE_2237691) BOUND_VARIABLE_2116342) BOUND_VARIABLE_2116343))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16143 BOUND_VARIABLE_2237691) BOUND_VARIABLE_2116342) BOUND_VARIABLE_2116343) BOUND_VARIABLE_2116344) BOUND_VARIABLE_2116345))))) (let ((_let_2849 (forall ((BOUND_VARIABLE_2116313 tptp.int) (BOUND_VARIABLE_2116314 tptp.int) (BOUND_VARIABLE_2116315 tptp.int) (BOUND_VARIABLE_2116316 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2116313) BOUND_VARIABLE_2116315))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2116314) BOUND_VARIABLE_2116316))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16144 BOUND_VARIABLE_2116313) BOUND_VARIABLE_2116314) BOUND_VARIABLE_2116315) BOUND_VARIABLE_2116316))))))) (let ((_let_2850 (forall ((BOUND_VARIABLE_2116216 tptp.nat) (BOUND_VARIABLE_2237789 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2116218 tptp.nat) (BOUND_VARIABLE_2116219 tptp.nat) (BOUND_VARIABLE_2116220 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2116220))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2116220))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2116218)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16145 BOUND_VARIABLE_2116216) BOUND_VARIABLE_2237789) BOUND_VARIABLE_2116218) BOUND_VARIABLE_2116219) BOUND_VARIABLE_2116220) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2237789 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2116216))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2237789 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2116219))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2851 (forall ((BOUND_VARIABLE_2116119 tptp.nat) (BOUND_VARIABLE_2237866 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2116121 tptp.nat) (BOUND_VARIABLE_2116122 tptp.nat) (BOUND_VARIABLE_2116123 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2116123))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2116123))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2116121)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16146 BOUND_VARIABLE_2116119) BOUND_VARIABLE_2237866) BOUND_VARIABLE_2116121) BOUND_VARIABLE_2116122) BOUND_VARIABLE_2116123) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2237866 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2116119))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2237866 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2116122))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2852 (forall ((BOUND_VARIABLE_2116027 tptp.nat) (BOUND_VARIABLE_2237891 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2116029 tptp.nat) (BOUND_VARIABLE_2116030 tptp.nat) (BOUND_VARIABLE_2116031 tptp.int) (BOUND_VARIABLE_2116032 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15406 BOUND_VARIABLE_2116032) BOUND_VARIABLE_2116031)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15407 BOUND_VARIABLE_2116027) BOUND_VARIABLE_2237891) BOUND_VARIABLE_2116029) BOUND_VARIABLE_2116030))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16147 BOUND_VARIABLE_2116027) BOUND_VARIABLE_2237891) BOUND_VARIABLE_2116029) BOUND_VARIABLE_2116030) BOUND_VARIABLE_2116031) BOUND_VARIABLE_2116032))))) (let ((_let_2853 (forall ((BOUND_VARIABLE_2115999 tptp.int) (BOUND_VARIABLE_2116000 tptp.int) (BOUND_VARIABLE_2116001 tptp.int) (BOUND_VARIABLE_2116002 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2115999) BOUND_VARIABLE_2116001))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2116000) BOUND_VARIABLE_2116002))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16148 BOUND_VARIABLE_2115999) BOUND_VARIABLE_2116000) BOUND_VARIABLE_2116001) BOUND_VARIABLE_2116002))))))) (let ((_let_2854 (forall ((BOUND_VARIABLE_2237992 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2115908 tptp.nat) (BOUND_VARIABLE_2115909 tptp.nat) (BOUND_VARIABLE_2115910 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2115910))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2115910))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2237992 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2115908)) (ho_15161 k_15160 BOUND_VARIABLE_2115909)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16149 BOUND_VARIABLE_2237992) BOUND_VARIABLE_2115908) BOUND_VARIABLE_2115909) BOUND_VARIABLE_2115910) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2855 (forall ((BOUND_VARIABLE_2238063 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2115816 tptp.nat) (BOUND_VARIABLE_2115817 tptp.nat) (BOUND_VARIABLE_2115818 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2115818))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2115818))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2238063 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2115816)) (ho_15161 k_15160 BOUND_VARIABLE_2115817)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16150 BOUND_VARIABLE_2238063) BOUND_VARIABLE_2115816) BOUND_VARIABLE_2115817) BOUND_VARIABLE_2115818) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2856 (forall ((BOUND_VARIABLE_2238082 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2115735 tptp.nat) (BOUND_VARIABLE_2115736 tptp.nat) (BOUND_VARIABLE_2115737 tptp.int) (BOUND_VARIABLE_2115738 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15408 BOUND_VARIABLE_2115738) BOUND_VARIABLE_2115737)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15409 BOUND_VARIABLE_2238082) BOUND_VARIABLE_2115735) BOUND_VARIABLE_2115736))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16151 BOUND_VARIABLE_2238082) BOUND_VARIABLE_2115735) BOUND_VARIABLE_2115736) BOUND_VARIABLE_2115737) BOUND_VARIABLE_2115738))))) (let ((_let_2857 (forall ((BOUND_VARIABLE_2115706 tptp.int) (BOUND_VARIABLE_2115707 tptp.int) (BOUND_VARIABLE_2115708 tptp.int) (BOUND_VARIABLE_2115709 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2115706) BOUND_VARIABLE_2115708))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2115707) BOUND_VARIABLE_2115709))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16152 BOUND_VARIABLE_2115706) BOUND_VARIABLE_2115707) BOUND_VARIABLE_2115708) BOUND_VARIABLE_2115709))))))) (let ((_let_2858 (forall ((BOUND_VARIABLE_2115609 tptp.nat) (BOUND_VARIABLE_2238180 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2115611 tptp.nat) (BOUND_VARIABLE_2115612 tptp.nat) (BOUND_VARIABLE_2115613 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2115613))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2115613))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2115611)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16153 BOUND_VARIABLE_2115609) BOUND_VARIABLE_2238180) BOUND_VARIABLE_2115611) BOUND_VARIABLE_2115612) BOUND_VARIABLE_2115613) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2238180 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2115609))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2238180 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2115612))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2859 (forall ((BOUND_VARIABLE_2115512 tptp.nat) (BOUND_VARIABLE_2238257 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2115514 tptp.nat) (BOUND_VARIABLE_2115515 tptp.nat) (BOUND_VARIABLE_2115516 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2115516))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2115516))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2115514)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16154 BOUND_VARIABLE_2115512) BOUND_VARIABLE_2238257) BOUND_VARIABLE_2115514) BOUND_VARIABLE_2115515) BOUND_VARIABLE_2115516) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2238257 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2115512))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2238257 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2115515))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2860 (forall ((BOUND_VARIABLE_2115420 tptp.nat) (BOUND_VARIABLE_2238282 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2115422 tptp.nat) (BOUND_VARIABLE_2115423 tptp.nat) (BOUND_VARIABLE_2115424 tptp.int) (BOUND_VARIABLE_2115425 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15410 BOUND_VARIABLE_2115425) BOUND_VARIABLE_2115424)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15411 BOUND_VARIABLE_2115420) BOUND_VARIABLE_2238282) BOUND_VARIABLE_2115422) BOUND_VARIABLE_2115423))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16155 BOUND_VARIABLE_2115420) BOUND_VARIABLE_2238282) BOUND_VARIABLE_2115422) BOUND_VARIABLE_2115423) BOUND_VARIABLE_2115424) BOUND_VARIABLE_2115425))))) (let ((_let_2861 (forall ((BOUND_VARIABLE_2115392 tptp.int) (BOUND_VARIABLE_2115393 tptp.int) (BOUND_VARIABLE_2115394 tptp.int) (BOUND_VARIABLE_2115395 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2115392) BOUND_VARIABLE_2115394))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2115393) BOUND_VARIABLE_2115395))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16156 BOUND_VARIABLE_2115392) BOUND_VARIABLE_2115393) BOUND_VARIABLE_2115394) BOUND_VARIABLE_2115395))))))) (let ((_let_2862 (forall ((BOUND_VARIABLE_2238383 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2115301 tptp.nat) (BOUND_VARIABLE_2115302 tptp.nat) (BOUND_VARIABLE_2115303 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2115303))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2115303))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2238383 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2115301)) (ho_15161 k_15160 BOUND_VARIABLE_2115302)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16157 BOUND_VARIABLE_2238383) BOUND_VARIABLE_2115301) BOUND_VARIABLE_2115302) BOUND_VARIABLE_2115303) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2863 (forall ((BOUND_VARIABLE_2238454 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2115209 tptp.nat) (BOUND_VARIABLE_2115210 tptp.nat) (BOUND_VARIABLE_2115211 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2115211))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2115211))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2238454 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2115209)) (ho_15161 k_15160 BOUND_VARIABLE_2115210)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16158 BOUND_VARIABLE_2238454) BOUND_VARIABLE_2115209) BOUND_VARIABLE_2115210) BOUND_VARIABLE_2115211) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2864 (forall ((BOUND_VARIABLE_2238473 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2115128 tptp.nat) (BOUND_VARIABLE_2115129 tptp.nat) (BOUND_VARIABLE_2115130 tptp.int) (BOUND_VARIABLE_2115131 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15412 BOUND_VARIABLE_2115131) BOUND_VARIABLE_2115130)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15413 BOUND_VARIABLE_2238473) BOUND_VARIABLE_2115128) BOUND_VARIABLE_2115129))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16159 BOUND_VARIABLE_2238473) BOUND_VARIABLE_2115128) BOUND_VARIABLE_2115129) BOUND_VARIABLE_2115130) BOUND_VARIABLE_2115131))))) (let ((_let_2865 (forall ((BOUND_VARIABLE_2115099 tptp.int) (BOUND_VARIABLE_2115100 tptp.int) (BOUND_VARIABLE_2115101 tptp.int) (BOUND_VARIABLE_2115102 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2115099) BOUND_VARIABLE_2115101))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2115100) BOUND_VARIABLE_2115102))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16160 BOUND_VARIABLE_2115099) BOUND_VARIABLE_2115100) BOUND_VARIABLE_2115101) BOUND_VARIABLE_2115102))))))) (let ((_let_2866 (forall ((BOUND_VARIABLE_2115055 tptp.int) (BOUND_VARIABLE_2115056 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15414 BOUND_VARIABLE_2115056) BOUND_VARIABLE_2115055)) (ho_15260 k_15259 k_16161)) (ho_15108 (ho_15107 k_16162 BOUND_VARIABLE_2115055) BOUND_VARIABLE_2115056))))) (let ((_let_2867 (forall ((BOUND_VARIABLE_2115027 tptp.int) (BOUND_VARIABLE_2115028 tptp.int) (BOUND_VARIABLE_2115029 tptp.int) (BOUND_VARIABLE_2115030 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2115027) BOUND_VARIABLE_2115029))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2115028) BOUND_VARIABLE_2115030))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16163 BOUND_VARIABLE_2115027) BOUND_VARIABLE_2115028) BOUND_VARIABLE_2115029) BOUND_VARIABLE_2115030))))))) (let ((_let_2868 (forall ((BOUND_VARIABLE_2114983 tptp.int) (BOUND_VARIABLE_2114984 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15415 BOUND_VARIABLE_2114984) BOUND_VARIABLE_2114983)) (ho_15260 k_15259 k_16164)) (ho_15108 (ho_15107 k_16165 BOUND_VARIABLE_2114983) BOUND_VARIABLE_2114984))))) (let ((_let_2869 (forall ((BOUND_VARIABLE_2114955 tptp.int) (BOUND_VARIABLE_2114956 tptp.int) (BOUND_VARIABLE_2114957 tptp.int) (BOUND_VARIABLE_2114958 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2114955) BOUND_VARIABLE_2114957))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2114956) BOUND_VARIABLE_2114958))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16166 BOUND_VARIABLE_2114955) BOUND_VARIABLE_2114956) BOUND_VARIABLE_2114957) BOUND_VARIABLE_2114958))))))) (let ((_let_2870 (forall ((BOUND_VARIABLE_2114911 tptp.int) (BOUND_VARIABLE_2114912 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15416 BOUND_VARIABLE_2114912) BOUND_VARIABLE_2114911)) (ho_15260 k_15259 k_16167)) (ho_15108 (ho_15107 k_16168 BOUND_VARIABLE_2114911) BOUND_VARIABLE_2114912))))) (let ((_let_2871 (forall ((BOUND_VARIABLE_2114883 tptp.int) (BOUND_VARIABLE_2114884 tptp.int) (BOUND_VARIABLE_2114885 tptp.int) (BOUND_VARIABLE_2114886 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2114883) BOUND_VARIABLE_2114885))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2114884) BOUND_VARIABLE_2114886))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16169 BOUND_VARIABLE_2114883) BOUND_VARIABLE_2114884) BOUND_VARIABLE_2114885) BOUND_VARIABLE_2114886))))))) (let ((_let_2872 (forall ((BOUND_VARIABLE_2114839 tptp.int) (BOUND_VARIABLE_2114840 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15417 BOUND_VARIABLE_2114840) BOUND_VARIABLE_2114839)) (ho_15260 k_15259 k_16170)) (ho_15108 (ho_15107 k_16171 BOUND_VARIABLE_2114839) BOUND_VARIABLE_2114840))))) (let ((_let_2873 (forall ((BOUND_VARIABLE_2114811 tptp.int) (BOUND_VARIABLE_2114812 tptp.int) (BOUND_VARIABLE_2114813 tptp.int) (BOUND_VARIABLE_2114814 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2114811) BOUND_VARIABLE_2114813))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2114812) BOUND_VARIABLE_2114814))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16172 BOUND_VARIABLE_2114811) BOUND_VARIABLE_2114812) BOUND_VARIABLE_2114813) BOUND_VARIABLE_2114814))))))) (let ((_let_2874 (forall ((BOUND_VARIABLE_2114714 tptp.nat) (BOUND_VARIABLE_2238715 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2114716 tptp.nat) (BOUND_VARIABLE_2114717 tptp.nat) (BOUND_VARIABLE_2114718 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2114718))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2114718))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2114716)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16173 BOUND_VARIABLE_2114714) BOUND_VARIABLE_2238715) BOUND_VARIABLE_2114716) BOUND_VARIABLE_2114717) BOUND_VARIABLE_2114718) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2238715 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2114714))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2238715 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2114717))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2875 (forall ((BOUND_VARIABLE_2114617 tptp.nat) (BOUND_VARIABLE_2238792 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2114619 tptp.nat) (BOUND_VARIABLE_2114620 tptp.nat) (BOUND_VARIABLE_2114621 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2114621))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2114621))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2114619)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16174 BOUND_VARIABLE_2114617) BOUND_VARIABLE_2238792) BOUND_VARIABLE_2114619) BOUND_VARIABLE_2114620) BOUND_VARIABLE_2114621) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2238792 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2114617))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2238792 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2114620))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2876 (forall ((BOUND_VARIABLE_2114525 tptp.nat) (BOUND_VARIABLE_2238817 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2114527 tptp.nat) (BOUND_VARIABLE_2114528 tptp.nat) (BOUND_VARIABLE_2114529 tptp.int) (BOUND_VARIABLE_2114530 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15418 BOUND_VARIABLE_2114530) BOUND_VARIABLE_2114529)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15419 BOUND_VARIABLE_2114525) BOUND_VARIABLE_2238817) BOUND_VARIABLE_2114527) BOUND_VARIABLE_2114528))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16175 BOUND_VARIABLE_2114525) BOUND_VARIABLE_2238817) BOUND_VARIABLE_2114527) BOUND_VARIABLE_2114528) BOUND_VARIABLE_2114529) BOUND_VARIABLE_2114530))))) (let ((_let_2877 (forall ((BOUND_VARIABLE_2114497 tptp.int) (BOUND_VARIABLE_2114498 tptp.int) (BOUND_VARIABLE_2114499 tptp.int) (BOUND_VARIABLE_2114500 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2114497) BOUND_VARIABLE_2114499))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2114498) BOUND_VARIABLE_2114500))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16176 BOUND_VARIABLE_2114497) BOUND_VARIABLE_2114498) BOUND_VARIABLE_2114499) BOUND_VARIABLE_2114500))))))) (let ((_let_2878 (forall ((BOUND_VARIABLE_2238918 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2114406 tptp.nat) (BOUND_VARIABLE_2114407 tptp.nat) (BOUND_VARIABLE_2114408 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2114408))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2114408))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2238918 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2114406)) (ho_15161 k_15160 BOUND_VARIABLE_2114407)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16177 BOUND_VARIABLE_2238918) BOUND_VARIABLE_2114406) BOUND_VARIABLE_2114407) BOUND_VARIABLE_2114408) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2879 (forall ((BOUND_VARIABLE_2238989 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2114314 tptp.nat) (BOUND_VARIABLE_2114315 tptp.nat) (BOUND_VARIABLE_2114316 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2114316))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2114316))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2238989 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2114314)) (ho_15161 k_15160 BOUND_VARIABLE_2114315)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16178 BOUND_VARIABLE_2238989) BOUND_VARIABLE_2114314) BOUND_VARIABLE_2114315) BOUND_VARIABLE_2114316) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2880 (forall ((BOUND_VARIABLE_2239008 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2114233 tptp.nat) (BOUND_VARIABLE_2114234 tptp.nat) (BOUND_VARIABLE_2114235 tptp.int) (BOUND_VARIABLE_2114236 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15420 BOUND_VARIABLE_2114236) BOUND_VARIABLE_2114235)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15421 BOUND_VARIABLE_2239008) BOUND_VARIABLE_2114233) BOUND_VARIABLE_2114234))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16179 BOUND_VARIABLE_2239008) BOUND_VARIABLE_2114233) BOUND_VARIABLE_2114234) BOUND_VARIABLE_2114235) BOUND_VARIABLE_2114236))))) (let ((_let_2881 (forall ((BOUND_VARIABLE_2114204 tptp.int) (BOUND_VARIABLE_2114205 tptp.int) (BOUND_VARIABLE_2114206 tptp.int) (BOUND_VARIABLE_2114207 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2114204) BOUND_VARIABLE_2114206))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2114205) BOUND_VARIABLE_2114207))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16180 BOUND_VARIABLE_2114204) BOUND_VARIABLE_2114205) BOUND_VARIABLE_2114206) BOUND_VARIABLE_2114207))))))) (let ((_let_2882 (forall ((BOUND_VARIABLE_2114107 tptp.nat) (BOUND_VARIABLE_2239106 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2114109 tptp.nat) (BOUND_VARIABLE_2114110 tptp.nat) (BOUND_VARIABLE_2114111 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2114111))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2114111))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2114109)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16181 BOUND_VARIABLE_2114107) BOUND_VARIABLE_2239106) BOUND_VARIABLE_2114109) BOUND_VARIABLE_2114110) BOUND_VARIABLE_2114111) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2239106 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2114107))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2239106 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2114110))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2883 (forall ((BOUND_VARIABLE_2114010 tptp.nat) (BOUND_VARIABLE_2239183 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2114012 tptp.nat) (BOUND_VARIABLE_2114013 tptp.nat) (BOUND_VARIABLE_2114014 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2114014))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2114014))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2114012)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16182 BOUND_VARIABLE_2114010) BOUND_VARIABLE_2239183) BOUND_VARIABLE_2114012) BOUND_VARIABLE_2114013) BOUND_VARIABLE_2114014) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2239183 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2114010))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2239183 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2114013))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2884 (forall ((BOUND_VARIABLE_2113918 tptp.nat) (BOUND_VARIABLE_2239208 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2113920 tptp.nat) (BOUND_VARIABLE_2113921 tptp.nat) (BOUND_VARIABLE_2113922 tptp.int) (BOUND_VARIABLE_2113923 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15422 BOUND_VARIABLE_2113923) BOUND_VARIABLE_2113922)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15423 BOUND_VARIABLE_2113918) BOUND_VARIABLE_2239208) BOUND_VARIABLE_2113920) BOUND_VARIABLE_2113921))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16183 BOUND_VARIABLE_2113918) BOUND_VARIABLE_2239208) BOUND_VARIABLE_2113920) BOUND_VARIABLE_2113921) BOUND_VARIABLE_2113922) BOUND_VARIABLE_2113923))))) (let ((_let_2885 (forall ((BOUND_VARIABLE_2113890 tptp.int) (BOUND_VARIABLE_2113891 tptp.int) (BOUND_VARIABLE_2113892 tptp.int) (BOUND_VARIABLE_2113893 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2113890) BOUND_VARIABLE_2113892))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2113891) BOUND_VARIABLE_2113893))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16184 BOUND_VARIABLE_2113890) BOUND_VARIABLE_2113891) BOUND_VARIABLE_2113892) BOUND_VARIABLE_2113893))))))) (let ((_let_2886 (forall ((BOUND_VARIABLE_2239309 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2113799 tptp.nat) (BOUND_VARIABLE_2113800 tptp.nat) (BOUND_VARIABLE_2113801 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2113801))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2113801))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2239309 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2113799)) (ho_15161 k_15160 BOUND_VARIABLE_2113800)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16185 BOUND_VARIABLE_2239309) BOUND_VARIABLE_2113799) BOUND_VARIABLE_2113800) BOUND_VARIABLE_2113801) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2887 (forall ((BOUND_VARIABLE_2239380 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2113707 tptp.nat) (BOUND_VARIABLE_2113708 tptp.nat) (BOUND_VARIABLE_2113709 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2113709))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2113709))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2239380 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2113707)) (ho_15161 k_15160 BOUND_VARIABLE_2113708)))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16186 BOUND_VARIABLE_2239380) BOUND_VARIABLE_2113707) BOUND_VARIABLE_2113708) BOUND_VARIABLE_2113709) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2888 (forall ((BOUND_VARIABLE_2239399 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2113626 tptp.nat) (BOUND_VARIABLE_2113627 tptp.nat) (BOUND_VARIABLE_2113628 tptp.int) (BOUND_VARIABLE_2113629 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15424 BOUND_VARIABLE_2113629) BOUND_VARIABLE_2113628)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15425 BOUND_VARIABLE_2239399) BOUND_VARIABLE_2113626) BOUND_VARIABLE_2113627))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16187 BOUND_VARIABLE_2239399) BOUND_VARIABLE_2113626) BOUND_VARIABLE_2113627) BOUND_VARIABLE_2113628) BOUND_VARIABLE_2113629))))) (let ((_let_2889 (forall ((BOUND_VARIABLE_2113597 tptp.int) (BOUND_VARIABLE_2113598 tptp.int) (BOUND_VARIABLE_2113599 tptp.int) (BOUND_VARIABLE_2113600 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2113597) BOUND_VARIABLE_2113599))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2113598) BOUND_VARIABLE_2113600))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16188 BOUND_VARIABLE_2113597) BOUND_VARIABLE_2113598) BOUND_VARIABLE_2113599) BOUND_VARIABLE_2113600))))))) (let ((_let_2890 (forall ((BOUND_VARIABLE_2239497 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2113511 tptp.nat) (BOUND_VARIABLE_2113512 tptp.nat) (BOUND_VARIABLE_2113513 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2113513))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2113513))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16189 BOUND_VARIABLE_2239497) BOUND_VARIABLE_2113511) BOUND_VARIABLE_2113512) BOUND_VARIABLE_2113513) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2239497 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2113511)) (ho_15161 k_15160 BOUND_VARIABLE_2113512))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2891 (forall ((BOUND_VARIABLE_2239565 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2113424 tptp.nat) (BOUND_VARIABLE_2113425 tptp.nat) (BOUND_VARIABLE_2113426 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2113426))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2113426))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16190 BOUND_VARIABLE_2239565) BOUND_VARIABLE_2113424) BOUND_VARIABLE_2113425) BOUND_VARIABLE_2113426) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2239565 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2113424)) (ho_15161 k_15160 BOUND_VARIABLE_2113425))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2892 (forall ((BOUND_VARIABLE_2239581 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2113349 tptp.nat) (BOUND_VARIABLE_2113350 tptp.nat) (BOUND_VARIABLE_2113351 tptp.int) (BOUND_VARIABLE_2113352 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15426 BOUND_VARIABLE_2113352) BOUND_VARIABLE_2113351)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15427 BOUND_VARIABLE_2239581) BOUND_VARIABLE_2113349) BOUND_VARIABLE_2113350))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16191 BOUND_VARIABLE_2239581) BOUND_VARIABLE_2113349) BOUND_VARIABLE_2113350) BOUND_VARIABLE_2113351) BOUND_VARIABLE_2113352))))) (let ((_let_2893 (forall ((BOUND_VARIABLE_2113320 tptp.int) (BOUND_VARIABLE_2113321 tptp.int) (BOUND_VARIABLE_2113322 tptp.int) (BOUND_VARIABLE_2113323 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2113320) BOUND_VARIABLE_2113322))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2113321) BOUND_VARIABLE_2113323))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16192 BOUND_VARIABLE_2113320) BOUND_VARIABLE_2113321) BOUND_VARIABLE_2113322) BOUND_VARIABLE_2113323))))))) (let ((_let_2894 (forall ((BOUND_VARIABLE_2113232 tptp.real) (BOUND_VARIABLE_2113233 tptp.nat) (BOUND_VARIABLE_2113234 tptp.nat) (BOUND_VARIABLE_2113235 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2113235))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2113235))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_16194 k_16193 BOUND_VARIABLE_2113232) BOUND_VARIABLE_2113233) BOUND_VARIABLE_2113234) BOUND_VARIABLE_2113235) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 (ho_15087 k_15086 BOUND_VARIABLE_2113232) (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2113233)) (ho_15161 k_15160 BOUND_VARIABLE_2113234))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2895 (forall ((BOUND_VARIABLE_2113204 tptp.int) (BOUND_VARIABLE_2113205 tptp.int) (BOUND_VARIABLE_2113206 tptp.int) (BOUND_VARIABLE_2113207 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2113204) BOUND_VARIABLE_2113206))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2113205) BOUND_VARIABLE_2113207))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16195 BOUND_VARIABLE_2113204) BOUND_VARIABLE_2113205) BOUND_VARIABLE_2113206) BOUND_VARIABLE_2113207))))))) (let ((_let_2896 (forall ((BOUND_VARIABLE_2113125 tptp.rat) (BOUND_VARIABLE_2113126 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2113126))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2113126))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2113125 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16196 BOUND_VARIABLE_2113125) BOUND_VARIABLE_2113126)))))))))))))) (let ((_let_2897 (forall ((BOUND_VARIABLE_2113097 tptp.int) (BOUND_VARIABLE_2113098 tptp.int) (BOUND_VARIABLE_2113099 tptp.int) (BOUND_VARIABLE_2113100 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2113097) BOUND_VARIABLE_2113099))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2113098) BOUND_VARIABLE_2113100))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16197 BOUND_VARIABLE_2113097) BOUND_VARIABLE_2113098) BOUND_VARIABLE_2113099) BOUND_VARIABLE_2113100))))))) (let ((_let_2898 (forall ((BOUND_VARIABLE_2113000 tptp.nat) (BOUND_VARIABLE_2239851 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2113002 tptp.nat) (BOUND_VARIABLE_2113003 tptp.nat) (BOUND_VARIABLE_2113004 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2113004))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2113004))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2113002)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16198 BOUND_VARIABLE_2113000) BOUND_VARIABLE_2239851) BOUND_VARIABLE_2113002) BOUND_VARIABLE_2113003) BOUND_VARIABLE_2113004) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2239851 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2113000))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2239851 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2113003))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2899 (forall ((BOUND_VARIABLE_2112903 tptp.nat) (BOUND_VARIABLE_2239928 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2112905 tptp.nat) (BOUND_VARIABLE_2112906 tptp.nat) (BOUND_VARIABLE_2112907 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2112907))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2112907))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2112905)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16199 BOUND_VARIABLE_2112903) BOUND_VARIABLE_2239928) BOUND_VARIABLE_2112905) BOUND_VARIABLE_2112906) BOUND_VARIABLE_2112907) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2239928 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112903))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2239928 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112906))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2900 (forall ((BOUND_VARIABLE_2112811 tptp.nat) (BOUND_VARIABLE_2239953 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2112813 tptp.nat) (BOUND_VARIABLE_2112814 tptp.nat) (BOUND_VARIABLE_2112815 tptp.int) (BOUND_VARIABLE_2112816 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15428 BOUND_VARIABLE_2112816) BOUND_VARIABLE_2112815)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15429 BOUND_VARIABLE_2112811) BOUND_VARIABLE_2239953) BOUND_VARIABLE_2112813) BOUND_VARIABLE_2112814))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16200 BOUND_VARIABLE_2112811) BOUND_VARIABLE_2239953) BOUND_VARIABLE_2112813) BOUND_VARIABLE_2112814) BOUND_VARIABLE_2112815) BOUND_VARIABLE_2112816))))) (let ((_let_2901 (forall ((BOUND_VARIABLE_2112783 tptp.int) (BOUND_VARIABLE_2112784 tptp.int) (BOUND_VARIABLE_2112785 tptp.int) (BOUND_VARIABLE_2112786 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2112783) BOUND_VARIABLE_2112785))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2112784) BOUND_VARIABLE_2112786))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16201 BOUND_VARIABLE_2112783) BOUND_VARIABLE_2112784) BOUND_VARIABLE_2112785) BOUND_VARIABLE_2112786))))))) (let ((_let_2902 (forall ((BOUND_VARIABLE_2112686 tptp.nat) (BOUND_VARIABLE_2240054 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2112688 tptp.nat) (BOUND_VARIABLE_2112689 tptp.nat) (BOUND_VARIABLE_2112690 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2112690))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2112690))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2112688)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16202 BOUND_VARIABLE_2112686) BOUND_VARIABLE_2240054) BOUND_VARIABLE_2112688) BOUND_VARIABLE_2112689) BOUND_VARIABLE_2112690) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2240054 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112686))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2240054 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112689))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2903 (forall ((BOUND_VARIABLE_2112589 tptp.nat) (BOUND_VARIABLE_2240131 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2112591 tptp.nat) (BOUND_VARIABLE_2112592 tptp.nat) (BOUND_VARIABLE_2112593 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2112593))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2112593))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2112591)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16203 BOUND_VARIABLE_2112589) BOUND_VARIABLE_2240131) BOUND_VARIABLE_2112591) BOUND_VARIABLE_2112592) BOUND_VARIABLE_2112593) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2240131 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112589))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2240131 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112592))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2904 (forall ((BOUND_VARIABLE_2112497 tptp.nat) (BOUND_VARIABLE_2240156 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2112499 tptp.nat) (BOUND_VARIABLE_2112500 tptp.nat) (BOUND_VARIABLE_2112501 tptp.int) (BOUND_VARIABLE_2112502 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15430 BOUND_VARIABLE_2112502) BOUND_VARIABLE_2112501)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15431 BOUND_VARIABLE_2112497) BOUND_VARIABLE_2240156) BOUND_VARIABLE_2112499) BOUND_VARIABLE_2112500))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16204 BOUND_VARIABLE_2112497) BOUND_VARIABLE_2240156) BOUND_VARIABLE_2112499) BOUND_VARIABLE_2112500) BOUND_VARIABLE_2112501) BOUND_VARIABLE_2112502))))) (let ((_let_2905 (forall ((BOUND_VARIABLE_2112469 tptp.int) (BOUND_VARIABLE_2112470 tptp.int) (BOUND_VARIABLE_2112471 tptp.int) (BOUND_VARIABLE_2112472 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2112469) BOUND_VARIABLE_2112471))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2112470) BOUND_VARIABLE_2112472))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16205 BOUND_VARIABLE_2112469) BOUND_VARIABLE_2112470) BOUND_VARIABLE_2112471) BOUND_VARIABLE_2112472))))))) (let ((_let_2906 (forall ((BOUND_VARIABLE_2112372 tptp.nat) (BOUND_VARIABLE_2240257 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2112374 tptp.nat) (BOUND_VARIABLE_2112375 tptp.nat) (BOUND_VARIABLE_2112376 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2112376))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2112376))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2112374)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16206 BOUND_VARIABLE_2112372) BOUND_VARIABLE_2240257) BOUND_VARIABLE_2112374) BOUND_VARIABLE_2112375) BOUND_VARIABLE_2112376) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2240257 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112372))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2240257 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112375))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2907 (forall ((BOUND_VARIABLE_2112275 tptp.nat) (BOUND_VARIABLE_2240334 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2112277 tptp.nat) (BOUND_VARIABLE_2112278 tptp.nat) (BOUND_VARIABLE_2112279 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2112279))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2112279))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2112277)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16207 BOUND_VARIABLE_2112275) BOUND_VARIABLE_2240334) BOUND_VARIABLE_2112277) BOUND_VARIABLE_2112278) BOUND_VARIABLE_2112279) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2240334 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112275))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2240334 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112278))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2908 (forall ((BOUND_VARIABLE_2112183 tptp.nat) (BOUND_VARIABLE_2240359 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2112185 tptp.nat) (BOUND_VARIABLE_2112186 tptp.nat) (BOUND_VARIABLE_2112187 tptp.int) (BOUND_VARIABLE_2112188 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15432 BOUND_VARIABLE_2112188) BOUND_VARIABLE_2112187)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15433 BOUND_VARIABLE_2112183) BOUND_VARIABLE_2240359) BOUND_VARIABLE_2112185) BOUND_VARIABLE_2112186))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16208 BOUND_VARIABLE_2112183) BOUND_VARIABLE_2240359) BOUND_VARIABLE_2112185) BOUND_VARIABLE_2112186) BOUND_VARIABLE_2112187) BOUND_VARIABLE_2112188))))) (let ((_let_2909 (forall ((BOUND_VARIABLE_2112155 tptp.int) (BOUND_VARIABLE_2112156 tptp.int) (BOUND_VARIABLE_2112157 tptp.int) (BOUND_VARIABLE_2112158 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2112155) BOUND_VARIABLE_2112157))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2112156) BOUND_VARIABLE_2112158))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16209 BOUND_VARIABLE_2112155) BOUND_VARIABLE_2112156) BOUND_VARIABLE_2112157) BOUND_VARIABLE_2112158))))))) (let ((_let_2910 (forall ((BOUND_VARIABLE_2112058 tptp.nat) (BOUND_VARIABLE_2240460 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2112060 tptp.nat) (BOUND_VARIABLE_2112061 tptp.nat) (BOUND_VARIABLE_2112062 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2112062))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2112062))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2112060)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16210 BOUND_VARIABLE_2112058) BOUND_VARIABLE_2240460) BOUND_VARIABLE_2112060) BOUND_VARIABLE_2112061) BOUND_VARIABLE_2112062) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2240460 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112058))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2240460 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2112061))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2911 (forall ((BOUND_VARIABLE_2111961 tptp.nat) (BOUND_VARIABLE_2240537 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2111963 tptp.nat) (BOUND_VARIABLE_2111964 tptp.nat) (BOUND_VARIABLE_2111965 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2111965))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2111965))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2111963)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16211 BOUND_VARIABLE_2111961) BOUND_VARIABLE_2240537) BOUND_VARIABLE_2111963) BOUND_VARIABLE_2111964) BOUND_VARIABLE_2111965) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2240537 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2111961))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2240537 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2111964))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2912 (forall ((BOUND_VARIABLE_2111869 tptp.nat) (BOUND_VARIABLE_2240562 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2111871 tptp.nat) (BOUND_VARIABLE_2111872 tptp.nat) (BOUND_VARIABLE_2111873 tptp.int) (BOUND_VARIABLE_2111874 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15434 BOUND_VARIABLE_2111874) BOUND_VARIABLE_2111873)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15435 BOUND_VARIABLE_2111869) BOUND_VARIABLE_2240562) BOUND_VARIABLE_2111871) BOUND_VARIABLE_2111872))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16212 BOUND_VARIABLE_2111869) BOUND_VARIABLE_2240562) BOUND_VARIABLE_2111871) BOUND_VARIABLE_2111872) BOUND_VARIABLE_2111873) BOUND_VARIABLE_2111874))))) (let ((_let_2913 (forall ((BOUND_VARIABLE_2111841 tptp.int) (BOUND_VARIABLE_2111842 tptp.int) (BOUND_VARIABLE_2111843 tptp.int) (BOUND_VARIABLE_2111844 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2111841) BOUND_VARIABLE_2111843))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2111842) BOUND_VARIABLE_2111844))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16213 BOUND_VARIABLE_2111841) BOUND_VARIABLE_2111842) BOUND_VARIABLE_2111843) BOUND_VARIABLE_2111844))))))) (let ((_let_2914 (forall ((BOUND_VARIABLE_2240666 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2240663 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2111749 tptp.nat) (BOUND_VARIABLE_2111750 tptp.nat) (BOUND_VARIABLE_2111751 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2111751))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2111751))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2111749)) (ho_15161 k_15160 BOUND_VARIABLE_2111750))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16214 BOUND_VARIABLE_2240666) BOUND_VARIABLE_2240663) BOUND_VARIABLE_2111749) BOUND_VARIABLE_2111750) BOUND_VARIABLE_2111751) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2240666 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2240663 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2915 (forall ((BOUND_VARIABLE_2240741 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2240738 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2111655 tptp.nat) (BOUND_VARIABLE_2111656 tptp.nat) (BOUND_VARIABLE_2111657 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2111657))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2111657))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2111655)) (ho_15161 k_15160 BOUND_VARIABLE_2111656))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16215 BOUND_VARIABLE_2240741) BOUND_VARIABLE_2240738) BOUND_VARIABLE_2111655) BOUND_VARIABLE_2111656) BOUND_VARIABLE_2111657) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2240741 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2240738 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2916 (forall ((BOUND_VARIABLE_2240762 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2240761 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2111569 tptp.nat) (BOUND_VARIABLE_2111570 tptp.nat) (BOUND_VARIABLE_2111571 tptp.int) (BOUND_VARIABLE_2111572 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15436 BOUND_VARIABLE_2111572) BOUND_VARIABLE_2111571)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15437 BOUND_VARIABLE_2240762) BOUND_VARIABLE_2240761) BOUND_VARIABLE_2111569) BOUND_VARIABLE_2111570))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 k_16216 BOUND_VARIABLE_2240762) BOUND_VARIABLE_2240761) BOUND_VARIABLE_2111569) BOUND_VARIABLE_2111570) BOUND_VARIABLE_2111571) BOUND_VARIABLE_2111572))))) (let ((_let_2917 (forall ((BOUND_VARIABLE_2111539 tptp.int) (BOUND_VARIABLE_2111540 tptp.int) (BOUND_VARIABLE_2111541 tptp.int) (BOUND_VARIABLE_2111542 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2111539) BOUND_VARIABLE_2111541))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2111540) BOUND_VARIABLE_2111542))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16217 BOUND_VARIABLE_2111539) BOUND_VARIABLE_2111540) BOUND_VARIABLE_2111541) BOUND_VARIABLE_2111542))))))) (let ((_let_2918 (forall ((BOUND_VARIABLE_2111442 tptp.nat) (BOUND_VARIABLE_2240863 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2111444 tptp.nat) (BOUND_VARIABLE_2111445 tptp.nat) (BOUND_VARIABLE_2111446 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2111446))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2111446))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2111444)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16218 BOUND_VARIABLE_2111442) BOUND_VARIABLE_2240863) BOUND_VARIABLE_2111444) BOUND_VARIABLE_2111445) BOUND_VARIABLE_2111446) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2240863 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2111442))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2240863 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2111445))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2919 (forall ((BOUND_VARIABLE_2111345 tptp.nat) (BOUND_VARIABLE_2240940 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2111347 tptp.nat) (BOUND_VARIABLE_2111348 tptp.nat) (BOUND_VARIABLE_2111349 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2111349))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2111349))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2111347)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16219 BOUND_VARIABLE_2111345) BOUND_VARIABLE_2240940) BOUND_VARIABLE_2111347) BOUND_VARIABLE_2111348) BOUND_VARIABLE_2111349) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2240940 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2111345))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2240940 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2111348))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2920 (forall ((BOUND_VARIABLE_2111253 tptp.nat) (BOUND_VARIABLE_2240965 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2111255 tptp.nat) (BOUND_VARIABLE_2111256 tptp.nat) (BOUND_VARIABLE_2111257 tptp.int) (BOUND_VARIABLE_2111258 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15438 BOUND_VARIABLE_2111258) BOUND_VARIABLE_2111257)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15439 BOUND_VARIABLE_2111253) BOUND_VARIABLE_2240965) BOUND_VARIABLE_2111255) BOUND_VARIABLE_2111256))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16220 BOUND_VARIABLE_2111253) BOUND_VARIABLE_2240965) BOUND_VARIABLE_2111255) BOUND_VARIABLE_2111256) BOUND_VARIABLE_2111257) BOUND_VARIABLE_2111258))))) (let ((_let_2921 (forall ((BOUND_VARIABLE_2111225 tptp.int) (BOUND_VARIABLE_2111226 tptp.int) (BOUND_VARIABLE_2111227 tptp.int) (BOUND_VARIABLE_2111228 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2111225) BOUND_VARIABLE_2111227))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2111226) BOUND_VARIABLE_2111228))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16221 BOUND_VARIABLE_2111225) BOUND_VARIABLE_2111226) BOUND_VARIABLE_2111227) BOUND_VARIABLE_2111228))))))) (let ((_let_2922 (forall ((BOUND_VARIABLE_2111128 tptp.nat) (BOUND_VARIABLE_2241066 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2111130 tptp.nat) (BOUND_VARIABLE_2111131 tptp.nat) (BOUND_VARIABLE_2111132 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2111132))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2111132))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2111130)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16222 BOUND_VARIABLE_2111128) BOUND_VARIABLE_2241066) BOUND_VARIABLE_2111130) BOUND_VARIABLE_2111131) BOUND_VARIABLE_2111132) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2241066 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2111128))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2241066 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2111131))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2923 (forall ((BOUND_VARIABLE_2111031 tptp.nat) (BOUND_VARIABLE_2241143 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2111033 tptp.nat) (BOUND_VARIABLE_2111034 tptp.nat) (BOUND_VARIABLE_2111035 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2111035))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2111035))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2111033)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16223 BOUND_VARIABLE_2111031) BOUND_VARIABLE_2241143) BOUND_VARIABLE_2111033) BOUND_VARIABLE_2111034) BOUND_VARIABLE_2111035) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2241143 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2111031))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2241143 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2111034))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2924 (forall ((BOUND_VARIABLE_2110939 tptp.nat) (BOUND_VARIABLE_2241168 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2110941 tptp.nat) (BOUND_VARIABLE_2110942 tptp.nat) (BOUND_VARIABLE_2110943 tptp.int) (BOUND_VARIABLE_2110944 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15440 BOUND_VARIABLE_2110944) BOUND_VARIABLE_2110943)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15441 BOUND_VARIABLE_2110939) BOUND_VARIABLE_2241168) BOUND_VARIABLE_2110941) BOUND_VARIABLE_2110942))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16224 BOUND_VARIABLE_2110939) BOUND_VARIABLE_2241168) BOUND_VARIABLE_2110941) BOUND_VARIABLE_2110942) BOUND_VARIABLE_2110943) BOUND_VARIABLE_2110944))))) (let ((_let_2925 (forall ((BOUND_VARIABLE_2110911 tptp.int) (BOUND_VARIABLE_2110912 tptp.int) (BOUND_VARIABLE_2110913 tptp.int) (BOUND_VARIABLE_2110914 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2110911) BOUND_VARIABLE_2110913))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2110912) BOUND_VARIABLE_2110914))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16225 BOUND_VARIABLE_2110911) BOUND_VARIABLE_2110912) BOUND_VARIABLE_2110913) BOUND_VARIABLE_2110914))))))) (let ((_let_2926 (forall ((BOUND_VARIABLE_2110814 tptp.nat) (BOUND_VARIABLE_2241269 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2110816 tptp.nat) (BOUND_VARIABLE_2110817 tptp.nat) (BOUND_VARIABLE_2110818 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2110818))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2110818))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2110816)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16226 BOUND_VARIABLE_2110814) BOUND_VARIABLE_2241269) BOUND_VARIABLE_2110816) BOUND_VARIABLE_2110817) BOUND_VARIABLE_2110818) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2241269 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110814))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2241269 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110817))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2927 (forall ((BOUND_VARIABLE_2110717 tptp.nat) (BOUND_VARIABLE_2241346 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2110719 tptp.nat) (BOUND_VARIABLE_2110720 tptp.nat) (BOUND_VARIABLE_2110721 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2110721))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2110721))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2110719)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16227 BOUND_VARIABLE_2110717) BOUND_VARIABLE_2241346) BOUND_VARIABLE_2110719) BOUND_VARIABLE_2110720) BOUND_VARIABLE_2110721) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2241346 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110717))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2241346 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110720))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2928 (forall ((BOUND_VARIABLE_2110625 tptp.nat) (BOUND_VARIABLE_2241371 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2110627 tptp.nat) (BOUND_VARIABLE_2110628 tptp.nat) (BOUND_VARIABLE_2110629 tptp.int) (BOUND_VARIABLE_2110630 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15442 BOUND_VARIABLE_2110630) BOUND_VARIABLE_2110629)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15443 BOUND_VARIABLE_2110625) BOUND_VARIABLE_2241371) BOUND_VARIABLE_2110627) BOUND_VARIABLE_2110628))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16228 BOUND_VARIABLE_2110625) BOUND_VARIABLE_2241371) BOUND_VARIABLE_2110627) BOUND_VARIABLE_2110628) BOUND_VARIABLE_2110629) BOUND_VARIABLE_2110630))))) (let ((_let_2929 (forall ((BOUND_VARIABLE_2110597 tptp.int) (BOUND_VARIABLE_2110598 tptp.int) (BOUND_VARIABLE_2110599 tptp.int) (BOUND_VARIABLE_2110600 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2110597) BOUND_VARIABLE_2110599))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2110598) BOUND_VARIABLE_2110600))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16229 BOUND_VARIABLE_2110597) BOUND_VARIABLE_2110598) BOUND_VARIABLE_2110599) BOUND_VARIABLE_2110600))))))) (let ((_let_2930 (forall ((BOUND_VARIABLE_2110500 tptp.nat) (BOUND_VARIABLE_2241472 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2110502 tptp.nat) (BOUND_VARIABLE_2110503 tptp.nat) (BOUND_VARIABLE_2110504 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2110504))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2110504))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2110502)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16230 BOUND_VARIABLE_2110500) BOUND_VARIABLE_2241472) BOUND_VARIABLE_2110502) BOUND_VARIABLE_2110503) BOUND_VARIABLE_2110504) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2241472 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110500))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2241472 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110503))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2931 (forall ((BOUND_VARIABLE_2110403 tptp.nat) (BOUND_VARIABLE_2241549 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2110405 tptp.nat) (BOUND_VARIABLE_2110406 tptp.nat) (BOUND_VARIABLE_2110407 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2110407))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2110407))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2110405)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16231 BOUND_VARIABLE_2110403) BOUND_VARIABLE_2241549) BOUND_VARIABLE_2110405) BOUND_VARIABLE_2110406) BOUND_VARIABLE_2110407) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2241549 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110403))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2241549 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110406))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2932 (forall ((BOUND_VARIABLE_2110311 tptp.nat) (BOUND_VARIABLE_2241574 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2110313 tptp.nat) (BOUND_VARIABLE_2110314 tptp.nat) (BOUND_VARIABLE_2110315 tptp.int) (BOUND_VARIABLE_2110316 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15444 BOUND_VARIABLE_2110316) BOUND_VARIABLE_2110315)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15445 BOUND_VARIABLE_2110311) BOUND_VARIABLE_2241574) BOUND_VARIABLE_2110313) BOUND_VARIABLE_2110314))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16232 BOUND_VARIABLE_2110311) BOUND_VARIABLE_2241574) BOUND_VARIABLE_2110313) BOUND_VARIABLE_2110314) BOUND_VARIABLE_2110315) BOUND_VARIABLE_2110316))))) (let ((_let_2933 (forall ((BOUND_VARIABLE_2110283 tptp.int) (BOUND_VARIABLE_2110284 tptp.int) (BOUND_VARIABLE_2110285 tptp.int) (BOUND_VARIABLE_2110286 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2110283) BOUND_VARIABLE_2110285))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2110284) BOUND_VARIABLE_2110286))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16233 BOUND_VARIABLE_2110283) BOUND_VARIABLE_2110284) BOUND_VARIABLE_2110285) BOUND_VARIABLE_2110286))))))) (let ((_let_2934 (forall ((BOUND_VARIABLE_2110186 tptp.nat) (BOUND_VARIABLE_2241675 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2110188 tptp.nat) (BOUND_VARIABLE_2110189 tptp.nat) (BOUND_VARIABLE_2110190 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2110190))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2110190))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2110188)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16234 BOUND_VARIABLE_2110186) BOUND_VARIABLE_2241675) BOUND_VARIABLE_2110188) BOUND_VARIABLE_2110189) BOUND_VARIABLE_2110190) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2241675 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110186))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2241675 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110189))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2935 (forall ((BOUND_VARIABLE_2110089 tptp.nat) (BOUND_VARIABLE_2241752 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2110091 tptp.nat) (BOUND_VARIABLE_2110092 tptp.nat) (BOUND_VARIABLE_2110093 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2110093))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2110093))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2110091)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16235 BOUND_VARIABLE_2110089) BOUND_VARIABLE_2241752) BOUND_VARIABLE_2110091) BOUND_VARIABLE_2110092) BOUND_VARIABLE_2110093) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2241752 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110089))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2241752 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2110092))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2936 (forall ((BOUND_VARIABLE_2109997 tptp.nat) (BOUND_VARIABLE_2241777 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2109999 tptp.nat) (BOUND_VARIABLE_2110000 tptp.nat) (BOUND_VARIABLE_2110001 tptp.int) (BOUND_VARIABLE_2110002 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15446 BOUND_VARIABLE_2110002) BOUND_VARIABLE_2110001)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15447 BOUND_VARIABLE_2109997) BOUND_VARIABLE_2241777) BOUND_VARIABLE_2109999) BOUND_VARIABLE_2110000))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16236 BOUND_VARIABLE_2109997) BOUND_VARIABLE_2241777) BOUND_VARIABLE_2109999) BOUND_VARIABLE_2110000) BOUND_VARIABLE_2110001) BOUND_VARIABLE_2110002))))) (let ((_let_2937 (forall ((BOUND_VARIABLE_2109969 tptp.int) (BOUND_VARIABLE_2109970 tptp.int) (BOUND_VARIABLE_2109971 tptp.int) (BOUND_VARIABLE_2109972 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2109969) BOUND_VARIABLE_2109971))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2109970) BOUND_VARIABLE_2109972))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16237 BOUND_VARIABLE_2109969) BOUND_VARIABLE_2109970) BOUND_VARIABLE_2109971) BOUND_VARIABLE_2109972))))))) (let ((_let_2938 (forall ((BOUND_VARIABLE_2109872 tptp.nat) (BOUND_VARIABLE_2241878 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2109874 tptp.nat) (BOUND_VARIABLE_2109875 tptp.nat) (BOUND_VARIABLE_2109876 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2109876))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2109876))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2109874)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16238 BOUND_VARIABLE_2109872) BOUND_VARIABLE_2241878) BOUND_VARIABLE_2109874) BOUND_VARIABLE_2109875) BOUND_VARIABLE_2109876) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2241878 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109872))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2241878 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109875))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2939 (forall ((BOUND_VARIABLE_2109775 tptp.nat) (BOUND_VARIABLE_2241955 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2109777 tptp.nat) (BOUND_VARIABLE_2109778 tptp.nat) (BOUND_VARIABLE_2109779 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2109779))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2109779))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2109777)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16239 BOUND_VARIABLE_2109775) BOUND_VARIABLE_2241955) BOUND_VARIABLE_2109777) BOUND_VARIABLE_2109778) BOUND_VARIABLE_2109779) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2241955 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109775))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2241955 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109778))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2940 (forall ((BOUND_VARIABLE_2109683 tptp.nat) (BOUND_VARIABLE_2241980 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2109685 tptp.nat) (BOUND_VARIABLE_2109686 tptp.nat) (BOUND_VARIABLE_2109687 tptp.int) (BOUND_VARIABLE_2109688 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15448 BOUND_VARIABLE_2109688) BOUND_VARIABLE_2109687)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15449 BOUND_VARIABLE_2109683) BOUND_VARIABLE_2241980) BOUND_VARIABLE_2109685) BOUND_VARIABLE_2109686))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16240 BOUND_VARIABLE_2109683) BOUND_VARIABLE_2241980) BOUND_VARIABLE_2109685) BOUND_VARIABLE_2109686) BOUND_VARIABLE_2109687) BOUND_VARIABLE_2109688))))) (let ((_let_2941 (forall ((BOUND_VARIABLE_2109655 tptp.int) (BOUND_VARIABLE_2109656 tptp.int) (BOUND_VARIABLE_2109657 tptp.int) (BOUND_VARIABLE_2109658 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2109655) BOUND_VARIABLE_2109657))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2109656) BOUND_VARIABLE_2109658))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16241 BOUND_VARIABLE_2109655) BOUND_VARIABLE_2109656) BOUND_VARIABLE_2109657) BOUND_VARIABLE_2109658))))))) (let ((_let_2942 (forall ((BOUND_VARIABLE_2109558 tptp.nat) (BOUND_VARIABLE_2242081 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2109560 tptp.nat) (BOUND_VARIABLE_2109561 tptp.nat) (BOUND_VARIABLE_2109562 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2109562))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2109562))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2109560)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16242 BOUND_VARIABLE_2109558) BOUND_VARIABLE_2242081) BOUND_VARIABLE_2109560) BOUND_VARIABLE_2109561) BOUND_VARIABLE_2109562) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2242081 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109558))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2242081 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109561))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2943 (forall ((BOUND_VARIABLE_2109461 tptp.nat) (BOUND_VARIABLE_2242158 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2109463 tptp.nat) (BOUND_VARIABLE_2109464 tptp.nat) (BOUND_VARIABLE_2109465 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2109465))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2109465))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2109463)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16243 BOUND_VARIABLE_2109461) BOUND_VARIABLE_2242158) BOUND_VARIABLE_2109463) BOUND_VARIABLE_2109464) BOUND_VARIABLE_2109465) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2242158 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109461))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2242158 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109464))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2944 (forall ((BOUND_VARIABLE_2109369 tptp.nat) (BOUND_VARIABLE_2242183 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2109371 tptp.nat) (BOUND_VARIABLE_2109372 tptp.nat) (BOUND_VARIABLE_2109373 tptp.int) (BOUND_VARIABLE_2109374 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15450 BOUND_VARIABLE_2109374) BOUND_VARIABLE_2109373)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15451 BOUND_VARIABLE_2109369) BOUND_VARIABLE_2242183) BOUND_VARIABLE_2109371) BOUND_VARIABLE_2109372))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16244 BOUND_VARIABLE_2109369) BOUND_VARIABLE_2242183) BOUND_VARIABLE_2109371) BOUND_VARIABLE_2109372) BOUND_VARIABLE_2109373) BOUND_VARIABLE_2109374))))) (let ((_let_2945 (forall ((BOUND_VARIABLE_2109341 tptp.int) (BOUND_VARIABLE_2109342 tptp.int) (BOUND_VARIABLE_2109343 tptp.int) (BOUND_VARIABLE_2109344 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2109341) BOUND_VARIABLE_2109343))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2109342) BOUND_VARIABLE_2109344))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16245 BOUND_VARIABLE_2109341) BOUND_VARIABLE_2109342) BOUND_VARIABLE_2109343) BOUND_VARIABLE_2109344))))))) (let ((_let_2946 (forall ((BOUND_VARIABLE_2109244 tptp.nat) (BOUND_VARIABLE_2242284 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2109246 tptp.nat) (BOUND_VARIABLE_2109247 tptp.nat) (BOUND_VARIABLE_2109248 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2109248))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2109248))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2109246)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16246 BOUND_VARIABLE_2109244) BOUND_VARIABLE_2242284) BOUND_VARIABLE_2109246) BOUND_VARIABLE_2109247) BOUND_VARIABLE_2109248) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2242284 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109244))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2242284 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109247))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2947 (forall ((BOUND_VARIABLE_2109147 tptp.nat) (BOUND_VARIABLE_2242361 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2109149 tptp.nat) (BOUND_VARIABLE_2109150 tptp.nat) (BOUND_VARIABLE_2109151 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2109151))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2109151))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2109149)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16247 BOUND_VARIABLE_2109147) BOUND_VARIABLE_2242361) BOUND_VARIABLE_2109149) BOUND_VARIABLE_2109150) BOUND_VARIABLE_2109151) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2242361 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109147))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2242361 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2109150))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2948 (forall ((BOUND_VARIABLE_2109055 tptp.nat) (BOUND_VARIABLE_2242386 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2109057 tptp.nat) (BOUND_VARIABLE_2109058 tptp.nat) (BOUND_VARIABLE_2109059 tptp.int) (BOUND_VARIABLE_2109060 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15452 BOUND_VARIABLE_2109060) BOUND_VARIABLE_2109059)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15453 BOUND_VARIABLE_2109055) BOUND_VARIABLE_2242386) BOUND_VARIABLE_2109057) BOUND_VARIABLE_2109058))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16248 BOUND_VARIABLE_2109055) BOUND_VARIABLE_2242386) BOUND_VARIABLE_2109057) BOUND_VARIABLE_2109058) BOUND_VARIABLE_2109059) BOUND_VARIABLE_2109060))))) (let ((_let_2949 (forall ((BOUND_VARIABLE_2109027 tptp.int) (BOUND_VARIABLE_2109028 tptp.int) (BOUND_VARIABLE_2109029 tptp.int) (BOUND_VARIABLE_2109030 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2109027) BOUND_VARIABLE_2109029))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2109028) BOUND_VARIABLE_2109030))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16249 BOUND_VARIABLE_2109027) BOUND_VARIABLE_2109028) BOUND_VARIABLE_2109029) BOUND_VARIABLE_2109030))))))) (let ((_let_2950 (forall ((BOUND_VARIABLE_2108930 tptp.nat) (BOUND_VARIABLE_2242487 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2108932 tptp.nat) (BOUND_VARIABLE_2108933 tptp.nat) (BOUND_VARIABLE_2108934 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2108934))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2108934))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2108932)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16250 BOUND_VARIABLE_2108930) BOUND_VARIABLE_2242487) BOUND_VARIABLE_2108932) BOUND_VARIABLE_2108933) BOUND_VARIABLE_2108934) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2242487 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2108930))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2242487 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2108933))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2951 (forall ((BOUND_VARIABLE_2108833 tptp.nat) (BOUND_VARIABLE_2242564 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2108835 tptp.nat) (BOUND_VARIABLE_2108836 tptp.nat) (BOUND_VARIABLE_2108837 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2108837))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2108837))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2108835)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16251 BOUND_VARIABLE_2108833) BOUND_VARIABLE_2242564) BOUND_VARIABLE_2108835) BOUND_VARIABLE_2108836) BOUND_VARIABLE_2108837) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2242564 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2108833))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2242564 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2108836))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2952 (forall ((BOUND_VARIABLE_2108741 tptp.nat) (BOUND_VARIABLE_2242589 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2108743 tptp.nat) (BOUND_VARIABLE_2108744 tptp.nat) (BOUND_VARIABLE_2108745 tptp.int) (BOUND_VARIABLE_2108746 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15454 BOUND_VARIABLE_2108746) BOUND_VARIABLE_2108745)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15455 BOUND_VARIABLE_2108741) BOUND_VARIABLE_2242589) BOUND_VARIABLE_2108743) BOUND_VARIABLE_2108744))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16252 BOUND_VARIABLE_2108741) BOUND_VARIABLE_2242589) BOUND_VARIABLE_2108743) BOUND_VARIABLE_2108744) BOUND_VARIABLE_2108745) BOUND_VARIABLE_2108746))))) (let ((_let_2953 (forall ((BOUND_VARIABLE_2108713 tptp.int) (BOUND_VARIABLE_2108714 tptp.int) (BOUND_VARIABLE_2108715 tptp.int) (BOUND_VARIABLE_2108716 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2108713) BOUND_VARIABLE_2108715))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2108714) BOUND_VARIABLE_2108716))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16253 BOUND_VARIABLE_2108713) BOUND_VARIABLE_2108714) BOUND_VARIABLE_2108715) BOUND_VARIABLE_2108716))))))) (let ((_let_2954 (forall ((BOUND_VARIABLE_2242690 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2108627 tptp.nat) (BOUND_VARIABLE_2108628 tptp.nat) (BOUND_VARIABLE_2108629 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2108629))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2108629))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16254 BOUND_VARIABLE_2242690) BOUND_VARIABLE_2108627) BOUND_VARIABLE_2108628) BOUND_VARIABLE_2108629) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2242690 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2108627)) (ho_15161 k_15160 BOUND_VARIABLE_2108628))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2955 (forall ((BOUND_VARIABLE_2242758 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2108540 tptp.nat) (BOUND_VARIABLE_2108541 tptp.nat) (BOUND_VARIABLE_2108542 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2108542))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2108542))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16255 BOUND_VARIABLE_2242758) BOUND_VARIABLE_2108540) BOUND_VARIABLE_2108541) BOUND_VARIABLE_2108542) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2242758 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2108540)) (ho_15161 k_15160 BOUND_VARIABLE_2108541))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2956 (forall ((BOUND_VARIABLE_2242774 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2108465 tptp.nat) (BOUND_VARIABLE_2108466 tptp.nat) (BOUND_VARIABLE_2108467 tptp.int) (BOUND_VARIABLE_2108468 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15456 BOUND_VARIABLE_2108468) BOUND_VARIABLE_2108467)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15457 BOUND_VARIABLE_2242774) BOUND_VARIABLE_2108465) BOUND_VARIABLE_2108466))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16256 BOUND_VARIABLE_2242774) BOUND_VARIABLE_2108465) BOUND_VARIABLE_2108466) BOUND_VARIABLE_2108467) BOUND_VARIABLE_2108468))))) (let ((_let_2957 (forall ((BOUND_VARIABLE_2108436 tptp.int) (BOUND_VARIABLE_2108437 tptp.int) (BOUND_VARIABLE_2108438 tptp.int) (BOUND_VARIABLE_2108439 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2108436) BOUND_VARIABLE_2108438))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2108437) BOUND_VARIABLE_2108439))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16257 BOUND_VARIABLE_2108436) BOUND_VARIABLE_2108437) BOUND_VARIABLE_2108438) BOUND_VARIABLE_2108439))))))) (let ((_let_2958 (forall ((BOUND_VARIABLE_2108339 tptp.nat) (BOUND_VARIABLE_2242872 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2108341 tptp.nat) (BOUND_VARIABLE_2108342 tptp.nat) (BOUND_VARIABLE_2108343 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2108343))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2108343))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2108341)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16258 BOUND_VARIABLE_2108339) BOUND_VARIABLE_2242872) BOUND_VARIABLE_2108341) BOUND_VARIABLE_2108342) BOUND_VARIABLE_2108343) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2242872 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2108339))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2242872 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2108342))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2959 (forall ((BOUND_VARIABLE_2108242 tptp.nat) (BOUND_VARIABLE_2242949 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2108244 tptp.nat) (BOUND_VARIABLE_2108245 tptp.nat) (BOUND_VARIABLE_2108246 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2108246))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2108246))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2108244)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16259 BOUND_VARIABLE_2108242) BOUND_VARIABLE_2242949) BOUND_VARIABLE_2108244) BOUND_VARIABLE_2108245) BOUND_VARIABLE_2108246) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2242949 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2108242))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2242949 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2108245))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2960 (forall ((BOUND_VARIABLE_2108150 tptp.nat) (BOUND_VARIABLE_2242974 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2108152 tptp.nat) (BOUND_VARIABLE_2108153 tptp.nat) (BOUND_VARIABLE_2108154 tptp.int) (BOUND_VARIABLE_2108155 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15458 BOUND_VARIABLE_2108155) BOUND_VARIABLE_2108154)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15459 BOUND_VARIABLE_2108150) BOUND_VARIABLE_2242974) BOUND_VARIABLE_2108152) BOUND_VARIABLE_2108153))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16260 BOUND_VARIABLE_2108150) BOUND_VARIABLE_2242974) BOUND_VARIABLE_2108152) BOUND_VARIABLE_2108153) BOUND_VARIABLE_2108154) BOUND_VARIABLE_2108155))))) (let ((_let_2961 (forall ((BOUND_VARIABLE_2108122 tptp.int) (BOUND_VARIABLE_2108123 tptp.int) (BOUND_VARIABLE_2108124 tptp.int) (BOUND_VARIABLE_2108125 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2108122) BOUND_VARIABLE_2108124))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2108123) BOUND_VARIABLE_2108125))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16261 BOUND_VARIABLE_2108122) BOUND_VARIABLE_2108123) BOUND_VARIABLE_2108124) BOUND_VARIABLE_2108125))))))) (let ((_let_2962 (forall ((BOUND_VARIABLE_2108025 tptp.nat) (BOUND_VARIABLE_2243075 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2108027 tptp.nat) (BOUND_VARIABLE_2108028 tptp.nat) (BOUND_VARIABLE_2108029 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2108029))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2108029))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2108027)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16262 BOUND_VARIABLE_2108025) BOUND_VARIABLE_2243075) BOUND_VARIABLE_2108027) BOUND_VARIABLE_2108028) BOUND_VARIABLE_2108029) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2243075 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2108025))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2243075 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2108028))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2963 (forall ((BOUND_VARIABLE_2107928 tptp.nat) (BOUND_VARIABLE_2243152 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2107930 tptp.nat) (BOUND_VARIABLE_2107931 tptp.nat) (BOUND_VARIABLE_2107932 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2107932))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2107932))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2107930)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16263 BOUND_VARIABLE_2107928) BOUND_VARIABLE_2243152) BOUND_VARIABLE_2107930) BOUND_VARIABLE_2107931) BOUND_VARIABLE_2107932) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2243152 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107928))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2243152 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107931))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2964 (forall ((BOUND_VARIABLE_2107836 tptp.nat) (BOUND_VARIABLE_2243177 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2107838 tptp.nat) (BOUND_VARIABLE_2107839 tptp.nat) (BOUND_VARIABLE_2107840 tptp.int) (BOUND_VARIABLE_2107841 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15460 BOUND_VARIABLE_2107841) BOUND_VARIABLE_2107840)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15461 BOUND_VARIABLE_2107836) BOUND_VARIABLE_2243177) BOUND_VARIABLE_2107838) BOUND_VARIABLE_2107839))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16264 BOUND_VARIABLE_2107836) BOUND_VARIABLE_2243177) BOUND_VARIABLE_2107838) BOUND_VARIABLE_2107839) BOUND_VARIABLE_2107840) BOUND_VARIABLE_2107841))))) (let ((_let_2965 (forall ((BOUND_VARIABLE_2107808 tptp.int) (BOUND_VARIABLE_2107809 tptp.int) (BOUND_VARIABLE_2107810 tptp.int) (BOUND_VARIABLE_2107811 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2107808) BOUND_VARIABLE_2107810))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2107809) BOUND_VARIABLE_2107811))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16265 BOUND_VARIABLE_2107808) BOUND_VARIABLE_2107809) BOUND_VARIABLE_2107810) BOUND_VARIABLE_2107811))))))) (let ((_let_2966 (forall ((BOUND_VARIABLE_2107711 tptp.nat) (BOUND_VARIABLE_2243278 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2107713 tptp.nat) (BOUND_VARIABLE_2107714 tptp.nat) (BOUND_VARIABLE_2107715 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2107715))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2107715))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2107713)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16266 BOUND_VARIABLE_2107711) BOUND_VARIABLE_2243278) BOUND_VARIABLE_2107713) BOUND_VARIABLE_2107714) BOUND_VARIABLE_2107715) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2243278 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107711))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2243278 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107714))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2967 (forall ((BOUND_VARIABLE_2107614 tptp.nat) (BOUND_VARIABLE_2243355 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2107616 tptp.nat) (BOUND_VARIABLE_2107617 tptp.nat) (BOUND_VARIABLE_2107618 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2107618))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2107618))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2107616)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16267 BOUND_VARIABLE_2107614) BOUND_VARIABLE_2243355) BOUND_VARIABLE_2107616) BOUND_VARIABLE_2107617) BOUND_VARIABLE_2107618) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2243355 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107614))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2243355 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107617))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2968 (forall ((BOUND_VARIABLE_2107522 tptp.nat) (BOUND_VARIABLE_2243380 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2107524 tptp.nat) (BOUND_VARIABLE_2107525 tptp.nat) (BOUND_VARIABLE_2107526 tptp.int) (BOUND_VARIABLE_2107527 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15462 BOUND_VARIABLE_2107527) BOUND_VARIABLE_2107526)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15463 BOUND_VARIABLE_2107522) BOUND_VARIABLE_2243380) BOUND_VARIABLE_2107524) BOUND_VARIABLE_2107525))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16268 BOUND_VARIABLE_2107522) BOUND_VARIABLE_2243380) BOUND_VARIABLE_2107524) BOUND_VARIABLE_2107525) BOUND_VARIABLE_2107526) BOUND_VARIABLE_2107527))))) (let ((_let_2969 (forall ((BOUND_VARIABLE_2107494 tptp.int) (BOUND_VARIABLE_2107495 tptp.int) (BOUND_VARIABLE_2107496 tptp.int) (BOUND_VARIABLE_2107497 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2107494) BOUND_VARIABLE_2107496))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2107495) BOUND_VARIABLE_2107497))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16269 BOUND_VARIABLE_2107494) BOUND_VARIABLE_2107495) BOUND_VARIABLE_2107496) BOUND_VARIABLE_2107497))))))) (let ((_let_2970 (forall ((BOUND_VARIABLE_2107466 tptp.int) (BOUND_VARIABLE_2107467 tptp.int) (BOUND_VARIABLE_2107468 tptp.int) (BOUND_VARIABLE_2107469 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2107466) BOUND_VARIABLE_2107468))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2107467) BOUND_VARIABLE_2107469))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16270 BOUND_VARIABLE_2107466) BOUND_VARIABLE_2107467) BOUND_VARIABLE_2107468) BOUND_VARIABLE_2107469))))))) (let ((_let_2971 (forall ((BOUND_VARIABLE_2107369 tptp.nat) (BOUND_VARIABLE_2243504 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2107371 tptp.nat) (BOUND_VARIABLE_2107372 tptp.nat) (BOUND_VARIABLE_2107373 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2107373))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2107373))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2107371)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16271 BOUND_VARIABLE_2107369) BOUND_VARIABLE_2243504) BOUND_VARIABLE_2107371) BOUND_VARIABLE_2107372) BOUND_VARIABLE_2107373) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2243504 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107369))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2243504 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107372))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2972 (forall ((BOUND_VARIABLE_2107325 tptp.int) (BOUND_VARIABLE_2107326 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15464 BOUND_VARIABLE_2107326) BOUND_VARIABLE_2107325)) (ho_15260 k_15259 k_16272)) (ho_15108 (ho_15107 k_16273 BOUND_VARIABLE_2107325) BOUND_VARIABLE_2107326))))) (let ((_let_2973 (forall ((BOUND_VARIABLE_2107228 tptp.nat) (BOUND_VARIABLE_2243594 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2107230 tptp.nat) (BOUND_VARIABLE_2107231 tptp.nat) (BOUND_VARIABLE_2107232 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2107232))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2107232))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2107230)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16274 BOUND_VARIABLE_2107228) BOUND_VARIABLE_2243594) BOUND_VARIABLE_2107230) BOUND_VARIABLE_2107231) BOUND_VARIABLE_2107232) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2243594 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107228))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2243594 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107231))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2974 (forall ((BOUND_VARIABLE_2107136 tptp.nat) (BOUND_VARIABLE_2243619 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2107138 tptp.nat) (BOUND_VARIABLE_2107139 tptp.nat) (BOUND_VARIABLE_2107140 tptp.int) (BOUND_VARIABLE_2107141 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15465 BOUND_VARIABLE_2107141) BOUND_VARIABLE_2107140)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15466 BOUND_VARIABLE_2107136) BOUND_VARIABLE_2243619) BOUND_VARIABLE_2107138) BOUND_VARIABLE_2107139))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16275 BOUND_VARIABLE_2107136) BOUND_VARIABLE_2243619) BOUND_VARIABLE_2107138) BOUND_VARIABLE_2107139) BOUND_VARIABLE_2107140) BOUND_VARIABLE_2107141))))) (let ((_let_2975 (forall ((BOUND_VARIABLE_2107108 tptp.int) (BOUND_VARIABLE_2107109 tptp.int) (BOUND_VARIABLE_2107110 tptp.int) (BOUND_VARIABLE_2107111 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2107108) BOUND_VARIABLE_2107110))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2107109) BOUND_VARIABLE_2107111))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16276 BOUND_VARIABLE_2107108) BOUND_VARIABLE_2107109) BOUND_VARIABLE_2107110) BOUND_VARIABLE_2107111))))))) (let ((_let_2976 (forall ((BOUND_VARIABLE_2107011 tptp.nat) (BOUND_VARIABLE_2243720 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2107013 tptp.nat) (BOUND_VARIABLE_2107014 tptp.nat) (BOUND_VARIABLE_2107015 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2107015))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2107015))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2107013)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16277 BOUND_VARIABLE_2107011) BOUND_VARIABLE_2243720) BOUND_VARIABLE_2107013) BOUND_VARIABLE_2107014) BOUND_VARIABLE_2107015) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2243720 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107011))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2243720 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2107014))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2977 (forall ((BOUND_VARIABLE_2106914 tptp.nat) (BOUND_VARIABLE_2243797 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2106916 tptp.nat) (BOUND_VARIABLE_2106917 tptp.nat) (BOUND_VARIABLE_2106918 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2106918))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2106918))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2106916)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16278 BOUND_VARIABLE_2106914) BOUND_VARIABLE_2243797) BOUND_VARIABLE_2106916) BOUND_VARIABLE_2106917) BOUND_VARIABLE_2106918) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2243797 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2106914))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2243797 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2106917))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2978 (forall ((BOUND_VARIABLE_2106822 tptp.nat) (BOUND_VARIABLE_2243822 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2106824 tptp.nat) (BOUND_VARIABLE_2106825 tptp.nat) (BOUND_VARIABLE_2106826 tptp.int) (BOUND_VARIABLE_2106827 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15467 BOUND_VARIABLE_2106827) BOUND_VARIABLE_2106826)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15468 BOUND_VARIABLE_2106822) BOUND_VARIABLE_2243822) BOUND_VARIABLE_2106824) BOUND_VARIABLE_2106825))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16279 BOUND_VARIABLE_2106822) BOUND_VARIABLE_2243822) BOUND_VARIABLE_2106824) BOUND_VARIABLE_2106825) BOUND_VARIABLE_2106826) BOUND_VARIABLE_2106827))))) (let ((_let_2979 (forall ((BOUND_VARIABLE_2106778 tptp.int) (BOUND_VARIABLE_2106779 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15469 BOUND_VARIABLE_2106779) BOUND_VARIABLE_2106778)) (ho_15260 k_15259 k_16280)) (ho_15108 (ho_15107 k_16281 BOUND_VARIABLE_2106778) BOUND_VARIABLE_2106779))))) (let ((_let_2980 (forall ((BOUND_VARIABLE_2243913 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2106692 tptp.nat) (BOUND_VARIABLE_2106693 tptp.nat) (BOUND_VARIABLE_2106694 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2106694))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2106694))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16282 BOUND_VARIABLE_2243913) BOUND_VARIABLE_2106692) BOUND_VARIABLE_2106693) BOUND_VARIABLE_2106694) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2243913 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2106692)) (ho_15161 k_15160 BOUND_VARIABLE_2106693))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2981 (forall ((BOUND_VARIABLE_2243929 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2106617 tptp.nat) (BOUND_VARIABLE_2106618 tptp.nat) (BOUND_VARIABLE_2106619 tptp.int) (BOUND_VARIABLE_2106620 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15470 BOUND_VARIABLE_2106620) BOUND_VARIABLE_2106619)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15471 BOUND_VARIABLE_2243929) BOUND_VARIABLE_2106617) BOUND_VARIABLE_2106618))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16283 BOUND_VARIABLE_2243929) BOUND_VARIABLE_2106617) BOUND_VARIABLE_2106618) BOUND_VARIABLE_2106619) BOUND_VARIABLE_2106620))))) (let ((_let_2982 (forall ((BOUND_VARIABLE_2106588 tptp.int) (BOUND_VARIABLE_2106589 tptp.int) (BOUND_VARIABLE_2106590 tptp.int) (BOUND_VARIABLE_2106591 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2106588) BOUND_VARIABLE_2106590))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2106589) BOUND_VARIABLE_2106591))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16284 BOUND_VARIABLE_2106588) BOUND_VARIABLE_2106589) BOUND_VARIABLE_2106590) BOUND_VARIABLE_2106591))))))) (let ((_let_2983 (forall ((BOUND_VARIABLE_2106560 tptp.int) (BOUND_VARIABLE_2106561 tptp.int) (BOUND_VARIABLE_2106562 tptp.int) (BOUND_VARIABLE_2106563 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2106560) BOUND_VARIABLE_2106562))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2106561) BOUND_VARIABLE_2106563))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16285 BOUND_VARIABLE_2106560) BOUND_VARIABLE_2106561) BOUND_VARIABLE_2106562) BOUND_VARIABLE_2106563))))))) (let ((_let_2984 (forall ((BOUND_VARIABLE_2244050 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2106474 tptp.nat) (BOUND_VARIABLE_2106475 tptp.nat) (BOUND_VARIABLE_2106476 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2106476))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2106476))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16286 BOUND_VARIABLE_2244050) BOUND_VARIABLE_2106474) BOUND_VARIABLE_2106475) BOUND_VARIABLE_2106476) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2244050 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2106474)) (ho_15161 k_15160 BOUND_VARIABLE_2106475))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2985 (forall ((BOUND_VARIABLE_2106445 tptp.int) (BOUND_VARIABLE_2106446 tptp.int) (BOUND_VARIABLE_2106447 tptp.int) (BOUND_VARIABLE_2106448 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2106445) BOUND_VARIABLE_2106447))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2106446) BOUND_VARIABLE_2106448))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16287 BOUND_VARIABLE_2106445) BOUND_VARIABLE_2106446) BOUND_VARIABLE_2106447) BOUND_VARIABLE_2106448))))))) (let ((_let_2986 (forall ((BOUND_VARIABLE_2244141 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2106359 tptp.nat) (BOUND_VARIABLE_2106360 tptp.nat) (BOUND_VARIABLE_2106361 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2106361))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2106361))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16288 BOUND_VARIABLE_2244141) BOUND_VARIABLE_2106359) BOUND_VARIABLE_2106360) BOUND_VARIABLE_2106361) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2244141 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2106359)) (ho_15161 k_15160 BOUND_VARIABLE_2106360))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2987 (forall ((BOUND_VARIABLE_2244209 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2106272 tptp.nat) (BOUND_VARIABLE_2106273 tptp.nat) (BOUND_VARIABLE_2106274 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2106274))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2106274))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16289 BOUND_VARIABLE_2244209) BOUND_VARIABLE_2106272) BOUND_VARIABLE_2106273) BOUND_VARIABLE_2106274) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2244209 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2106272)) (ho_15161 k_15160 BOUND_VARIABLE_2106273))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2988 (forall ((BOUND_VARIABLE_2244225 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2106197 tptp.nat) (BOUND_VARIABLE_2106198 tptp.nat) (BOUND_VARIABLE_2106199 tptp.int) (BOUND_VARIABLE_2106200 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15472 BOUND_VARIABLE_2106200) BOUND_VARIABLE_2106199)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15473 BOUND_VARIABLE_2244225) BOUND_VARIABLE_2106197) BOUND_VARIABLE_2106198))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16290 BOUND_VARIABLE_2244225) BOUND_VARIABLE_2106197) BOUND_VARIABLE_2106198) BOUND_VARIABLE_2106199) BOUND_VARIABLE_2106200))))) (let ((_let_2989 (forall ((BOUND_VARIABLE_2106168 tptp.int) (BOUND_VARIABLE_2106169 tptp.int) (BOUND_VARIABLE_2106170 tptp.int) (BOUND_VARIABLE_2106171 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2106168) BOUND_VARIABLE_2106170))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2106169) BOUND_VARIABLE_2106171))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16291 BOUND_VARIABLE_2106168) BOUND_VARIABLE_2106169) BOUND_VARIABLE_2106170) BOUND_VARIABLE_2106171))))))) (let ((_let_2990 (forall ((BOUND_VARIABLE_2106071 tptp.nat) (BOUND_VARIABLE_2244323 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2106073 tptp.nat) (BOUND_VARIABLE_2106074 tptp.nat) (BOUND_VARIABLE_2106075 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2106075))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2106075))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2106073)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16292 BOUND_VARIABLE_2106071) BOUND_VARIABLE_2244323) BOUND_VARIABLE_2106073) BOUND_VARIABLE_2106074) BOUND_VARIABLE_2106075) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2244323 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2106071))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2244323 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2106074))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2991 (forall ((BOUND_VARIABLE_2105974 tptp.nat) (BOUND_VARIABLE_2244400 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2105976 tptp.nat) (BOUND_VARIABLE_2105977 tptp.nat) (BOUND_VARIABLE_2105978 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2105978))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2105978))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2105976)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16293 BOUND_VARIABLE_2105974) BOUND_VARIABLE_2244400) BOUND_VARIABLE_2105976) BOUND_VARIABLE_2105977) BOUND_VARIABLE_2105978) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2244400 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2105974))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2244400 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2105977))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2992 (forall ((BOUND_VARIABLE_2105882 tptp.nat) (BOUND_VARIABLE_2244425 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2105884 tptp.nat) (BOUND_VARIABLE_2105885 tptp.nat) (BOUND_VARIABLE_2105886 tptp.int) (BOUND_VARIABLE_2105887 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15474 BOUND_VARIABLE_2105887) BOUND_VARIABLE_2105886)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15475 BOUND_VARIABLE_2105882) BOUND_VARIABLE_2244425) BOUND_VARIABLE_2105884) BOUND_VARIABLE_2105885))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16294 BOUND_VARIABLE_2105882) BOUND_VARIABLE_2244425) BOUND_VARIABLE_2105884) BOUND_VARIABLE_2105885) BOUND_VARIABLE_2105886) BOUND_VARIABLE_2105887))))) (let ((_let_2993 (forall ((BOUND_VARIABLE_2105854 tptp.int) (BOUND_VARIABLE_2105855 tptp.int) (BOUND_VARIABLE_2105856 tptp.int) (BOUND_VARIABLE_2105857 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2105854) BOUND_VARIABLE_2105856))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2105855) BOUND_VARIABLE_2105857))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16295 BOUND_VARIABLE_2105854) BOUND_VARIABLE_2105855) BOUND_VARIABLE_2105856) BOUND_VARIABLE_2105857))))))) (let ((_let_2994 (forall ((BOUND_VARIABLE_2244526 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2105768 tptp.nat) (BOUND_VARIABLE_2105769 tptp.nat) (BOUND_VARIABLE_2105770 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2105770))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2105770))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16296 BOUND_VARIABLE_2244526) BOUND_VARIABLE_2105768) BOUND_VARIABLE_2105769) BOUND_VARIABLE_2105770) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2244526 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2105768)) (ho_15161 k_15160 BOUND_VARIABLE_2105769))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2995 (forall ((BOUND_VARIABLE_2244594 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2105681 tptp.nat) (BOUND_VARIABLE_2105682 tptp.nat) (BOUND_VARIABLE_2105683 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2105683))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2105683))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16297 BOUND_VARIABLE_2244594) BOUND_VARIABLE_2105681) BOUND_VARIABLE_2105682) BOUND_VARIABLE_2105683) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2244594 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2105681)) (ho_15161 k_15160 BOUND_VARIABLE_2105682))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_2996 (forall ((BOUND_VARIABLE_2244610 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2105606 tptp.nat) (BOUND_VARIABLE_2105607 tptp.nat) (BOUND_VARIABLE_2105608 tptp.int) (BOUND_VARIABLE_2105609 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15476 BOUND_VARIABLE_2105609) BOUND_VARIABLE_2105608)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15477 BOUND_VARIABLE_2244610) BOUND_VARIABLE_2105606) BOUND_VARIABLE_2105607))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16298 BOUND_VARIABLE_2244610) BOUND_VARIABLE_2105606) BOUND_VARIABLE_2105607) BOUND_VARIABLE_2105608) BOUND_VARIABLE_2105609))))) (let ((_let_2997 (forall ((BOUND_VARIABLE_2105577 tptp.int) (BOUND_VARIABLE_2105578 tptp.int) (BOUND_VARIABLE_2105579 tptp.int) (BOUND_VARIABLE_2105580 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2105577) BOUND_VARIABLE_2105579))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2105578) BOUND_VARIABLE_2105580))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16299 BOUND_VARIABLE_2105577) BOUND_VARIABLE_2105578) BOUND_VARIABLE_2105579) BOUND_VARIABLE_2105580))))))) (let ((_let_2998 (forall ((BOUND_VARIABLE_2105480 tptp.nat) (BOUND_VARIABLE_2244708 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2105482 tptp.nat) (BOUND_VARIABLE_2105483 tptp.nat) (BOUND_VARIABLE_2105484 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2105484))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2105484))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2105482)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16300 BOUND_VARIABLE_2105480) BOUND_VARIABLE_2244708) BOUND_VARIABLE_2105482) BOUND_VARIABLE_2105483) BOUND_VARIABLE_2105484) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2244708 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2105480))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2244708 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2105483))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_2999 (forall ((BOUND_VARIABLE_2105383 tptp.nat) (BOUND_VARIABLE_2244785 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2105385 tptp.nat) (BOUND_VARIABLE_2105386 tptp.nat) (BOUND_VARIABLE_2105387 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2105387))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2105387))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2105385)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16301 BOUND_VARIABLE_2105383) BOUND_VARIABLE_2244785) BOUND_VARIABLE_2105385) BOUND_VARIABLE_2105386) BOUND_VARIABLE_2105387) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2244785 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2105383))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2244785 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2105386))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3000 (forall ((BOUND_VARIABLE_2105291 tptp.nat) (BOUND_VARIABLE_2244810 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2105293 tptp.nat) (BOUND_VARIABLE_2105294 tptp.nat) (BOUND_VARIABLE_2105295 tptp.int) (BOUND_VARIABLE_2105296 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15478 BOUND_VARIABLE_2105296) BOUND_VARIABLE_2105295)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15479 BOUND_VARIABLE_2105291) BOUND_VARIABLE_2244810) BOUND_VARIABLE_2105293) BOUND_VARIABLE_2105294))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16302 BOUND_VARIABLE_2105291) BOUND_VARIABLE_2244810) BOUND_VARIABLE_2105293) BOUND_VARIABLE_2105294) BOUND_VARIABLE_2105295) BOUND_VARIABLE_2105296))))) (let ((_let_3001 (forall ((BOUND_VARIABLE_2105263 tptp.int) (BOUND_VARIABLE_2105264 tptp.int) (BOUND_VARIABLE_2105265 tptp.int) (BOUND_VARIABLE_2105266 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2105263) BOUND_VARIABLE_2105265))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2105264) BOUND_VARIABLE_2105266))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16303 BOUND_VARIABLE_2105263) BOUND_VARIABLE_2105264) BOUND_VARIABLE_2105265) BOUND_VARIABLE_2105266))))))) (let ((_let_3002 (forall ((BOUND_VARIABLE_2105166 tptp.nat) (BOUND_VARIABLE_2244911 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2105168 tptp.nat) (BOUND_VARIABLE_2105169 tptp.nat) (BOUND_VARIABLE_2105170 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2105170))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2105170))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2105168)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16304 BOUND_VARIABLE_2105166) BOUND_VARIABLE_2244911) BOUND_VARIABLE_2105168) BOUND_VARIABLE_2105169) BOUND_VARIABLE_2105170) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2244911 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2105166))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2244911 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2105169))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3003 (forall ((BOUND_VARIABLE_2105069 tptp.nat) (BOUND_VARIABLE_2244988 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2105071 tptp.nat) (BOUND_VARIABLE_2105072 tptp.nat) (BOUND_VARIABLE_2105073 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2105073))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2105073))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2105071)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16305 BOUND_VARIABLE_2105069) BOUND_VARIABLE_2244988) BOUND_VARIABLE_2105071) BOUND_VARIABLE_2105072) BOUND_VARIABLE_2105073) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2244988 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2105069))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2244988 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2105072))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3004 (forall ((BOUND_VARIABLE_2104977 tptp.nat) (BOUND_VARIABLE_2245013 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2104979 tptp.nat) (BOUND_VARIABLE_2104980 tptp.nat) (BOUND_VARIABLE_2104981 tptp.int) (BOUND_VARIABLE_2104982 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15480 BOUND_VARIABLE_2104982) BOUND_VARIABLE_2104981)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15481 BOUND_VARIABLE_2104977) BOUND_VARIABLE_2245013) BOUND_VARIABLE_2104979) BOUND_VARIABLE_2104980))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16306 BOUND_VARIABLE_2104977) BOUND_VARIABLE_2245013) BOUND_VARIABLE_2104979) BOUND_VARIABLE_2104980) BOUND_VARIABLE_2104981) BOUND_VARIABLE_2104982))))) (let ((_let_3005 (forall ((BOUND_VARIABLE_2104949 tptp.int) (BOUND_VARIABLE_2104950 tptp.int) (BOUND_VARIABLE_2104951 tptp.int) (BOUND_VARIABLE_2104952 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2104949) BOUND_VARIABLE_2104951))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2104950) BOUND_VARIABLE_2104952))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16307 BOUND_VARIABLE_2104949) BOUND_VARIABLE_2104950) BOUND_VARIABLE_2104951) BOUND_VARIABLE_2104952))))))) (let ((_let_3006 (forall ((BOUND_VARIABLE_2245117 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2245114 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2104857 tptp.nat) (BOUND_VARIABLE_2104858 tptp.nat) (BOUND_VARIABLE_2104859 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2104859))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2104859))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2104857)) (ho_15161 k_15160 BOUND_VARIABLE_2104858))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16308 BOUND_VARIABLE_2245117) BOUND_VARIABLE_2245114) BOUND_VARIABLE_2104857) BOUND_VARIABLE_2104858) BOUND_VARIABLE_2104859) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2245117 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2245114 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3007 (forall ((BOUND_VARIABLE_2245192 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2245189 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2104763 tptp.nat) (BOUND_VARIABLE_2104764 tptp.nat) (BOUND_VARIABLE_2104765 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2104765))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2104765))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2104763)) (ho_15161 k_15160 BOUND_VARIABLE_2104764))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16309 BOUND_VARIABLE_2245192) BOUND_VARIABLE_2245189) BOUND_VARIABLE_2104763) BOUND_VARIABLE_2104764) BOUND_VARIABLE_2104765) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2245192 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2245189 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3008 (forall ((BOUND_VARIABLE_2245213 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2245212 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2104677 tptp.nat) (BOUND_VARIABLE_2104678 tptp.nat) (BOUND_VARIABLE_2104679 tptp.int) (BOUND_VARIABLE_2104680 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15482 BOUND_VARIABLE_2104680) BOUND_VARIABLE_2104679)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15483 BOUND_VARIABLE_2245213) BOUND_VARIABLE_2245212) BOUND_VARIABLE_2104677) BOUND_VARIABLE_2104678))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 k_16310 BOUND_VARIABLE_2245213) BOUND_VARIABLE_2245212) BOUND_VARIABLE_2104677) BOUND_VARIABLE_2104678) BOUND_VARIABLE_2104679) BOUND_VARIABLE_2104680))))) (let ((_let_3009 (forall ((BOUND_VARIABLE_2104647 tptp.int) (BOUND_VARIABLE_2104648 tptp.int) (BOUND_VARIABLE_2104649 tptp.int) (BOUND_VARIABLE_2104650 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2104647) BOUND_VARIABLE_2104649))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2104648) BOUND_VARIABLE_2104650))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16311 BOUND_VARIABLE_2104647) BOUND_VARIABLE_2104648) BOUND_VARIABLE_2104649) BOUND_VARIABLE_2104650))))))) (let ((_let_3010 (forall ((BOUND_VARIABLE_2245314 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2104561 tptp.nat) (BOUND_VARIABLE_2104562 tptp.nat) (BOUND_VARIABLE_2104563 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2104563))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2104563))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16312 BOUND_VARIABLE_2245314) BOUND_VARIABLE_2104561) BOUND_VARIABLE_2104562) BOUND_VARIABLE_2104563) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2245314 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2104561)) (ho_15161 k_15160 BOUND_VARIABLE_2104562))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3011 (forall ((BOUND_VARIABLE_2245382 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2104474 tptp.nat) (BOUND_VARIABLE_2104475 tptp.nat) (BOUND_VARIABLE_2104476 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2104476))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2104476))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16313 BOUND_VARIABLE_2245382) BOUND_VARIABLE_2104474) BOUND_VARIABLE_2104475) BOUND_VARIABLE_2104476) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2245382 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2104474)) (ho_15161 k_15160 BOUND_VARIABLE_2104475))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3012 (forall ((BOUND_VARIABLE_2245398 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2104399 tptp.nat) (BOUND_VARIABLE_2104400 tptp.nat) (BOUND_VARIABLE_2104401 tptp.int) (BOUND_VARIABLE_2104402 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15484 BOUND_VARIABLE_2104402) BOUND_VARIABLE_2104401)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15485 BOUND_VARIABLE_2245398) BOUND_VARIABLE_2104399) BOUND_VARIABLE_2104400))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16314 BOUND_VARIABLE_2245398) BOUND_VARIABLE_2104399) BOUND_VARIABLE_2104400) BOUND_VARIABLE_2104401) BOUND_VARIABLE_2104402))))) (let ((_let_3013 (forall ((BOUND_VARIABLE_2104370 tptp.int) (BOUND_VARIABLE_2104371 tptp.int) (BOUND_VARIABLE_2104372 tptp.int) (BOUND_VARIABLE_2104373 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2104370) BOUND_VARIABLE_2104372))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2104371) BOUND_VARIABLE_2104373))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16315 BOUND_VARIABLE_2104370) BOUND_VARIABLE_2104371) BOUND_VARIABLE_2104372) BOUND_VARIABLE_2104373))))))) (let ((_let_3014 (forall ((BOUND_VARIABLE_2245496 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2104284 tptp.nat) (BOUND_VARIABLE_2104285 tptp.nat) (BOUND_VARIABLE_2104286 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2104286))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2104286))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16316 BOUND_VARIABLE_2245496) BOUND_VARIABLE_2104284) BOUND_VARIABLE_2104285) BOUND_VARIABLE_2104286) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2245496 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2104284)) (ho_15161 k_15160 BOUND_VARIABLE_2104285))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3015 (forall ((BOUND_VARIABLE_2245564 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2104197 tptp.nat) (BOUND_VARIABLE_2104198 tptp.nat) (BOUND_VARIABLE_2104199 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2104199))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2104199))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16317 BOUND_VARIABLE_2245564) BOUND_VARIABLE_2104197) BOUND_VARIABLE_2104198) BOUND_VARIABLE_2104199) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2245564 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2104197)) (ho_15161 k_15160 BOUND_VARIABLE_2104198))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3016 (forall ((BOUND_VARIABLE_2245580 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2104122 tptp.nat) (BOUND_VARIABLE_2104123 tptp.nat) (BOUND_VARIABLE_2104124 tptp.int) (BOUND_VARIABLE_2104125 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15486 BOUND_VARIABLE_2104125) BOUND_VARIABLE_2104124)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15487 BOUND_VARIABLE_2245580) BOUND_VARIABLE_2104122) BOUND_VARIABLE_2104123))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16318 BOUND_VARIABLE_2245580) BOUND_VARIABLE_2104122) BOUND_VARIABLE_2104123) BOUND_VARIABLE_2104124) BOUND_VARIABLE_2104125))))) (let ((_let_3017 (forall ((BOUND_VARIABLE_2104093 tptp.int) (BOUND_VARIABLE_2104094 tptp.int) (BOUND_VARIABLE_2104095 tptp.int) (BOUND_VARIABLE_2104096 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2104093) BOUND_VARIABLE_2104095))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2104094) BOUND_VARIABLE_2104096))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16319 BOUND_VARIABLE_2104093) BOUND_VARIABLE_2104094) BOUND_VARIABLE_2104095) BOUND_VARIABLE_2104096))))))) (let ((_let_3018 (forall ((BOUND_VARIABLE_2245682 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2245678 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2103999 tptp.nat) (BOUND_VARIABLE_2104000 tptp.nat) (BOUND_VARIABLE_2104001 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2104001))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2104001))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2103999)) (ho_15161 k_15160 BOUND_VARIABLE_2104000))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16320 BOUND_VARIABLE_2245682) BOUND_VARIABLE_2245678) BOUND_VARIABLE_2103999) BOUND_VARIABLE_2104000) BOUND_VARIABLE_2104001) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2245682 _let_9))) (ho_15122 k_15121 (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2245678 _let_9))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3019 (forall ((BOUND_VARIABLE_2245759 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2245755 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2103903 tptp.nat) (BOUND_VARIABLE_2103904 tptp.nat) (BOUND_VARIABLE_2103905 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2103905))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2103905))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2103903)) (ho_15161 k_15160 BOUND_VARIABLE_2103904))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16321 BOUND_VARIABLE_2245759) BOUND_VARIABLE_2245755) BOUND_VARIABLE_2103903) BOUND_VARIABLE_2103904) BOUND_VARIABLE_2103905) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2245759 _let_9))) (ho_15122 k_15121 (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2245755 _let_9))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3020 (forall ((BOUND_VARIABLE_2245781 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2245780 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2103813 tptp.nat) (BOUND_VARIABLE_2103814 tptp.nat) (BOUND_VARIABLE_2103815 tptp.int) (BOUND_VARIABLE_2103816 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15488 BOUND_VARIABLE_2103816) BOUND_VARIABLE_2103815)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15489 BOUND_VARIABLE_2245781) BOUND_VARIABLE_2245780) BOUND_VARIABLE_2103813) BOUND_VARIABLE_2103814))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 k_16322 BOUND_VARIABLE_2245781) BOUND_VARIABLE_2245780) BOUND_VARIABLE_2103813) BOUND_VARIABLE_2103814) BOUND_VARIABLE_2103815) BOUND_VARIABLE_2103816))))) (let ((_let_3021 (forall ((BOUND_VARIABLE_2103783 tptp.int) (BOUND_VARIABLE_2103784 tptp.int) (BOUND_VARIABLE_2103785 tptp.int) (BOUND_VARIABLE_2103786 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2103783) BOUND_VARIABLE_2103785))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2103784) BOUND_VARIABLE_2103786))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16323 BOUND_VARIABLE_2103783) BOUND_VARIABLE_2103784) BOUND_VARIABLE_2103785) BOUND_VARIABLE_2103786))))))) (let ((_let_3022 (forall ((BOUND_VARIABLE_2103686 tptp.nat) (BOUND_VARIABLE_2245882 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2103688 tptp.nat) (BOUND_VARIABLE_2103689 tptp.nat) (BOUND_VARIABLE_2103690 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2103690))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2103690))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2103688)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16324 BOUND_VARIABLE_2103686) BOUND_VARIABLE_2245882) BOUND_VARIABLE_2103688) BOUND_VARIABLE_2103689) BOUND_VARIABLE_2103690) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2245882 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2103686))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2245882 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2103689))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3023 (forall ((BOUND_VARIABLE_2103589 tptp.nat) (BOUND_VARIABLE_2245959 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2103591 tptp.nat) (BOUND_VARIABLE_2103592 tptp.nat) (BOUND_VARIABLE_2103593 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2103593))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2103593))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2103591)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16325 BOUND_VARIABLE_2103589) BOUND_VARIABLE_2245959) BOUND_VARIABLE_2103591) BOUND_VARIABLE_2103592) BOUND_VARIABLE_2103593) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2245959 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2103589))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2245959 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2103592))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3024 (forall ((BOUND_VARIABLE_2103497 tptp.nat) (BOUND_VARIABLE_2245984 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2103499 tptp.nat) (BOUND_VARIABLE_2103500 tptp.nat) (BOUND_VARIABLE_2103501 tptp.int) (BOUND_VARIABLE_2103502 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15490 BOUND_VARIABLE_2103502) BOUND_VARIABLE_2103501)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15491 BOUND_VARIABLE_2103497) BOUND_VARIABLE_2245984) BOUND_VARIABLE_2103499) BOUND_VARIABLE_2103500))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16326 BOUND_VARIABLE_2103497) BOUND_VARIABLE_2245984) BOUND_VARIABLE_2103499) BOUND_VARIABLE_2103500) BOUND_VARIABLE_2103501) BOUND_VARIABLE_2103502))))) (let ((_let_3025 (forall ((BOUND_VARIABLE_2103469 tptp.int) (BOUND_VARIABLE_2103470 tptp.int) (BOUND_VARIABLE_2103471 tptp.int) (BOUND_VARIABLE_2103472 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2103469) BOUND_VARIABLE_2103471))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2103470) BOUND_VARIABLE_2103472))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16327 BOUND_VARIABLE_2103469) BOUND_VARIABLE_2103470) BOUND_VARIABLE_2103471) BOUND_VARIABLE_2103472))))))) (let ((_let_3026 (forall ((BOUND_VARIABLE_2103441 tptp.int) (BOUND_VARIABLE_2103442 tptp.int) (BOUND_VARIABLE_2103443 tptp.int) (BOUND_VARIABLE_2103444 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2103441) BOUND_VARIABLE_2103443))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2103442) BOUND_VARIABLE_2103444))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16328 BOUND_VARIABLE_2103441) BOUND_VARIABLE_2103442) BOUND_VARIABLE_2103443) BOUND_VARIABLE_2103444))))))) (let ((_let_3027 (forall ((BOUND_VARIABLE_2246103 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2103361 tptp.nat) (BOUND_VARIABLE_2103362 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2103362))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2103362))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15495 k_16329 BOUND_VARIABLE_2246103) BOUND_VARIABLE_2103361) BOUND_VARIABLE_2103362) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2246103 BOUND_VARIABLE_2103361)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3028 (forall ((BOUND_VARIABLE_2103316 tptp.int) (BOUND_VARIABLE_2103317 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15492 BOUND_VARIABLE_2103317) BOUND_VARIABLE_2103316)) (ho_15260 k_15259 k_16330)) (ho_15108 (ho_15107 k_16331 BOUND_VARIABLE_2103316) BOUND_VARIABLE_2103317))))) (let ((_let_3029 (forall ((BOUND_VARIABLE_2246177 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2103236 tptp.nat) (BOUND_VARIABLE_2103237 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2103237))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2103237))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15495 k_16332 BOUND_VARIABLE_2246177) BOUND_VARIABLE_2103236) BOUND_VARIABLE_2103237) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2246177 BOUND_VARIABLE_2103236)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3030 (forall ((BOUND_VARIABLE_2246191 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2103174 tptp.nat) (BOUND_VARIABLE_2103175 tptp.int) (BOUND_VARIABLE_2103176 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15493 BOUND_VARIABLE_2103176) BOUND_VARIABLE_2103175)) (ho_15260 k_15259 (ho_15165 (ho_15495 k_15494 BOUND_VARIABLE_2246191) BOUND_VARIABLE_2103174))) (ho_15108 (ho_15107 (ho_15345 (ho_16334 k_16333 BOUND_VARIABLE_2246191) BOUND_VARIABLE_2103174) BOUND_VARIABLE_2103175) BOUND_VARIABLE_2103176))))) (let ((_let_3031 (forall ((BOUND_VARIABLE_2103145 tptp.int) (BOUND_VARIABLE_2103146 tptp.int) (BOUND_VARIABLE_2103147 tptp.int) (BOUND_VARIABLE_2103148 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2103145) BOUND_VARIABLE_2103147))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2103146) BOUND_VARIABLE_2103148))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16335 BOUND_VARIABLE_2103145) BOUND_VARIABLE_2103146) BOUND_VARIABLE_2103147) BOUND_VARIABLE_2103148))))))) (let ((_let_3032 (forall ((BOUND_VARIABLE_2103048 tptp.nat) (BOUND_VARIABLE_2246290 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2103050 tptp.nat) (BOUND_VARIABLE_2103051 tptp.nat) (BOUND_VARIABLE_2103052 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2103052))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2103052))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2103050)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16336 BOUND_VARIABLE_2103048) BOUND_VARIABLE_2246290) BOUND_VARIABLE_2103050) BOUND_VARIABLE_2103051) BOUND_VARIABLE_2103052) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2246290 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2103048))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2246290 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2103051))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3033 (forall ((BOUND_VARIABLE_2102951 tptp.nat) (BOUND_VARIABLE_2246367 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2102953 tptp.nat) (BOUND_VARIABLE_2102954 tptp.nat) (BOUND_VARIABLE_2102955 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2102955))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2102955))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2102953)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16337 BOUND_VARIABLE_2102951) BOUND_VARIABLE_2246367) BOUND_VARIABLE_2102953) BOUND_VARIABLE_2102954) BOUND_VARIABLE_2102955) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2246367 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102951))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2246367 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102954))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3034 (forall ((BOUND_VARIABLE_2102859 tptp.nat) (BOUND_VARIABLE_2246392 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2102861 tptp.nat) (BOUND_VARIABLE_2102862 tptp.nat) (BOUND_VARIABLE_2102863 tptp.int) (BOUND_VARIABLE_2102864 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15496 BOUND_VARIABLE_2102864) BOUND_VARIABLE_2102863)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15497 BOUND_VARIABLE_2102859) BOUND_VARIABLE_2246392) BOUND_VARIABLE_2102861) BOUND_VARIABLE_2102862))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16338 BOUND_VARIABLE_2102859) BOUND_VARIABLE_2246392) BOUND_VARIABLE_2102861) BOUND_VARIABLE_2102862) BOUND_VARIABLE_2102863) BOUND_VARIABLE_2102864))))) (let ((_let_3035 (forall ((BOUND_VARIABLE_2102831 tptp.int) (BOUND_VARIABLE_2102832 tptp.int) (BOUND_VARIABLE_2102833 tptp.int) (BOUND_VARIABLE_2102834 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2102831) BOUND_VARIABLE_2102833))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2102832) BOUND_VARIABLE_2102834))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16339 BOUND_VARIABLE_2102831) BOUND_VARIABLE_2102832) BOUND_VARIABLE_2102833) BOUND_VARIABLE_2102834))))))) (let ((_let_3036 (forall ((BOUND_VARIABLE_2102734 tptp.nat) (BOUND_VARIABLE_2246493 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2102736 tptp.nat) (BOUND_VARIABLE_2102737 tptp.nat) (BOUND_VARIABLE_2102738 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2102738))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2102738))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2102736)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16340 BOUND_VARIABLE_2102734) BOUND_VARIABLE_2246493) BOUND_VARIABLE_2102736) BOUND_VARIABLE_2102737) BOUND_VARIABLE_2102738) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2246493 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102734))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2246493 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102737))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3037 (forall ((BOUND_VARIABLE_2102637 tptp.nat) (BOUND_VARIABLE_2246570 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2102639 tptp.nat) (BOUND_VARIABLE_2102640 tptp.nat) (BOUND_VARIABLE_2102641 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2102641))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2102641))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2102639)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16341 BOUND_VARIABLE_2102637) BOUND_VARIABLE_2246570) BOUND_VARIABLE_2102639) BOUND_VARIABLE_2102640) BOUND_VARIABLE_2102641) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2246570 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102637))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2246570 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102640))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3038 (forall ((BOUND_VARIABLE_2102545 tptp.nat) (BOUND_VARIABLE_2246595 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2102547 tptp.nat) (BOUND_VARIABLE_2102548 tptp.nat) (BOUND_VARIABLE_2102549 tptp.int) (BOUND_VARIABLE_2102550 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15498 BOUND_VARIABLE_2102550) BOUND_VARIABLE_2102549)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15499 BOUND_VARIABLE_2102545) BOUND_VARIABLE_2246595) BOUND_VARIABLE_2102547) BOUND_VARIABLE_2102548))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16342 BOUND_VARIABLE_2102545) BOUND_VARIABLE_2246595) BOUND_VARIABLE_2102547) BOUND_VARIABLE_2102548) BOUND_VARIABLE_2102549) BOUND_VARIABLE_2102550))))) (let ((_let_3039 (forall ((BOUND_VARIABLE_2102517 tptp.int) (BOUND_VARIABLE_2102518 tptp.int) (BOUND_VARIABLE_2102519 tptp.int) (BOUND_VARIABLE_2102520 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2102517) BOUND_VARIABLE_2102519))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2102518) BOUND_VARIABLE_2102520))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16343 BOUND_VARIABLE_2102517) BOUND_VARIABLE_2102518) BOUND_VARIABLE_2102519) BOUND_VARIABLE_2102520))))))) (let ((_let_3040 (forall ((BOUND_VARIABLE_2102408 tptp.nat) (BOUND_VARIABLE_2246698 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2246696 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2102411 tptp.nat) (BOUND_VARIABLE_2102412 tptp.nat) (BOUND_VARIABLE_2102413 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2102413))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2102413))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2102411)))) (let ((_let_10 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102412))))) (let ((_let_11 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_12 (ho_15139 _let_11 k_15153))) (let ((_let_13 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102408))))) (let ((_let_14 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_16344 BOUND_VARIABLE_2102408) BOUND_VARIABLE_2246698) BOUND_VARIABLE_2246696) BOUND_VARIABLE_2102411) BOUND_VARIABLE_2102412) BOUND_VARIABLE_2102413) (and (= (ho_15122 (ho_15125 (ho_15139 _let_11 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_12 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2246698 _let_13)) (ho_15120 BOUND_VARIABLE_2246696 _let_13))) (ho_15122 k_15121 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2246698 _let_10)) (ho_15120 BOUND_VARIABLE_2246696 _let_10))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))))) (let ((_let_3041 (forall ((BOUND_VARIABLE_2102299 tptp.nat) (BOUND_VARIABLE_2246784 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2246782 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2102302 tptp.nat) (BOUND_VARIABLE_2102303 tptp.nat) (BOUND_VARIABLE_2102304 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2102304))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2102304))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2102302)))) (let ((_let_10 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102303))))) (let ((_let_11 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_12 (ho_15139 _let_11 k_15153))) (let ((_let_13 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102299))))) (let ((_let_14 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_16345 BOUND_VARIABLE_2102299) BOUND_VARIABLE_2246784) BOUND_VARIABLE_2246782) BOUND_VARIABLE_2102302) BOUND_VARIABLE_2102303) BOUND_VARIABLE_2102304) (and (= (ho_15122 (ho_15125 (ho_15139 _let_11 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_12 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2246784 _let_13)) (ho_15120 BOUND_VARIABLE_2246782 _let_13))) (ho_15122 k_15121 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2246784 _let_10)) (ho_15120 BOUND_VARIABLE_2246782 _let_10))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))))) (let ((_let_3042 (forall ((BOUND_VARIABLE_2102192 tptp.nat) (BOUND_VARIABLE_2246817 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2246816 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2102195 tptp.nat) (BOUND_VARIABLE_2102196 tptp.nat) (BOUND_VARIABLE_2102197 tptp.int) (BOUND_VARIABLE_2102198 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15500 BOUND_VARIABLE_2102198) BOUND_VARIABLE_2102197)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_15501 BOUND_VARIABLE_2102192) BOUND_VARIABLE_2246817) BOUND_VARIABLE_2246816) BOUND_VARIABLE_2102195) BOUND_VARIABLE_2102196))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 (ho_16347 k_16346 BOUND_VARIABLE_2102192) BOUND_VARIABLE_2246817) BOUND_VARIABLE_2246816) BOUND_VARIABLE_2102195) BOUND_VARIABLE_2102196) BOUND_VARIABLE_2102197) BOUND_VARIABLE_2102198))))) (let ((_let_3043 (forall ((BOUND_VARIABLE_2102164 tptp.int) (BOUND_VARIABLE_2102165 tptp.int) (BOUND_VARIABLE_2102166 tptp.int) (BOUND_VARIABLE_2102167 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2102164) BOUND_VARIABLE_2102166))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2102165) BOUND_VARIABLE_2102167))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16348 BOUND_VARIABLE_2102164) BOUND_VARIABLE_2102165) BOUND_VARIABLE_2102166) BOUND_VARIABLE_2102167))))))) (let ((_let_3044 (forall ((BOUND_VARIABLE_2102067 tptp.nat) (BOUND_VARIABLE_2246925 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2102069 tptp.nat) (BOUND_VARIABLE_2102070 tptp.nat) (BOUND_VARIABLE_2102071 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2102071))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2102071))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2102069)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16349 BOUND_VARIABLE_2102067) BOUND_VARIABLE_2246925) BOUND_VARIABLE_2102069) BOUND_VARIABLE_2102070) BOUND_VARIABLE_2102071) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2246925 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102067))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2246925 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2102070))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3045 (forall ((BOUND_VARIABLE_2101970 tptp.nat) (BOUND_VARIABLE_2247002 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2101972 tptp.nat) (BOUND_VARIABLE_2101973 tptp.nat) (BOUND_VARIABLE_2101974 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2101974))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2101974))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2101972)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16350 BOUND_VARIABLE_2101970) BOUND_VARIABLE_2247002) BOUND_VARIABLE_2101972) BOUND_VARIABLE_2101973) BOUND_VARIABLE_2101974) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2247002 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2101970))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2247002 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2101973))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3046 (forall ((BOUND_VARIABLE_2101878 tptp.nat) (BOUND_VARIABLE_2247027 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2101880 tptp.nat) (BOUND_VARIABLE_2101881 tptp.nat) (BOUND_VARIABLE_2101882 tptp.int) (BOUND_VARIABLE_2101883 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15503 BOUND_VARIABLE_2101883) BOUND_VARIABLE_2101882)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15504 BOUND_VARIABLE_2101878) BOUND_VARIABLE_2247027) BOUND_VARIABLE_2101880) BOUND_VARIABLE_2101881))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16351 BOUND_VARIABLE_2101878) BOUND_VARIABLE_2247027) BOUND_VARIABLE_2101880) BOUND_VARIABLE_2101881) BOUND_VARIABLE_2101882) BOUND_VARIABLE_2101883))))) (let ((_let_3047 (forall ((BOUND_VARIABLE_2101850 tptp.int) (BOUND_VARIABLE_2101851 tptp.int) (BOUND_VARIABLE_2101852 tptp.int) (BOUND_VARIABLE_2101853 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2101850) BOUND_VARIABLE_2101852))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2101851) BOUND_VARIABLE_2101853))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16352 BOUND_VARIABLE_2101850) BOUND_VARIABLE_2101851) BOUND_VARIABLE_2101852) BOUND_VARIABLE_2101853))))))) (let ((_let_3048 (forall ((BOUND_VARIABLE_2101751 tptp.nat) (BOUND_VARIABLE_2247128 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2101753 tptp.nat) (BOUND_VARIABLE_2101754 tptp.nat) (BOUND_VARIABLE_2101755 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2101755))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2101755))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2101753)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16353 BOUND_VARIABLE_2101751) BOUND_VARIABLE_2247128) BOUND_VARIABLE_2101753) BOUND_VARIABLE_2101754) BOUND_VARIABLE_2101755) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2247128 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2101751)))))) (ho_15122 k_15121 (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2247128 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2101754)))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3049 (forall ((BOUND_VARIABLE_2101652 tptp.nat) (BOUND_VARIABLE_2247207 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2101654 tptp.nat) (BOUND_VARIABLE_2101655 tptp.nat) (BOUND_VARIABLE_2101656 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2101656))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2101656))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2101654)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16354 BOUND_VARIABLE_2101652) BOUND_VARIABLE_2247207) BOUND_VARIABLE_2101654) BOUND_VARIABLE_2101655) BOUND_VARIABLE_2101656) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2247207 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2101652)))))) (ho_15122 k_15121 (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2247207 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2101655)))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3050 (forall ((BOUND_VARIABLE_2101556 tptp.nat) (BOUND_VARIABLE_2247234 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2101558 tptp.nat) (BOUND_VARIABLE_2101559 tptp.nat) (BOUND_VARIABLE_2101560 tptp.int) (BOUND_VARIABLE_2101561 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15505 BOUND_VARIABLE_2101561) BOUND_VARIABLE_2101560)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15506 BOUND_VARIABLE_2101556) BOUND_VARIABLE_2247234) BOUND_VARIABLE_2101558) BOUND_VARIABLE_2101559))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16355 BOUND_VARIABLE_2101556) BOUND_VARIABLE_2247234) BOUND_VARIABLE_2101558) BOUND_VARIABLE_2101559) BOUND_VARIABLE_2101560) BOUND_VARIABLE_2101561))))) (let ((_let_3051 (forall ((BOUND_VARIABLE_2101528 tptp.int) (BOUND_VARIABLE_2101529 tptp.int) (BOUND_VARIABLE_2101530 tptp.int) (BOUND_VARIABLE_2101531 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2101528) BOUND_VARIABLE_2101530))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2101529) BOUND_VARIABLE_2101531))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16356 BOUND_VARIABLE_2101528) BOUND_VARIABLE_2101529) BOUND_VARIABLE_2101530) BOUND_VARIABLE_2101531))))))) (let ((_let_3052 (forall ((BOUND_VARIABLE_2101444 tptp.rat) (BOUND_VARIABLE_2101445 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2101445))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2101445))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 k_16357 BOUND_VARIABLE_2101444) BOUND_VARIABLE_2101445) (and (= (ho_15122 (ho_15125 (ho_15139 _let_9 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2101444) (ho_15122 k_15121 BOUND_VARIABLE_2101444))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3053 (forall ((BOUND_VARIABLE_2101360 tptp.rat) (BOUND_VARIABLE_2101361 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2101361))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2101361))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 k_16358 BOUND_VARIABLE_2101360) BOUND_VARIABLE_2101361) (and (= (ho_15122 (ho_15125 (ho_15139 _let_9 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2101360) (ho_15122 k_15121 BOUND_VARIABLE_2101360))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3054 (forall ((BOUND_VARIABLE_2101297 tptp.rat) (BOUND_VARIABLE_2101298 tptp.int) (BOUND_VARIABLE_2101299 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15507 BOUND_VARIABLE_2101299) BOUND_VARIABLE_2101298)) (ho_15260 k_15259 (ho_15145 k_15508 BOUND_VARIABLE_2101297))) (ho_15108 (ho_15107 (ho_15266 k_16359 BOUND_VARIABLE_2101297) BOUND_VARIABLE_2101298) BOUND_VARIABLE_2101299))))) (let ((_let_3055 (forall ((BOUND_VARIABLE_2101269 tptp.int) (BOUND_VARIABLE_2101270 tptp.int) (BOUND_VARIABLE_2101271 tptp.int) (BOUND_VARIABLE_2101272 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2101269) BOUND_VARIABLE_2101271))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2101270) BOUND_VARIABLE_2101272))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16360 BOUND_VARIABLE_2101269) BOUND_VARIABLE_2101270) BOUND_VARIABLE_2101271) BOUND_VARIABLE_2101272))))))) (let ((_let_3056 (forall ((BOUND_VARIABLE_2101172 tptp.nat) (BOUND_VARIABLE_2247491 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2101174 tptp.nat) (BOUND_VARIABLE_2101175 tptp.nat) (BOUND_VARIABLE_2101176 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2101176))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2101176))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2101174)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16361 BOUND_VARIABLE_2101172) BOUND_VARIABLE_2247491) BOUND_VARIABLE_2101174) BOUND_VARIABLE_2101175) BOUND_VARIABLE_2101176) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2247491 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2101172))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2247491 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2101175))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3057 (forall ((BOUND_VARIABLE_2101075 tptp.nat) (BOUND_VARIABLE_2247568 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2101077 tptp.nat) (BOUND_VARIABLE_2101078 tptp.nat) (BOUND_VARIABLE_2101079 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2101079))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2101079))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2101077)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16362 BOUND_VARIABLE_2101075) BOUND_VARIABLE_2247568) BOUND_VARIABLE_2101077) BOUND_VARIABLE_2101078) BOUND_VARIABLE_2101079) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2247568 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2101075))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2247568 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2101078))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3058 (forall ((BOUND_VARIABLE_2100983 tptp.nat) (BOUND_VARIABLE_2247593 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2100985 tptp.nat) (BOUND_VARIABLE_2100986 tptp.nat) (BOUND_VARIABLE_2100987 tptp.int) (BOUND_VARIABLE_2100988 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15509 BOUND_VARIABLE_2100988) BOUND_VARIABLE_2100987)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15510 BOUND_VARIABLE_2100983) BOUND_VARIABLE_2247593) BOUND_VARIABLE_2100985) BOUND_VARIABLE_2100986))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16363 BOUND_VARIABLE_2100983) BOUND_VARIABLE_2247593) BOUND_VARIABLE_2100985) BOUND_VARIABLE_2100986) BOUND_VARIABLE_2100987) BOUND_VARIABLE_2100988))))) (let ((_let_3059 (forall ((BOUND_VARIABLE_2100955 tptp.int) (BOUND_VARIABLE_2100956 tptp.int) (BOUND_VARIABLE_2100957 tptp.int) (BOUND_VARIABLE_2100958 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2100955) BOUND_VARIABLE_2100957))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2100956) BOUND_VARIABLE_2100958))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16364 BOUND_VARIABLE_2100955) BOUND_VARIABLE_2100956) BOUND_VARIABLE_2100957) BOUND_VARIABLE_2100958))))))) (let ((_let_3060 (forall ((BOUND_VARIABLE_2100858 tptp.nat) (BOUND_VARIABLE_2247694 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2100860 tptp.nat) (BOUND_VARIABLE_2100861 tptp.nat) (BOUND_VARIABLE_2100862 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2100862))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2100862))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2100860)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16365 BOUND_VARIABLE_2100858) BOUND_VARIABLE_2247694) BOUND_VARIABLE_2100860) BOUND_VARIABLE_2100861) BOUND_VARIABLE_2100862) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2247694 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100858))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2247694 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100861))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3061 (forall ((BOUND_VARIABLE_2100761 tptp.nat) (BOUND_VARIABLE_2247771 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2100763 tptp.nat) (BOUND_VARIABLE_2100764 tptp.nat) (BOUND_VARIABLE_2100765 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2100765))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2100765))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2100763)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16366 BOUND_VARIABLE_2100761) BOUND_VARIABLE_2247771) BOUND_VARIABLE_2100763) BOUND_VARIABLE_2100764) BOUND_VARIABLE_2100765) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2247771 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100761))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2247771 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100764))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3062 (forall ((BOUND_VARIABLE_2100669 tptp.nat) (BOUND_VARIABLE_2247796 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2100671 tptp.nat) (BOUND_VARIABLE_2100672 tptp.nat) (BOUND_VARIABLE_2100673 tptp.int) (BOUND_VARIABLE_2100674 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15511 BOUND_VARIABLE_2100674) BOUND_VARIABLE_2100673)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15512 BOUND_VARIABLE_2100669) BOUND_VARIABLE_2247796) BOUND_VARIABLE_2100671) BOUND_VARIABLE_2100672))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16367 BOUND_VARIABLE_2100669) BOUND_VARIABLE_2247796) BOUND_VARIABLE_2100671) BOUND_VARIABLE_2100672) BOUND_VARIABLE_2100673) BOUND_VARIABLE_2100674))))) (let ((_let_3063 (forall ((BOUND_VARIABLE_2100641 tptp.int) (BOUND_VARIABLE_2100642 tptp.int) (BOUND_VARIABLE_2100643 tptp.int) (BOUND_VARIABLE_2100644 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2100641) BOUND_VARIABLE_2100643))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2100642) BOUND_VARIABLE_2100644))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16368 BOUND_VARIABLE_2100641) BOUND_VARIABLE_2100642) BOUND_VARIABLE_2100643) BOUND_VARIABLE_2100644))))))) (let ((_let_3064 (forall ((BOUND_VARIABLE_2100532 tptp.nat) (BOUND_VARIABLE_2247899 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2247897 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2100535 tptp.nat) (BOUND_VARIABLE_2100536 tptp.nat) (BOUND_VARIABLE_2100537 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2100537))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2100537))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2100535)))) (let ((_let_10 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100536))))) (let ((_let_11 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_12 (ho_15139 _let_11 k_15127))) (let ((_let_13 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100532))))) (let ((_let_14 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_16369 BOUND_VARIABLE_2100532) BOUND_VARIABLE_2247899) BOUND_VARIABLE_2247897) BOUND_VARIABLE_2100535) BOUND_VARIABLE_2100536) BOUND_VARIABLE_2100537) (and (= (ho_15122 (ho_15125 _let_12 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_11 k_15153) (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2247899 _let_13)) (ho_15120 BOUND_VARIABLE_2247897 _let_13))) (ho_15122 k_15121 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2247899 _let_10)) (ho_15120 BOUND_VARIABLE_2247897 _let_10))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))))) (let ((_let_3065 (forall ((BOUND_VARIABLE_2100423 tptp.nat) (BOUND_VARIABLE_2247985 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2247983 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2100426 tptp.nat) (BOUND_VARIABLE_2100427 tptp.nat) (BOUND_VARIABLE_2100428 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2100428))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2100428))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2100426)))) (let ((_let_10 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100427))))) (let ((_let_11 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_12 (ho_15139 _let_11 k_15127))) (let ((_let_13 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100423))))) (let ((_let_14 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_16370 BOUND_VARIABLE_2100423) BOUND_VARIABLE_2247985) BOUND_VARIABLE_2247983) BOUND_VARIABLE_2100426) BOUND_VARIABLE_2100427) BOUND_VARIABLE_2100428) (and (= (ho_15122 (ho_15125 _let_12 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_11 k_15153) (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2247985 _let_13)) (ho_15120 BOUND_VARIABLE_2247983 _let_13))) (ho_15122 k_15121 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2247985 _let_10)) (ho_15120 BOUND_VARIABLE_2247983 _let_10))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))))) (let ((_let_3066 (forall ((BOUND_VARIABLE_2100316 tptp.nat) (BOUND_VARIABLE_2248018 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2248017 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2100319 tptp.nat) (BOUND_VARIABLE_2100320 tptp.nat) (BOUND_VARIABLE_2100321 tptp.int) (BOUND_VARIABLE_2100322 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15513 BOUND_VARIABLE_2100322) BOUND_VARIABLE_2100321)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_15514 BOUND_VARIABLE_2100316) BOUND_VARIABLE_2248018) BOUND_VARIABLE_2248017) BOUND_VARIABLE_2100319) BOUND_VARIABLE_2100320))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 (ho_16347 k_16371 BOUND_VARIABLE_2100316) BOUND_VARIABLE_2248018) BOUND_VARIABLE_2248017) BOUND_VARIABLE_2100319) BOUND_VARIABLE_2100320) BOUND_VARIABLE_2100321) BOUND_VARIABLE_2100322))))) (let ((_let_3067 (forall ((BOUND_VARIABLE_2100288 tptp.int) (BOUND_VARIABLE_2100289 tptp.int) (BOUND_VARIABLE_2100290 tptp.int) (BOUND_VARIABLE_2100291 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2100288) BOUND_VARIABLE_2100290))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2100289) BOUND_VARIABLE_2100291))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16372 BOUND_VARIABLE_2100288) BOUND_VARIABLE_2100289) BOUND_VARIABLE_2100290) BOUND_VARIABLE_2100291))))))) (let ((_let_3068 (forall ((BOUND_VARIABLE_2100191 tptp.nat) (BOUND_VARIABLE_2248122 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2100193 tptp.nat) (BOUND_VARIABLE_2100194 tptp.nat) (BOUND_VARIABLE_2100195 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2100195))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2100195))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2100193)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16373 BOUND_VARIABLE_2100191) BOUND_VARIABLE_2248122) BOUND_VARIABLE_2100193) BOUND_VARIABLE_2100194) BOUND_VARIABLE_2100195) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2248122 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100191))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2248122 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100194))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3069 (forall ((BOUND_VARIABLE_2100094 tptp.nat) (BOUND_VARIABLE_2248199 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2100096 tptp.nat) (BOUND_VARIABLE_2100097 tptp.nat) (BOUND_VARIABLE_2100098 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2100098))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2100098))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2100096)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16374 BOUND_VARIABLE_2100094) BOUND_VARIABLE_2248199) BOUND_VARIABLE_2100096) BOUND_VARIABLE_2100097) BOUND_VARIABLE_2100098) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2248199 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100094))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2248199 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2100097))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3070 (forall ((BOUND_VARIABLE_2100002 tptp.nat) (BOUND_VARIABLE_2248224 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2100004 tptp.nat) (BOUND_VARIABLE_2100005 tptp.nat) (BOUND_VARIABLE_2100006 tptp.int) (BOUND_VARIABLE_2100007 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15515 BOUND_VARIABLE_2100007) BOUND_VARIABLE_2100006)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15516 BOUND_VARIABLE_2100002) BOUND_VARIABLE_2248224) BOUND_VARIABLE_2100004) BOUND_VARIABLE_2100005))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16375 BOUND_VARIABLE_2100002) BOUND_VARIABLE_2248224) BOUND_VARIABLE_2100004) BOUND_VARIABLE_2100005) BOUND_VARIABLE_2100006) BOUND_VARIABLE_2100007))))) (let ((_let_3071 (forall ((BOUND_VARIABLE_2099974 tptp.int) (BOUND_VARIABLE_2099975 tptp.int) (BOUND_VARIABLE_2099976 tptp.int) (BOUND_VARIABLE_2099977 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2099974) BOUND_VARIABLE_2099976))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2099975) BOUND_VARIABLE_2099977))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16376 BOUND_VARIABLE_2099974) BOUND_VARIABLE_2099975) BOUND_VARIABLE_2099976) BOUND_VARIABLE_2099977))))))) (let ((_let_3072 (forall ((BOUND_VARIABLE_2099877 tptp.nat) (BOUND_VARIABLE_2248325 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2099879 tptp.nat) (BOUND_VARIABLE_2099880 tptp.nat) (BOUND_VARIABLE_2099881 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2099881))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2099881))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2099879)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16377 BOUND_VARIABLE_2099877) BOUND_VARIABLE_2248325) BOUND_VARIABLE_2099879) BOUND_VARIABLE_2099880) BOUND_VARIABLE_2099881) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2248325 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099877))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2248325 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099880))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3073 (forall ((BOUND_VARIABLE_2099780 tptp.nat) (BOUND_VARIABLE_2248402 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2099782 tptp.nat) (BOUND_VARIABLE_2099783 tptp.nat) (BOUND_VARIABLE_2099784 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2099784))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2099784))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2099782)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16378 BOUND_VARIABLE_2099780) BOUND_VARIABLE_2248402) BOUND_VARIABLE_2099782) BOUND_VARIABLE_2099783) BOUND_VARIABLE_2099784) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2248402 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099780))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2248402 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099783))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3074 (forall ((BOUND_VARIABLE_2099688 tptp.nat) (BOUND_VARIABLE_2248427 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2099690 tptp.nat) (BOUND_VARIABLE_2099691 tptp.nat) (BOUND_VARIABLE_2099692 tptp.int) (BOUND_VARIABLE_2099693 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15517 BOUND_VARIABLE_2099693) BOUND_VARIABLE_2099692)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15518 BOUND_VARIABLE_2099688) BOUND_VARIABLE_2248427) BOUND_VARIABLE_2099690) BOUND_VARIABLE_2099691))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16379 BOUND_VARIABLE_2099688) BOUND_VARIABLE_2248427) BOUND_VARIABLE_2099690) BOUND_VARIABLE_2099691) BOUND_VARIABLE_2099692) BOUND_VARIABLE_2099693))))) (let ((_let_3075 (forall ((BOUND_VARIABLE_2099660 tptp.int) (BOUND_VARIABLE_2099661 tptp.int) (BOUND_VARIABLE_2099662 tptp.int) (BOUND_VARIABLE_2099663 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2099660) BOUND_VARIABLE_2099662))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2099661) BOUND_VARIABLE_2099663))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16380 BOUND_VARIABLE_2099660) BOUND_VARIABLE_2099661) BOUND_VARIABLE_2099662) BOUND_VARIABLE_2099663))))))) (let ((_let_3076 (forall ((BOUND_VARIABLE_2099549 tptp.nat) (BOUND_VARIABLE_2248531 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2248528 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2099552 tptp.nat) (BOUND_VARIABLE_2099553 tptp.nat) (BOUND_VARIABLE_2099554 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2099554))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2099554))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2099552)))) (let ((_let_10 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099553))))) (let ((_let_11 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_12 (ho_15139 _let_11 k_15153))) (let ((_let_13 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099549))))) (let ((_let_14 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_16381 BOUND_VARIABLE_2099549) BOUND_VARIABLE_2248531) BOUND_VARIABLE_2248528) BOUND_VARIABLE_2099552) BOUND_VARIABLE_2099553) BOUND_VARIABLE_2099554) (and (= (ho_15122 (ho_15125 (ho_15139 _let_11 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_12 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2248531 _let_13)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2248528 _let_13)))) (ho_15122 k_15121 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2248531 _let_10)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2248528 _let_10)))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))))) (let ((_let_3077 (forall ((BOUND_VARIABLE_2099438 tptp.nat) (BOUND_VARIABLE_2248619 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2248616 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2099441 tptp.nat) (BOUND_VARIABLE_2099442 tptp.nat) (BOUND_VARIABLE_2099443 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2099443))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2099443))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2099441)))) (let ((_let_10 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099442))))) (let ((_let_11 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_12 (ho_15139 _let_11 k_15153))) (let ((_let_13 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099438))))) (let ((_let_14 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_16382 BOUND_VARIABLE_2099438) BOUND_VARIABLE_2248619) BOUND_VARIABLE_2248616) BOUND_VARIABLE_2099441) BOUND_VARIABLE_2099442) BOUND_VARIABLE_2099443) (and (= (ho_15122 (ho_15125 (ho_15139 _let_11 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_14 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_12 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2248619 _let_13)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2248616 _let_13)))) (ho_15122 k_15121 (ho_15122 (ho_15125 _let_12 (ho_15120 BOUND_VARIABLE_2248619 _let_10)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2248616 _let_10)))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))))) (let ((_let_3078 (forall ((BOUND_VARIABLE_2099327 tptp.nat) (BOUND_VARIABLE_2248653 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2248652 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2099330 tptp.nat) (BOUND_VARIABLE_2099331 tptp.nat) (BOUND_VARIABLE_2099332 tptp.int) (BOUND_VARIABLE_2099333 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15519 BOUND_VARIABLE_2099333) BOUND_VARIABLE_2099332)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 (ho_15502 k_15520 BOUND_VARIABLE_2099327) BOUND_VARIABLE_2248653) BOUND_VARIABLE_2248652) BOUND_VARIABLE_2099330) BOUND_VARIABLE_2099331))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 (ho_16347 k_16383 BOUND_VARIABLE_2099327) BOUND_VARIABLE_2248653) BOUND_VARIABLE_2248652) BOUND_VARIABLE_2099330) BOUND_VARIABLE_2099331) BOUND_VARIABLE_2099332) BOUND_VARIABLE_2099333))))) (let ((_let_3079 (forall ((BOUND_VARIABLE_2099299 tptp.int) (BOUND_VARIABLE_2099300 tptp.int) (BOUND_VARIABLE_2099301 tptp.int) (BOUND_VARIABLE_2099302 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2099299) BOUND_VARIABLE_2099301))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2099300) BOUND_VARIABLE_2099302))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16384 BOUND_VARIABLE_2099299) BOUND_VARIABLE_2099300) BOUND_VARIABLE_2099301) BOUND_VARIABLE_2099302))))))) (let ((_let_3080 (forall ((BOUND_VARIABLE_2099202 tptp.nat) (BOUND_VARIABLE_2248757 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2099204 tptp.nat) (BOUND_VARIABLE_2099205 tptp.nat) (BOUND_VARIABLE_2099206 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2099206))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2099206))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2099204)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16385 BOUND_VARIABLE_2099202) BOUND_VARIABLE_2248757) BOUND_VARIABLE_2099204) BOUND_VARIABLE_2099205) BOUND_VARIABLE_2099206) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2248757 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099202))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2248757 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099205))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3081 (forall ((BOUND_VARIABLE_2099105 tptp.nat) (BOUND_VARIABLE_2248834 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2099107 tptp.nat) (BOUND_VARIABLE_2099108 tptp.nat) (BOUND_VARIABLE_2099109 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2099109))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2099109))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2099107)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16386 BOUND_VARIABLE_2099105) BOUND_VARIABLE_2248834) BOUND_VARIABLE_2099107) BOUND_VARIABLE_2099108) BOUND_VARIABLE_2099109) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2248834 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099105))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2248834 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2099108))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3082 (forall ((BOUND_VARIABLE_2099013 tptp.nat) (BOUND_VARIABLE_2248859 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2099015 tptp.nat) (BOUND_VARIABLE_2099016 tptp.nat) (BOUND_VARIABLE_2099017 tptp.int) (BOUND_VARIABLE_2099018 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15521 BOUND_VARIABLE_2099018) BOUND_VARIABLE_2099017)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15522 BOUND_VARIABLE_2099013) BOUND_VARIABLE_2248859) BOUND_VARIABLE_2099015) BOUND_VARIABLE_2099016))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16387 BOUND_VARIABLE_2099013) BOUND_VARIABLE_2248859) BOUND_VARIABLE_2099015) BOUND_VARIABLE_2099016) BOUND_VARIABLE_2099017) BOUND_VARIABLE_2099018))))) (let ((_let_3083 (forall ((BOUND_VARIABLE_2098985 tptp.int) (BOUND_VARIABLE_2098986 tptp.int) (BOUND_VARIABLE_2098987 tptp.int) (BOUND_VARIABLE_2098988 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2098985) BOUND_VARIABLE_2098987))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2098986) BOUND_VARIABLE_2098988))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16388 BOUND_VARIABLE_2098985) BOUND_VARIABLE_2098986) BOUND_VARIABLE_2098987) BOUND_VARIABLE_2098988))))))) (let ((_let_3084 (forall ((BOUND_VARIABLE_2248960 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2098899 tptp.nat) (BOUND_VARIABLE_2098900 tptp.nat) (BOUND_VARIABLE_2098901 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2098901))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2098901))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16389 BOUND_VARIABLE_2248960) BOUND_VARIABLE_2098899) BOUND_VARIABLE_2098900) BOUND_VARIABLE_2098901) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2248960 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2098899)) (ho_15161 k_15160 BOUND_VARIABLE_2098900))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3085 (forall ((BOUND_VARIABLE_2249028 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2098812 tptp.nat) (BOUND_VARIABLE_2098813 tptp.nat) (BOUND_VARIABLE_2098814 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2098814))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2098814))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16390 BOUND_VARIABLE_2249028) BOUND_VARIABLE_2098812) BOUND_VARIABLE_2098813) BOUND_VARIABLE_2098814) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2249028 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2098812)) (ho_15161 k_15160 BOUND_VARIABLE_2098813))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3086 (forall ((BOUND_VARIABLE_2249044 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2098737 tptp.nat) (BOUND_VARIABLE_2098738 tptp.nat) (BOUND_VARIABLE_2098739 tptp.int) (BOUND_VARIABLE_2098740 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15523 BOUND_VARIABLE_2098740) BOUND_VARIABLE_2098739)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15524 BOUND_VARIABLE_2249044) BOUND_VARIABLE_2098737) BOUND_VARIABLE_2098738))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16391 BOUND_VARIABLE_2249044) BOUND_VARIABLE_2098737) BOUND_VARIABLE_2098738) BOUND_VARIABLE_2098739) BOUND_VARIABLE_2098740))))) (let ((_let_3087 (forall ((BOUND_VARIABLE_2098708 tptp.int) (BOUND_VARIABLE_2098709 tptp.int) (BOUND_VARIABLE_2098710 tptp.int) (BOUND_VARIABLE_2098711 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2098708) BOUND_VARIABLE_2098710))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2098709) BOUND_VARIABLE_2098711))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16392 BOUND_VARIABLE_2098708) BOUND_VARIABLE_2098709) BOUND_VARIABLE_2098710) BOUND_VARIABLE_2098711))))))) (let ((_let_3088 (forall ((BOUND_VARIABLE_2098609 tptp.nat) (BOUND_VARIABLE_2249142 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2098611 tptp.nat) (BOUND_VARIABLE_2098612 tptp.nat) (BOUND_VARIABLE_2098613 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2098613))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2098613))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2098611)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16393 BOUND_VARIABLE_2098609) BOUND_VARIABLE_2249142) BOUND_VARIABLE_2098611) BOUND_VARIABLE_2098612) BOUND_VARIABLE_2098613) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2249142 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2098609)))))) (ho_15122 k_15121 (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2249142 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2098612)))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3089 (forall ((BOUND_VARIABLE_2098510 tptp.nat) (BOUND_VARIABLE_2249221 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2098512 tptp.nat) (BOUND_VARIABLE_2098513 tptp.nat) (BOUND_VARIABLE_2098514 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2098514))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2098514))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2098512)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16394 BOUND_VARIABLE_2098510) BOUND_VARIABLE_2249221) BOUND_VARIABLE_2098512) BOUND_VARIABLE_2098513) BOUND_VARIABLE_2098514) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2249221 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2098510)))))) (ho_15122 k_15121 (ho_15122 k_15126 (ho_15120 BOUND_VARIABLE_2249221 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2098513)))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3090 (forall ((BOUND_VARIABLE_2098414 tptp.nat) (BOUND_VARIABLE_2249248 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2098416 tptp.nat) (BOUND_VARIABLE_2098417 tptp.nat) (BOUND_VARIABLE_2098418 tptp.int) (BOUND_VARIABLE_2098419 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15525 BOUND_VARIABLE_2098419) BOUND_VARIABLE_2098418)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15526 BOUND_VARIABLE_2098414) BOUND_VARIABLE_2249248) BOUND_VARIABLE_2098416) BOUND_VARIABLE_2098417))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16395 BOUND_VARIABLE_2098414) BOUND_VARIABLE_2249248) BOUND_VARIABLE_2098416) BOUND_VARIABLE_2098417) BOUND_VARIABLE_2098418) BOUND_VARIABLE_2098419))))) (let ((_let_3091 (forall ((BOUND_VARIABLE_2098386 tptp.int) (BOUND_VARIABLE_2098387 tptp.int) (BOUND_VARIABLE_2098388 tptp.int) (BOUND_VARIABLE_2098389 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2098386) BOUND_VARIABLE_2098388))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2098387) BOUND_VARIABLE_2098389))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16396 BOUND_VARIABLE_2098386) BOUND_VARIABLE_2098387) BOUND_VARIABLE_2098388) BOUND_VARIABLE_2098389))))))) (let ((_let_3092 (forall ((BOUND_VARIABLE_2098358 tptp.int) (BOUND_VARIABLE_2098359 tptp.int) (BOUND_VARIABLE_2098360 tptp.int) (BOUND_VARIABLE_2098361 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2098358) BOUND_VARIABLE_2098360))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2098359) BOUND_VARIABLE_2098361))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16397 BOUND_VARIABLE_2098358) BOUND_VARIABLE_2098359) BOUND_VARIABLE_2098360) BOUND_VARIABLE_2098361))))))) (let ((_let_3093 (forall ((BOUND_VARIABLE_2098261 tptp.nat) (BOUND_VARIABLE_2249372 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2098263 tptp.nat) (BOUND_VARIABLE_2098264 tptp.nat) (BOUND_VARIABLE_2098265 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2098265))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2098265))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2098263)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16398 BOUND_VARIABLE_2098261) BOUND_VARIABLE_2249372) BOUND_VARIABLE_2098263) BOUND_VARIABLE_2098264) BOUND_VARIABLE_2098265) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2249372 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2098261))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2249372 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2098264))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3094 (forall ((BOUND_VARIABLE_2098217 tptp.int) (BOUND_VARIABLE_2098218 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15527 BOUND_VARIABLE_2098218) BOUND_VARIABLE_2098217)) (ho_15260 k_15259 k_16399)) (ho_15108 (ho_15107 k_16400 BOUND_VARIABLE_2098217) BOUND_VARIABLE_2098218))))) (let ((_let_3095 (forall ((BOUND_VARIABLE_2098120 tptp.nat) (BOUND_VARIABLE_2249462 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2098122 tptp.nat) (BOUND_VARIABLE_2098123 tptp.nat) (BOUND_VARIABLE_2098124 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2098124))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2098124))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2098122)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16401 BOUND_VARIABLE_2098120) BOUND_VARIABLE_2249462) BOUND_VARIABLE_2098122) BOUND_VARIABLE_2098123) BOUND_VARIABLE_2098124) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2249462 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2098120))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2249462 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2098123))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3096 (forall ((BOUND_VARIABLE_2098028 tptp.nat) (BOUND_VARIABLE_2249487 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2098030 tptp.nat) (BOUND_VARIABLE_2098031 tptp.nat) (BOUND_VARIABLE_2098032 tptp.int) (BOUND_VARIABLE_2098033 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15528 BOUND_VARIABLE_2098033) BOUND_VARIABLE_2098032)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15529 BOUND_VARIABLE_2098028) BOUND_VARIABLE_2249487) BOUND_VARIABLE_2098030) BOUND_VARIABLE_2098031))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16402 BOUND_VARIABLE_2098028) BOUND_VARIABLE_2249487) BOUND_VARIABLE_2098030) BOUND_VARIABLE_2098031) BOUND_VARIABLE_2098032) BOUND_VARIABLE_2098033))))) (let ((_let_3097 (forall ((BOUND_VARIABLE_2098000 tptp.int) (BOUND_VARIABLE_2098001 tptp.int) (BOUND_VARIABLE_2098002 tptp.int) (BOUND_VARIABLE_2098003 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2098000) BOUND_VARIABLE_2098002))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2098001) BOUND_VARIABLE_2098003))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16403 BOUND_VARIABLE_2098000) BOUND_VARIABLE_2098001) BOUND_VARIABLE_2098002) BOUND_VARIABLE_2098003))))))) (let ((_let_3098 (forall ((BOUND_VARIABLE_2097972 tptp.int) (BOUND_VARIABLE_2097973 tptp.int) (BOUND_VARIABLE_2097974 tptp.int) (BOUND_VARIABLE_2097975 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2097972) BOUND_VARIABLE_2097974))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2097973) BOUND_VARIABLE_2097975))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16404 BOUND_VARIABLE_2097972) BOUND_VARIABLE_2097973) BOUND_VARIABLE_2097974) BOUND_VARIABLE_2097975))))))) (let ((_let_3099 (forall ((BOUND_VARIABLE_2097875 tptp.nat) (BOUND_VARIABLE_2249611 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2097877 tptp.nat) (BOUND_VARIABLE_2097878 tptp.nat) (BOUND_VARIABLE_2097879 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2097879))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2097879))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2097877)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16405 BOUND_VARIABLE_2097875) BOUND_VARIABLE_2249611) BOUND_VARIABLE_2097877) BOUND_VARIABLE_2097878) BOUND_VARIABLE_2097879) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2249611 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2097875))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2249611 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2097878))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3100 (forall ((BOUND_VARIABLE_2097831 tptp.int) (BOUND_VARIABLE_2097832 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15530 BOUND_VARIABLE_2097832) BOUND_VARIABLE_2097831)) (ho_15260 k_15259 k_16049)) (ho_15108 (ho_15107 k_16050 BOUND_VARIABLE_2097831) BOUND_VARIABLE_2097832))))) (let ((_let_3101 (forall ((BOUND_VARIABLE_2097734 tptp.nat) (BOUND_VARIABLE_2249698 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2097736 tptp.nat) (BOUND_VARIABLE_2097737 tptp.nat) (BOUND_VARIABLE_2097738 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2097738))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2097738))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2097736)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16406 BOUND_VARIABLE_2097734) BOUND_VARIABLE_2249698) BOUND_VARIABLE_2097736) BOUND_VARIABLE_2097737) BOUND_VARIABLE_2097738) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2249698 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2097734))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2249698 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2097737))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3102 (forall ((BOUND_VARIABLE_2097642 tptp.nat) (BOUND_VARIABLE_2249723 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2097644 tptp.nat) (BOUND_VARIABLE_2097645 tptp.nat) (BOUND_VARIABLE_2097646 tptp.int) (BOUND_VARIABLE_2097647 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15531 BOUND_VARIABLE_2097647) BOUND_VARIABLE_2097646)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15532 BOUND_VARIABLE_2097642) BOUND_VARIABLE_2249723) BOUND_VARIABLE_2097644) BOUND_VARIABLE_2097645))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16407 BOUND_VARIABLE_2097642) BOUND_VARIABLE_2249723) BOUND_VARIABLE_2097644) BOUND_VARIABLE_2097645) BOUND_VARIABLE_2097646) BOUND_VARIABLE_2097647))))) (let ((_let_3103 (forall ((BOUND_VARIABLE_2097545 tptp.nat) (BOUND_VARIABLE_2249801 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2097547 tptp.nat) (BOUND_VARIABLE_2097548 tptp.nat) (BOUND_VARIABLE_2097549 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2097549))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2097549))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2097547)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16408 BOUND_VARIABLE_2097545) BOUND_VARIABLE_2249801) BOUND_VARIABLE_2097547) BOUND_VARIABLE_2097548) BOUND_VARIABLE_2097549) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2249801 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2097545))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2249801 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2097548))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3104 (forall ((BOUND_VARIABLE_2097453 tptp.nat) (BOUND_VARIABLE_2249826 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2097455 tptp.nat) (BOUND_VARIABLE_2097456 tptp.nat) (BOUND_VARIABLE_2097457 tptp.int) (BOUND_VARIABLE_2097458 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15533 BOUND_VARIABLE_2097458) BOUND_VARIABLE_2097457)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15534 BOUND_VARIABLE_2097453) BOUND_VARIABLE_2249826) BOUND_VARIABLE_2097455) BOUND_VARIABLE_2097456))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16409 BOUND_VARIABLE_2097453) BOUND_VARIABLE_2249826) BOUND_VARIABLE_2097455) BOUND_VARIABLE_2097456) BOUND_VARIABLE_2097457) BOUND_VARIABLE_2097458))))) (let ((_let_3105 (forall ((BOUND_VARIABLE_2097425 tptp.int) (BOUND_VARIABLE_2097426 tptp.int) (BOUND_VARIABLE_2097427 tptp.int) (BOUND_VARIABLE_2097428 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2097425) BOUND_VARIABLE_2097427))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2097426) BOUND_VARIABLE_2097428))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16410 BOUND_VARIABLE_2097425) BOUND_VARIABLE_2097426) BOUND_VARIABLE_2097427) BOUND_VARIABLE_2097428))))))) (let ((_let_3106 (forall ((BOUND_VARIABLE_2097248 tptp.nat) (BOUND_VARIABLE_2249927 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2097250 tptp.nat) (BOUND_VARIABLE_2097251 tptp.nat) (BOUND_VARIABLE_2097252 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2097252))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2097252))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2097250)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2249927 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2097248))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2249927 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2097251)))))))) (let ((_let_12 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16411 BOUND_VARIABLE_2097248) BOUND_VARIABLE_2249927) BOUND_VARIABLE_2097250) BOUND_VARIABLE_2097251) BOUND_VARIABLE_2097252) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16050) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15535 BOUND_VARIABLE_2097248) BOUND_VARIABLE_2249927) BOUND_VARIABLE_2097250) BOUND_VARIABLE_2097251))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15536 BOUND_VARIABLE_2097248) BOUND_VARIABLE_2249927) BOUND_VARIABLE_2097250) BOUND_VARIABLE_2097251)) (ho_15260 k_15259 k_16049))))) (ho_15122 k_15121 _let_11)) _let_11)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))) (let ((_let_3107 (forall ((BOUND_VARIABLE_2097204 tptp.int) (BOUND_VARIABLE_2097205 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15537 BOUND_VARIABLE_2097205) BOUND_VARIABLE_2097204)) (ho_15260 k_15259 k_15540)) (ho_15108 (ho_15107 k_16412 BOUND_VARIABLE_2097204) BOUND_VARIABLE_2097205))))) (let ((_let_3108 (forall ((BOUND_VARIABLE_2097107 tptp.nat) (BOUND_VARIABLE_2250033 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2097109 tptp.nat) (BOUND_VARIABLE_2097110 tptp.nat) (BOUND_VARIABLE_2097111 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2097111))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2097111))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2097109)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16413 BOUND_VARIABLE_2097107) BOUND_VARIABLE_2250033) BOUND_VARIABLE_2097109) BOUND_VARIABLE_2097110) BOUND_VARIABLE_2097111) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2250033 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2097107))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2250033 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2097110))))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3109 (forall ((BOUND_VARIABLE_2097015 tptp.nat) (BOUND_VARIABLE_2250058 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2097017 tptp.nat) (BOUND_VARIABLE_2097018 tptp.nat) (BOUND_VARIABLE_2097019 tptp.int) (BOUND_VARIABLE_2097020 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15538 BOUND_VARIABLE_2097020) BOUND_VARIABLE_2097019)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15539 BOUND_VARIABLE_2097015) BOUND_VARIABLE_2250058) BOUND_VARIABLE_2097017) BOUND_VARIABLE_2097018))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_16414 BOUND_VARIABLE_2097015) BOUND_VARIABLE_2250058) BOUND_VARIABLE_2097017) BOUND_VARIABLE_2097018) BOUND_VARIABLE_2097019) BOUND_VARIABLE_2097020))))) (let ((_let_3110 (forall ((BOUND_VARIABLE_2096937 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2096937))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2096937))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15150 k_15149 tptp.one))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 k_15540 BOUND_VARIABLE_2096937) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_9) (ho_15122 k_15121 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3111 (forall ((BOUND_VARIABLE_2096909 tptp.int) (BOUND_VARIABLE_2096910 tptp.int) (BOUND_VARIABLE_2096911 tptp.int) (BOUND_VARIABLE_2096912 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2096909) BOUND_VARIABLE_2096911))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2096910) BOUND_VARIABLE_2096912))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16415 BOUND_VARIABLE_2096909) BOUND_VARIABLE_2096910) BOUND_VARIABLE_2096911) BOUND_VARIABLE_2096912))))))) (let ((_let_3112 (forall ((BOUND_VARIABLE_2096730 tptp.nat) (BOUND_VARIABLE_2250215 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2096732 tptp.nat) (BOUND_VARIABLE_2096733 tptp.nat) (BOUND_VARIABLE_2096734 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2096734))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2096734))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2096732)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2250215 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2096730))))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2250215 (ho_15118 k_15117 (ho_15079 _let_9 (ho_15161 k_15160 BOUND_VARIABLE_2096733)))))))) (let ((_let_12 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_16416 BOUND_VARIABLE_2096730) BOUND_VARIABLE_2250215) BOUND_VARIABLE_2096732) BOUND_VARIABLE_2096733) BOUND_VARIABLE_2096734) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_12 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_15541) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15168 k_15542 BOUND_VARIABLE_2096730) BOUND_VARIABLE_2250215) BOUND_VARIABLE_2096732) BOUND_VARIABLE_2096733))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 (ho_15350 k_15543 BOUND_VARIABLE_2096730) BOUND_VARIABLE_2250215) BOUND_VARIABLE_2096732) BOUND_VARIABLE_2096733)) (ho_15260 k_15259 k_15540))))) (ho_15122 k_15121 _let_11)) _let_11)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))))) (let ((_let_3113 (forall ((BOUND_VARIABLE_2250311 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2096644 tptp.nat) (BOUND_VARIABLE_2096645 tptp.nat) (BOUND_VARIABLE_2096646 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2096646))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2096646))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16417 BOUND_VARIABLE_2250311) BOUND_VARIABLE_2096644) BOUND_VARIABLE_2096645) BOUND_VARIABLE_2096646) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2250311 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2096644)) (ho_15161 k_15160 BOUND_VARIABLE_2096645))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3114 (forall ((BOUND_VARIABLE_2250327 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2096569 tptp.nat) (BOUND_VARIABLE_2096570 tptp.nat) (BOUND_VARIABLE_2096571 tptp.int) (BOUND_VARIABLE_2096572 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15544 BOUND_VARIABLE_2096572) BOUND_VARIABLE_2096571)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15545 BOUND_VARIABLE_2250327) BOUND_VARIABLE_2096569) BOUND_VARIABLE_2096570))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16418 BOUND_VARIABLE_2250327) BOUND_VARIABLE_2096569) BOUND_VARIABLE_2096570) BOUND_VARIABLE_2096571) BOUND_VARIABLE_2096572))))) (let ((_let_3115 (forall ((BOUND_VARIABLE_2096540 tptp.int) (BOUND_VARIABLE_2096541 tptp.int) (BOUND_VARIABLE_2096542 tptp.int) (BOUND_VARIABLE_2096543 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2096540) BOUND_VARIABLE_2096542))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2096541) BOUND_VARIABLE_2096543))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16419 BOUND_VARIABLE_2096540) BOUND_VARIABLE_2096541) BOUND_VARIABLE_2096542) BOUND_VARIABLE_2096543))))))) (let ((_let_3116 (forall ((BOUND_VARIABLE_2250425 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2096393 tptp.nat) (BOUND_VARIABLE_2096394 tptp.nat) (BOUND_VARIABLE_2096395 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2096395))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2096395))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2250425 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2096393)) (ho_15161 k_15160 BOUND_VARIABLE_2096394)))))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16420 BOUND_VARIABLE_2250425) BOUND_VARIABLE_2096393) BOUND_VARIABLE_2096394) BOUND_VARIABLE_2096395) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_16044) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15546 BOUND_VARIABLE_2250425) BOUND_VARIABLE_2096393) BOUND_VARIABLE_2096394))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 k_15547 BOUND_VARIABLE_2250425) BOUND_VARIABLE_2096393) BOUND_VARIABLE_2096394)) (ho_15260 k_15259 k_16043))))) (ho_15122 k_15121 _let_9)) _let_9)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3117 (forall ((BOUND_VARIABLE_2096348 tptp.int) (BOUND_VARIABLE_2096349 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15548 BOUND_VARIABLE_2096349) BOUND_VARIABLE_2096348)) (ho_15260 k_15259 k_15551)) (ho_15108 (ho_15107 k_16421 BOUND_VARIABLE_2096348) BOUND_VARIABLE_2096349))))) (let ((_let_3118 (forall ((BOUND_VARIABLE_2250520 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2096262 tptp.nat) (BOUND_VARIABLE_2096263 tptp.nat) (BOUND_VARIABLE_2096264 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2096264))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2096264))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16422 BOUND_VARIABLE_2250520) BOUND_VARIABLE_2096262) BOUND_VARIABLE_2096263) BOUND_VARIABLE_2096264) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2250520 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2096262)) (ho_15161 k_15160 BOUND_VARIABLE_2096263))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3119 (forall ((BOUND_VARIABLE_2250536 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2096187 tptp.nat) (BOUND_VARIABLE_2096188 tptp.nat) (BOUND_VARIABLE_2096189 tptp.int) (BOUND_VARIABLE_2096190 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15549 BOUND_VARIABLE_2096190) BOUND_VARIABLE_2096189)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15550 BOUND_VARIABLE_2250536) BOUND_VARIABLE_2096187) BOUND_VARIABLE_2096188))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16423 BOUND_VARIABLE_2250536) BOUND_VARIABLE_2096187) BOUND_VARIABLE_2096188) BOUND_VARIABLE_2096189) BOUND_VARIABLE_2096190))))) (let ((_let_3120 (forall ((BOUND_VARIABLE_2096108 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2096108))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2096108))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15150 k_15149 tptp.one))) (= (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_11) (ho_15122 k_15121 _let_11)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 k_15551 BOUND_VARIABLE_2096108)))))))))))))))) (let ((_let_3121 (forall ((BOUND_VARIABLE_2096080 tptp.int) (BOUND_VARIABLE_2096081 tptp.int) (BOUND_VARIABLE_2096082 tptp.int) (BOUND_VARIABLE_2096083 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2096080) BOUND_VARIABLE_2096082))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2096081) BOUND_VARIABLE_2096083))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16424 BOUND_VARIABLE_2096080) BOUND_VARIABLE_2096081) BOUND_VARIABLE_2096082) BOUND_VARIABLE_2096083))))))) (let ((_let_3122 (forall ((BOUND_VARIABLE_2250687 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2095931 tptp.nat) (BOUND_VARIABLE_2095932 tptp.nat) (BOUND_VARIABLE_2095933 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2095933))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2095933))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15120 BOUND_VARIABLE_2250687 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2095931)) (ho_15161 k_15160 BOUND_VARIABLE_2095932)))))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16425 BOUND_VARIABLE_2250687) BOUND_VARIABLE_2095931) BOUND_VARIABLE_2095932) BOUND_VARIABLE_2095933) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (and (ho_15142 (ho_15262 k_15261 k_15552) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15553 BOUND_VARIABLE_2250687) BOUND_VARIABLE_2095931) BOUND_VARIABLE_2095932))) (not (ho_15142 (ho_15262 k_15261 (ho_15345 (ho_15344 (ho_15343 k_15554 BOUND_VARIABLE_2250687) BOUND_VARIABLE_2095931) BOUND_VARIABLE_2095932)) (ho_15260 k_15259 k_15551))))) (ho_15122 k_15121 _let_9)) _let_9)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3123 (forall ((BOUND_VARIABLE_2095902 tptp.int) (BOUND_VARIABLE_2095903 tptp.int) (BOUND_VARIABLE_2095904 tptp.int) (BOUND_VARIABLE_2095905 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2095902) BOUND_VARIABLE_2095904))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2095903) BOUND_VARIABLE_2095905))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16426 BOUND_VARIABLE_2095902) BOUND_VARIABLE_2095903) BOUND_VARIABLE_2095904) BOUND_VARIABLE_2095905))))))) (let ((_let_3124 (forall ((BOUND_VARIABLE_2095874 tptp.int) (BOUND_VARIABLE_2095875 tptp.int) (BOUND_VARIABLE_2095876 tptp.int) (BOUND_VARIABLE_2095877 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2095874) BOUND_VARIABLE_2095876))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2095875) BOUND_VARIABLE_2095877))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16427 BOUND_VARIABLE_2095874) BOUND_VARIABLE_2095875) BOUND_VARIABLE_2095876) BOUND_VARIABLE_2095877))))))) (let ((_let_3125 (forall ((BOUND_VARIABLE_2250818 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2095788 tptp.nat) (BOUND_VARIABLE_2095789 tptp.nat) (BOUND_VARIABLE_2095790 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2095790))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2095790))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16428 BOUND_VARIABLE_2250818) BOUND_VARIABLE_2095788) BOUND_VARIABLE_2095789) BOUND_VARIABLE_2095790) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2250818 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2095788)) (ho_15161 k_15160 BOUND_VARIABLE_2095789))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3126 (forall ((BOUND_VARIABLE_2095743 tptp.int) (BOUND_VARIABLE_2095744 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15555 BOUND_VARIABLE_2095744) BOUND_VARIABLE_2095743)) (ho_15260 k_15259 k_16429)) (ho_15108 (ho_15107 k_16430 BOUND_VARIABLE_2095743) BOUND_VARIABLE_2095744))))) (let ((_let_3127 (forall ((BOUND_VARIABLE_2250899 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2095657 tptp.nat) (BOUND_VARIABLE_2095658 tptp.nat) (BOUND_VARIABLE_2095659 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2095659))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2095659))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16431 BOUND_VARIABLE_2250899) BOUND_VARIABLE_2095657) BOUND_VARIABLE_2095658) BOUND_VARIABLE_2095659) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2250899 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2095657)) (ho_15161 k_15160 BOUND_VARIABLE_2095658))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3128 (forall ((BOUND_VARIABLE_2250915 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2095582 tptp.nat) (BOUND_VARIABLE_2095583 tptp.nat) (BOUND_VARIABLE_2095584 tptp.int) (BOUND_VARIABLE_2095585 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15556 BOUND_VARIABLE_2095585) BOUND_VARIABLE_2095584)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15557 BOUND_VARIABLE_2250915) BOUND_VARIABLE_2095582) BOUND_VARIABLE_2095583))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16432 BOUND_VARIABLE_2250915) BOUND_VARIABLE_2095582) BOUND_VARIABLE_2095583) BOUND_VARIABLE_2095584) BOUND_VARIABLE_2095585))))) (let ((_let_3129 (forall ((BOUND_VARIABLE_2095553 tptp.int) (BOUND_VARIABLE_2095554 tptp.int) (BOUND_VARIABLE_2095555 tptp.int) (BOUND_VARIABLE_2095556 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2095553) BOUND_VARIABLE_2095555))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2095554) BOUND_VARIABLE_2095556))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16433 BOUND_VARIABLE_2095553) BOUND_VARIABLE_2095554) BOUND_VARIABLE_2095555) BOUND_VARIABLE_2095556))))))) (let ((_let_3130 (forall ((BOUND_VARIABLE_2251013 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2095467 tptp.nat) (BOUND_VARIABLE_2095468 tptp.nat) (BOUND_VARIABLE_2095469 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2095469))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2095469))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16434 BOUND_VARIABLE_2251013) BOUND_VARIABLE_2095467) BOUND_VARIABLE_2095468) BOUND_VARIABLE_2095469) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2251013 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2095467)) (ho_15161 k_15160 BOUND_VARIABLE_2095468))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3131 (forall ((BOUND_VARIABLE_2251081 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2095380 tptp.nat) (BOUND_VARIABLE_2095381 tptp.nat) (BOUND_VARIABLE_2095382 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2095382))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2095382))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16435 BOUND_VARIABLE_2251081) BOUND_VARIABLE_2095380) BOUND_VARIABLE_2095381) BOUND_VARIABLE_2095382) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2251081 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2095380)) (ho_15161 k_15160 BOUND_VARIABLE_2095381))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3132 (forall ((BOUND_VARIABLE_2251097 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2095305 tptp.nat) (BOUND_VARIABLE_2095306 tptp.nat) (BOUND_VARIABLE_2095307 tptp.int) (BOUND_VARIABLE_2095308 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15558 BOUND_VARIABLE_2095308) BOUND_VARIABLE_2095307)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15559 BOUND_VARIABLE_2251097) BOUND_VARIABLE_2095305) BOUND_VARIABLE_2095306))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16436 BOUND_VARIABLE_2251097) BOUND_VARIABLE_2095305) BOUND_VARIABLE_2095306) BOUND_VARIABLE_2095307) BOUND_VARIABLE_2095308))))) (let ((_let_3133 (forall ((BOUND_VARIABLE_2095276 tptp.int) (BOUND_VARIABLE_2095277 tptp.int) (BOUND_VARIABLE_2095278 tptp.int) (BOUND_VARIABLE_2095279 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2095276) BOUND_VARIABLE_2095278))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2095277) BOUND_VARIABLE_2095279))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16437 BOUND_VARIABLE_2095276) BOUND_VARIABLE_2095277) BOUND_VARIABLE_2095278) BOUND_VARIABLE_2095279))))))) (let ((_let_3134 (forall ((BOUND_VARIABLE_2251195 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2095190 tptp.nat) (BOUND_VARIABLE_2095191 tptp.nat) (BOUND_VARIABLE_2095192 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2095192))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2095192))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16438 BOUND_VARIABLE_2251195) BOUND_VARIABLE_2095190) BOUND_VARIABLE_2095191) BOUND_VARIABLE_2095192) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2251195 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2095190)) (ho_15161 k_15160 BOUND_VARIABLE_2095191))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3135 (forall ((BOUND_VARIABLE_2251263 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2095103 tptp.nat) (BOUND_VARIABLE_2095104 tptp.nat) (BOUND_VARIABLE_2095105 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2095105))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2095105))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16439 BOUND_VARIABLE_2251263) BOUND_VARIABLE_2095103) BOUND_VARIABLE_2095104) BOUND_VARIABLE_2095105) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2251263 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2095103)) (ho_15161 k_15160 BOUND_VARIABLE_2095104))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3136 (forall ((BOUND_VARIABLE_2251279 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2095028 tptp.nat) (BOUND_VARIABLE_2095029 tptp.nat) (BOUND_VARIABLE_2095030 tptp.int) (BOUND_VARIABLE_2095031 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15560 BOUND_VARIABLE_2095031) BOUND_VARIABLE_2095030)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15561 BOUND_VARIABLE_2251279) BOUND_VARIABLE_2095028) BOUND_VARIABLE_2095029))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16440 BOUND_VARIABLE_2251279) BOUND_VARIABLE_2095028) BOUND_VARIABLE_2095029) BOUND_VARIABLE_2095030) BOUND_VARIABLE_2095031))))) (let ((_let_3137 (forall ((BOUND_VARIABLE_2094999 tptp.int) (BOUND_VARIABLE_2095000 tptp.int) (BOUND_VARIABLE_2095001 tptp.int) (BOUND_VARIABLE_2095002 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2094999) BOUND_VARIABLE_2095001))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2095000) BOUND_VARIABLE_2095002))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16441 BOUND_VARIABLE_2094999) BOUND_VARIABLE_2095000) BOUND_VARIABLE_2095001) BOUND_VARIABLE_2095002))))))) (let ((_let_3138 (forall ((BOUND_VARIABLE_2094971 tptp.int) (BOUND_VARIABLE_2094972 tptp.int) (BOUND_VARIABLE_2094973 tptp.int) (BOUND_VARIABLE_2094974 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2094971) BOUND_VARIABLE_2094973))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2094972) BOUND_VARIABLE_2094974))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16442 BOUND_VARIABLE_2094971) BOUND_VARIABLE_2094972) BOUND_VARIABLE_2094973) BOUND_VARIABLE_2094974))))))) (let ((_let_3139 (forall ((BOUND_VARIABLE_2251400 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2094885 tptp.nat) (BOUND_VARIABLE_2094886 tptp.nat) (BOUND_VARIABLE_2094887 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2094887))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2094887))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16443 BOUND_VARIABLE_2251400) BOUND_VARIABLE_2094885) BOUND_VARIABLE_2094886) BOUND_VARIABLE_2094887) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2251400 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2094885)) (ho_15161 k_15160 BOUND_VARIABLE_2094886))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3140 (forall ((BOUND_VARIABLE_2094840 tptp.int) (BOUND_VARIABLE_2094841 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15562 BOUND_VARIABLE_2094841) BOUND_VARIABLE_2094840)) (ho_15260 k_15259 k_16444)) (ho_15108 (ho_15107 k_16445 BOUND_VARIABLE_2094840) BOUND_VARIABLE_2094841))))) (let ((_let_3141 (forall ((BOUND_VARIABLE_2251481 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2094754 tptp.nat) (BOUND_VARIABLE_2094755 tptp.nat) (BOUND_VARIABLE_2094756 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2094756))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2094756))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16446 BOUND_VARIABLE_2251481) BOUND_VARIABLE_2094754) BOUND_VARIABLE_2094755) BOUND_VARIABLE_2094756) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2251481 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2094754)) (ho_15161 k_15160 BOUND_VARIABLE_2094755))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3142 (forall ((BOUND_VARIABLE_2251497 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2094679 tptp.nat) (BOUND_VARIABLE_2094680 tptp.nat) (BOUND_VARIABLE_2094681 tptp.int) (BOUND_VARIABLE_2094682 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15563 BOUND_VARIABLE_2094682) BOUND_VARIABLE_2094681)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15564 BOUND_VARIABLE_2251497) BOUND_VARIABLE_2094679) BOUND_VARIABLE_2094680))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16447 BOUND_VARIABLE_2251497) BOUND_VARIABLE_2094679) BOUND_VARIABLE_2094680) BOUND_VARIABLE_2094681) BOUND_VARIABLE_2094682))))) (let ((_let_3143 (forall ((BOUND_VARIABLE_2094650 tptp.int) (BOUND_VARIABLE_2094651 tptp.int) (BOUND_VARIABLE_2094652 tptp.int) (BOUND_VARIABLE_2094653 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2094650) BOUND_VARIABLE_2094652))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2094651) BOUND_VARIABLE_2094653))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16448 BOUND_VARIABLE_2094650) BOUND_VARIABLE_2094651) BOUND_VARIABLE_2094652) BOUND_VARIABLE_2094653))))))) (let ((_let_3144 (forall ((BOUND_VARIABLE_2251595 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2094564 tptp.nat) (BOUND_VARIABLE_2094565 tptp.nat) (BOUND_VARIABLE_2094566 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2094566))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2094566))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16449 BOUND_VARIABLE_2251595) BOUND_VARIABLE_2094564) BOUND_VARIABLE_2094565) BOUND_VARIABLE_2094566) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2251595 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2094564)) (ho_15161 k_15160 BOUND_VARIABLE_2094565))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3145 (forall ((BOUND_VARIABLE_2251663 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2094477 tptp.nat) (BOUND_VARIABLE_2094478 tptp.nat) (BOUND_VARIABLE_2094479 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2094479))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2094479))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16450 BOUND_VARIABLE_2251663) BOUND_VARIABLE_2094477) BOUND_VARIABLE_2094478) BOUND_VARIABLE_2094479) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2251663 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2094477)) (ho_15161 k_15160 BOUND_VARIABLE_2094478))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3146 (forall ((BOUND_VARIABLE_2251679 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2094402 tptp.nat) (BOUND_VARIABLE_2094403 tptp.nat) (BOUND_VARIABLE_2094404 tptp.int) (BOUND_VARIABLE_2094405 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15565 BOUND_VARIABLE_2094405) BOUND_VARIABLE_2094404)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15566 BOUND_VARIABLE_2251679) BOUND_VARIABLE_2094402) BOUND_VARIABLE_2094403))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16451 BOUND_VARIABLE_2251679) BOUND_VARIABLE_2094402) BOUND_VARIABLE_2094403) BOUND_VARIABLE_2094404) BOUND_VARIABLE_2094405))))) (let ((_let_3147 (forall ((BOUND_VARIABLE_2094373 tptp.int) (BOUND_VARIABLE_2094374 tptp.int) (BOUND_VARIABLE_2094375 tptp.int) (BOUND_VARIABLE_2094376 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2094373) BOUND_VARIABLE_2094375))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2094374) BOUND_VARIABLE_2094376))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16452 BOUND_VARIABLE_2094373) BOUND_VARIABLE_2094374) BOUND_VARIABLE_2094375) BOUND_VARIABLE_2094376))))))) (let ((_let_3148 (forall ((BOUND_VARIABLE_2251777 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2094287 tptp.nat) (BOUND_VARIABLE_2094288 tptp.nat) (BOUND_VARIABLE_2094289 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2094289))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2094289))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16453 BOUND_VARIABLE_2251777) BOUND_VARIABLE_2094287) BOUND_VARIABLE_2094288) BOUND_VARIABLE_2094289) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2251777 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2094287)) (ho_15161 k_15160 BOUND_VARIABLE_2094288))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3149 (forall ((BOUND_VARIABLE_2251845 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2094200 tptp.nat) (BOUND_VARIABLE_2094201 tptp.nat) (BOUND_VARIABLE_2094202 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2094202))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2094202))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16454 BOUND_VARIABLE_2251845) BOUND_VARIABLE_2094200) BOUND_VARIABLE_2094201) BOUND_VARIABLE_2094202) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2251845 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2094200)) (ho_15161 k_15160 BOUND_VARIABLE_2094201))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3150 (forall ((BOUND_VARIABLE_2251861 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2094125 tptp.nat) (BOUND_VARIABLE_2094126 tptp.nat) (BOUND_VARIABLE_2094127 tptp.int) (BOUND_VARIABLE_2094128 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15567 BOUND_VARIABLE_2094128) BOUND_VARIABLE_2094127)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15568 BOUND_VARIABLE_2251861) BOUND_VARIABLE_2094125) BOUND_VARIABLE_2094126))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16455 BOUND_VARIABLE_2251861) BOUND_VARIABLE_2094125) BOUND_VARIABLE_2094126) BOUND_VARIABLE_2094127) BOUND_VARIABLE_2094128))))) (let ((_let_3151 (forall ((BOUND_VARIABLE_2094096 tptp.int) (BOUND_VARIABLE_2094097 tptp.int) (BOUND_VARIABLE_2094098 tptp.int) (BOUND_VARIABLE_2094099 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2094096) BOUND_VARIABLE_2094098))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2094097) BOUND_VARIABLE_2094099))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16456 BOUND_VARIABLE_2094096) BOUND_VARIABLE_2094097) BOUND_VARIABLE_2094098) BOUND_VARIABLE_2094099))))))) (let ((_let_3152 (forall ((BOUND_VARIABLE_2251962 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2251959 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2094004 tptp.nat) (BOUND_VARIABLE_2094005 tptp.nat) (BOUND_VARIABLE_2094006 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2094006))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2094006))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2094004)) (ho_15161 k_15160 BOUND_VARIABLE_2094005))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16457 BOUND_VARIABLE_2251962) BOUND_VARIABLE_2251959) BOUND_VARIABLE_2094004) BOUND_VARIABLE_2094005) BOUND_VARIABLE_2094006) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2251962 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2251959 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3153 (forall ((BOUND_VARIABLE_2252037 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2252034 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2093910 tptp.nat) (BOUND_VARIABLE_2093911 tptp.nat) (BOUND_VARIABLE_2093912 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2093912))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2093912))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2093910)) (ho_15161 k_15160 BOUND_VARIABLE_2093911))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16458 BOUND_VARIABLE_2252037) BOUND_VARIABLE_2252034) BOUND_VARIABLE_2093910) BOUND_VARIABLE_2093911) BOUND_VARIABLE_2093912) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2252037 _let_9)) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2252034 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3154 (forall ((BOUND_VARIABLE_2252058 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2252057 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2093824 tptp.nat) (BOUND_VARIABLE_2093825 tptp.nat) (BOUND_VARIABLE_2093826 tptp.int) (BOUND_VARIABLE_2093827 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15569 BOUND_VARIABLE_2093827) BOUND_VARIABLE_2093826)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15570 BOUND_VARIABLE_2252058) BOUND_VARIABLE_2252057) BOUND_VARIABLE_2093824) BOUND_VARIABLE_2093825))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 k_16459 BOUND_VARIABLE_2252058) BOUND_VARIABLE_2252057) BOUND_VARIABLE_2093824) BOUND_VARIABLE_2093825) BOUND_VARIABLE_2093826) BOUND_VARIABLE_2093827))))) (let ((_let_3155 (forall ((BOUND_VARIABLE_2093794 tptp.int) (BOUND_VARIABLE_2093795 tptp.int) (BOUND_VARIABLE_2093796 tptp.int) (BOUND_VARIABLE_2093797 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2093794) BOUND_VARIABLE_2093796))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2093795) BOUND_VARIABLE_2093797))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16460 BOUND_VARIABLE_2093794) BOUND_VARIABLE_2093795) BOUND_VARIABLE_2093796) BOUND_VARIABLE_2093797))))))) (let ((_let_3156 (forall ((BOUND_VARIABLE_2252159 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2093708 tptp.nat) (BOUND_VARIABLE_2093709 tptp.nat) (BOUND_VARIABLE_2093710 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2093710))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2093710))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16461 BOUND_VARIABLE_2252159) BOUND_VARIABLE_2093708) BOUND_VARIABLE_2093709) BOUND_VARIABLE_2093710) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2252159 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2093708)) (ho_15161 k_15160 BOUND_VARIABLE_2093709))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3157 (forall ((BOUND_VARIABLE_2252227 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2093621 tptp.nat) (BOUND_VARIABLE_2093622 tptp.nat) (BOUND_VARIABLE_2093623 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2093623))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2093623))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16462 BOUND_VARIABLE_2252227) BOUND_VARIABLE_2093621) BOUND_VARIABLE_2093622) BOUND_VARIABLE_2093623) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2252227 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2093621)) (ho_15161 k_15160 BOUND_VARIABLE_2093622))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3158 (forall ((BOUND_VARIABLE_2252243 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2093546 tptp.nat) (BOUND_VARIABLE_2093547 tptp.nat) (BOUND_VARIABLE_2093548 tptp.int) (BOUND_VARIABLE_2093549 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15571 BOUND_VARIABLE_2093549) BOUND_VARIABLE_2093548)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15572 BOUND_VARIABLE_2252243) BOUND_VARIABLE_2093546) BOUND_VARIABLE_2093547))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16463 BOUND_VARIABLE_2252243) BOUND_VARIABLE_2093546) BOUND_VARIABLE_2093547) BOUND_VARIABLE_2093548) BOUND_VARIABLE_2093549))))) (let ((_let_3159 (forall ((BOUND_VARIABLE_2093517 tptp.int) (BOUND_VARIABLE_2093518 tptp.int) (BOUND_VARIABLE_2093519 tptp.int) (BOUND_VARIABLE_2093520 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2093517) BOUND_VARIABLE_2093519))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2093518) BOUND_VARIABLE_2093520))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16464 BOUND_VARIABLE_2093517) BOUND_VARIABLE_2093518) BOUND_VARIABLE_2093519) BOUND_VARIABLE_2093520))))))) (let ((_let_3160 (forall ((BOUND_VARIABLE_2252341 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2093431 tptp.nat) (BOUND_VARIABLE_2093432 tptp.nat) (BOUND_VARIABLE_2093433 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2093433))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2093433))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16465 BOUND_VARIABLE_2252341) BOUND_VARIABLE_2093431) BOUND_VARIABLE_2093432) BOUND_VARIABLE_2093433) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2252341 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2093431)) (ho_15161 k_15160 BOUND_VARIABLE_2093432))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3161 (forall ((BOUND_VARIABLE_2252409 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2093344 tptp.nat) (BOUND_VARIABLE_2093345 tptp.nat) (BOUND_VARIABLE_2093346 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2093346))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2093346))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16466 BOUND_VARIABLE_2252409) BOUND_VARIABLE_2093344) BOUND_VARIABLE_2093345) BOUND_VARIABLE_2093346) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2252409 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2093344)) (ho_15161 k_15160 BOUND_VARIABLE_2093345))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3162 (forall ((BOUND_VARIABLE_2252425 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2093269 tptp.nat) (BOUND_VARIABLE_2093270 tptp.nat) (BOUND_VARIABLE_2093271 tptp.int) (BOUND_VARIABLE_2093272 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15573 BOUND_VARIABLE_2093272) BOUND_VARIABLE_2093271)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15574 BOUND_VARIABLE_2252425) BOUND_VARIABLE_2093269) BOUND_VARIABLE_2093270))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16467 BOUND_VARIABLE_2252425) BOUND_VARIABLE_2093269) BOUND_VARIABLE_2093270) BOUND_VARIABLE_2093271) BOUND_VARIABLE_2093272))))) (let ((_let_3163 (forall ((BOUND_VARIABLE_2093240 tptp.int) (BOUND_VARIABLE_2093241 tptp.int) (BOUND_VARIABLE_2093242 tptp.int) (BOUND_VARIABLE_2093243 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2093240) BOUND_VARIABLE_2093242))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2093241) BOUND_VARIABLE_2093243))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16468 BOUND_VARIABLE_2093240) BOUND_VARIABLE_2093241) BOUND_VARIABLE_2093242) BOUND_VARIABLE_2093243))))))) (let ((_let_3164 (forall ((BOUND_VARIABLE_2252525 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2252523 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2093149 tptp.nat) (BOUND_VARIABLE_2093150 tptp.nat) (BOUND_VARIABLE_2093151 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2093151))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2093151))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2093149)) (ho_15161 k_15160 BOUND_VARIABLE_2093150))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16469 BOUND_VARIABLE_2252525) BOUND_VARIABLE_2252523) BOUND_VARIABLE_2093149) BOUND_VARIABLE_2093150) BOUND_VARIABLE_2093151) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2252525 _let_9)) (ho_15120 BOUND_VARIABLE_2252523 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3165 (forall ((BOUND_VARIABLE_2252599 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2252597 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2093056 tptp.nat) (BOUND_VARIABLE_2093057 tptp.nat) (BOUND_VARIABLE_2093058 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2093058))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2093058))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2093056)) (ho_15161 k_15160 BOUND_VARIABLE_2093057))))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16470 BOUND_VARIABLE_2252599) BOUND_VARIABLE_2252597) BOUND_VARIABLE_2093056) BOUND_VARIABLE_2093057) BOUND_VARIABLE_2093058) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) (ho_15120 BOUND_VARIABLE_2252599 _let_9)) (ho_15120 BOUND_VARIABLE_2252597 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3166 (forall ((BOUND_VARIABLE_2252620 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2252619 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2092972 tptp.nat) (BOUND_VARIABLE_2092973 tptp.nat) (BOUND_VARIABLE_2092974 tptp.int) (BOUND_VARIABLE_2092975 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15575 BOUND_VARIABLE_2092975) BOUND_VARIABLE_2092974)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15576 BOUND_VARIABLE_2252620) BOUND_VARIABLE_2252619) BOUND_VARIABLE_2092972) BOUND_VARIABLE_2092973))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 k_16471 BOUND_VARIABLE_2252620) BOUND_VARIABLE_2252619) BOUND_VARIABLE_2092972) BOUND_VARIABLE_2092973) BOUND_VARIABLE_2092974) BOUND_VARIABLE_2092975))))) (let ((_let_3167 (forall ((BOUND_VARIABLE_2092942 tptp.int) (BOUND_VARIABLE_2092943 tptp.int) (BOUND_VARIABLE_2092944 tptp.int) (BOUND_VARIABLE_2092945 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2092942) BOUND_VARIABLE_2092944))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2092943) BOUND_VARIABLE_2092945))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16472 BOUND_VARIABLE_2092942) BOUND_VARIABLE_2092943) BOUND_VARIABLE_2092944) BOUND_VARIABLE_2092945))))))) (let ((_let_3168 (forall ((BOUND_VARIABLE_2252721 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2092856 tptp.nat) (BOUND_VARIABLE_2092857 tptp.nat) (BOUND_VARIABLE_2092858 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2092858))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2092858))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16473 BOUND_VARIABLE_2252721) BOUND_VARIABLE_2092856) BOUND_VARIABLE_2092857) BOUND_VARIABLE_2092858) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2252721 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2092856)) (ho_15161 k_15160 BOUND_VARIABLE_2092857))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3169 (forall ((BOUND_VARIABLE_2252789 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2092769 tptp.nat) (BOUND_VARIABLE_2092770 tptp.nat) (BOUND_VARIABLE_2092771 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2092771))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2092771))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16474 BOUND_VARIABLE_2252789) BOUND_VARIABLE_2092769) BOUND_VARIABLE_2092770) BOUND_VARIABLE_2092771) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2252789 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2092769)) (ho_15161 k_15160 BOUND_VARIABLE_2092770))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3170 (forall ((BOUND_VARIABLE_2252805 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2092694 tptp.nat) (BOUND_VARIABLE_2092695 tptp.nat) (BOUND_VARIABLE_2092696 tptp.int) (BOUND_VARIABLE_2092697 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15577 BOUND_VARIABLE_2092697) BOUND_VARIABLE_2092696)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15578 BOUND_VARIABLE_2252805) BOUND_VARIABLE_2092694) BOUND_VARIABLE_2092695))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16475 BOUND_VARIABLE_2252805) BOUND_VARIABLE_2092694) BOUND_VARIABLE_2092695) BOUND_VARIABLE_2092696) BOUND_VARIABLE_2092697))))) (let ((_let_3171 (forall ((BOUND_VARIABLE_2092665 tptp.int) (BOUND_VARIABLE_2092666 tptp.int) (BOUND_VARIABLE_2092667 tptp.int) (BOUND_VARIABLE_2092668 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2092665) BOUND_VARIABLE_2092667))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2092666) BOUND_VARIABLE_2092668))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16476 BOUND_VARIABLE_2092665) BOUND_VARIABLE_2092666) BOUND_VARIABLE_2092667) BOUND_VARIABLE_2092668))))))) (let ((_let_3172 (forall ((BOUND_VARIABLE_2252903 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2092578 tptp.nat) (BOUND_VARIABLE_2092579 tptp.nat) (BOUND_VARIABLE_2092580 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2092580))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2092580))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16477 BOUND_VARIABLE_2252903) BOUND_VARIABLE_2092578) BOUND_VARIABLE_2092579) BOUND_VARIABLE_2092580) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2252903 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2092578)) (ho_15161 k_15160 BOUND_VARIABLE_2092579)))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3173 (forall ((BOUND_VARIABLE_2252972 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2092490 tptp.nat) (BOUND_VARIABLE_2092491 tptp.nat) (BOUND_VARIABLE_2092492 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2092492))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2092492))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16478 BOUND_VARIABLE_2252972) BOUND_VARIABLE_2092490) BOUND_VARIABLE_2092491) BOUND_VARIABLE_2092492) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 k_15121 (ho_15120 BOUND_VARIABLE_2252972 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2092490)) (ho_15161 k_15160 BOUND_VARIABLE_2092491)))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3174 (forall ((BOUND_VARIABLE_2252989 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2092413 tptp.nat) (BOUND_VARIABLE_2092414 tptp.nat) (BOUND_VARIABLE_2092415 tptp.int) (BOUND_VARIABLE_2092416 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15579 BOUND_VARIABLE_2092416) BOUND_VARIABLE_2092415)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15580 BOUND_VARIABLE_2252989) BOUND_VARIABLE_2092413) BOUND_VARIABLE_2092414))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16479 BOUND_VARIABLE_2252989) BOUND_VARIABLE_2092413) BOUND_VARIABLE_2092414) BOUND_VARIABLE_2092415) BOUND_VARIABLE_2092416))))) (let ((_let_3175 (forall ((BOUND_VARIABLE_2092384 tptp.int) (BOUND_VARIABLE_2092385 tptp.int) (BOUND_VARIABLE_2092386 tptp.int) (BOUND_VARIABLE_2092387 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2092384) BOUND_VARIABLE_2092386))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2092385) BOUND_VARIABLE_2092387))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16480 BOUND_VARIABLE_2092384) BOUND_VARIABLE_2092385) BOUND_VARIABLE_2092386) BOUND_VARIABLE_2092387))))))) (let ((_let_3176 (forall ((BOUND_VARIABLE_2092305 tptp.rat) (BOUND_VARIABLE_2092306 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2092306))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2092306))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2092305 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16481 BOUND_VARIABLE_2092305) BOUND_VARIABLE_2092306)))))))))))))) (let ((_let_3177 (forall ((BOUND_VARIABLE_2092226 tptp.rat) (BOUND_VARIABLE_2092227 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2092227))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2092227))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2092226 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16482 BOUND_VARIABLE_2092226) BOUND_VARIABLE_2092227)))))))))))))) (let ((_let_3178 (forall ((BOUND_VARIABLE_2092169 tptp.rat) (BOUND_VARIABLE_2092170 tptp.int) (BOUND_VARIABLE_2092171 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15581 BOUND_VARIABLE_2092171) BOUND_VARIABLE_2092170)) (ho_15260 k_15259 (ho_15145 k_15582 BOUND_VARIABLE_2092169))) (ho_15108 (ho_15107 (ho_15266 k_16483 BOUND_VARIABLE_2092169) BOUND_VARIABLE_2092170) BOUND_VARIABLE_2092171))))) (let ((_let_3179 (forall ((BOUND_VARIABLE_2092141 tptp.int) (BOUND_VARIABLE_2092142 tptp.int) (BOUND_VARIABLE_2092143 tptp.int) (BOUND_VARIABLE_2092144 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2092141) BOUND_VARIABLE_2092143))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2092142) BOUND_VARIABLE_2092144))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16484 BOUND_VARIABLE_2092141) BOUND_VARIABLE_2092142) BOUND_VARIABLE_2092143) BOUND_VARIABLE_2092144))))))) (let ((_let_3180 (forall ((BOUND_VARIABLE_2253237 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2092055 tptp.nat) (BOUND_VARIABLE_2092056 tptp.nat) (BOUND_VARIABLE_2092057 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2092057))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2092057))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16485 BOUND_VARIABLE_2253237) BOUND_VARIABLE_2092055) BOUND_VARIABLE_2092056) BOUND_VARIABLE_2092057) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2253237 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2092055)) (ho_15161 k_15160 BOUND_VARIABLE_2092056))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3181 (forall ((BOUND_VARIABLE_2253305 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2091968 tptp.nat) (BOUND_VARIABLE_2091969 tptp.nat) (BOUND_VARIABLE_2091970 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2091970))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2091970))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 k_16486 BOUND_VARIABLE_2253305) BOUND_VARIABLE_2091968) BOUND_VARIABLE_2091969) BOUND_VARIABLE_2091970) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2253305 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2091968)) (ho_15161 k_15160 BOUND_VARIABLE_2091969))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3182 (forall ((BOUND_VARIABLE_2253321 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2091893 tptp.nat) (BOUND_VARIABLE_2091894 tptp.nat) (BOUND_VARIABLE_2091895 tptp.int) (BOUND_VARIABLE_2091896 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15583 BOUND_VARIABLE_2091896) BOUND_VARIABLE_2091895)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 k_15584 BOUND_VARIABLE_2253321) BOUND_VARIABLE_2091893) BOUND_VARIABLE_2091894))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 k_16487 BOUND_VARIABLE_2253321) BOUND_VARIABLE_2091893) BOUND_VARIABLE_2091894) BOUND_VARIABLE_2091895) BOUND_VARIABLE_2091896))))) (let ((_let_3183 (forall ((BOUND_VARIABLE_2091864 tptp.int) (BOUND_VARIABLE_2091865 tptp.int) (BOUND_VARIABLE_2091866 tptp.int) (BOUND_VARIABLE_2091867 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2091864) BOUND_VARIABLE_2091866))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2091865) BOUND_VARIABLE_2091867))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16488 BOUND_VARIABLE_2091864) BOUND_VARIABLE_2091865) BOUND_VARIABLE_2091866) BOUND_VARIABLE_2091867))))))) (let ((_let_3184 (forall ((BOUND_VARIABLE_2091836 tptp.int) (BOUND_VARIABLE_2091837 tptp.int) (BOUND_VARIABLE_2091838 tptp.int) (BOUND_VARIABLE_2091839 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2091836) BOUND_VARIABLE_2091838))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2091837) BOUND_VARIABLE_2091839))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16489 BOUND_VARIABLE_2091836) BOUND_VARIABLE_2091837) BOUND_VARIABLE_2091838) BOUND_VARIABLE_2091839))))))) (let ((_let_3185 (forall ((BOUND_VARIABLE_2253437 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2091756 tptp.nat) (BOUND_VARIABLE_2091757 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2091757))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2091757))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15495 k_16490 BOUND_VARIABLE_2253437) BOUND_VARIABLE_2091756) BOUND_VARIABLE_2091757) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2253437 BOUND_VARIABLE_2091756)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3186 (forall ((BOUND_VARIABLE_2091711 tptp.int) (BOUND_VARIABLE_2091712 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15585 BOUND_VARIABLE_2091712) BOUND_VARIABLE_2091711)) (ho_15260 k_15259 k_16491)) (ho_15108 (ho_15107 k_16492 BOUND_VARIABLE_2091711) BOUND_VARIABLE_2091712))))) (let ((_let_3187 (forall ((BOUND_VARIABLE_2253511 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2091631 tptp.nat) (BOUND_VARIABLE_2091632 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2091632))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2091632))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15495 k_16493 BOUND_VARIABLE_2253511) BOUND_VARIABLE_2091631) BOUND_VARIABLE_2091632) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15120 BOUND_VARIABLE_2253511 BOUND_VARIABLE_2091631)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3188 (forall ((BOUND_VARIABLE_2253525 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2091569 tptp.nat) (BOUND_VARIABLE_2091570 tptp.int) (BOUND_VARIABLE_2091571 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15586 BOUND_VARIABLE_2091571) BOUND_VARIABLE_2091570)) (ho_15260 k_15259 (ho_15165 (ho_15495 k_15587 BOUND_VARIABLE_2253525) BOUND_VARIABLE_2091569))) (ho_15108 (ho_15107 (ho_15345 (ho_16334 k_16494 BOUND_VARIABLE_2253525) BOUND_VARIABLE_2091569) BOUND_VARIABLE_2091570) BOUND_VARIABLE_2091571))))) (let ((_let_3189 (forall ((BOUND_VARIABLE_2091540 tptp.int) (BOUND_VARIABLE_2091541 tptp.int) (BOUND_VARIABLE_2091542 tptp.int) (BOUND_VARIABLE_2091543 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2091540) BOUND_VARIABLE_2091542))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2091541) BOUND_VARIABLE_2091543))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16495 BOUND_VARIABLE_2091540) BOUND_VARIABLE_2091541) BOUND_VARIABLE_2091542) BOUND_VARIABLE_2091543))))))) (let ((_let_3190 (forall ((BOUND_VARIABLE_2091512 tptp.int) (BOUND_VARIABLE_2091513 tptp.int) (BOUND_VARIABLE_2091514 tptp.int) (BOUND_VARIABLE_2091515 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2091512) BOUND_VARIABLE_2091514))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2091513) BOUND_VARIABLE_2091515))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16496 BOUND_VARIABLE_2091512) BOUND_VARIABLE_2091513) BOUND_VARIABLE_2091514) BOUND_VARIABLE_2091515))))))) (let ((_let_3191 (forall ((BOUND_VARIABLE_2253645 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2253643 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2091421 tptp.nat) (BOUND_VARIABLE_2091422 tptp.nat) (BOUND_VARIABLE_2091423 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2091423))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2091423))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2091421)) (ho_15161 k_15160 BOUND_VARIABLE_2091422))))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16497 BOUND_VARIABLE_2253645) BOUND_VARIABLE_2253643) BOUND_VARIABLE_2091421) BOUND_VARIABLE_2091422) BOUND_VARIABLE_2091423) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_10 (ho_15120 BOUND_VARIABLE_2253645 _let_9)) (ho_15120 BOUND_VARIABLE_2253643 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3192 (forall ((BOUND_VARIABLE_2091375 tptp.int) (BOUND_VARIABLE_2091376 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15588 BOUND_VARIABLE_2091376) BOUND_VARIABLE_2091375)) (ho_15260 k_15259 k_16043)) (ho_15108 (ho_15107 k_16044 BOUND_VARIABLE_2091375) BOUND_VARIABLE_2091376))))) (let ((_let_3193 (forall ((BOUND_VARIABLE_2253729 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2253727 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2091284 tptp.nat) (BOUND_VARIABLE_2091285 tptp.nat) (BOUND_VARIABLE_2091286 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2091286))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2091286))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2091284)) (ho_15161 k_15160 BOUND_VARIABLE_2091285))))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (let ((_let_11 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_16498 BOUND_VARIABLE_2253729) BOUND_VARIABLE_2253727) BOUND_VARIABLE_2091284) BOUND_VARIABLE_2091285) BOUND_VARIABLE_2091286) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_11 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_10 (ho_15120 BOUND_VARIABLE_2253729 _let_9)) (ho_15120 BOUND_VARIABLE_2253727 _let_9))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))))) (let ((_let_3194 (forall ((BOUND_VARIABLE_2253750 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2253749 |u_(-> tptp.nat tptp.rat)|) (BOUND_VARIABLE_2091200 tptp.nat) (BOUND_VARIABLE_2091201 tptp.nat) (BOUND_VARIABLE_2091202 tptp.int) (BOUND_VARIABLE_2091203 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15589 BOUND_VARIABLE_2091203) BOUND_VARIABLE_2091202)) (ho_15260 k_15259 (ho_15165 (ho_15164 (ho_15163 (ho_15183 k_15590 BOUND_VARIABLE_2253750) BOUND_VARIABLE_2253749) BOUND_VARIABLE_2091200) BOUND_VARIABLE_2091201))) (ho_15108 (ho_15107 (ho_15345 (ho_15344 (ho_15343 (ho_15379 k_16499 BOUND_VARIABLE_2253750) BOUND_VARIABLE_2253749) BOUND_VARIABLE_2091200) BOUND_VARIABLE_2091201) BOUND_VARIABLE_2091202) BOUND_VARIABLE_2091203))))) (let ((_let_3195 (forall ((BOUND_VARIABLE_2091168 tptp.int) (BOUND_VARIABLE_2091169 tptp.int) (BOUND_VARIABLE_2091170 tptp.int) (BOUND_VARIABLE_2091171 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2091168) BOUND_VARIABLE_2091170))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2091169) BOUND_VARIABLE_2091171)) (ho_15114 k_15113 tptp.one)))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16500 BOUND_VARIABLE_2091168) BOUND_VARIABLE_2091169) BOUND_VARIABLE_2091170) BOUND_VARIABLE_2091171))))))) (let ((_let_3196 (forall ((BOUND_VARIABLE_2091089 tptp.rat) (BOUND_VARIABLE_2091090 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2091090))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2091090))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2091089 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16501 BOUND_VARIABLE_2091089) BOUND_VARIABLE_2091090)))))))))))))) (let ((_let_3197 (forall ((BOUND_VARIABLE_2091074 tptp.nat) (BOUND_VARIABLE_2091075 tptp.nat)) (= (ho_15120 (ho_16503 k_16502 BOUND_VARIABLE_2091074) BOUND_VARIABLE_2091075) (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15077 (ho_15161 k_15160 BOUND_VARIABLE_2091074)) (ho_15161 k_15160 (ho_15118 k_15117 (ho_15114 k_15113 (ho_15152 k_15151 tptp.one)))))))) (ho_15161 k_15160 (ho_15118 k_15117 (ho_15114 k_15113 tptp.one)))))))))) (let ((_let_3198 (forall ((BOUND_VARIABLE_2090992 tptp.num) (BOUND_VARIABLE_2090993 tptp.nat)) (= (ho_15195 (ho_16507 (ho_16506 (ho_16505 k_16504 (ho_15195 k_15196 tptp.one)) (ho_15608 k_15607 BOUND_VARIABLE_2090993)) (ho_15608 k_15609 BOUND_VARIABLE_2090993)) BOUND_VARIABLE_2090992) (ho_16510 (ho_16509 k_16508 BOUND_VARIABLE_2090992) BOUND_VARIABLE_2090993))))) (let ((_let_3199 (forall ((BOUND_VARIABLE_2090964 tptp.int) (BOUND_VARIABLE_2090965 tptp.int) (BOUND_VARIABLE_2090966 tptp.int) (BOUND_VARIABLE_2090967 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090964) BOUND_VARIABLE_2090966))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090965) BOUND_VARIABLE_2090967))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16511 BOUND_VARIABLE_2090964) BOUND_VARIABLE_2090965) BOUND_VARIABLE_2090966) BOUND_VARIABLE_2090967))))))) (let ((_let_3200 (forall ((BOUND_VARIABLE_2090860 tptp.int) (BOUND_VARIABLE_2090861 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2090861))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2090861))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2090860) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16512 BOUND_VARIABLE_2090860) BOUND_VARIABLE_2090861) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3201 (forall ((BOUND_VARIABLE_2090832 tptp.int) (BOUND_VARIABLE_2090833 tptp.int) (BOUND_VARIABLE_2090834 tptp.int) (BOUND_VARIABLE_2090835 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090832) BOUND_VARIABLE_2090834))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090833) BOUND_VARIABLE_2090835))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16513 BOUND_VARIABLE_2090832) BOUND_VARIABLE_2090833) BOUND_VARIABLE_2090834) BOUND_VARIABLE_2090835))))))) (let ((_let_3202 (forall ((BOUND_VARIABLE_2090700 tptp.int) (BOUND_VARIABLE_2090701 tptp.int) (BOUND_VARIABLE_2090702 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2090702))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2090702))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15141 (ho_16515 k_16514 BOUND_VARIABLE_2090700) BOUND_VARIABLE_2090701) BOUND_VARIABLE_2090702) (and (= (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2090700) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2090700)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2090700))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2090701) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2090701)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2090701))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3203 (forall ((BOUND_VARIABLE_2090670 tptp.nat) (BOUND_VARIABLE_2090671 tptp.nat) (BOUND_VARIABLE_2090672 tptp.nat) (BOUND_VARIABLE_2090673 tptp.nat)) (= (ho_16520 (ho_16519 (ho_16518 (ho_16517 k_16516 BOUND_VARIABLE_2090670) BOUND_VARIABLE_2090671) BOUND_VARIABLE_2090672) BOUND_VARIABLE_2090673) (not (forall ((K3 tptp.nat)) (not (= (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2090672)) (ho_15161 k_15160 BOUND_VARIABLE_2090671))) (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2090670)) (ho_15161 k_15160 BOUND_VARIABLE_2090673))))) (ho_15161 k_15160 (ho_15118 k_15117 (ho_15114 k_15113 tptp.one))))))) (ho_15161 k_15160 K3))))))))))) (let ((_let_3204 (forall ((BOUND_VARIABLE_2090644 tptp.nat) (BOUND_VARIABLE_2090645 tptp.nat) (BOUND_VARIABLE_2090646 tptp.nat) (BOUND_VARIABLE_2090647 tptp.nat)) (= (ho_16520 (ho_16519 (ho_16518 (ho_16517 k_16521 BOUND_VARIABLE_2090644) BOUND_VARIABLE_2090645) BOUND_VARIABLE_2090646) BOUND_VARIABLE_2090647) (not (forall ((K3 tptp.nat)) (not (= (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2090646)) (ho_15161 k_15160 BOUND_VARIABLE_2090645))) (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2090644)) (ho_15161 k_15160 BOUND_VARIABLE_2090647))))) (ho_15161 k_15160 K3))))))))))) (let ((_let_3205 (forall ((BOUND_VARIABLE_2090616 tptp.int) (BOUND_VARIABLE_2090617 tptp.int) (BOUND_VARIABLE_2090618 tptp.int) (BOUND_VARIABLE_2090619 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090616) BOUND_VARIABLE_2090618))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090617) BOUND_VARIABLE_2090619))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16522 BOUND_VARIABLE_2090616) BOUND_VARIABLE_2090617) BOUND_VARIABLE_2090618) BOUND_VARIABLE_2090619))))))) (let ((_let_3206 (forall ((BOUND_VARIABLE_2090537 tptp.rat) (BOUND_VARIABLE_2090538 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2090538))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2090538))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2090537 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16523 BOUND_VARIABLE_2090537) BOUND_VARIABLE_2090538)))))))))))))) (let ((_let_3207 (forall ((BOUND_VARIABLE_2090509 tptp.int) (BOUND_VARIABLE_2090510 tptp.int) (BOUND_VARIABLE_2090511 tptp.int) (BOUND_VARIABLE_2090512 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090509) BOUND_VARIABLE_2090511))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090510) BOUND_VARIABLE_2090512))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16524 BOUND_VARIABLE_2090509) BOUND_VARIABLE_2090510) BOUND_VARIABLE_2090511) BOUND_VARIABLE_2090512))))))) (let ((_let_3208 (forall ((BOUND_VARIABLE_2090430 tptp.rat) (BOUND_VARIABLE_2090431 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2090431))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2090431))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2090430 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16525 BOUND_VARIABLE_2090430) BOUND_VARIABLE_2090431)))))))))))))) (let ((_let_3209 (forall ((BOUND_VARIABLE_2090402 tptp.int) (BOUND_VARIABLE_2090403 tptp.int) (BOUND_VARIABLE_2090404 tptp.int) (BOUND_VARIABLE_2090405 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090402) BOUND_VARIABLE_2090404))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090403) BOUND_VARIABLE_2090405))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16526 BOUND_VARIABLE_2090402) BOUND_VARIABLE_2090403) BOUND_VARIABLE_2090404) BOUND_VARIABLE_2090405))))))) (let ((_let_3210 (forall ((BOUND_VARIABLE_2090323 tptp.rat) (BOUND_VARIABLE_2090324 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2090324))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2090324))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2090323 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16527 BOUND_VARIABLE_2090323) BOUND_VARIABLE_2090324)))))))))))))) (let ((_let_3211 (forall ((BOUND_VARIABLE_2090295 tptp.int) (BOUND_VARIABLE_2090296 tptp.int) (BOUND_VARIABLE_2090297 tptp.int) (BOUND_VARIABLE_2090298 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090295) BOUND_VARIABLE_2090297))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090296) BOUND_VARIABLE_2090298))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16528 BOUND_VARIABLE_2090295) BOUND_VARIABLE_2090296) BOUND_VARIABLE_2090297) BOUND_VARIABLE_2090298))))))) (let ((_let_3212 (forall ((BOUND_VARIABLE_2090216 tptp.rat) (BOUND_VARIABLE_2090217 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2090217))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2090217))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2090216 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16529 BOUND_VARIABLE_2090216) BOUND_VARIABLE_2090217)))))))))))))) (let ((_let_3213 (forall ((BOUND_VARIABLE_2090188 tptp.int) (BOUND_VARIABLE_2090189 tptp.int) (BOUND_VARIABLE_2090190 tptp.int) (BOUND_VARIABLE_2090191 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090188) BOUND_VARIABLE_2090190))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090189) BOUND_VARIABLE_2090191))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16530 BOUND_VARIABLE_2090188) BOUND_VARIABLE_2090189) BOUND_VARIABLE_2090190) BOUND_VARIABLE_2090191))))))) (let ((_let_3214 (forall ((BOUND_VARIABLE_2090109 tptp.rat) (BOUND_VARIABLE_2090110 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2090110))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2090110))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2090109 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16531 BOUND_VARIABLE_2090109) BOUND_VARIABLE_2090110)))))))))))))) (let ((_let_3215 (forall ((BOUND_VARIABLE_2090102 tptp.nat) (BOUND_VARIABLE_2090103 tptp.nat)) (= (ho_15120 (ho_16503 k_16532 BOUND_VARIABLE_2090102) BOUND_VARIABLE_2090103) (ho_15120 k_15119 BOUND_VARIABLE_2090102))))) (let ((_let_3216 (forall ((BOUND_VARIABLE_2090086 tptp.nat) (BOUND_VARIABLE_2090087 tptp.nat) (BOUND_VARIABLE_2090088 tptp.nat)) (= (ho_15120 (ho_16503 (ho_16534 k_16533 BOUND_VARIABLE_2090086) BOUND_VARIABLE_2090087) BOUND_VARIABLE_2090088) (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2090086)) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 (ho_15161 k_15160 BOUND_VARIABLE_2090087))) (ho_15114 k_15113 tptp.one))))))))) (let ((_let_3217 (forall ((BOUND_VARIABLE_2090081 tptp.nat)) (= BOUND_VARIABLE_2090081 (ho_15593 k_16535 BOUND_VARIABLE_2090081))))) (let ((_let_3218 (forall ((BOUND_VARIABLE_2090060 tptp.nat) (BOUND_VARIABLE_2090061 tptp.nat)) (= (ho_16520 (ho_16519 k_16536 BOUND_VARIABLE_2090060) BOUND_VARIABLE_2090061) (not (forall ((I2 tptp.nat) (BOUND_VARIABLE_358980 tptp.nat)) (let ((_let_1 (ho_15118 k_15117 (ho_15114 k_15113 tptp.one)))) (let ((_let_2 (ho_15161 k_15160 _let_1))) (let ((_let_3 (ho_16539 (ho_16538 k_16537 _let_1) (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 BOUND_VARIABLE_2090060)) _let_2))))) (or (not (= BOUND_VARIABLE_2090061 (ho_15593 (ho_16543 k_16542 _let_3) I2))) (not (= (ho_16541 k_16540 _let_3) (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15161 k_15160 I2)) _let_2)))) (ho_15161 k_15160 BOUND_VARIABLE_358980))))))))))))))) (let ((_let_3219 (forall ((BOUND_VARIABLE_2090053 tptp.nat) (BOUND_VARIABLE_2090054 tptp.nat)) (= (ho_15120 (ho_16503 k_16544 BOUND_VARIABLE_2090053) BOUND_VARIABLE_2090054) (ho_15120 k_15119 BOUND_VARIABLE_2090053))))) (let ((_let_3220 (forall ((BOUND_VARIABLE_2090025 tptp.int) (BOUND_VARIABLE_2090026 tptp.int) (BOUND_VARIABLE_2090027 tptp.int) (BOUND_VARIABLE_2090028 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090025) BOUND_VARIABLE_2090027))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2090026) BOUND_VARIABLE_2090028))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16545 BOUND_VARIABLE_2090025) BOUND_VARIABLE_2090026) BOUND_VARIABLE_2090027) BOUND_VARIABLE_2090028))))))) (let ((_let_3221 (forall ((BOUND_VARIABLE_2089946 tptp.rat) (BOUND_VARIABLE_2089947 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2089947))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2089947))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2089946 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16546 BOUND_VARIABLE_2089946) BOUND_VARIABLE_2089947)))))))))))))) (let ((_let_3222 (forall ((BOUND_VARIABLE_2089918 tptp.int) (BOUND_VARIABLE_2089919 tptp.int) (BOUND_VARIABLE_2089920 tptp.int) (BOUND_VARIABLE_2089921 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089918) BOUND_VARIABLE_2089920))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089919) BOUND_VARIABLE_2089921))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16547 BOUND_VARIABLE_2089918) BOUND_VARIABLE_2089919) BOUND_VARIABLE_2089920) BOUND_VARIABLE_2089921))))))) (let ((_let_3223 (forall ((BOUND_VARIABLE_2089839 tptp.rat) (BOUND_VARIABLE_2089840 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2089840))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2089840))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2089839 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16548 BOUND_VARIABLE_2089839) BOUND_VARIABLE_2089840)))))))))))))) (let ((_let_3224 (forall ((BOUND_VARIABLE_2089811 tptp.int) (BOUND_VARIABLE_2089812 tptp.int) (BOUND_VARIABLE_2089813 tptp.int) (BOUND_VARIABLE_2089814 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089811) BOUND_VARIABLE_2089813))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089812) BOUND_VARIABLE_2089814))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16549 BOUND_VARIABLE_2089811) BOUND_VARIABLE_2089812) BOUND_VARIABLE_2089813) BOUND_VARIABLE_2089814))))))) (let ((_let_3225 (forall ((BOUND_VARIABLE_2089732 tptp.rat) (BOUND_VARIABLE_2089733 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2089733))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2089733))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2089732 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16550 BOUND_VARIABLE_2089732) BOUND_VARIABLE_2089733)))))))))))))) (let ((_let_3226 (forall ((BOUND_VARIABLE_2089704 tptp.int) (BOUND_VARIABLE_2089705 tptp.int) (BOUND_VARIABLE_2089706 tptp.int) (BOUND_VARIABLE_2089707 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089704) BOUND_VARIABLE_2089706))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089705) BOUND_VARIABLE_2089707))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16551 BOUND_VARIABLE_2089704) BOUND_VARIABLE_2089705) BOUND_VARIABLE_2089706) BOUND_VARIABLE_2089707))))))) (let ((_let_3227 (forall ((BOUND_VARIABLE_2089625 tptp.rat) (BOUND_VARIABLE_2089626 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2089626))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2089626))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2089625 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16552 BOUND_VARIABLE_2089625) BOUND_VARIABLE_2089626)))))))))))))) (let ((_let_3228 (forall ((BOUND_VARIABLE_2089597 tptp.int) (BOUND_VARIABLE_2089598 tptp.int) (BOUND_VARIABLE_2089599 tptp.int) (BOUND_VARIABLE_2089600 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089597) BOUND_VARIABLE_2089599))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089598) BOUND_VARIABLE_2089600))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16553 BOUND_VARIABLE_2089597) BOUND_VARIABLE_2089598) BOUND_VARIABLE_2089599) BOUND_VARIABLE_2089600))))))) (let ((_let_3229 (forall ((BOUND_VARIABLE_2089518 tptp.rat) (BOUND_VARIABLE_2089519 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2089519))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2089519))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2089518 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16554 BOUND_VARIABLE_2089518) BOUND_VARIABLE_2089519)))))))))))))) (let ((_let_3230 (forall ((BOUND_VARIABLE_2089490 tptp.int) (BOUND_VARIABLE_2089491 tptp.int) (BOUND_VARIABLE_2089492 tptp.int) (BOUND_VARIABLE_2089493 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089490) BOUND_VARIABLE_2089492))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089491) BOUND_VARIABLE_2089493))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16555 BOUND_VARIABLE_2089490) BOUND_VARIABLE_2089491) BOUND_VARIABLE_2089492) BOUND_VARIABLE_2089493))))))) (let ((_let_3231 (forall ((BOUND_VARIABLE_2089411 tptp.rat) (BOUND_VARIABLE_2089412 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2089412))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2089412))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2089411 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16556 BOUND_VARIABLE_2089411) BOUND_VARIABLE_2089412)))))))))))))) (let ((_let_3232 (forall ((BOUND_VARIABLE_2089383 tptp.int) (BOUND_VARIABLE_2089384 tptp.int) (BOUND_VARIABLE_2089385 tptp.int) (BOUND_VARIABLE_2089386 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089383) BOUND_VARIABLE_2089385))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089384) BOUND_VARIABLE_2089386))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16557 BOUND_VARIABLE_2089383) BOUND_VARIABLE_2089384) BOUND_VARIABLE_2089385) BOUND_VARIABLE_2089386))))))) (let ((_let_3233 (forall ((BOUND_VARIABLE_2089304 tptp.rat) (BOUND_VARIABLE_2089305 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2089305))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2089305))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2089304 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16558 BOUND_VARIABLE_2089304) BOUND_VARIABLE_2089305)))))))))))))) (let ((_let_3234 (forall ((BOUND_VARIABLE_2089276 tptp.int) (BOUND_VARIABLE_2089277 tptp.int) (BOUND_VARIABLE_2089278 tptp.int) (BOUND_VARIABLE_2089279 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089276) BOUND_VARIABLE_2089278))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089277) BOUND_VARIABLE_2089279))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16559 BOUND_VARIABLE_2089276) BOUND_VARIABLE_2089277) BOUND_VARIABLE_2089278) BOUND_VARIABLE_2089279))))))) (let ((_let_3235 (forall ((BOUND_VARIABLE_2089197 tptp.rat) (BOUND_VARIABLE_2089198 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2089198))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2089198))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2089197 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16560 BOUND_VARIABLE_2089197) BOUND_VARIABLE_2089198)))))))))))))) (let ((_let_3236 (forall ((BOUND_VARIABLE_2089169 tptp.int) (BOUND_VARIABLE_2089170 tptp.int) (BOUND_VARIABLE_2089171 tptp.int) (BOUND_VARIABLE_2089172 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089169) BOUND_VARIABLE_2089171))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089170) BOUND_VARIABLE_2089172))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16561 BOUND_VARIABLE_2089169) BOUND_VARIABLE_2089170) BOUND_VARIABLE_2089171) BOUND_VARIABLE_2089172))))))) (let ((_let_3237 (forall ((BOUND_VARIABLE_2089090 tptp.rat) (BOUND_VARIABLE_2089091 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2089091))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2089091))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2089090 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16562 BOUND_VARIABLE_2089090) BOUND_VARIABLE_2089091)))))))))))))) (let ((_let_3238 (forall ((BOUND_VARIABLE_2089062 tptp.int) (BOUND_VARIABLE_2089063 tptp.int) (BOUND_VARIABLE_2089064 tptp.int) (BOUND_VARIABLE_2089065 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089062) BOUND_VARIABLE_2089064))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2089063) BOUND_VARIABLE_2089065))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16563 BOUND_VARIABLE_2089062) BOUND_VARIABLE_2089063) BOUND_VARIABLE_2089064) BOUND_VARIABLE_2089065))))))) (let ((_let_3239 (forall ((BOUND_VARIABLE_2088983 tptp.rat) (BOUND_VARIABLE_2088984 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2088984))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2088984))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2088983 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16564 BOUND_VARIABLE_2088983) BOUND_VARIABLE_2088984)))))))))))))) (let ((_let_3240 (forall ((BOUND_VARIABLE_2088955 tptp.int) (BOUND_VARIABLE_2088956 tptp.int) (BOUND_VARIABLE_2088957 tptp.int) (BOUND_VARIABLE_2088958 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088955) BOUND_VARIABLE_2088957))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088956) BOUND_VARIABLE_2088958))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16565 BOUND_VARIABLE_2088955) BOUND_VARIABLE_2088956) BOUND_VARIABLE_2088957) BOUND_VARIABLE_2088958))))))) (let ((_let_3241 (forall ((BOUND_VARIABLE_2088876 tptp.rat) (BOUND_VARIABLE_2088877 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2088877))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2088877))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2088876 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16566 BOUND_VARIABLE_2088876) BOUND_VARIABLE_2088877)))))))))))))) (let ((_let_3242 (forall ((BOUND_VARIABLE_2088848 tptp.int) (BOUND_VARIABLE_2088849 tptp.int) (BOUND_VARIABLE_2088850 tptp.int) (BOUND_VARIABLE_2088851 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088848) BOUND_VARIABLE_2088850))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088849) BOUND_VARIABLE_2088851))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16567 BOUND_VARIABLE_2088848) BOUND_VARIABLE_2088849) BOUND_VARIABLE_2088850) BOUND_VARIABLE_2088851))))))) (let ((_let_3243 (forall ((BOUND_VARIABLE_2088769 tptp.rat) (BOUND_VARIABLE_2088770 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2088770))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2088770))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2088769 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16568 BOUND_VARIABLE_2088769) BOUND_VARIABLE_2088770)))))))))))))) (let ((_let_3244 (forall ((BOUND_VARIABLE_2088741 tptp.int) (BOUND_VARIABLE_2088742 tptp.int) (BOUND_VARIABLE_2088743 tptp.int) (BOUND_VARIABLE_2088744 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088741) BOUND_VARIABLE_2088743))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088742) BOUND_VARIABLE_2088744))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16569 BOUND_VARIABLE_2088741) BOUND_VARIABLE_2088742) BOUND_VARIABLE_2088743) BOUND_VARIABLE_2088744))))))) (let ((_let_3245 (forall ((BOUND_VARIABLE_2088662 tptp.rat) (BOUND_VARIABLE_2088663 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2088663))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2088663))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2088662 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16570 BOUND_VARIABLE_2088662) BOUND_VARIABLE_2088663)))))))))))))) (let ((_let_3246 (forall ((BOUND_VARIABLE_2088634 tptp.int) (BOUND_VARIABLE_2088635 tptp.int) (BOUND_VARIABLE_2088636 tptp.int) (BOUND_VARIABLE_2088637 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088634) BOUND_VARIABLE_2088636))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088635) BOUND_VARIABLE_2088637))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16571 BOUND_VARIABLE_2088634) BOUND_VARIABLE_2088635) BOUND_VARIABLE_2088636) BOUND_VARIABLE_2088637))))))) (let ((_let_3247 (forall ((BOUND_VARIABLE_2088555 tptp.rat) (BOUND_VARIABLE_2088556 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2088556))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2088556))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2088555 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16572 BOUND_VARIABLE_2088555) BOUND_VARIABLE_2088556)))))))))))))) (let ((_let_3248 (forall ((BOUND_VARIABLE_2088527 tptp.int) (BOUND_VARIABLE_2088528 tptp.int) (BOUND_VARIABLE_2088529 tptp.int) (BOUND_VARIABLE_2088530 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088527) BOUND_VARIABLE_2088529))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088528) BOUND_VARIABLE_2088530))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16573 BOUND_VARIABLE_2088527) BOUND_VARIABLE_2088528) BOUND_VARIABLE_2088529) BOUND_VARIABLE_2088530))))))) (let ((_let_3249 (forall ((BOUND_VARIABLE_2088448 tptp.rat) (BOUND_VARIABLE_2088449 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2088449))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2088449))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2088448 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16574 BOUND_VARIABLE_2088448) BOUND_VARIABLE_2088449)))))))))))))) (let ((_let_3250 (forall ((BOUND_VARIABLE_2088420 tptp.int) (BOUND_VARIABLE_2088421 tptp.int) (BOUND_VARIABLE_2088422 tptp.int) (BOUND_VARIABLE_2088423 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088420) BOUND_VARIABLE_2088422))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088421) BOUND_VARIABLE_2088423))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16575 BOUND_VARIABLE_2088420) BOUND_VARIABLE_2088421) BOUND_VARIABLE_2088422) BOUND_VARIABLE_2088423))))))) (let ((_let_3251 (forall ((BOUND_VARIABLE_2088341 tptp.rat) (BOUND_VARIABLE_2088342 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2088342))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2088342))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2088341 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16576 BOUND_VARIABLE_2088341) BOUND_VARIABLE_2088342)))))))))))))) (let ((_let_3252 (forall ((BOUND_VARIABLE_2088313 tptp.int) (BOUND_VARIABLE_2088314 tptp.int) (BOUND_VARIABLE_2088315 tptp.int) (BOUND_VARIABLE_2088316 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088313) BOUND_VARIABLE_2088315))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088314) BOUND_VARIABLE_2088316))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16577 BOUND_VARIABLE_2088313) BOUND_VARIABLE_2088314) BOUND_VARIABLE_2088315) BOUND_VARIABLE_2088316))))))) (let ((_let_3253 (forall ((BOUND_VARIABLE_2088234 tptp.rat) (BOUND_VARIABLE_2088235 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2088235))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2088235))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2088234 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16578 BOUND_VARIABLE_2088234) BOUND_VARIABLE_2088235)))))))))))))) (let ((_let_3254 (forall ((BOUND_VARIABLE_2088206 tptp.int) (BOUND_VARIABLE_2088207 tptp.int) (BOUND_VARIABLE_2088208 tptp.int) (BOUND_VARIABLE_2088209 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088206) BOUND_VARIABLE_2088208))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088207) BOUND_VARIABLE_2088209))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16579 BOUND_VARIABLE_2088206) BOUND_VARIABLE_2088207) BOUND_VARIABLE_2088208) BOUND_VARIABLE_2088209))))))) (let ((_let_3255 (forall ((BOUND_VARIABLE_2088127 tptp.rat) (BOUND_VARIABLE_2088128 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2088128))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2088128))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2088127 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16580 BOUND_VARIABLE_2088127) BOUND_VARIABLE_2088128)))))))))))))) (let ((_let_3256 (forall ((BOUND_VARIABLE_2088099 tptp.int) (BOUND_VARIABLE_2088100 tptp.int) (BOUND_VARIABLE_2088101 tptp.int) (BOUND_VARIABLE_2088102 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088099) BOUND_VARIABLE_2088101))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2088100) BOUND_VARIABLE_2088102))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16581 BOUND_VARIABLE_2088099) BOUND_VARIABLE_2088100) BOUND_VARIABLE_2088101) BOUND_VARIABLE_2088102))))))) (let ((_let_3257 (forall ((BOUND_VARIABLE_2088020 tptp.rat) (BOUND_VARIABLE_2088021 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2088021))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2088021))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2088020 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16582 BOUND_VARIABLE_2088020) BOUND_VARIABLE_2088021)))))))))))))) (let ((_let_3258 (forall ((BOUND_VARIABLE_2088013 tptp.nat) (BOUND_VARIABLE_2088014 tptp.nat)) (= (ho_15120 (ho_16503 k_16583 BOUND_VARIABLE_2088013) BOUND_VARIABLE_2088014) (ho_15120 k_15119 BOUND_VARIABLE_2088013))))) (let ((_let_3259 (forall ((BOUND_VARIABLE_2088006 tptp.nat) (BOUND_VARIABLE_2088007 tptp.nat)) (= (ho_15120 (ho_16503 k_16584 BOUND_VARIABLE_2088006) BOUND_VARIABLE_2088007) (ho_15120 k_15119 BOUND_VARIABLE_2088006))))) (let ((_let_3260 (forall ((BOUND_VARIABLE_2087978 tptp.int) (BOUND_VARIABLE_2087979 tptp.int) (BOUND_VARIABLE_2087980 tptp.int) (BOUND_VARIABLE_2087981 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087978) BOUND_VARIABLE_2087980))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087979) BOUND_VARIABLE_2087981))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16585 BOUND_VARIABLE_2087978) BOUND_VARIABLE_2087979) BOUND_VARIABLE_2087980) BOUND_VARIABLE_2087981))))))) (let ((_let_3261 (forall ((BOUND_VARIABLE_2087874 tptp.int) (BOUND_VARIABLE_2087875 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2087875))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2087875))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2087874) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16586 BOUND_VARIABLE_2087874) BOUND_VARIABLE_2087875) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3262 (forall ((BOUND_VARIABLE_2087846 tptp.int) (BOUND_VARIABLE_2087847 tptp.int) (BOUND_VARIABLE_2087848 tptp.int) (BOUND_VARIABLE_2087849 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087846) BOUND_VARIABLE_2087848))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087847) BOUND_VARIABLE_2087849))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16587 BOUND_VARIABLE_2087846) BOUND_VARIABLE_2087847) BOUND_VARIABLE_2087848) BOUND_VARIABLE_2087849))))))) (let ((_let_3263 (forall ((BOUND_VARIABLE_2087767 tptp.rat) (BOUND_VARIABLE_2087768 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2087768))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2087768))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2087767 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16588 BOUND_VARIABLE_2087767) BOUND_VARIABLE_2087768)))))))))))))) (let ((_let_3264 (forall ((BOUND_VARIABLE_2087739 tptp.int) (BOUND_VARIABLE_2087740 tptp.int) (BOUND_VARIABLE_2087741 tptp.int) (BOUND_VARIABLE_2087742 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087739) BOUND_VARIABLE_2087741))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087740) BOUND_VARIABLE_2087742))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16589 BOUND_VARIABLE_2087739) BOUND_VARIABLE_2087740) BOUND_VARIABLE_2087741) BOUND_VARIABLE_2087742))))))) (let ((_let_3265 (forall ((BOUND_VARIABLE_2087635 tptp.int) (BOUND_VARIABLE_2087636 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2087636))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2087636))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 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_let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3266 (forall ((BOUND_VARIABLE_2087607 tptp.int) (BOUND_VARIABLE_2087608 tptp.int) (BOUND_VARIABLE_2087609 tptp.int) (BOUND_VARIABLE_2087610 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087607) BOUND_VARIABLE_2087609))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087608) BOUND_VARIABLE_2087610))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16591 BOUND_VARIABLE_2087607) BOUND_VARIABLE_2087608) BOUND_VARIABLE_2087609) BOUND_VARIABLE_2087610))))))) (let ((_let_3267 (forall ((BOUND_VARIABLE_2087528 tptp.rat) (BOUND_VARIABLE_2087529 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2087529))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2087529))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2087528 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16592 BOUND_VARIABLE_2087528) BOUND_VARIABLE_2087529)))))))))))))) (let ((_let_3268 (forall ((BOUND_VARIABLE_2087500 tptp.int) (BOUND_VARIABLE_2087501 tptp.int) (BOUND_VARIABLE_2087502 tptp.int) (BOUND_VARIABLE_2087503 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087500) BOUND_VARIABLE_2087502))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087501) BOUND_VARIABLE_2087503))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16593 BOUND_VARIABLE_2087500) BOUND_VARIABLE_2087501) BOUND_VARIABLE_2087502) BOUND_VARIABLE_2087503))))))) (let ((_let_3269 (forall ((BOUND_VARIABLE_2087396 tptp.int) (BOUND_VARIABLE_2087397 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2087397))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2087397))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2087396) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16594 BOUND_VARIABLE_2087396) BOUND_VARIABLE_2087397) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3270 (forall ((BOUND_VARIABLE_2087368 tptp.int) (BOUND_VARIABLE_2087369 tptp.int) (BOUND_VARIABLE_2087370 tptp.int) (BOUND_VARIABLE_2087371 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087368) BOUND_VARIABLE_2087370))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2087369) BOUND_VARIABLE_2087371))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16595 BOUND_VARIABLE_2087368) BOUND_VARIABLE_2087369) BOUND_VARIABLE_2087370) BOUND_VARIABLE_2087371))))))) (let ((_let_3271 (forall ((BOUND_VARIABLE_2087284 tptp.rat) (BOUND_VARIABLE_2087285 tptp.rat) (BOUND_VARIABLE_2087286 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2087286))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2087286))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 (ho_15209 k_16596 BOUND_VARIABLE_2087284) BOUND_VARIABLE_2087285) BOUND_VARIABLE_2087286) (and (= (ho_15122 (ho_15125 _let_9 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_9 BOUND_VARIABLE_2087284) BOUND_VARIABLE_2087285)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3272 (forall ((BOUND_VARIABLE_2087113 tptp.rat) (BOUND_VARIABLE_2087114 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15618 BOUND_VARIABLE_2087113)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15615 BOUND_VARIABLE_2087114))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15616 BOUND_VARIABLE_2087114)) (ho_15260 k_15259 (ho_15145 k_15617 BOUND_VARIABLE_2087113))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15619 BOUND_VARIABLE_2087114))))) (ho_15108 (ho_15783 k_16597 BOUND_VARIABLE_2087113) BOUND_VARIABLE_2087114)))))) (let ((_let_3273 (forall ((BOUND_VARIABLE_2086942 tptp.rat) (BOUND_VARIABLE_2086943 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15623 BOUND_VARIABLE_2086942)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15620 BOUND_VARIABLE_2086943))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15621 BOUND_VARIABLE_2086943)) (ho_15260 k_15259 (ho_15145 k_15622 BOUND_VARIABLE_2086942))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15624 BOUND_VARIABLE_2086943))))) (ho_15108 (ho_15783 k_16598 BOUND_VARIABLE_2086942) BOUND_VARIABLE_2086943)))))) (let ((_let_3274 (forall ((BOUND_VARIABLE_2086840 tptp.int) (BOUND_VARIABLE_2086841 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2086841))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2086841))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16599 BOUND_VARIABLE_2086840) BOUND_VARIABLE_2086841) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2086840) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2086840)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2086840))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3275 (forall ((BOUND_VARIABLE_2086745 tptp.int) (BOUND_VARIABLE_2086746 tptp.int) (BOUND_VARIABLE_2086747 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15625 BOUND_VARIABLE_2086747) BOUND_VARIABLE_2086746)) (ho_15260 k_15259 (ho_15141 k_15626 BOUND_VARIABLE_2086745))) (ho_15108 (ho_15107 (ho_15106 k_16600 BOUND_VARIABLE_2086745) BOUND_VARIABLE_2086746) BOUND_VARIABLE_2086747))))) (let ((_let_3276 (forall ((BOUND_VARIABLE_2086661 tptp.rat) (BOUND_VARIABLE_2086662 tptp.rat) (BOUND_VARIABLE_2086663 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2086663))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2086663))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (= (ho_15142 (ho_15145 (ho_15209 k_16601 BOUND_VARIABLE_2086661) BOUND_VARIABLE_2086662) BOUND_VARIABLE_2086663) (and (= (ho_15122 (ho_15125 _let_10 BOUND_VARIABLE_2086661) BOUND_VARIABLE_2086662) (ho_15122 (ho_15125 _let_10 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3277 (forall ((BOUND_VARIABLE_2086597 tptp.rat) (BOUND_VARIABLE_2086598 tptp.rat) (BOUND_VARIABLE_2086599 tptp.int) (BOUND_VARIABLE_2086600 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15627 BOUND_VARIABLE_2086600) BOUND_VARIABLE_2086599)) (ho_15260 k_15259 (ho_15145 (ho_15209 k_15628 BOUND_VARIABLE_2086597) BOUND_VARIABLE_2086598))) (ho_15108 (ho_15107 (ho_15266 (ho_15633 k_16602 BOUND_VARIABLE_2086597) BOUND_VARIABLE_2086598) BOUND_VARIABLE_2086599) BOUND_VARIABLE_2086600))))) (let ((_let_3278 (forall ((BOUND_VARIABLE_2086493 tptp.int) (BOUND_VARIABLE_2086494 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2086494))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2086494))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2086493) _let_3))) (= (ho_15142 (ho_15141 k_16603 BOUND_VARIABLE_2086493) BOUND_VARIABLE_2086494) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3279 (forall ((BOUND_VARIABLE_2086465 tptp.int) (BOUND_VARIABLE_2086466 tptp.int) (BOUND_VARIABLE_2086467 tptp.int) (BOUND_VARIABLE_2086468 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2086465) BOUND_VARIABLE_2086467))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2086466) BOUND_VARIABLE_2086468))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16604 BOUND_VARIABLE_2086465) BOUND_VARIABLE_2086466) BOUND_VARIABLE_2086467) BOUND_VARIABLE_2086468))))))) (let ((_let_3280 (forall ((BOUND_VARIABLE_2086361 tptp.int) (BOUND_VARIABLE_2086362 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2086362))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2086362))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2086361) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16605 BOUND_VARIABLE_2086361) BOUND_VARIABLE_2086362) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3281 (forall ((BOUND_VARIABLE_2086333 tptp.int) (BOUND_VARIABLE_2086334 tptp.int) (BOUND_VARIABLE_2086335 tptp.int) (BOUND_VARIABLE_2086336 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2086333) BOUND_VARIABLE_2086335))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2086334) BOUND_VARIABLE_2086336))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16606 BOUND_VARIABLE_2086333) BOUND_VARIABLE_2086334) BOUND_VARIABLE_2086335) BOUND_VARIABLE_2086336))))))) (let ((_let_3282 (forall ((BOUND_VARIABLE_2086249 tptp.rat) (BOUND_VARIABLE_2086250 tptp.rat) (BOUND_VARIABLE_2086251 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2086251))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2086251))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 (ho_15209 k_16607 BOUND_VARIABLE_2086249) BOUND_VARIABLE_2086250) BOUND_VARIABLE_2086251) (and (= (ho_15122 (ho_15125 _let_9 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_9 BOUND_VARIABLE_2086249) BOUND_VARIABLE_2086250)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3283 (forall ((BOUND_VARIABLE_2086221 tptp.int) (BOUND_VARIABLE_2086222 tptp.int) (BOUND_VARIABLE_2086223 tptp.int) (BOUND_VARIABLE_2086224 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2086221) BOUND_VARIABLE_2086223))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2086222) BOUND_VARIABLE_2086224))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16608 BOUND_VARIABLE_2086221) BOUND_VARIABLE_2086222) BOUND_VARIABLE_2086223) BOUND_VARIABLE_2086224))))))) (let ((_let_3284 (forall ((BOUND_VARIABLE_2086117 tptp.int) (BOUND_VARIABLE_2086118 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2086118))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2086118))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2086117) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16609 BOUND_VARIABLE_2086117) BOUND_VARIABLE_2086118) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3285 (forall ((BOUND_VARIABLE_2086089 tptp.int) (BOUND_VARIABLE_2086090 tptp.int) (BOUND_VARIABLE_2086091 tptp.int) (BOUND_VARIABLE_2086092 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 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k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2086010 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16611 BOUND_VARIABLE_2086010) BOUND_VARIABLE_2086011)))))))))))))) (let ((_let_3287 (forall ((BOUND_VARIABLE_2085982 tptp.int) (BOUND_VARIABLE_2085983 tptp.int) (BOUND_VARIABLE_2085984 tptp.int) (BOUND_VARIABLE_2085985 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085982) BOUND_VARIABLE_2085984))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085983) BOUND_VARIABLE_2085985))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16612 BOUND_VARIABLE_2085982) BOUND_VARIABLE_2085983) BOUND_VARIABLE_2085984) BOUND_VARIABLE_2085985))))))) (let ((_let_3288 (forall ((BOUND_VARIABLE_2085878 tptp.int) (BOUND_VARIABLE_2085879 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2085879))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2085879))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2085878) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16613 BOUND_VARIABLE_2085878) BOUND_VARIABLE_2085879) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3289 (forall ((BOUND_VARIABLE_2085850 tptp.int) (BOUND_VARIABLE_2085851 tptp.int) (BOUND_VARIABLE_2085852 tptp.int) (BOUND_VARIABLE_2085853 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085850) BOUND_VARIABLE_2085852))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085851) BOUND_VARIABLE_2085853))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16614 BOUND_VARIABLE_2085850) BOUND_VARIABLE_2085851) BOUND_VARIABLE_2085852) BOUND_VARIABLE_2085853))))))) (let ((_let_3290 (forall ((BOUND_VARIABLE_2085771 tptp.rat) (BOUND_VARIABLE_2085772 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2085772))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2085772))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2085771 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16615 BOUND_VARIABLE_2085771) BOUND_VARIABLE_2085772)))))))))))))) (let ((_let_3291 (forall ((BOUND_VARIABLE_2085738 tptp.real) (BOUND_VARIABLE_2085739 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15091 _let_1 k_15082))) (let ((_let_3 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (let ((_let_4 (ho_15081 k_15080 BOUND_VARIABLE_2085739))) (= (and (or (ho_15103 k_15102 (ho_15092 (ho_15101 _let_3 BOUND_VARIABLE_2085738) (ho_15092 _let_2 _let_4))) (= BOUND_VARIABLE_2085738 _let_4)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_3 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2085739) (ho_15114 k_15113 tptp.one)))) (ho_15092 _let_2 BOUND_VARIABLE_2085738)))) (ho_15108 (ho_16617 k_16616 BOUND_VARIABLE_2085738) BOUND_VARIABLE_2085739))))))))) (let ((_let_3292 (forall ((BOUND_VARIABLE_2085705 tptp.real) (BOUND_VARIABLE_2085706 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15091 _let_1 k_15082))) (let ((_let_3 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (let ((_let_4 (ho_15081 k_15080 BOUND_VARIABLE_2085706))) (= (and (or (ho_15103 k_15102 (ho_15092 (ho_15101 _let_3 BOUND_VARIABLE_2085705) (ho_15092 _let_2 _let_4))) (= BOUND_VARIABLE_2085705 _let_4)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_3 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2085706) (ho_15114 k_15113 tptp.one)))) (ho_15092 _let_2 BOUND_VARIABLE_2085705)))) (ho_15108 (ho_16617 k_16618 BOUND_VARIABLE_2085705) BOUND_VARIABLE_2085706))))))))) (let ((_let_3293 (forall ((BOUND_VARIABLE_2085677 tptp.int) (BOUND_VARIABLE_2085678 tptp.int) (BOUND_VARIABLE_2085679 tptp.int) (BOUND_VARIABLE_2085680 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085677) BOUND_VARIABLE_2085679))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085678) BOUND_VARIABLE_2085680))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16619 BOUND_VARIABLE_2085677) BOUND_VARIABLE_2085678) BOUND_VARIABLE_2085679) BOUND_VARIABLE_2085680))))))) (let ((_let_3294 (forall ((BOUND_VARIABLE_2085573 tptp.int) (BOUND_VARIABLE_2085574 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2085574))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2085574))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2085573) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16620 BOUND_VARIABLE_2085573) BOUND_VARIABLE_2085574) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3295 (forall ((BOUND_VARIABLE_2085545 tptp.int) (BOUND_VARIABLE_2085546 tptp.int) (BOUND_VARIABLE_2085547 tptp.int) (BOUND_VARIABLE_2085548 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085545) BOUND_VARIABLE_2085547))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085546) BOUND_VARIABLE_2085548))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16621 BOUND_VARIABLE_2085545) BOUND_VARIABLE_2085546) BOUND_VARIABLE_2085547) BOUND_VARIABLE_2085548))))))) (let ((_let_3296 (forall ((BOUND_VARIABLE_2085466 tptp.rat) (BOUND_VARIABLE_2085467 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2085467))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2085467))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2085466 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16622 BOUND_VARIABLE_2085466) BOUND_VARIABLE_2085467)))))))))))))) (let ((_let_3297 (forall ((BOUND_VARIABLE_2085438 tptp.int) (BOUND_VARIABLE_2085439 tptp.int) (BOUND_VARIABLE_2085440 tptp.int) (BOUND_VARIABLE_2085441 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085438) BOUND_VARIABLE_2085440))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085439) BOUND_VARIABLE_2085441))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16623 BOUND_VARIABLE_2085438) BOUND_VARIABLE_2085439) BOUND_VARIABLE_2085440) BOUND_VARIABLE_2085441))))))) (let ((_let_3298 (forall ((BOUND_VARIABLE_2085334 tptp.int) (BOUND_VARIABLE_2085335 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2085335))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2085335))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2085334) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16624 BOUND_VARIABLE_2085334) BOUND_VARIABLE_2085335) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3299 (forall ((BOUND_VARIABLE_2085306 tptp.int) (BOUND_VARIABLE_2085307 tptp.int) (BOUND_VARIABLE_2085308 tptp.int) (BOUND_VARIABLE_2085309 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085306) BOUND_VARIABLE_2085308))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085307) BOUND_VARIABLE_2085309))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16625 BOUND_VARIABLE_2085306) BOUND_VARIABLE_2085307) BOUND_VARIABLE_2085308) BOUND_VARIABLE_2085309))))))) (let ((_let_3300 (forall ((BOUND_VARIABLE_2085222 tptp.rat) (BOUND_VARIABLE_2085223 tptp.rat) (BOUND_VARIABLE_2085224 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2085224))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2085224))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 (ho_15209 k_16626 BOUND_VARIABLE_2085222) BOUND_VARIABLE_2085223) BOUND_VARIABLE_2085224) (and (= (ho_15122 (ho_15125 _let_9 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_9 BOUND_VARIABLE_2085222) BOUND_VARIABLE_2085223)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3301 (forall ((BOUND_VARIABLE_2085194 tptp.int) (BOUND_VARIABLE_2085195 tptp.int) (BOUND_VARIABLE_2085196 tptp.int) (BOUND_VARIABLE_2085197 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085194) BOUND_VARIABLE_2085196))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085195) BOUND_VARIABLE_2085197))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16627 BOUND_VARIABLE_2085194) BOUND_VARIABLE_2085195) BOUND_VARIABLE_2085196) BOUND_VARIABLE_2085197))))))) (let ((_let_3302 (forall ((BOUND_VARIABLE_2085090 tptp.int) (BOUND_VARIABLE_2085091 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2085091))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2085091))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2085090) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16628 BOUND_VARIABLE_2085090) BOUND_VARIABLE_2085091) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3303 (forall ((BOUND_VARIABLE_2085062 tptp.int) (BOUND_VARIABLE_2085063 tptp.int) (BOUND_VARIABLE_2085064 tptp.int) (BOUND_VARIABLE_2085065 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085062) BOUND_VARIABLE_2085064))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2085063) BOUND_VARIABLE_2085065))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16629 BOUND_VARIABLE_2085062) BOUND_VARIABLE_2085063) BOUND_VARIABLE_2085064) BOUND_VARIABLE_2085065))))))) (let ((_let_3304 (forall ((BOUND_VARIABLE_2084983 tptp.rat) (BOUND_VARIABLE_2084984 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2084984))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2084984))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2084983 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16630 BOUND_VARIABLE_2084983) BOUND_VARIABLE_2084984)))))))))))))) (let ((_let_3305 (forall ((BOUND_VARIABLE_2084955 tptp.int) (BOUND_VARIABLE_2084956 tptp.int) (BOUND_VARIABLE_2084957 tptp.int) (BOUND_VARIABLE_2084958 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2084955) BOUND_VARIABLE_2084957))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2084956) BOUND_VARIABLE_2084958))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16631 BOUND_VARIABLE_2084955) BOUND_VARIABLE_2084956) BOUND_VARIABLE_2084957) BOUND_VARIABLE_2084958))))))) (let ((_let_3306 (forall ((BOUND_VARIABLE_2084851 tptp.int) (BOUND_VARIABLE_2084852 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2084852))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2084852))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2084851) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16632 BOUND_VARIABLE_2084851) BOUND_VARIABLE_2084852) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3307 (forall ((BOUND_VARIABLE_2084823 tptp.int) (BOUND_VARIABLE_2084824 tptp.int) (BOUND_VARIABLE_2084825 tptp.int) (BOUND_VARIABLE_2084826 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2084823) BOUND_VARIABLE_2084825))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2084824) BOUND_VARIABLE_2084826))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16633 BOUND_VARIABLE_2084823) BOUND_VARIABLE_2084824) BOUND_VARIABLE_2084825) BOUND_VARIABLE_2084826))))))) (let ((_let_3308 (forall ((BOUND_VARIABLE_2084744 tptp.rat) (BOUND_VARIABLE_2084745 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2084745))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2084745))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2084744 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16634 BOUND_VARIABLE_2084744) BOUND_VARIABLE_2084745)))))))))))))) (let ((_let_3309 (forall ((BOUND_VARIABLE_2084562 tptp.rat) (BOUND_VARIABLE_2084563 tptp.rat) (BOUND_VARIABLE_2084564 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 (ho_15633 k_15632 BOUND_VARIABLE_2084562) BOUND_VARIABLE_2084563)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15629 BOUND_VARIABLE_2084564))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15630 BOUND_VARIABLE_2084564)) (ho_15260 k_15259 (ho_15145 (ho_15209 k_15631 BOUND_VARIABLE_2084562) BOUND_VARIABLE_2084563))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15634 BOUND_VARIABLE_2084564))))) (ho_15108 (ho_15783 (ho_16636 k_16635 BOUND_VARIABLE_2084562) BOUND_VARIABLE_2084563) BOUND_VARIABLE_2084564)))))) (let ((_let_3310 (forall ((BOUND_VARIABLE_2084460 tptp.int) (BOUND_VARIABLE_2084461 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2084461))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2084461))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16637 BOUND_VARIABLE_2084460) BOUND_VARIABLE_2084461) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2084460) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2084460)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2084460))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3311 (forall ((BOUND_VARIABLE_2084365 tptp.int) (BOUND_VARIABLE_2084366 tptp.int) (BOUND_VARIABLE_2084367 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15635 BOUND_VARIABLE_2084367) BOUND_VARIABLE_2084366)) (ho_15260 k_15259 (ho_15141 k_15636 BOUND_VARIABLE_2084365))) (ho_15108 (ho_15107 (ho_15106 k_16638 BOUND_VARIABLE_2084365) BOUND_VARIABLE_2084366) BOUND_VARIABLE_2084367))))) (let ((_let_3312 (forall ((BOUND_VARIABLE_2084286 tptp.rat) (BOUND_VARIABLE_2084287 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2084287))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2084287))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2084286 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16639 BOUND_VARIABLE_2084286) BOUND_VARIABLE_2084287)))))))))))))) (let ((_let_3313 (forall ((BOUND_VARIABLE_2084229 tptp.rat) (BOUND_VARIABLE_2084230 tptp.int) (BOUND_VARIABLE_2084231 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15637 BOUND_VARIABLE_2084231) BOUND_VARIABLE_2084230)) (ho_15260 k_15259 (ho_15145 k_15638 BOUND_VARIABLE_2084229))) (ho_15108 (ho_15107 (ho_15266 k_16640 BOUND_VARIABLE_2084229) BOUND_VARIABLE_2084230) BOUND_VARIABLE_2084231))))) (let ((_let_3314 (forall ((BOUND_VARIABLE_2084125 tptp.int) (BOUND_VARIABLE_2084126 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2084126))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2084126))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2084125) _let_3))) (= (ho_15142 (ho_15141 k_16641 BOUND_VARIABLE_2084125) BOUND_VARIABLE_2084126) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3315 (forall ((BOUND_VARIABLE_2084023 tptp.int) (BOUND_VARIABLE_2084024 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2084024))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2084024))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16642 BOUND_VARIABLE_2084023) BOUND_VARIABLE_2084024) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2084023) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2084023)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2084023))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 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(ho_15106 k_16643 BOUND_VARIABLE_2083928) BOUND_VARIABLE_2083929) BOUND_VARIABLE_2083930))))) (let ((_let_3317 (forall ((BOUND_VARIABLE_2083849 tptp.rat) (BOUND_VARIABLE_2083850 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2083850))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2083850))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2083849 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16644 BOUND_VARIABLE_2083849) BOUND_VARIABLE_2083850)))))))))))))) (let ((_let_3318 (forall ((BOUND_VARIABLE_2083792 tptp.rat) (BOUND_VARIABLE_2083793 tptp.int) (BOUND_VARIABLE_2083794 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15641 BOUND_VARIABLE_2083794) BOUND_VARIABLE_2083793)) (ho_15260 k_15259 (ho_15145 k_15642 BOUND_VARIABLE_2083792))) (ho_15108 (ho_15107 (ho_15266 k_16645 BOUND_VARIABLE_2083792) BOUND_VARIABLE_2083793) BOUND_VARIABLE_2083794))))) (let ((_let_3319 (forall ((BOUND_VARIABLE_2083688 tptp.int) (BOUND_VARIABLE_2083689 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2083689))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2083689))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2083688) _let_3))) (= (ho_15142 (ho_15141 k_16646 BOUND_VARIABLE_2083688) BOUND_VARIABLE_2083689) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3320 (forall ((BOUND_VARIABLE_2083660 tptp.int) (BOUND_VARIABLE_2083661 tptp.int) (BOUND_VARIABLE_2083662 tptp.int) (BOUND_VARIABLE_2083663 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083660) BOUND_VARIABLE_2083662))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083661) BOUND_VARIABLE_2083663))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16647 BOUND_VARIABLE_2083660) BOUND_VARIABLE_2083661) BOUND_VARIABLE_2083662) BOUND_VARIABLE_2083663))))))) (let ((_let_3321 (forall ((BOUND_VARIABLE_2083556 tptp.int) (BOUND_VARIABLE_2083557 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2083557))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2083557))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2083556) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16648 BOUND_VARIABLE_2083556) BOUND_VARIABLE_2083557) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3322 (forall ((BOUND_VARIABLE_2083528 tptp.int) (BOUND_VARIABLE_2083529 tptp.int) (BOUND_VARIABLE_2083530 tptp.int) (BOUND_VARIABLE_2083531 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083528) BOUND_VARIABLE_2083530))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083529) BOUND_VARIABLE_2083531))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16649 BOUND_VARIABLE_2083528) BOUND_VARIABLE_2083529) BOUND_VARIABLE_2083530) BOUND_VARIABLE_2083531))))))) (let ((_let_3323 (forall ((BOUND_VARIABLE_2083449 tptp.rat) (BOUND_VARIABLE_2083450 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2083450))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2083450))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2083449 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16650 BOUND_VARIABLE_2083449) BOUND_VARIABLE_2083450)))))))))))))) (let ((_let_3324 (forall ((BOUND_VARIABLE_2083421 tptp.int) (BOUND_VARIABLE_2083422 tptp.int) (BOUND_VARIABLE_2083423 tptp.int) (BOUND_VARIABLE_2083424 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083421) BOUND_VARIABLE_2083423))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083422) BOUND_VARIABLE_2083424))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16651 BOUND_VARIABLE_2083421) BOUND_VARIABLE_2083422) BOUND_VARIABLE_2083423) BOUND_VARIABLE_2083424))))))) (let ((_let_3325 (forall ((BOUND_VARIABLE_2083317 tptp.int) (BOUND_VARIABLE_2083318 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2083318))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2083318))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2083317) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16652 BOUND_VARIABLE_2083317) BOUND_VARIABLE_2083318) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3326 (forall ((BOUND_VARIABLE_2083289 tptp.int) (BOUND_VARIABLE_2083290 tptp.int) (BOUND_VARIABLE_2083291 tptp.int) (BOUND_VARIABLE_2083292 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083289) BOUND_VARIABLE_2083291))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083290) BOUND_VARIABLE_2083292))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16653 BOUND_VARIABLE_2083289) BOUND_VARIABLE_2083290) BOUND_VARIABLE_2083291) BOUND_VARIABLE_2083292))))))) (let ((_let_3327 (forall ((BOUND_VARIABLE_2083210 tptp.rat) (BOUND_VARIABLE_2083211 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2083211))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2083211))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2083210 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16654 BOUND_VARIABLE_2083210) BOUND_VARIABLE_2083211)))))))))))))) (let ((_let_3328 (forall ((BOUND_VARIABLE_2083182 tptp.int) (BOUND_VARIABLE_2083183 tptp.int) (BOUND_VARIABLE_2083184 tptp.int) (BOUND_VARIABLE_2083185 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083182) BOUND_VARIABLE_2083184))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083183) BOUND_VARIABLE_2083185))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16655 BOUND_VARIABLE_2083182) BOUND_VARIABLE_2083183) BOUND_VARIABLE_2083184) BOUND_VARIABLE_2083185))))))) (let ((_let_3329 (forall ((BOUND_VARIABLE_2083078 tptp.int) (BOUND_VARIABLE_2083079 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2083079))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2083079))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2083078) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16656 BOUND_VARIABLE_2083078) BOUND_VARIABLE_2083079) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3330 (forall ((BOUND_VARIABLE_2083050 tptp.int) (BOUND_VARIABLE_2083051 tptp.int) (BOUND_VARIABLE_2083052 tptp.int) (BOUND_VARIABLE_2083053 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083050) BOUND_VARIABLE_2083052))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2083051) BOUND_VARIABLE_2083053))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16657 BOUND_VARIABLE_2083050) BOUND_VARIABLE_2083051) BOUND_VARIABLE_2083052) BOUND_VARIABLE_2083053))))))) (let ((_let_3331 (forall ((BOUND_VARIABLE_2082966 tptp.rat) (BOUND_VARIABLE_2082967 tptp.rat) (BOUND_VARIABLE_2082968 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2082968))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2082968))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 (ho_15209 k_16658 BOUND_VARIABLE_2082966) BOUND_VARIABLE_2082967) BOUND_VARIABLE_2082968) (and (= (ho_15122 (ho_15125 _let_9 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_9 BOUND_VARIABLE_2082966) BOUND_VARIABLE_2082967)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3332 (forall ((BOUND_VARIABLE_2082927 tptp.real) (BOUND_VARIABLE_2082928 tptp.real) (BOUND_VARIABLE_2082929 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15099 (ho_15098 k_15097 k_15086) _let_1))) (let ((_let_3 (ho_15092 (ho_15101 (ho_15100 _let_2 k_16659) BOUND_VARIABLE_2082927) BOUND_VARIABLE_2082928))) (let ((_let_4 (ho_15091 _let_1 k_15082))) (let ((_let_5 (ho_15100 _let_2 k_15095))) (let ((_let_6 (ho_15081 k_15080 BOUND_VARIABLE_2082929))) (= (ho_15108 (ho_16617 (ho_16661 k_16660 BOUND_VARIABLE_2082927) BOUND_VARIABLE_2082928) BOUND_VARIABLE_2082929) (and (or (ho_15103 k_15102 (ho_15092 (ho_15101 _let_5 _let_3) (ho_15092 _let_4 _let_6))) (= _let_3 _let_6)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_5 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2082929) (ho_15114 k_15113 tptp.one)))) (ho_15092 _let_4 _let_3)))))))))))))) (let ((_let_3333 (forall ((BOUND_VARIABLE_2082920 tptp.nat) (BOUND_VARIABLE_2082921 tptp.nat)) (= (ho_15120 (ho_16503 k_16662 BOUND_VARIABLE_2082920) BOUND_VARIABLE_2082921) (ho_15120 k_15119 BOUND_VARIABLE_2082920))))) (let ((_let_3334 (forall ((BOUND_VARIABLE_2082913 tptp.nat) (BOUND_VARIABLE_2082914 tptp.nat)) (= (ho_15120 (ho_16503 k_16663 BOUND_VARIABLE_2082913) BOUND_VARIABLE_2082914) (ho_15120 k_15119 BOUND_VARIABLE_2082913))))) (let ((_let_3335 (forall ((BOUND_VARIABLE_2082906 tptp.nat) (BOUND_VARIABLE_2082907 tptp.nat)) (= (ho_15120 (ho_16503 k_16664 BOUND_VARIABLE_2082906) BOUND_VARIABLE_2082907) (ho_15120 k_15119 BOUND_VARIABLE_2082906))))) (let ((_let_3336 (forall ((BOUND_VARIABLE_2082878 tptp.int) (BOUND_VARIABLE_2082879 tptp.int) (BOUND_VARIABLE_2082880 tptp.int) (BOUND_VARIABLE_2082881 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082878) BOUND_VARIABLE_2082880))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082879) BOUND_VARIABLE_2082881))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16665 BOUND_VARIABLE_2082878) BOUND_VARIABLE_2082879) BOUND_VARIABLE_2082880) BOUND_VARIABLE_2082881))))))) (let ((_let_3337 (forall ((BOUND_VARIABLE_2082774 tptp.int) (BOUND_VARIABLE_2082775 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2082775))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2082775))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2082774) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16666 BOUND_VARIABLE_2082774) BOUND_VARIABLE_2082775) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3338 (forall ((BOUND_VARIABLE_2082746 tptp.int) (BOUND_VARIABLE_2082747 tptp.int) (BOUND_VARIABLE_2082748 tptp.int) (BOUND_VARIABLE_2082749 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 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(ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 k_16668 BOUND_VARIABLE_2082666) BOUND_VARIABLE_2082667) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 k_15121 BOUND_VARIABLE_2082666)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3340 (forall ((BOUND_VARIABLE_2082638 tptp.int) (BOUND_VARIABLE_2082639 tptp.int) (BOUND_VARIABLE_2082640 tptp.int) (BOUND_VARIABLE_2082641 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082638) BOUND_VARIABLE_2082640))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082639) BOUND_VARIABLE_2082641))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16669 BOUND_VARIABLE_2082638) BOUND_VARIABLE_2082639) BOUND_VARIABLE_2082640) BOUND_VARIABLE_2082641))))))) (let ((_let_3341 (forall ((BOUND_VARIABLE_2082534 tptp.int) (BOUND_VARIABLE_2082535 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2082535))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2082535))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2082534) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16670 BOUND_VARIABLE_2082534) BOUND_VARIABLE_2082535) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3342 (forall ((BOUND_VARIABLE_2082506 tptp.int) (BOUND_VARIABLE_2082507 tptp.int) (BOUND_VARIABLE_2082508 tptp.int) (BOUND_VARIABLE_2082509 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082506) BOUND_VARIABLE_2082508))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082507) BOUND_VARIABLE_2082509))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16671 BOUND_VARIABLE_2082506) BOUND_VARIABLE_2082507) BOUND_VARIABLE_2082508) BOUND_VARIABLE_2082509))))))) (let ((_let_3343 (forall ((BOUND_VARIABLE_2082426 tptp.rat) (BOUND_VARIABLE_2082427 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2082427))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2082427))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 k_16672 BOUND_VARIABLE_2082426) BOUND_VARIABLE_2082427) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 k_15121 BOUND_VARIABLE_2082426)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3344 (forall ((BOUND_VARIABLE_2082398 tptp.int) (BOUND_VARIABLE_2082399 tptp.int) (BOUND_VARIABLE_2082400 tptp.int) (BOUND_VARIABLE_2082401 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082398) BOUND_VARIABLE_2082400))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082399) BOUND_VARIABLE_2082401))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16673 BOUND_VARIABLE_2082398) BOUND_VARIABLE_2082399) BOUND_VARIABLE_2082400) BOUND_VARIABLE_2082401))))))) (let ((_let_3345 (forall ((BOUND_VARIABLE_2082294 tptp.int) (BOUND_VARIABLE_2082295 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2082295))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2082295))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2082294) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16674 BOUND_VARIABLE_2082294) BOUND_VARIABLE_2082295) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3346 (forall ((BOUND_VARIABLE_2082266 tptp.int) (BOUND_VARIABLE_2082267 tptp.int) (BOUND_VARIABLE_2082268 tptp.int) (BOUND_VARIABLE_2082269 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082266) BOUND_VARIABLE_2082268))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082267) BOUND_VARIABLE_2082269))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16675 BOUND_VARIABLE_2082266) BOUND_VARIABLE_2082267) BOUND_VARIABLE_2082268) BOUND_VARIABLE_2082269))))))) (let ((_let_3347 (forall ((BOUND_VARIABLE_2082187 tptp.rat) (BOUND_VARIABLE_2082188 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2082188))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2082188))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2082187 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16676 BOUND_VARIABLE_2082187) BOUND_VARIABLE_2082188)))))))))))))) (let ((_let_3348 (forall ((BOUND_VARIABLE_2082159 tptp.int) (BOUND_VARIABLE_2082160 tptp.int) (BOUND_VARIABLE_2082161 tptp.int) (BOUND_VARIABLE_2082162 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082159) BOUND_VARIABLE_2082161))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082160) BOUND_VARIABLE_2082162))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16677 BOUND_VARIABLE_2082159) BOUND_VARIABLE_2082160) BOUND_VARIABLE_2082161) BOUND_VARIABLE_2082162))))))) (let ((_let_3349 (forall ((BOUND_VARIABLE_2082131 tptp.int) (BOUND_VARIABLE_2082132 tptp.int) (BOUND_VARIABLE_2082133 tptp.int) (BOUND_VARIABLE_2082134 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082131) BOUND_VARIABLE_2082133))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2082132) BOUND_VARIABLE_2082134))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16678 BOUND_VARIABLE_2082131) BOUND_VARIABLE_2082132) BOUND_VARIABLE_2082133) BOUND_VARIABLE_2082134))))))) (let ((_let_3350 (forall ((BOUND_VARIABLE_2082046 tptp.rat) (BOUND_VARIABLE_2082047 tptp.rat) (BOUND_VARIABLE_2082048 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2082048))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2082048))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15145 (ho_15209 k_16679 BOUND_VARIABLE_2082046) BOUND_VARIABLE_2082047) BOUND_VARIABLE_2082048) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2082046) (ho_15122 k_15121 BOUND_VARIABLE_2082047)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3351 (forall ((BOUND_VARIABLE_2082002 tptp.int) (BOUND_VARIABLE_2082003 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15643 BOUND_VARIABLE_2082003) BOUND_VARIABLE_2082002)) (ho_15260 k_15259 k_16680)) (ho_15108 (ho_15107 k_16681 BOUND_VARIABLE_2082002) BOUND_VARIABLE_2082003))))) (let ((_let_3352 (forall ((BOUND_VARIABLE_2081917 tptp.rat) (BOUND_VARIABLE_2081918 tptp.rat) (BOUND_VARIABLE_2081919 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2081919))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2081919))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15142 (ho_15145 (ho_15209 k_16682 BOUND_VARIABLE_2081917) BOUND_VARIABLE_2081918) BOUND_VARIABLE_2081919) (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) BOUND_VARIABLE_2081917) (ho_15122 k_15121 BOUND_VARIABLE_2081918)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3353 (forall ((BOUND_VARIABLE_2081851 tptp.rat) (BOUND_VARIABLE_2081852 tptp.rat) (BOUND_VARIABLE_2081853 tptp.int) (BOUND_VARIABLE_2081854 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15644 BOUND_VARIABLE_2081854) BOUND_VARIABLE_2081853)) (ho_15260 k_15259 (ho_15145 (ho_15209 k_15645 BOUND_VARIABLE_2081851) BOUND_VARIABLE_2081852))) (ho_15108 (ho_15107 (ho_15266 (ho_15633 k_16683 BOUND_VARIABLE_2081851) BOUND_VARIABLE_2081852) BOUND_VARIABLE_2081853) BOUND_VARIABLE_2081854))))) (let ((_let_3354 (forall ((BOUND_VARIABLE_2081823 tptp.int) (BOUND_VARIABLE_2081824 tptp.int) (BOUND_VARIABLE_2081825 tptp.int) (BOUND_VARIABLE_2081826 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2081823) BOUND_VARIABLE_2081825))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2081824) BOUND_VARIABLE_2081826))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16684 BOUND_VARIABLE_2081823) BOUND_VARIABLE_2081824) BOUND_VARIABLE_2081825) BOUND_VARIABLE_2081826))))))) (let ((_let_3355 (forall ((BOUND_VARIABLE_2081795 tptp.int) (BOUND_VARIABLE_2081796 tptp.int) (BOUND_VARIABLE_2081797 tptp.int) (BOUND_VARIABLE_2081798 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2081795) BOUND_VARIABLE_2081797))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2081796) BOUND_VARIABLE_2081798))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16685 BOUND_VARIABLE_2081795) BOUND_VARIABLE_2081796) BOUND_VARIABLE_2081797) BOUND_VARIABLE_2081798))))))) (let ((_let_3356 (forall ((BOUND_VARIABLE_2081716 tptp.rat) (BOUND_VARIABLE_2081717 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2081717))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2081717))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2081716 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16686 BOUND_VARIABLE_2081716) BOUND_VARIABLE_2081717)))))))))))))) (let ((_let_3357 (forall ((BOUND_VARIABLE_2081672 tptp.int) (BOUND_VARIABLE_2081673 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15646 BOUND_VARIABLE_2081673) BOUND_VARIABLE_2081672)) (ho_15260 k_15259 k_16687)) (ho_15108 (ho_15107 k_16688 BOUND_VARIABLE_2081672) BOUND_VARIABLE_2081673))))) (let ((_let_3358 (forall ((BOUND_VARIABLE_2081593 tptp.rat) (BOUND_VARIABLE_2081594 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2081594))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2081594))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2081593 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16689 BOUND_VARIABLE_2081593) BOUND_VARIABLE_2081594)))))))))))))) (let ((_let_3359 (forall ((BOUND_VARIABLE_2081536 tptp.rat) (BOUND_VARIABLE_2081537 tptp.int) (BOUND_VARIABLE_2081538 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15647 BOUND_VARIABLE_2081538) BOUND_VARIABLE_2081537)) (ho_15260 k_15259 (ho_15145 k_15648 BOUND_VARIABLE_2081536))) (ho_15108 (ho_15107 (ho_15266 k_16690 BOUND_VARIABLE_2081536) BOUND_VARIABLE_2081537) BOUND_VARIABLE_2081538))))) (let ((_let_3360 (forall ((BOUND_VARIABLE_2081492 tptp.int) (BOUND_VARIABLE_2081493 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15649 BOUND_VARIABLE_2081493) BOUND_VARIABLE_2081492)) (ho_15260 k_15259 k_16691)) (ho_15108 (ho_15107 k_16692 BOUND_VARIABLE_2081492) BOUND_VARIABLE_2081493))))) (let ((_let_3361 (forall ((BOUND_VARIABLE_2081413 tptp.rat) (BOUND_VARIABLE_2081414 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2081414))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2081414))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2081413 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16693 BOUND_VARIABLE_2081413) BOUND_VARIABLE_2081414)))))))))))))) (let ((_let_3362 (forall ((BOUND_VARIABLE_2081356 tptp.rat) (BOUND_VARIABLE_2081357 tptp.int) (BOUND_VARIABLE_2081358 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15650 BOUND_VARIABLE_2081358) BOUND_VARIABLE_2081357)) (ho_15260 k_15259 (ho_15145 k_15651 BOUND_VARIABLE_2081356))) (ho_15108 (ho_15107 (ho_15266 k_16694 BOUND_VARIABLE_2081356) BOUND_VARIABLE_2081357) BOUND_VARIABLE_2081358))))) (let ((_let_3363 (forall ((BOUND_VARIABLE_2081278 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2081278))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2081278))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_11 (ho_15150 k_15149 tptp.one))) (= (and (= (ho_15122 (ho_15125 (ho_15139 _let_10 k_15153) _let_11) (ho_15122 k_15121 _let_11)) (ho_15122 (ho_15125 (ho_15139 _let_10 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 k_16691 BOUND_VARIABLE_2081278)))))))))))))))) (let ((_let_3364 (forall ((BOUND_VARIABLE_2081259 tptp.rat) (BOUND_VARIABLE_2081260 tptp.nat) (BOUND_VARIABLE_2081261 tptp.rat)) (let ((_let_1 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (= (ho_15122 (ho_15125 (ho_15139 _let_1 k_15127) (ho_15122 (ho_15125 (ho_15139 _let_1 k_15153) (ho_15122 k_15121 BOUND_VARIABLE_2081259)) (ho_15120 k_15119 BOUND_VARIABLE_2081260))) BOUND_VARIABLE_2081261) (ho_15122 (ho_16697 (ho_16696 k_16695 BOUND_VARIABLE_2081259) BOUND_VARIABLE_2081260) BOUND_VARIABLE_2081261)))))) (let ((_let_3365 (forall ((BOUND_VARIABLE_2081088 tptp.rat) (BOUND_VARIABLE_2081089 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15655 BOUND_VARIABLE_2081088)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15652 BOUND_VARIABLE_2081089))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15653 BOUND_VARIABLE_2081089)) (ho_15260 k_15259 (ho_15145 k_15654 BOUND_VARIABLE_2081088))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15656 BOUND_VARIABLE_2081089))))) (ho_15108 (ho_15783 k_16698 BOUND_VARIABLE_2081088) BOUND_VARIABLE_2081089)))))) (let ((_let_3366 (forall ((BOUND_VARIABLE_2080986 tptp.int) (BOUND_VARIABLE_2080987 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2080987))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2080987))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16699 BOUND_VARIABLE_2080986) BOUND_VARIABLE_2080987) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2080986) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2080986)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2080986))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3367 (forall ((BOUND_VARIABLE_2080891 tptp.int) (BOUND_VARIABLE_2080892 tptp.int) (BOUND_VARIABLE_2080893 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15657 BOUND_VARIABLE_2080893) BOUND_VARIABLE_2080892)) (ho_15260 k_15259 (ho_15141 k_15658 BOUND_VARIABLE_2080891))) (ho_15108 (ho_15107 (ho_15106 k_16700 BOUND_VARIABLE_2080891) BOUND_VARIABLE_2080892) BOUND_VARIABLE_2080893))))) (let ((_let_3368 (forall ((BOUND_VARIABLE_2080812 tptp.rat) (BOUND_VARIABLE_2080813 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2080813))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2080813))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2080812 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16701 BOUND_VARIABLE_2080812) BOUND_VARIABLE_2080813)))))))))))))) (let ((_let_3369 (forall ((BOUND_VARIABLE_2080755 tptp.rat) (BOUND_VARIABLE_2080756 tptp.int) (BOUND_VARIABLE_2080757 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15659 BOUND_VARIABLE_2080757) BOUND_VARIABLE_2080756)) (ho_15260 k_15259 (ho_15145 k_15660 BOUND_VARIABLE_2080755))) (ho_15108 (ho_15107 (ho_15266 k_16702 BOUND_VARIABLE_2080755) BOUND_VARIABLE_2080756) BOUND_VARIABLE_2080757))))) (let ((_let_3370 (forall ((BOUND_VARIABLE_2080651 tptp.int) (BOUND_VARIABLE_2080652 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2080652))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2080652))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2080651) _let_3))) (= (ho_15142 (ho_15141 k_16703 BOUND_VARIABLE_2080651) BOUND_VARIABLE_2080652) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3371 (forall ((BOUND_VARIABLE_2080623 tptp.int) (BOUND_VARIABLE_2080624 tptp.int) (BOUND_VARIABLE_2080625 tptp.int) (BOUND_VARIABLE_2080626 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080623) BOUND_VARIABLE_2080625))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080624) BOUND_VARIABLE_2080626))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16704 BOUND_VARIABLE_2080623) BOUND_VARIABLE_2080624) BOUND_VARIABLE_2080625) BOUND_VARIABLE_2080626))))))) (let ((_let_3372 (forall ((BOUND_VARIABLE_2080519 tptp.int) (BOUND_VARIABLE_2080520 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2080520))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2080520))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2080519) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16705 BOUND_VARIABLE_2080519) BOUND_VARIABLE_2080520) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3373 (forall ((BOUND_VARIABLE_2080491 tptp.int) (BOUND_VARIABLE_2080492 tptp.int) (BOUND_VARIABLE_2080493 tptp.int) (BOUND_VARIABLE_2080494 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080491) BOUND_VARIABLE_2080493))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080492) BOUND_VARIABLE_2080494))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16706 BOUND_VARIABLE_2080491) BOUND_VARIABLE_2080492) BOUND_VARIABLE_2080493) BOUND_VARIABLE_2080494))))))) (let ((_let_3374 (forall ((BOUND_VARIABLE_2080407 tptp.rat) (BOUND_VARIABLE_2080408 tptp.rat) (BOUND_VARIABLE_2080409 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2080409))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2080409))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 (ho_15209 k_16707 BOUND_VARIABLE_2080407) BOUND_VARIABLE_2080408) BOUND_VARIABLE_2080409) (and (= (ho_15122 (ho_15125 (ho_15139 _let_9 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2080407) BOUND_VARIABLE_2080408)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3375 (forall ((BOUND_VARIABLE_2080379 tptp.int) (BOUND_VARIABLE_2080380 tptp.int) (BOUND_VARIABLE_2080381 tptp.int) (BOUND_VARIABLE_2080382 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080379) BOUND_VARIABLE_2080381))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080380) BOUND_VARIABLE_2080382))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16708 BOUND_VARIABLE_2080379) BOUND_VARIABLE_2080380) BOUND_VARIABLE_2080381) BOUND_VARIABLE_2080382))))))) (let ((_let_3376 (forall ((BOUND_VARIABLE_2080275 tptp.int) (BOUND_VARIABLE_2080276 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2080276))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2080276))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2080275) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16709 BOUND_VARIABLE_2080275) BOUND_VARIABLE_2080276) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3377 (forall ((BOUND_VARIABLE_2080247 tptp.int) (BOUND_VARIABLE_2080248 tptp.int) (BOUND_VARIABLE_2080249 tptp.int) (BOUND_VARIABLE_2080250 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080247) BOUND_VARIABLE_2080249))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080248) BOUND_VARIABLE_2080250))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16710 BOUND_VARIABLE_2080247) BOUND_VARIABLE_2080248) BOUND_VARIABLE_2080249) BOUND_VARIABLE_2080250))))))) (let ((_let_3378 (forall ((BOUND_VARIABLE_2080168 tptp.rat) (BOUND_VARIABLE_2080169 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2080169))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2080169))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2080168 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16711 BOUND_VARIABLE_2080168) BOUND_VARIABLE_2080169)))))))))))))) (let ((_let_3379 (forall ((BOUND_VARIABLE_2080140 tptp.int) (BOUND_VARIABLE_2080141 tptp.int) (BOUND_VARIABLE_2080142 tptp.int) (BOUND_VARIABLE_2080143 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080140) BOUND_VARIABLE_2080142))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080141) BOUND_VARIABLE_2080143))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16712 BOUND_VARIABLE_2080140) BOUND_VARIABLE_2080141) BOUND_VARIABLE_2080142) BOUND_VARIABLE_2080143))))))) (let ((_let_3380 (forall ((BOUND_VARIABLE_2080036 tptp.int) (BOUND_VARIABLE_2080037 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2080037))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2080037))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2080036) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16713 BOUND_VARIABLE_2080036) BOUND_VARIABLE_2080037) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3381 (forall ((BOUND_VARIABLE_2080008 tptp.int) (BOUND_VARIABLE_2080009 tptp.int) (BOUND_VARIABLE_2080010 tptp.int) (BOUND_VARIABLE_2080011 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080008) BOUND_VARIABLE_2080010))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2080009) BOUND_VARIABLE_2080011))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16714 BOUND_VARIABLE_2080008) BOUND_VARIABLE_2080009) BOUND_VARIABLE_2080010) BOUND_VARIABLE_2080011))))))) (let ((_let_3382 (forall ((BOUND_VARIABLE_2079929 tptp.rat) (BOUND_VARIABLE_2079930 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2079930))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2079930))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2079929 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16715 BOUND_VARIABLE_2079929) BOUND_VARIABLE_2079930)))))))))))))) (let ((_let_3383 (forall ((BOUND_VARIABLE_2079901 tptp.int) (BOUND_VARIABLE_2079902 tptp.int) (BOUND_VARIABLE_2079903 tptp.int) (BOUND_VARIABLE_2079904 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079901) BOUND_VARIABLE_2079903))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079902) BOUND_VARIABLE_2079904))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16716 BOUND_VARIABLE_2079901) BOUND_VARIABLE_2079902) BOUND_VARIABLE_2079903) BOUND_VARIABLE_2079904))))))) (let ((_let_3384 (forall ((BOUND_VARIABLE_2079797 tptp.int) (BOUND_VARIABLE_2079798 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2079798))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2079798))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2079797) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16717 BOUND_VARIABLE_2079797) BOUND_VARIABLE_2079798) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3385 (forall ((BOUND_VARIABLE_2079769 tptp.int) (BOUND_VARIABLE_2079770 tptp.int) (BOUND_VARIABLE_2079771 tptp.int) (BOUND_VARIABLE_2079772 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079769) BOUND_VARIABLE_2079771))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079770) BOUND_VARIABLE_2079772))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16718 BOUND_VARIABLE_2079769) BOUND_VARIABLE_2079770) BOUND_VARIABLE_2079771) BOUND_VARIABLE_2079772))))))) (let ((_let_3386 (forall ((BOUND_VARIABLE_2079690 tptp.rat) (BOUND_VARIABLE_2079691 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2079691))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2079691))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2079690 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16719 BOUND_VARIABLE_2079690) BOUND_VARIABLE_2079691)))))))))))))) (let ((_let_3387 (forall ((BOUND_VARIABLE_2079662 tptp.int) (BOUND_VARIABLE_2079663 tptp.int) (BOUND_VARIABLE_2079664 tptp.int) (BOUND_VARIABLE_2079665 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079662) BOUND_VARIABLE_2079664))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079663) BOUND_VARIABLE_2079665))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16720 BOUND_VARIABLE_2079662) BOUND_VARIABLE_2079663) BOUND_VARIABLE_2079664) BOUND_VARIABLE_2079665))))))) (let ((_let_3388 (forall ((BOUND_VARIABLE_2079558 tptp.int) (BOUND_VARIABLE_2079559 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2079559))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2079559))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2079558) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16721 BOUND_VARIABLE_2079558) BOUND_VARIABLE_2079559) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3389 (forall ((BOUND_VARIABLE_2079530 tptp.int) (BOUND_VARIABLE_2079531 tptp.int) (BOUND_VARIABLE_2079532 tptp.int) (BOUND_VARIABLE_2079533 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079530) BOUND_VARIABLE_2079532))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079531) BOUND_VARIABLE_2079533))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16722 BOUND_VARIABLE_2079530) BOUND_VARIABLE_2079531) BOUND_VARIABLE_2079532) BOUND_VARIABLE_2079533))))))) (let ((_let_3390 (forall ((BOUND_VARIABLE_2079451 tptp.rat) (BOUND_VARIABLE_2079452 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2079452))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2079452))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2079451 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16723 BOUND_VARIABLE_2079451) BOUND_VARIABLE_2079452)))))))))))))) (let ((_let_3391 (forall ((BOUND_VARIABLE_2079423 tptp.int) (BOUND_VARIABLE_2079424 tptp.int) (BOUND_VARIABLE_2079425 tptp.int) (BOUND_VARIABLE_2079426 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079423) BOUND_VARIABLE_2079425))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079424) BOUND_VARIABLE_2079426))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16724 BOUND_VARIABLE_2079423) BOUND_VARIABLE_2079424) BOUND_VARIABLE_2079425) BOUND_VARIABLE_2079426))))))) (let ((_let_3392 (forall ((BOUND_VARIABLE_2079319 tptp.int) (BOUND_VARIABLE_2079320 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2079320))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2079320))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2079319) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16725 BOUND_VARIABLE_2079319) BOUND_VARIABLE_2079320) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3393 (forall ((BOUND_VARIABLE_2079291 tptp.int) (BOUND_VARIABLE_2079292 tptp.int) (BOUND_VARIABLE_2079293 tptp.int) (BOUND_VARIABLE_2079294 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079291) BOUND_VARIABLE_2079293))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2079292) BOUND_VARIABLE_2079294))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16726 BOUND_VARIABLE_2079291) BOUND_VARIABLE_2079292) BOUND_VARIABLE_2079293) BOUND_VARIABLE_2079294))))))) (let ((_let_3394 (forall ((BOUND_VARIABLE_2079207 tptp.rat) (BOUND_VARIABLE_2079208 tptp.rat) (BOUND_VARIABLE_2079209 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2079209))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2079209))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 (ho_15209 k_16727 BOUND_VARIABLE_2079207) BOUND_VARIABLE_2079208) BOUND_VARIABLE_2079209) (and (= (ho_15122 (ho_15125 _let_9 (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 _let_9 BOUND_VARIABLE_2079207) BOUND_VARIABLE_2079208)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3395 (forall ((BOUND_VARIABLE_2079105 tptp.int) (BOUND_VARIABLE_2079106 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2079106))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2079106))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16728 BOUND_VARIABLE_2079105) BOUND_VARIABLE_2079106) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2079105) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2079105)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2079105))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3396 (forall ((BOUND_VARIABLE_2079010 tptp.int) (BOUND_VARIABLE_2079011 tptp.int) (BOUND_VARIABLE_2079012 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15661 BOUND_VARIABLE_2079012) BOUND_VARIABLE_2079011)) (ho_15260 k_15259 (ho_15141 k_15662 BOUND_VARIABLE_2079010))) (ho_15108 (ho_15107 (ho_15106 k_16729 BOUND_VARIABLE_2079010) BOUND_VARIABLE_2079011) BOUND_VARIABLE_2079012))))) (let ((_let_3397 (forall ((BOUND_VARIABLE_2078931 tptp.rat) (BOUND_VARIABLE_2078932 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2078932))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2078932))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2078931 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16730 BOUND_VARIABLE_2078931) BOUND_VARIABLE_2078932)))))))))))))) (let ((_let_3398 (forall ((BOUND_VARIABLE_2078874 tptp.rat) (BOUND_VARIABLE_2078875 tptp.int) (BOUND_VARIABLE_2078876 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15663 BOUND_VARIABLE_2078876) BOUND_VARIABLE_2078875)) (ho_15260 k_15259 (ho_15145 k_15664 BOUND_VARIABLE_2078874))) (ho_15108 (ho_15107 (ho_15266 k_16731 BOUND_VARIABLE_2078874) BOUND_VARIABLE_2078875) BOUND_VARIABLE_2078876))))) (let ((_let_3399 (forall ((BOUND_VARIABLE_2078770 tptp.int) (BOUND_VARIABLE_2078771 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2078771))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2078771))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2078770) _let_3))) (= (ho_15142 (ho_15141 k_16732 BOUND_VARIABLE_2078770) BOUND_VARIABLE_2078771) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3400 (forall ((BOUND_VARIABLE_2078599 tptp.rat) (BOUND_VARIABLE_2078600 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15668 BOUND_VARIABLE_2078599)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15665 BOUND_VARIABLE_2078600))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15666 BOUND_VARIABLE_2078600)) (ho_15260 k_15259 (ho_15145 k_15667 BOUND_VARIABLE_2078599))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15669 BOUND_VARIABLE_2078600))))) (ho_15108 (ho_15783 k_16733 BOUND_VARIABLE_2078599) BOUND_VARIABLE_2078600)))))) (let ((_let_3401 (forall ((BOUND_VARIABLE_2078571 tptp.int) (BOUND_VARIABLE_2078572 tptp.int) (BOUND_VARIABLE_2078573 tptp.int) (BOUND_VARIABLE_2078574 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2078571) BOUND_VARIABLE_2078573))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2078572) BOUND_VARIABLE_2078574))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16734 BOUND_VARIABLE_2078571) BOUND_VARIABLE_2078572) BOUND_VARIABLE_2078573) BOUND_VARIABLE_2078574))))))) (let ((_let_3402 (forall ((BOUND_VARIABLE_2078527 tptp.int) (BOUND_VARIABLE_2078528 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15670 BOUND_VARIABLE_2078528) BOUND_VARIABLE_2078527)) (ho_15260 k_15259 k_16735)) (ho_15108 (ho_15107 k_16736 BOUND_VARIABLE_2078527) BOUND_VARIABLE_2078528))))) (let ((_let_3403 (forall ((BOUND_VARIABLE_2078499 tptp.int) (BOUND_VARIABLE_2078500 tptp.int) (BOUND_VARIABLE_2078501 tptp.int) (BOUND_VARIABLE_2078502 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2078499) BOUND_VARIABLE_2078501))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2078500) BOUND_VARIABLE_2078502))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16737 BOUND_VARIABLE_2078499) BOUND_VARIABLE_2078500) BOUND_VARIABLE_2078501) BOUND_VARIABLE_2078502))))))) (let ((_let_3404 (forall ((BOUND_VARIABLE_2078420 tptp.rat) (BOUND_VARIABLE_2078421 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2078421))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2078421))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2078420 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16738 BOUND_VARIABLE_2078420) BOUND_VARIABLE_2078421)))))))))))))) (let ((_let_3405 (forall ((BOUND_VARIABLE_2078392 tptp.int) (BOUND_VARIABLE_2078393 tptp.int) (BOUND_VARIABLE_2078394 tptp.int) (BOUND_VARIABLE_2078395 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2078392) BOUND_VARIABLE_2078394))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2078393) BOUND_VARIABLE_2078395))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16739 BOUND_VARIABLE_2078392) BOUND_VARIABLE_2078393) BOUND_VARIABLE_2078394) BOUND_VARIABLE_2078395))))))) (let ((_let_3406 (forall ((BOUND_VARIABLE_2078335 tptp.rat) (BOUND_VARIABLE_2078336 tptp.int) (BOUND_VARIABLE_2078337 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15671 BOUND_VARIABLE_2078337) BOUND_VARIABLE_2078336)) (ho_15260 k_15259 (ho_15145 k_15672 BOUND_VARIABLE_2078335))) (ho_15108 (ho_15107 (ho_15266 k_16740 BOUND_VARIABLE_2078335) BOUND_VARIABLE_2078336) BOUND_VARIABLE_2078337))))) (let ((_let_3407 (forall ((BOUND_VARIABLE_2078291 tptp.int) (BOUND_VARIABLE_2078292 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15673 BOUND_VARIABLE_2078292) BOUND_VARIABLE_2078291)) (ho_15260 k_15259 k_16741)) (ho_15108 (ho_15107 k_16742 BOUND_VARIABLE_2078291) BOUND_VARIABLE_2078292))))) (let ((_let_3408 (forall ((BOUND_VARIABLE_2078212 tptp.rat) (BOUND_VARIABLE_2078213 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2078213))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2078213))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2078212 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16743 BOUND_VARIABLE_2078212) BOUND_VARIABLE_2078213)))))))))))))) (let ((_let_3409 (forall ((BOUND_VARIABLE_2078184 tptp.int) (BOUND_VARIABLE_2078185 tptp.int) (BOUND_VARIABLE_2078186 tptp.int) (BOUND_VARIABLE_2078187 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2078184) BOUND_VARIABLE_2078186))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2078185) BOUND_VARIABLE_2078187))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16744 BOUND_VARIABLE_2078184) BOUND_VARIABLE_2078185) BOUND_VARIABLE_2078186) BOUND_VARIABLE_2078187))))))) (let ((_let_3410 (forall ((BOUND_VARIABLE_2078105 tptp.rat) (BOUND_VARIABLE_2078106 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2078106))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2078106))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2078105 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16745 BOUND_VARIABLE_2078105) BOUND_VARIABLE_2078106)))))))))))))) (let ((_let_3411 (forall ((BOUND_VARIABLE_2078077 tptp.int) (BOUND_VARIABLE_2078078 tptp.int) (BOUND_VARIABLE_2078079 tptp.int) (BOUND_VARIABLE_2078080 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2078077) BOUND_VARIABLE_2078079))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2078078) BOUND_VARIABLE_2078080))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16746 BOUND_VARIABLE_2078077) BOUND_VARIABLE_2078078) BOUND_VARIABLE_2078079) BOUND_VARIABLE_2078080))))))) (let ((_let_3412 (forall ((BOUND_VARIABLE_2077998 tptp.rat) (BOUND_VARIABLE_2077999 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2077999))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2077999))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2077998 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16747 BOUND_VARIABLE_2077998) BOUND_VARIABLE_2077999)))))))))))))) (let ((_let_3413 (forall ((BOUND_VARIABLE_2077970 tptp.int) (BOUND_VARIABLE_2077971 tptp.int) (BOUND_VARIABLE_2077972 tptp.int) (BOUND_VARIABLE_2077973 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077970) BOUND_VARIABLE_2077972))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077971) BOUND_VARIABLE_2077973))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16748 BOUND_VARIABLE_2077970) BOUND_VARIABLE_2077971) BOUND_VARIABLE_2077972) BOUND_VARIABLE_2077973))))))) (let ((_let_3414 (forall ((BOUND_VARIABLE_2077913 tptp.rat) (BOUND_VARIABLE_2077914 tptp.int) (BOUND_VARIABLE_2077915 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15674 BOUND_VARIABLE_2077915) BOUND_VARIABLE_2077914)) (ho_15260 k_15259 (ho_15145 k_15675 BOUND_VARIABLE_2077913))) (ho_15108 (ho_15107 (ho_15266 k_16749 BOUND_VARIABLE_2077913) BOUND_VARIABLE_2077914) BOUND_VARIABLE_2077915))))) (let ((_let_3415 (forall ((BOUND_VARIABLE_2077869 tptp.int) (BOUND_VARIABLE_2077870 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15676 BOUND_VARIABLE_2077870) BOUND_VARIABLE_2077869)) (ho_15260 k_15259 k_16750)) (ho_15108 (ho_15107 k_16751 BOUND_VARIABLE_2077869) BOUND_VARIABLE_2077870))))) (let ((_let_3416 (forall ((BOUND_VARIABLE_2077790 tptp.rat) (BOUND_VARIABLE_2077791 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2077791))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2077791))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2077790 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16752 BOUND_VARIABLE_2077790) BOUND_VARIABLE_2077791)))))))))))))) (let ((_let_3417 (forall ((BOUND_VARIABLE_2077746 tptp.int) (BOUND_VARIABLE_2077747 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15677 BOUND_VARIABLE_2077747) BOUND_VARIABLE_2077746)) (ho_15260 k_15259 k_16753)) (ho_15108 (ho_15107 k_16754 BOUND_VARIABLE_2077746) BOUND_VARIABLE_2077747))))) (let ((_let_3418 (forall ((BOUND_VARIABLE_2077667 tptp.rat) (BOUND_VARIABLE_2077668 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2077668))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2077668))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2077667 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16755 BOUND_VARIABLE_2077667) BOUND_VARIABLE_2077668)))))))))))))) (let ((_let_3419 (forall ((BOUND_VARIABLE_2077610 tptp.rat) (BOUND_VARIABLE_2077611 tptp.int) (BOUND_VARIABLE_2077612 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15678 BOUND_VARIABLE_2077612) BOUND_VARIABLE_2077611)) (ho_15260 k_15259 (ho_15145 k_15679 BOUND_VARIABLE_2077610))) (ho_15108 (ho_15107 (ho_15266 k_16756 BOUND_VARIABLE_2077610) BOUND_VARIABLE_2077611) BOUND_VARIABLE_2077612))))) (let ((_let_3420 (forall ((BOUND_VARIABLE_2077582 tptp.int) (BOUND_VARIABLE_2077583 tptp.int) (BOUND_VARIABLE_2077584 tptp.int) (BOUND_VARIABLE_2077585 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077582) BOUND_VARIABLE_2077584))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077583) BOUND_VARIABLE_2077585))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16757 BOUND_VARIABLE_2077582) BOUND_VARIABLE_2077583) BOUND_VARIABLE_2077584) BOUND_VARIABLE_2077585))))))) (let ((_let_3421 (forall ((BOUND_VARIABLE_2077554 tptp.int) (BOUND_VARIABLE_2077555 tptp.int) (BOUND_VARIABLE_2077556 tptp.int) (BOUND_VARIABLE_2077557 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077554) BOUND_VARIABLE_2077556))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077555) BOUND_VARIABLE_2077557))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16758 BOUND_VARIABLE_2077554) BOUND_VARIABLE_2077555) BOUND_VARIABLE_2077556) BOUND_VARIABLE_2077557))))))) (let ((_let_3422 (forall ((BOUND_VARIABLE_2077475 tptp.rat) (BOUND_VARIABLE_2077476 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2077476))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2077476))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2077475 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16759 BOUND_VARIABLE_2077475) BOUND_VARIABLE_2077476)))))))))))))) (let ((_let_3423 (forall ((BOUND_VARIABLE_2077447 tptp.int) (BOUND_VARIABLE_2077448 tptp.int) (BOUND_VARIABLE_2077449 tptp.int) (BOUND_VARIABLE_2077450 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077447) BOUND_VARIABLE_2077449))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077448) BOUND_VARIABLE_2077450))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16760 BOUND_VARIABLE_2077447) BOUND_VARIABLE_2077448) BOUND_VARIABLE_2077449) BOUND_VARIABLE_2077450))))))) (let ((_let_3424 (forall ((BOUND_VARIABLE_2077368 tptp.rat) (BOUND_VARIABLE_2077369 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2077369))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2077369))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2077368 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16761 BOUND_VARIABLE_2077368) BOUND_VARIABLE_2077369)))))))))))))) (let ((_let_3425 (forall ((BOUND_VARIABLE_2077340 tptp.int) (BOUND_VARIABLE_2077341 tptp.int) (BOUND_VARIABLE_2077342 tptp.int) (BOUND_VARIABLE_2077343 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077340) BOUND_VARIABLE_2077342))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077341) BOUND_VARIABLE_2077343))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16762 BOUND_VARIABLE_2077340) BOUND_VARIABLE_2077341) BOUND_VARIABLE_2077342) BOUND_VARIABLE_2077343))))))) (let ((_let_3426 (forall ((BOUND_VARIABLE_2077283 tptp.rat) (BOUND_VARIABLE_2077284 tptp.int) (BOUND_VARIABLE_2077285 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15680 BOUND_VARIABLE_2077285) BOUND_VARIABLE_2077284)) (ho_15260 k_15259 (ho_15145 k_15681 BOUND_VARIABLE_2077283))) (ho_15108 (ho_15107 (ho_15266 k_16763 BOUND_VARIABLE_2077283) BOUND_VARIABLE_2077284) BOUND_VARIABLE_2077285))))) (let ((_let_3427 (forall ((BOUND_VARIABLE_2077239 tptp.int) (BOUND_VARIABLE_2077240 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15682 BOUND_VARIABLE_2077240) BOUND_VARIABLE_2077239)) (ho_15260 k_15259 k_16764)) (ho_15108 (ho_15107 k_16765 BOUND_VARIABLE_2077239) BOUND_VARIABLE_2077240))))) (let ((_let_3428 (forall ((BOUND_VARIABLE_2077160 tptp.rat) (BOUND_VARIABLE_2077161 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2077161))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2077161))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2077160 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16766 BOUND_VARIABLE_2077160) BOUND_VARIABLE_2077161)))))))))))))) (let ((_let_3429 (forall ((BOUND_VARIABLE_2077132 tptp.int) (BOUND_VARIABLE_2077133 tptp.int) (BOUND_VARIABLE_2077134 tptp.int) (BOUND_VARIABLE_2077135 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077132) BOUND_VARIABLE_2077134))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2077133) BOUND_VARIABLE_2077135))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16767 BOUND_VARIABLE_2077132) BOUND_VARIABLE_2077133) BOUND_VARIABLE_2077134) BOUND_VARIABLE_2077135))))))) (let ((_let_3430 (forall ((BOUND_VARIABLE_2077053 tptp.rat) (BOUND_VARIABLE_2077054 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2077054))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2077054))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2077053 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 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BOUND_VARIABLE_2077027) BOUND_VARIABLE_2077028))))))) (let ((_let_3432 (forall ((BOUND_VARIABLE_2076968 tptp.rat) (BOUND_VARIABLE_2076969 tptp.int) (BOUND_VARIABLE_2076970 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15683 BOUND_VARIABLE_2076970) BOUND_VARIABLE_2076969)) (ho_15260 k_15259 (ho_15145 k_15684 BOUND_VARIABLE_2076968))) (ho_15108 (ho_15107 (ho_15266 k_16770 BOUND_VARIABLE_2076968) BOUND_VARIABLE_2076969) BOUND_VARIABLE_2076970))))) (let ((_let_3433 (forall ((BOUND_VARIABLE_2076924 tptp.int) (BOUND_VARIABLE_2076925 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15685 BOUND_VARIABLE_2076925) BOUND_VARIABLE_2076924)) (ho_15260 k_15259 k_16771)) (ho_15108 (ho_15107 k_16772 BOUND_VARIABLE_2076924) BOUND_VARIABLE_2076925))))) (let ((_let_3434 (forall ((BOUND_VARIABLE_2076845 tptp.rat) (BOUND_VARIABLE_2076846 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2076846))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2076846))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2076845 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16773 BOUND_VARIABLE_2076845) BOUND_VARIABLE_2076846)))))))))))))) (let ((_let_3435 (forall ((BOUND_VARIABLE_2076788 tptp.rat) (BOUND_VARIABLE_2076789 tptp.int) (BOUND_VARIABLE_2076790 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15686 BOUND_VARIABLE_2076790) BOUND_VARIABLE_2076789)) (ho_15260 k_15259 (ho_15145 k_15687 BOUND_VARIABLE_2076788))) (ho_15108 (ho_15107 (ho_15266 k_16774 BOUND_VARIABLE_2076788) BOUND_VARIABLE_2076789) BOUND_VARIABLE_2076790))))) (let ((_let_3436 (forall ((BOUND_VARIABLE_2076744 tptp.int) (BOUND_VARIABLE_2076745 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15688 BOUND_VARIABLE_2076745) BOUND_VARIABLE_2076744)) (ho_15260 k_15259 k_16775)) (ho_15108 (ho_15107 k_16776 BOUND_VARIABLE_2076744) BOUND_VARIABLE_2076745))))) (let ((_let_3437 (forall ((BOUND_VARIABLE_2076665 tptp.rat) (BOUND_VARIABLE_2076666 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2076666))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2076666))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2076665 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 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BOUND_VARIABLE_2076639) BOUND_VARIABLE_2076640))))))) (let ((_let_3439 (forall ((BOUND_VARIABLE_2076558 tptp.rat) (BOUND_VARIABLE_2076559 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2076559))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2076559))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2076558 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16779 BOUND_VARIABLE_2076558) BOUND_VARIABLE_2076559)))))))))))))) (let ((_let_3440 (forall ((BOUND_VARIABLE_2076530 tptp.int) (BOUND_VARIABLE_2076531 tptp.int) (BOUND_VARIABLE_2076532 tptp.int) (BOUND_VARIABLE_2076533 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2076530) BOUND_VARIABLE_2076532))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2076531) BOUND_VARIABLE_2076533))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16780 BOUND_VARIABLE_2076530) BOUND_VARIABLE_2076531) BOUND_VARIABLE_2076532) BOUND_VARIABLE_2076533))))))) (let ((_let_3441 (forall ((BOUND_VARIABLE_2076473 tptp.rat) (BOUND_VARIABLE_2076474 tptp.int) (BOUND_VARIABLE_2076475 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15689 BOUND_VARIABLE_2076475) BOUND_VARIABLE_2076474)) (ho_15260 k_15259 (ho_15145 k_15690 BOUND_VARIABLE_2076473))) (ho_15108 (ho_15107 (ho_15266 k_16781 BOUND_VARIABLE_2076473) BOUND_VARIABLE_2076474) BOUND_VARIABLE_2076475))))) (let ((_let_3442 (forall ((BOUND_VARIABLE_2076429 tptp.int) (BOUND_VARIABLE_2076430 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15691 BOUND_VARIABLE_2076430) BOUND_VARIABLE_2076429)) (ho_15260 k_15259 k_16782)) (ho_15108 (ho_15107 k_16783 BOUND_VARIABLE_2076429) BOUND_VARIABLE_2076430))))) (let ((_let_3443 (forall ((BOUND_VARIABLE_2076350 tptp.rat) (BOUND_VARIABLE_2076351 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2076351))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2076351))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2076350 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16784 BOUND_VARIABLE_2076350) BOUND_VARIABLE_2076351)))))))))))))) (let ((_let_3444 (forall ((BOUND_VARIABLE_2076322 tptp.int) (BOUND_VARIABLE_2076323 tptp.int) (BOUND_VARIABLE_2076324 tptp.int) (BOUND_VARIABLE_2076325 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2076322) BOUND_VARIABLE_2076324))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2076323) BOUND_VARIABLE_2076325))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16785 BOUND_VARIABLE_2076322) BOUND_VARIABLE_2076323) BOUND_VARIABLE_2076324) BOUND_VARIABLE_2076325))))))) (let ((_let_3445 (forall ((BOUND_VARIABLE_2076243 tptp.rat) (BOUND_VARIABLE_2076244 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2076244))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2076244))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2076243 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 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((_let_3446 (forall ((BOUND_VARIABLE_2076215 tptp.int) (BOUND_VARIABLE_2076216 tptp.int) (BOUND_VARIABLE_2076217 tptp.int) (BOUND_VARIABLE_2076218 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2076215) BOUND_VARIABLE_2076217))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2076216) BOUND_VARIABLE_2076218))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16787 BOUND_VARIABLE_2076215) BOUND_VARIABLE_2076216) BOUND_VARIABLE_2076217) BOUND_VARIABLE_2076218))))))) (let ((_let_3447 (forall ((BOUND_VARIABLE_2076113 tptp.int) (BOUND_VARIABLE_2076114 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2076114))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2076114))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16788 BOUND_VARIABLE_2076113) BOUND_VARIABLE_2076114) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2076113) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2076113)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2076113))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3448 (forall ((BOUND_VARIABLE_2076018 tptp.int) (BOUND_VARIABLE_2076019 tptp.int) (BOUND_VARIABLE_2076020 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15692 BOUND_VARIABLE_2076020) BOUND_VARIABLE_2076019)) (ho_15260 k_15259 (ho_15141 k_15693 BOUND_VARIABLE_2076018))) (ho_15108 (ho_15107 (ho_15106 k_16789 BOUND_VARIABLE_2076018) BOUND_VARIABLE_2076019) BOUND_VARIABLE_2076020))))) (let ((_let_3449 (forall ((BOUND_VARIABLE_2075939 tptp.rat) (BOUND_VARIABLE_2075940 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2075940))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2075940))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2075939 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16790 BOUND_VARIABLE_2075939) BOUND_VARIABLE_2075940)))))))))))))) (let ((_let_3450 (forall ((BOUND_VARIABLE_2075882 tptp.rat) (BOUND_VARIABLE_2075883 tptp.int) (BOUND_VARIABLE_2075884 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15694 BOUND_VARIABLE_2075884) BOUND_VARIABLE_2075883)) (ho_15260 k_15259 (ho_15145 k_15695 BOUND_VARIABLE_2075882))) (ho_15108 (ho_15107 (ho_15266 k_16791 BOUND_VARIABLE_2075882) BOUND_VARIABLE_2075883) BOUND_VARIABLE_2075884))))) (let ((_let_3451 (forall ((BOUND_VARIABLE_2075778 tptp.int) (BOUND_VARIABLE_2075779 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2075779))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2075779))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2075778) _let_3))) (= (ho_15142 (ho_15141 k_16792 BOUND_VARIABLE_2075778) BOUND_VARIABLE_2075779) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3452 (forall ((BOUND_VARIABLE_2075676 tptp.int) (BOUND_VARIABLE_2075677 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2075677))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2075677))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16793 BOUND_VARIABLE_2075676) BOUND_VARIABLE_2075677) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2075676) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2075676)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2075676))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3453 (forall ((BOUND_VARIABLE_2075581 tptp.int) (BOUND_VARIABLE_2075582 tptp.int) (BOUND_VARIABLE_2075583 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15696 BOUND_VARIABLE_2075583) BOUND_VARIABLE_2075582)) (ho_15260 k_15259 (ho_15141 k_15697 BOUND_VARIABLE_2075581))) (ho_15108 (ho_15107 (ho_15106 k_16794 BOUND_VARIABLE_2075581) BOUND_VARIABLE_2075582) BOUND_VARIABLE_2075583))))) (let ((_let_3454 (forall ((BOUND_VARIABLE_2075502 tptp.rat) (BOUND_VARIABLE_2075503 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2075503))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2075503))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2075502 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16795 BOUND_VARIABLE_2075502) BOUND_VARIABLE_2075503)))))))))))))) (let ((_let_3455 (forall ((BOUND_VARIABLE_2075445 tptp.rat) (BOUND_VARIABLE_2075446 tptp.int) (BOUND_VARIABLE_2075447 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15698 BOUND_VARIABLE_2075447) BOUND_VARIABLE_2075446)) (ho_15260 k_15259 (ho_15145 k_15699 BOUND_VARIABLE_2075445))) (ho_15108 (ho_15107 (ho_15266 k_16796 BOUND_VARIABLE_2075445) BOUND_VARIABLE_2075446) BOUND_VARIABLE_2075447))))) (let ((_let_3456 (forall ((BOUND_VARIABLE_2075341 tptp.int) (BOUND_VARIABLE_2075342 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2075342))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2075342))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2075341) _let_3))) (= (ho_15142 (ho_15141 k_16797 BOUND_VARIABLE_2075341) BOUND_VARIABLE_2075342) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3457 (forall ((BOUND_VARIABLE_2075170 tptp.rat) (BOUND_VARIABLE_2075171 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15703 BOUND_VARIABLE_2075170)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15700 BOUND_VARIABLE_2075171))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15701 BOUND_VARIABLE_2075171)) (ho_15260 k_15259 (ho_15145 k_15702 BOUND_VARIABLE_2075170))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15704 BOUND_VARIABLE_2075171))))) (ho_15108 (ho_15783 k_16798 BOUND_VARIABLE_2075170) BOUND_VARIABLE_2075171)))))) (let ((_let_3458 (forall ((BOUND_VARIABLE_2074999 tptp.rat) (BOUND_VARIABLE_2075000 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15708 BOUND_VARIABLE_2074999)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15705 BOUND_VARIABLE_2075000))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15706 BOUND_VARIABLE_2075000)) (ho_15260 k_15259 (ho_15145 k_15707 BOUND_VARIABLE_2074999))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15709 BOUND_VARIABLE_2075000))))) (ho_15108 (ho_15783 k_16799 BOUND_VARIABLE_2074999) BOUND_VARIABLE_2075000)))))) (let ((_let_3459 (forall ((BOUND_VARIABLE_2074971 tptp.int) (BOUND_VARIABLE_2074972 tptp.int) (BOUND_VARIABLE_2074973 tptp.int) (BOUND_VARIABLE_2074974 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074971) BOUND_VARIABLE_2074973))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074972) BOUND_VARIABLE_2074974))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16800 BOUND_VARIABLE_2074971) BOUND_VARIABLE_2074972) BOUND_VARIABLE_2074973) BOUND_VARIABLE_2074974))))))) (let ((_let_3460 (forall ((BOUND_VARIABLE_2074867 tptp.int) (BOUND_VARIABLE_2074868 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2074868))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2074868))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2074867) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16801 BOUND_VARIABLE_2074867) BOUND_VARIABLE_2074868) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3461 (forall ((BOUND_VARIABLE_2074839 tptp.int) (BOUND_VARIABLE_2074840 tptp.int) (BOUND_VARIABLE_2074841 tptp.int) (BOUND_VARIABLE_2074842 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074839) BOUND_VARIABLE_2074841))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074840) BOUND_VARIABLE_2074842))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16802 BOUND_VARIABLE_2074839) BOUND_VARIABLE_2074840) BOUND_VARIABLE_2074841) BOUND_VARIABLE_2074842))))))) (let ((_let_3462 (forall ((BOUND_VARIABLE_2074760 tptp.rat) (BOUND_VARIABLE_2074761 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2074761))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2074761))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2074760 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16803 BOUND_VARIABLE_2074760) BOUND_VARIABLE_2074761)))))))))))))) (let ((_let_3463 (forall ((BOUND_VARIABLE_2074732 tptp.int) (BOUND_VARIABLE_2074733 tptp.int) (BOUND_VARIABLE_2074734 tptp.int) (BOUND_VARIABLE_2074735 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074732) BOUND_VARIABLE_2074734))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074733) BOUND_VARIABLE_2074735))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16804 BOUND_VARIABLE_2074732) BOUND_VARIABLE_2074733) BOUND_VARIABLE_2074734) BOUND_VARIABLE_2074735))))))) (let ((_let_3464 (forall ((BOUND_VARIABLE_2074628 tptp.int) (BOUND_VARIABLE_2074629 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2074629))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2074629))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2074628) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16805 BOUND_VARIABLE_2074628) BOUND_VARIABLE_2074629) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3465 (forall ((BOUND_VARIABLE_2074600 tptp.int) (BOUND_VARIABLE_2074601 tptp.int) (BOUND_VARIABLE_2074602 tptp.int) (BOUND_VARIABLE_2074603 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074600) BOUND_VARIABLE_2074602))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074601) BOUND_VARIABLE_2074603))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16806 BOUND_VARIABLE_2074600) BOUND_VARIABLE_2074601) BOUND_VARIABLE_2074602) BOUND_VARIABLE_2074603))))))) (let ((_let_3466 (forall ((BOUND_VARIABLE_2074521 tptp.rat) (BOUND_VARIABLE_2074522 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2074522))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2074522))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2074521 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16807 BOUND_VARIABLE_2074521) BOUND_VARIABLE_2074522)))))))))))))) (let ((_let_3467 (forall ((BOUND_VARIABLE_2074493 tptp.int) (BOUND_VARIABLE_2074494 tptp.int) (BOUND_VARIABLE_2074495 tptp.int) (BOUND_VARIABLE_2074496 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074493) BOUND_VARIABLE_2074495))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074494) BOUND_VARIABLE_2074496))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16808 BOUND_VARIABLE_2074493) BOUND_VARIABLE_2074494) BOUND_VARIABLE_2074495) BOUND_VARIABLE_2074496))))))) (let ((_let_3468 (forall ((BOUND_VARIABLE_2074389 tptp.int) (BOUND_VARIABLE_2074390 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2074390))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2074390))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2074389) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16809 BOUND_VARIABLE_2074389) BOUND_VARIABLE_2074390) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3469 (forall ((BOUND_VARIABLE_2074361 tptp.int) (BOUND_VARIABLE_2074362 tptp.int) (BOUND_VARIABLE_2074363 tptp.int) (BOUND_VARIABLE_2074364 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074361) BOUND_VARIABLE_2074363))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2074362) BOUND_VARIABLE_2074364))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16810 BOUND_VARIABLE_2074361) BOUND_VARIABLE_2074362) BOUND_VARIABLE_2074363) BOUND_VARIABLE_2074364))))))) (let ((_let_3470 (forall ((BOUND_VARIABLE_2074277 tptp.rat) (BOUND_VARIABLE_2074278 tptp.rat) (BOUND_VARIABLE_2074279 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2074279))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2074279))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 (ho_15209 k_16811 BOUND_VARIABLE_2074277) BOUND_VARIABLE_2074278) BOUND_VARIABLE_2074279) (and (= (ho_15122 (ho_15125 (ho_15139 _let_9 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2074277) BOUND_VARIABLE_2074278)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3471 (forall ((BOUND_VARIABLE_2074175 tptp.int) (BOUND_VARIABLE_2074176 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2074176))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2074176))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16812 BOUND_VARIABLE_2074175) BOUND_VARIABLE_2074176) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2074175) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2074175)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2074175))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3472 (forall ((BOUND_VARIABLE_2074080 tptp.int) (BOUND_VARIABLE_2074081 tptp.int) (BOUND_VARIABLE_2074082 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15710 BOUND_VARIABLE_2074082) BOUND_VARIABLE_2074081)) (ho_15260 k_15259 (ho_15141 k_15711 BOUND_VARIABLE_2074080))) (ho_15108 (ho_15107 (ho_15106 k_16813 BOUND_VARIABLE_2074080) BOUND_VARIABLE_2074081) BOUND_VARIABLE_2074082))))) (let ((_let_3473 (forall ((BOUND_VARIABLE_2074001 tptp.rat) (BOUND_VARIABLE_2074002 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2074002))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2074002))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2074001 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16814 BOUND_VARIABLE_2074001) BOUND_VARIABLE_2074002)))))))))))))) (let ((_let_3474 (forall ((BOUND_VARIABLE_2073944 tptp.rat) (BOUND_VARIABLE_2073945 tptp.int) (BOUND_VARIABLE_2073946 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15712 BOUND_VARIABLE_2073946) BOUND_VARIABLE_2073945)) (ho_15260 k_15259 (ho_15145 k_15713 BOUND_VARIABLE_2073944))) (ho_15108 (ho_15107 (ho_15266 k_16815 BOUND_VARIABLE_2073944) BOUND_VARIABLE_2073945) BOUND_VARIABLE_2073946))))) (let ((_let_3475 (forall ((BOUND_VARIABLE_2073840 tptp.int) (BOUND_VARIABLE_2073841 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2073841))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2073841))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2073840) _let_3))) (= (ho_15142 (ho_15141 k_16816 BOUND_VARIABLE_2073840) BOUND_VARIABLE_2073841) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3476 (forall ((BOUND_VARIABLE_2073738 tptp.int) (BOUND_VARIABLE_2073739 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2073739))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2073739))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16817 BOUND_VARIABLE_2073738) BOUND_VARIABLE_2073739) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2073738) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2073738)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2073738))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 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((BOUND_VARIABLE_2073643 tptp.int) (BOUND_VARIABLE_2073644 tptp.int) (BOUND_VARIABLE_2073645 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15714 BOUND_VARIABLE_2073645) BOUND_VARIABLE_2073644)) (ho_15260 k_15259 (ho_15141 k_15715 BOUND_VARIABLE_2073643))) (ho_15108 (ho_15107 (ho_15106 k_16818 BOUND_VARIABLE_2073643) BOUND_VARIABLE_2073644) BOUND_VARIABLE_2073645))))) (let ((_let_3478 (forall ((BOUND_VARIABLE_2073564 tptp.rat) (BOUND_VARIABLE_2073565 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2073565))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2073565))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2073564 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16819 BOUND_VARIABLE_2073564) BOUND_VARIABLE_2073565)))))))))))))) (let ((_let_3479 (forall ((BOUND_VARIABLE_2073507 tptp.rat) (BOUND_VARIABLE_2073508 tptp.int) (BOUND_VARIABLE_2073509 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15716 BOUND_VARIABLE_2073509) BOUND_VARIABLE_2073508)) (ho_15260 k_15259 (ho_15145 k_15717 BOUND_VARIABLE_2073507))) (ho_15108 (ho_15107 (ho_15266 k_16820 BOUND_VARIABLE_2073507) BOUND_VARIABLE_2073508) BOUND_VARIABLE_2073509))))) (let ((_let_3480 (forall ((BOUND_VARIABLE_2073403 tptp.int) (BOUND_VARIABLE_2073404 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2073404))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2073404))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2073403) _let_3))) (= (ho_15142 (ho_15141 k_16821 BOUND_VARIABLE_2073403) BOUND_VARIABLE_2073404) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3481 (forall ((BOUND_VARIABLE_2073232 tptp.rat) (BOUND_VARIABLE_2073233 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15721 BOUND_VARIABLE_2073232)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15718 BOUND_VARIABLE_2073233))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15719 BOUND_VARIABLE_2073233)) (ho_15260 k_15259 (ho_15145 k_15720 BOUND_VARIABLE_2073232))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15722 BOUND_VARIABLE_2073233))))) (ho_15108 (ho_15783 k_16822 BOUND_VARIABLE_2073232) BOUND_VARIABLE_2073233)))))) (let ((_let_3482 (forall ((BOUND_VARIABLE_2073061 tptp.rat) (BOUND_VARIABLE_2073062 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15726 BOUND_VARIABLE_2073061)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15723 BOUND_VARIABLE_2073062))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15724 BOUND_VARIABLE_2073062)) (ho_15260 k_15259 (ho_15145 k_15725 BOUND_VARIABLE_2073061))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15727 BOUND_VARIABLE_2073062))))) (ho_15108 (ho_15783 k_16823 BOUND_VARIABLE_2073061) BOUND_VARIABLE_2073062)))))) (let ((_let_3483 (forall ((BOUND_VARIABLE_2073033 tptp.int) (BOUND_VARIABLE_2073034 tptp.int) (BOUND_VARIABLE_2073035 tptp.int) (BOUND_VARIABLE_2073036 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2073033) BOUND_VARIABLE_2073035))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2073034) BOUND_VARIABLE_2073036))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16824 BOUND_VARIABLE_2073033) BOUND_VARIABLE_2073034) BOUND_VARIABLE_2073035) BOUND_VARIABLE_2073036))))))) (let ((_let_3484 (forall ((BOUND_VARIABLE_2072929 tptp.int) (BOUND_VARIABLE_2072930 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2072930))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2072930))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2072929) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16825 BOUND_VARIABLE_2072929) BOUND_VARIABLE_2072930) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3485 (forall ((BOUND_VARIABLE_2072901 tptp.int) (BOUND_VARIABLE_2072902 tptp.int) (BOUND_VARIABLE_2072903 tptp.int) (BOUND_VARIABLE_2072904 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2072901) BOUND_VARIABLE_2072903))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2072902) BOUND_VARIABLE_2072904))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16826 BOUND_VARIABLE_2072901) BOUND_VARIABLE_2072902) BOUND_VARIABLE_2072903) BOUND_VARIABLE_2072904))))))) (let ((_let_3486 (forall ((BOUND_VARIABLE_2072817 tptp.rat) (BOUND_VARIABLE_2072818 tptp.rat) (BOUND_VARIABLE_2072819 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2072819))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2072819))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 (ho_15209 k_16827 BOUND_VARIABLE_2072817) BOUND_VARIABLE_2072818) BOUND_VARIABLE_2072819) (and (= (ho_15122 (ho_15125 (ho_15139 _let_9 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2072817) BOUND_VARIABLE_2072818)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3487 (forall ((BOUND_VARIABLE_2072789 tptp.int) (BOUND_VARIABLE_2072790 tptp.int) (BOUND_VARIABLE_2072791 tptp.int) (BOUND_VARIABLE_2072792 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2072789) BOUND_VARIABLE_2072791))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2072790) BOUND_VARIABLE_2072792))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16828 BOUND_VARIABLE_2072789) BOUND_VARIABLE_2072790) BOUND_VARIABLE_2072791) BOUND_VARIABLE_2072792))))))) (let ((_let_3488 (forall ((BOUND_VARIABLE_2072685 tptp.int) (BOUND_VARIABLE_2072686 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2072686))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2072686))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2072685) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16829 BOUND_VARIABLE_2072685) BOUND_VARIABLE_2072686) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3489 (forall ((BOUND_VARIABLE_2072657 tptp.int) (BOUND_VARIABLE_2072658 tptp.int) (BOUND_VARIABLE_2072659 tptp.int) (BOUND_VARIABLE_2072660 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2072657) BOUND_VARIABLE_2072659))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2072658) BOUND_VARIABLE_2072660))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16830 BOUND_VARIABLE_2072657) BOUND_VARIABLE_2072658) BOUND_VARIABLE_2072659) BOUND_VARIABLE_2072660))))))) (let ((_let_3490 (forall ((BOUND_VARIABLE_2072578 tptp.rat) (BOUND_VARIABLE_2072579 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2072579))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2072579))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2072578 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16831 BOUND_VARIABLE_2072578) BOUND_VARIABLE_2072579)))))))))))))) (let ((_let_3491 (forall ((BOUND_VARIABLE_2072550 tptp.int) (BOUND_VARIABLE_2072551 tptp.int) (BOUND_VARIABLE_2072552 tptp.int) (BOUND_VARIABLE_2072553 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2072550) BOUND_VARIABLE_2072552))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2072551) BOUND_VARIABLE_2072553))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16832 BOUND_VARIABLE_2072550) BOUND_VARIABLE_2072551) BOUND_VARIABLE_2072552) BOUND_VARIABLE_2072553))))))) (let ((_let_3492 (forall ((BOUND_VARIABLE_2072446 tptp.int) (BOUND_VARIABLE_2072447 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2072447))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2072447))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2072446) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16833 BOUND_VARIABLE_2072446) BOUND_VARIABLE_2072447) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3493 (forall ((BOUND_VARIABLE_2072418 tptp.int) (BOUND_VARIABLE_2072419 tptp.int) (BOUND_VARIABLE_2072420 tptp.int) (BOUND_VARIABLE_2072421 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2072418) BOUND_VARIABLE_2072420))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2072419) BOUND_VARIABLE_2072421))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16834 BOUND_VARIABLE_2072418) BOUND_VARIABLE_2072419) BOUND_VARIABLE_2072420) BOUND_VARIABLE_2072421))))))) (let ((_let_3494 (forall ((BOUND_VARIABLE_2072339 tptp.rat) (BOUND_VARIABLE_2072340 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2072340))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2072340))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2072339 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16835 BOUND_VARIABLE_2072339) BOUND_VARIABLE_2072340)))))))))))))) (let ((_let_3495 (forall ((BOUND_VARIABLE_2072237 tptp.int) (BOUND_VARIABLE_2072238 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2072238))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2072238))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16836 BOUND_VARIABLE_2072237) BOUND_VARIABLE_2072238) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2072237) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2072237)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2072237))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3496 (forall ((BOUND_VARIABLE_2072142 tptp.int) (BOUND_VARIABLE_2072143 tptp.int) (BOUND_VARIABLE_2072144 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15728 BOUND_VARIABLE_2072144) BOUND_VARIABLE_2072143)) (ho_15260 k_15259 (ho_15141 k_15729 BOUND_VARIABLE_2072142))) (ho_15108 (ho_15107 (ho_15106 k_16837 BOUND_VARIABLE_2072142) BOUND_VARIABLE_2072143) BOUND_VARIABLE_2072144))))) (let ((_let_3497 (forall ((BOUND_VARIABLE_2072063 tptp.rat) (BOUND_VARIABLE_2072064 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2072064))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2072064))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2072063 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16838 BOUND_VARIABLE_2072063) BOUND_VARIABLE_2072064)))))))))))))) (let ((_let_3498 (forall ((BOUND_VARIABLE_2072006 tptp.rat) (BOUND_VARIABLE_2072007 tptp.int) (BOUND_VARIABLE_2072008 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15730 BOUND_VARIABLE_2072008) BOUND_VARIABLE_2072007)) (ho_15260 k_15259 (ho_15145 k_15731 BOUND_VARIABLE_2072006))) (ho_15108 (ho_15107 (ho_15266 k_16839 BOUND_VARIABLE_2072006) BOUND_VARIABLE_2072007) BOUND_VARIABLE_2072008))))) (let ((_let_3499 (forall ((BOUND_VARIABLE_2071902 tptp.int) (BOUND_VARIABLE_2071903 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2071903))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2071903))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2071902) _let_3))) (= (ho_15142 (ho_15141 k_16840 BOUND_VARIABLE_2071902) BOUND_VARIABLE_2071903) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3500 (forall ((BOUND_VARIABLE_2071800 tptp.int) (BOUND_VARIABLE_2071801 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2071801))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2071801))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16841 BOUND_VARIABLE_2071800) BOUND_VARIABLE_2071801) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2071800) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2071800)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2071800))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3501 (forall ((BOUND_VARIABLE_2071705 tptp.int) (BOUND_VARIABLE_2071706 tptp.int) (BOUND_VARIABLE_2071707 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15732 BOUND_VARIABLE_2071707) BOUND_VARIABLE_2071706)) (ho_15260 k_15259 (ho_15141 k_15733 BOUND_VARIABLE_2071705))) (ho_15108 (ho_15107 (ho_15106 k_16842 BOUND_VARIABLE_2071705) BOUND_VARIABLE_2071706) BOUND_VARIABLE_2071707))))) (let ((_let_3502 (forall ((BOUND_VARIABLE_2071626 tptp.rat) (BOUND_VARIABLE_2071627 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2071627))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2071627))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2071626 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16843 BOUND_VARIABLE_2071626) BOUND_VARIABLE_2071627)))))))))))))) (let ((_let_3503 (forall ((BOUND_VARIABLE_2071569 tptp.rat) (BOUND_VARIABLE_2071570 tptp.int) (BOUND_VARIABLE_2071571 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15734 BOUND_VARIABLE_2071571) BOUND_VARIABLE_2071570)) (ho_15260 k_15259 (ho_15145 k_15735 BOUND_VARIABLE_2071569))) (ho_15108 (ho_15107 (ho_15266 k_16844 BOUND_VARIABLE_2071569) BOUND_VARIABLE_2071570) BOUND_VARIABLE_2071571))))) (let ((_let_3504 (forall ((BOUND_VARIABLE_2071465 tptp.int) (BOUND_VARIABLE_2071466 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2071466))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2071466))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (let ((_let_10 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2071465) _let_3))) (= (ho_15142 (ho_15141 k_16845 BOUND_VARIABLE_2071465) BOUND_VARIABLE_2071466) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_10) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_10)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_10))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3505 (forall ((BOUND_VARIABLE_2071294 tptp.rat) (BOUND_VARIABLE_2071295 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15739 BOUND_VARIABLE_2071294)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15736 BOUND_VARIABLE_2071295))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15737 BOUND_VARIABLE_2071295)) (ho_15260 k_15259 (ho_15145 k_15738 BOUND_VARIABLE_2071294))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15740 BOUND_VARIABLE_2071295))))) (ho_15108 (ho_15783 k_16846 BOUND_VARIABLE_2071294) BOUND_VARIABLE_2071295)))))) (let ((_let_3506 (forall ((BOUND_VARIABLE_2071123 tptp.rat) (BOUND_VARIABLE_2071124 tptp.int)) (let ((_let_1 (ho_15262 k_15261 (ho_15266 k_15744 BOUND_VARIABLE_2071123)))) (= (and (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15741 BOUND_VARIABLE_2071124))) (ho_15142 (ho_15262 k_15261 (ho_15106 k_15742 BOUND_VARIABLE_2071124)) (ho_15260 k_15259 (ho_15145 k_15743 BOUND_VARIABLE_2071123))) (not (ho_15142 _let_1 (ho_15260 k_15259 (ho_15141 k_15745 BOUND_VARIABLE_2071124))))) (ho_15108 (ho_15783 k_16847 BOUND_VARIABLE_2071123) BOUND_VARIABLE_2071124)))))) (let ((_let_3507 (forall ((BOUND_VARIABLE_2071095 tptp.int) (BOUND_VARIABLE_2071096 tptp.int) (BOUND_VARIABLE_2071097 tptp.int) (BOUND_VARIABLE_2071098 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2071095) BOUND_VARIABLE_2071097))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2071096) BOUND_VARIABLE_2071098))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16848 BOUND_VARIABLE_2071095) BOUND_VARIABLE_2071096) BOUND_VARIABLE_2071097) BOUND_VARIABLE_2071098))))))) (let ((_let_3508 (forall ((BOUND_VARIABLE_2070991 tptp.int) (BOUND_VARIABLE_2070992 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2070992))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2070992))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2070991) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16849 BOUND_VARIABLE_2070991) BOUND_VARIABLE_2070992) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3509 (forall ((BOUND_VARIABLE_2070963 tptp.int) (BOUND_VARIABLE_2070964 tptp.int) (BOUND_VARIABLE_2070965 tptp.int) (BOUND_VARIABLE_2070966 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2070963) BOUND_VARIABLE_2070965))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2070964) BOUND_VARIABLE_2070966))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16850 BOUND_VARIABLE_2070963) BOUND_VARIABLE_2070964) BOUND_VARIABLE_2070965) BOUND_VARIABLE_2070966))))))) (let ((_let_3510 (forall ((BOUND_VARIABLE_2070884 tptp.rat) (BOUND_VARIABLE_2070885 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2070885))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2070885))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2070884 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16851 BOUND_VARIABLE_2070884) BOUND_VARIABLE_2070885)))))))))))))) (let ((_let_3511 (forall ((BOUND_VARIABLE_2070856 tptp.int) (BOUND_VARIABLE_2070857 tptp.int) (BOUND_VARIABLE_2070858 tptp.int) (BOUND_VARIABLE_2070859 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2070856) BOUND_VARIABLE_2070858))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2070857) BOUND_VARIABLE_2070859))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16852 BOUND_VARIABLE_2070856) BOUND_VARIABLE_2070857) BOUND_VARIABLE_2070858) BOUND_VARIABLE_2070859))))))) (let ((_let_3512 (forall ((BOUND_VARIABLE_2070752 tptp.int) (BOUND_VARIABLE_2070753 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2070753))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2070753))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2070752) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16853 BOUND_VARIABLE_2070752) BOUND_VARIABLE_2070753) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3513 (forall ((BOUND_VARIABLE_2070724 tptp.int) (BOUND_VARIABLE_2070725 tptp.int) (BOUND_VARIABLE_2070726 tptp.int) (BOUND_VARIABLE_2070727 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2070724) BOUND_VARIABLE_2070726))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2070725) BOUND_VARIABLE_2070727))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16854 BOUND_VARIABLE_2070724) BOUND_VARIABLE_2070725) BOUND_VARIABLE_2070726) BOUND_VARIABLE_2070727))))))) (let ((_let_3514 (forall ((BOUND_VARIABLE_2070645 tptp.rat) (BOUND_VARIABLE_2070646 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2070646))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2070646))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2070645 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16855 BOUND_VARIABLE_2070645) BOUND_VARIABLE_2070646)))))))))))))) (let ((_let_3515 (forall ((BOUND_VARIABLE_2070617 tptp.int) (BOUND_VARIABLE_2070618 tptp.int) (BOUND_VARIABLE_2070619 tptp.int) (BOUND_VARIABLE_2070620 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2070617) BOUND_VARIABLE_2070619))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2070618) BOUND_VARIABLE_2070620))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16856 BOUND_VARIABLE_2070617) BOUND_VARIABLE_2070618) BOUND_VARIABLE_2070619) BOUND_VARIABLE_2070620))))))) (let ((_let_3516 (forall ((BOUND_VARIABLE_2070513 tptp.int) (BOUND_VARIABLE_2070514 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2070514))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2070514))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2070513) _let_3))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16857 BOUND_VARIABLE_2070513) BOUND_VARIABLE_2070514) (and (= (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_9) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_9)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_9)))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3517 (forall ((BOUND_VARIABLE_2070485 tptp.int) (BOUND_VARIABLE_2070486 tptp.int) (BOUND_VARIABLE_2070487 tptp.int) (BOUND_VARIABLE_2070488 tptp.int)) (let ((_let_1 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_2 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_1) k_15095))) (= (ho_15103 k_15102 (ho_15092 (ho_15101 _let_2 (ho_15092 (ho_15101 _let_2 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2070485) BOUND_VARIABLE_2070487))) (ho_15094 k_15093 tptp.one))) (ho_15092 (ho_15091 _let_1 k_15082) (ho_15081 k_15080 (ho_15079 (ho_15078 k_15077 BOUND_VARIABLE_2070486) BOUND_VARIABLE_2070488))))) (ho_15108 (ho_15107 (ho_15106 (ho_15105 k_16858 BOUND_VARIABLE_2070485) BOUND_VARIABLE_2070486) BOUND_VARIABLE_2070487) BOUND_VARIABLE_2070488))))))) (let ((_let_3518 (forall ((BOUND_VARIABLE_2070401 tptp.rat) (BOUND_VARIABLE_2070402 tptp.rat) (BOUND_VARIABLE_2070403 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2070403))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2070403))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)))) (let ((_let_10 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15145 (ho_15209 k_16859 BOUND_VARIABLE_2070401) BOUND_VARIABLE_2070402) BOUND_VARIABLE_2070403) (and (= (ho_15122 (ho_15125 (ho_15139 _let_9 k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_10 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2)))) (ho_15122 (ho_15125 (ho_15139 _let_9 k_15153) BOUND_VARIABLE_2070401) BOUND_VARIABLE_2070402)) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)))))))))))))))) (let ((_let_3519 (forall ((BOUND_VARIABLE_2070299 tptp.int) (BOUND_VARIABLE_2070300 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2070300))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2070300))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (ho_15142 (ho_15141 k_16860 BOUND_VARIABLE_2070299) BOUND_VARIABLE_2070300) (and (= (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 BOUND_VARIABLE_2070299) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 BOUND_VARIABLE_2070299)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 BOUND_VARIABLE_2070299))) (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1))))))))))))))) (let ((_let_3520 (forall ((BOUND_VARIABLE_2070204 tptp.int) (BOUND_VARIABLE_2070205 tptp.int) (BOUND_VARIABLE_2070206 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15746 BOUND_VARIABLE_2070206) BOUND_VARIABLE_2070205)) (ho_15260 k_15259 (ho_15141 k_15747 BOUND_VARIABLE_2070204))) (ho_15108 (ho_15107 (ho_15106 k_16861 BOUND_VARIABLE_2070204) BOUND_VARIABLE_2070205) BOUND_VARIABLE_2070206))))) (let ((_let_3521 (forall ((BOUND_VARIABLE_2070125 tptp.rat) (BOUND_VARIABLE_2070126 tptp.product_prod_int_int)) (let ((_let_1 (ho_15110 k_15109 BOUND_VARIABLE_2070126))) (let ((_let_2 (ho_15110 k_15111 BOUND_VARIABLE_2070126))) (let ((_let_3 (ho_15114 k_15113 tptp.one))) (let ((_let_4 (ho_15079 (ho_15078 k_15116 _let_3) (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_3)) _let_3)))) (let ((_let_5 (ho_15090 (ho_15089 k_15088 k_15086) k_15084))) (let ((_let_6 (ho_15091 _let_5 k_15082))) (let ((_let_7 (ho_15094 k_15093 tptp.one))) (let ((_let_8 (ho_15100 (ho_15099 (ho_15098 k_15097 k_15086) _let_5) k_15095))) (let ((_let_9 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_4)) _let_7)))) (= (and (= BOUND_VARIABLE_2070125 (ho_15122 (ho_15125 (ho_15139 (ho_15138 (ho_15137 k_15136 k_15131) (ho_15135 (ho_15134 k_15133 k_15131) k_15129)) k_15127) (ho_15122 k_15126 (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_1) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_1)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_1))))) (ho_15122 (ho_15125 (ho_15124 k_15123 (ho_15103 k_15102 (ho_15092 _let_9 (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_2) _let_3)))))) (ho_15122 k_15121 (ho_15120 k_15119 (ho_15118 k_15117 (ho_15079 (ho_15078 k_15116 (ho_15079 k_15115 _let_2)) _let_3))))) (ho_15120 k_15119 (ho_15118 k_15117 _let_2))))) (ho_15103 k_15102 (ho_15092 (ho_15101 _let_8 (ho_15092 (ho_15101 _let_8 (ho_15081 k_15080 _let_1)) _let_7)) (ho_15092 _let_6 (ho_15081 k_15080 (ho_15079 (ho_15078 k_15116 _let_4) _let_3))))) (ho_15108 (ho_15107 k_15112 _let_2) _let_1)) (ho_15142 (ho_15145 k_16862 BOUND_VARIABLE_2070125) BOUND_VARIABLE_2070126)))))))))))))) (let ((_let_3522 (forall ((BOUND_VARIABLE_2070068 tptp.rat) (BOUND_VARIABLE_2070069 tptp.int) (BOUND_VARIABLE_2070070 tptp.int)) (= (ho_15142 (ho_15262 k_15261 (ho_15106 (ho_15105 k_15748 BOUND_VARIABLE_2070070) BOUND_VARIABLE_2070069)) (ho_15260 k_15259 (ho_15145 k_15749 BOUND_VARIABLE_2070068))) (ho_15108 (ho_15107 (ho_15266 k_1686